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This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan;
(2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan;
(3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan;
(4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan;
(5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. Table of Links Abstract and Intro Setup Result Summary and Discussion Appendix A. Dual Energy Formalism B. Convergence of Results C. Change of the Mass Loss Rate in MHD Regime References 2. SETUP We conduct a series of numerical simulations of a rotating magnetic wind from a massive WD merger product with a stable nuclear burning occurring at the near surface region. We first describe the general numerical setup including the governing equations, the Riemann solver, the mesh decomposition, and the boundary conditions in Sec. 2.1. We then describe the source term that represents the injection of mass and internal energy at the near surface nuclear burning region in Sec. 2.2. Finally, we elaborate on setups related to magnetic fields. 2.1. Magnetohydrodynamic (MHD) equations We numerically integrate ideal MHD equations with central gravity; We use the HLLD approximate Riemann solver for the MHD equations (Miyoshi & Kusano 2005) with the secondorder piecewise linear reconstruction method (PLM). The time integration is carried out by the second-order RungeKutta method with Courant-Friedrich-Lewy number of 0.1. The computational domain is resolved with the mesh number of 128 for [0.9, 30] R∗ in the radial direction and 128 for [0, π] in the polar direction. We employ a non-uniform mesh in the radial direction, where the radial grid size is proportional to the radius. The fiducial value of the grid size ratio ∆r(i + 1)/∆r(i) is 1.02 so that the smallest cell size is 0.05, where i stands for the grid index. In this paper, we consider the cases with Ω∗ = [0.05, 0.07, 0.12, 0.16, 0.23, 0.35, 0.46] s−1, which correpsonds to ∼ 5-50 % of the mass shedding limit. In terms of the inner ghost cell’s density and pressure, we carefully prescribe their values to achieve a specific thermally-driven wind mass loss rate (see Sec. 2.2). Initially, we distribute a cold and homogeneous gas throughout the entire computational domain and inject the thermally-driven wind from the designated launching region. As the thermally-driven outflow reaches the outer boundary, we initiate an aligned dipole field at the inner boundary, facilitating the transformation of the wind into a rotating magnetic wind (see Sec. 2.3). 2.2. Wind launching region We initialize our simulation with a cold, homogeneous, isotropic and non-magnetized atmosphere, and set up a “wind launching region” [2] with a width of D near the WD surface, where the mass is injected to the computational domain to mimic the mass loading due to the carbon burning around the surface of massive WD merger product. To do that, we implement an isotropic relaxation function for both matter and energy source terms to update density and pressure in wind launching region: where ρ∗ and p∗ correspond to the density and pressure at the outer edge of the wind launching region. The actual value of the relaxation timescale τ is chosen to satisfy the condition, 2.3. Rotating magnetic wind The launched gas will then corotate with the rotating magnetic field, and the magnetic torque, which depends on the resultant magnetospheric structure and the polar angle, can also contribute to the wind acceleration in addition to the thermal pressure gradient. As a result, we expect a rotating magnetic wind to start blowing in an angle dependent manner, and relax to a quasi-steady state when it reaches to the outer boundary. We simulate the rotating magnetic wind for a few 10 × the spin period after turning on the magnetic field. [2] Note that this is originally called damping layer in the context of accreting stellar system (see Takasao et al. 2019) This paper is available on arxiv under CC 4.0 license. Authors: (1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; (2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan; (3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan; (4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; (5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; (2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan; (3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan; (4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; (5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. Table of Links Abstract and Intro Abstract and Intro Setup Setup Result Result Summary and Discussion Summary and Discussion Appendix Appendix A. Dual Energy Formalism A. Dual Energy Formalism B. Convergence of Results B. Convergence of Results C. Change of the Mass Loss Rate in MHD Regime C. Change of the Mass Loss Rate in MHD Regime References References 2. SETUP We conduct a series of numerical simulations of a rotating magnetic wind from a massive WD merger product with a stable nuclear burning occurring at the near surface region. We first describe the general numerical setup including the governing equations, the Riemann solver, the mesh decomposition, and the boundary conditions in Sec. 2.1. We then describe the source term that represents the injection of mass and internal energy at the near surface nuclear burning region in Sec. 2.2. Finally, we elaborate on setups related to magnetic fields. 2.1. Magnetohydrodynamic (MHD) equations Magnetohydrodynamic (MHD) equations We numerically integrate ideal MHD equations with central gravity; We use the HLLD approximate Riemann solver for the MHD equations (Miyoshi & Kusano 2005) with the secondorder piecewise linear reconstruction method (PLM). The time integration is carried out by the second-order RungeKutta method with Courant-Friedrich-Lewy number of 0.1. The computational domain is resolved with the mesh number of 128 for [0.9, 30] R∗ in the radial direction and 128 for [0, π] in the polar direction. We employ a non-uniform mesh in the radial direction, where the radial grid size is proportional to the radius. The fiducial value of the grid size ratio ∆r( i + 1)/∆r( i ) is 1.02 so that the smallest cell size is 0.05, where i stands for the grid index. i i i In this paper, we consider the cases with Ω∗ = [0.05, 0.07, 0.12, 0.16, 0.23, 0.35, 0.46] s−1, which correpsonds to ∼ 5-50 % of the mass shedding limit. In terms of the inner ghost cell’s density and pressure, we carefully prescribe their values to achieve a specific thermally-driven wind mass loss rate (see Sec. 2.2). Initially, we distribute a cold and homogeneous gas throughout the entire computational domain and inject the thermally-driven wind from the designated launching region. As the thermally-driven outflow reaches the outer boundary, we initiate an aligned dipole field at the inner boundary, facilitating the transformation of the wind into a rotating magnetic wind (see Sec. 2.3). 2.2. Wind launching region Wind launching region We initialize our simulation with a cold, homogeneous, isotropic and non-magnetized atmosphere, and set up a “wind launching region” [2] with a width of D near the WD surface, where the mass is injected to the computational domain to mimic the mass loading due to the carbon burning around the surface of massive WD merger product. To do that, we implement an isotropic relaxation function for both matter and energy source terms to update density and pressure in wind launching region: where ρ∗ and p∗ correspond to the density and pressure at the outer edge of the wind launching region. The actual value of the relaxation timescale τ is chosen to satisfy the condition, 2.3. Rotating magnetic wind Rotating magnetic wind The launched gas will then corotate with the rotating magnetic field, and the magnetic torque, which depends on the resultant magnetospheric structure and the polar angle, can also contribute to the wind acceleration in addition to the thermal pressure gradient. As a result, we expect a rotating magnetic wind to start blowing in an angle dependent manner, and relax to a quasi-steady state when it reaches to the outer boundary. We simulate the rotating magnetic wind for a few 10 × the spin period after turning on the magnetic field. [2] Note that this is originally called damping layer in the context of accreting stellar system (see Takasao et al. 2019)

Magnetic Wind From a Massive White Dwarf Merger: Setup

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan;
(2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan;
(3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan;
(4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan;
(5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. Table of Links Abstract and Intro Setup Result Summary and Discussion Appendix A. Dual Energy Formalism B. Convergence of Results C. Change of the Mass Loss Rate in MHD Regime References 4. SUMMARY AND DISCUSSION Hence, even if the currently observed wind of WD J005311 is a rotating magnetic one and continues to blow for a Kelvin-Helmholtz timescale of the central WD, which is ∼ 1, 000-10, 000, yr, the spin-down will be negligible. When the carbon burning in the near-surface region ceases, the mass loss rate will significantly decrease, which increases the dimensionless parameter σ. The rotating magnetic wind will then become relativistic and eventually enter the force-free regime without significantly spinning down the WD. In this case, the remnant WD may serve as a non-thermal radiation source, or or the so-called WD pulsar (e.g., Kashiyama et al. 2011). Finally, we address some caveats in our numerical simulations. We have implemented a simple prescription for the near-surface carbon burning region as source terms (Eqs. 13 and 14), referred to as the wind launching region. However, the actual near-surface carbon burning region should be convective, and can be affected by the strong magnetic field. The structure of the convective region, the resulting wind launch, and its chemical composition would also be influenced by the radiative transfer. For accurate multi-wavelength spectrum calculations, it is desirable to conduct a comprehensive radiative MHD simulation that covers from the carbon burning layer to the photosphere radius. Also, we only investigate the aligned rotating dipole magnetic fields in this paper, while a more complicated field configuration such as oblique or off-centered dipole may be realized for the remnant WD system. Finally, the deformation of the central WD due to its rapid rotation and anisotropic carbon burning can alter the observed properties as well. We save the investigations into the above topics for our future work. This paper is available on arxiv under CC 4.0 license. Authors: (1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; (2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan; (3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan; (4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; (5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; (2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan; (3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan; (4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; (5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. Table of Links Abstract and Intro Abstract and Intro Setup Setup Result Result Summary and Discussion Summary and Discussion Appendix Appendix A. Dual Energy Formalism A. Dual Energy Formalism B. Convergence of Results B. Convergence of Results C. Change of the Mass Loss Rate in MHD Regime C. Change of the Mass Loss Rate in MHD Regime References References 4. SUMMARY AND DISCUSSION Hence, even if the currently observed wind of WD J005311 is a rotating magnetic one and continues to blow for a Kelvin-Helmholtz timescale of the central WD, which is ∼ 1, 000-10, 000, yr, the spin-down will be negligible. When the carbon burning in the near-surface region ceases, the mass loss rate will significantly decrease, which increases the dimensionless parameter σ. The rotating magnetic wind will then become relativistic and eventually enter the force-free regime without significantly spinning down the WD. In this case, the remnant WD may serve as a non-thermal radiation source, or or the so-called WD pulsar (e.g., Kashiyama et al. 2011). Finally, we address some caveats in our numerical simulations. We have implemented a simple prescription for the near-surface carbon burning region as source terms (Eqs. 13 and 14), referred to as the wind launching region. However, the actual near-surface carbon burning region should be convective, and can be affected by the strong magnetic field. The structure of the convective region, the resulting wind launch, and its chemical composition would also be influenced by the radiative transfer. For accurate multi-wavelength spectrum calculations, it is desirable to conduct a comprehensive radiative MHD simulation that covers from the carbon burning layer to the photosphere radius. Also, we only investigate the aligned rotating dipole magnetic fields in this paper, while a more complicated field configuration such as oblique or off-centered dipole may be realized for the remnant WD system. Finally, the deformation of the central WD due to its rapid rotation and anisotropic carbon burning can alter the observed properties as well. We save the investigations into the above topics for our future work.

Magnetic Wind From a Massive White Dwarf Merger: Summary and Discussion

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan;
(2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan;
(3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan;
(4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan;
(5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. Table of Links Abstract and Intro Setup Result Summary and Discussion Appendix A. Dual Energy Formalism B. Convergence of Results C. Change of the Mass Loss Rate in MHD Regime References 3. RESULT Table. 3 shows a summary of our simulation. A model BxΩy corresponds to the case with B∗ = x and Ω∗ = y in the cgs unit. When the rotating magnetic wind becomes quasi-steady, it can be characterized by the mass loss rate wind luminosity and spindown torque estimated at the outer boundary. As we show later, the strength of rotating magnetic winds can be characterized by a dimensionless parameter Hereafter we take B1.5e6Ω0.23 with σ = 34.3 as the fiducial model, and first show the multi-dimensional structure of the rotating magnetic wind in Sec. 3.1. We then investigate the time variability of the system primarily focusing on the impacts of quasi-periodic eruption along with the equatorial plane in Sec. 3.2. Finally, we show how the time-averaged spin-down torque scales with system parameters in Sec. 3.3. 3.1. Anisotropic wind structure In the equatorial direction (80◦ ≲ θ ≲ 100◦), magnetic fields are closed at small radii, forming a corotating magnetosphere. Beyond the last closed loop, the magnetic field lines are open with a predominant toroidal component, having opposite polarities with respect to the equatorial plane. The transition of the magnetic field configuration is mediated by reconnection occurring at around the tip of the last closed loop, or the Y point. As can be observed from the top-right panel of Fig. 1, the plasma beta in this transition region is higher than those along the open magnetic fields, implying that the gas is trapped mainly by magnetic tensions. In this high plasma-beta region sandwiched by low plasma beta regions, gases are pinched and radially accelerated in the reconnection region, eventually become supersonic at around r ∼ 5 R∗. The latitudinal angle dependence of the wind at the outer boundary is illustrated in Fig. 2, where the gray shaded regions represent the dynamical range of radial velocity (top-left), luminosity (top-right), torque (bottom-left), and mass loss rate (bottom-right). As described in the previous paragraphs, radial velocities in the near-equatorial direction can reach and transiently exceed the Michel velocity (represented by the horizontal dotted line) during eruptions caused by reconnection at the Y-point. Consequently, the wind luminosity, dominated by the radial kinetic term, also exhibits a sharp peak in the equatorial direction. On the other hand, the torque is primarily exerted by corotation with the magnetic fields and reaches its peak slightly off the equatorial plane (θ ∼ 85◦), corresponding to the edge of the concave shape of the Alfven radius. 3.2. Time variability The acceleration of the rotating magnetic wind in the equatorial direction occurs in a time-variable manner, associated with magnetic reconnection at the Y-point. Consequently, the overall flux of mass, energy, and angular momentum from the central WD can also vary with time. Fig. 3 displays the time evolution of the mass loss rate (M˙ ), luminosity (L), and torque (T) in our fiducial model. All quantities are normalized by their time-averaged values. The lower panel of Fig. 3, which provides a long-term perspective, reveals a recurrent eruptive behavior. A recurrent cycle consists of pre-eruption, reconnection, post-eruption phases: In the pre-eruption phase, gases injected into the near-equatorial plane become trapped within the closed field lines. Due to the centrifugal force, the gases accumulate at the tip of the last closed loop, resulting in a continuous decrease in plasma beta in that region. When the centrifugal force acting on the accumulated gases exceeds the tension of the closed magnetic fields, the tip of the closed zone starts expanding radially and is subsequently ejected as a plasmoid through reconnection. Such a plasmoid can be observed at r ∼ 4 - 5 R∗ in Fig. 1. Afterwards, the cycle returns to the pre-eruption phase and restores the gases within the closed magnetic field lines. This type of recurrent eruptions has been known as slingshot prominence in the context of magnetically-active rapidly-rotating stars (e.g., Ferreira 2000; Townsend & Owocki 2005; Jardine & Collier Cameron 2019). The upper panel of Fig. 3 focuses on the fluxes during a rotation period (t = 15-16 [2π/Ω∗]), as also depicted in Fig. 2. In comparison to the pre- and post-eruption phases, represented by the purple and red lines, respectively, the observed fluxes of mass, energy, and angular momentum consistently increase as the erupted plasmoids reach the outer boundary, indicated by the green lines. Notably, the magnetic torque significantly contributes to the overall torque increase during the eruption phase and plays a dominant role in the central WD’s spin-down. We note that the specifics of reconnection dynamics, such as the frequency of recurrent eruptions and the resulting time evolution of mass, energy, and angular momentum fluxes, may be influenced by our numerical parameters, including spatial resolution (which governs numerical resistivity) and the width of the wind launching region. However, we have verified that the time-averaged values of wind velocities, mass loss rate, luminosity, and torque have all reached convergence concerning the spatial resolution in our simulations and the width of the wind launching region (see Appendix B). 3.3. Scaling relation of the spin-down torque Here we consider how the spin-down torque of rotating magnetic wind depends on the system parameters based on our numerical results. As we show in the previous sub-sections, the time-averaged torque is essentially determined by the magnetic torque exerted on the gases at the tip of the last closed field lines, or the Y-point, where the field configuration is still roughly compatible with the rotating dipole. In this case, the (electro)magnetic torque at the Y point can be estimated as [3] In relativistic MHD regime, speed of light c is conventionally used as the characteristic speed of the system (e.g., see the definition of σ0 in Bucciantini et al. 2006). This paper is available on arxiv under CC 4.0 license. Authors: (1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; (2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan; (3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan; (4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; (5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Yici Zhong, Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan; (2) Kazumi Kashiyama, Research Center for the Early Universe, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan and Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU,WPI), The University of Tokyo, Chiba 277-8582, Japan; (3) Shinsuke Takasao, Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan; (4) Toshikazu Shigeyama, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Astronomy, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan; (5) Kotaro Fujisawa, Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan and Department of Liberal Arts, Tokyo University of Technology, Ota-ku, Tokyo 144-0051, Japan. Table of Links Abstract and Intro Abstract and Intro Setup Setup Result Result Summary and Discussion Summary and Discussion Appendix Appendix A. Dual Energy Formalism A. Dual Energy Formalism B. Convergence of Results B. Convergence of Results C. Change of the Mass Loss Rate in MHD Regime C. Change of the Mass Loss Rate in MHD Regime References References 3. RESULT Table. 3 shows a summary of our simulation. A model BxΩy corresponds to the case with B∗ = x and Ω∗ = y in the cgs unit. When the rotating magnetic wind becomes quasi-steady, it can be characterized by the mass loss rate wind luminosity and spindown torque estimated at the outer boundary. As we show later, the strength of rotating magnetic winds can be characterized by a dimensionless parameter Hereafter we take B1.5e6Ω0.23 with σ = 34.3 as the fiducial model, and first show the multi-dimensional structure of the rotating magnetic wind in Sec. 3.1. We then investigate the time variability of the system primarily focusing on the impacts of quasi-periodic eruption along with the equatorial plane in Sec. 3.2. Finally, we show how the time-averaged spin-down torque scales with system parameters in Sec. 3.3. 3.1. Anisotropic wind structure Anisotropic wind structure In the equatorial direction (80◦ ≲ θ ≲ 100◦), magnetic fields are closed at small radii, forming a corotating magnetosphere. Beyond the last closed loop, the magnetic field lines are open with a predominant toroidal component, having opposite polarities with respect to the equatorial plane. The transition of the magnetic field configuration is mediated by reconnection occurring at around the tip of the last closed loop, or the Y point. As can be observed from the top-right panel of Fig. 1, the plasma beta in this transition region is higher than those along the open magnetic fields, implying that the gas is trapped mainly by magnetic tensions. In this high plasma-beta region sandwiched by low plasma beta regions, gases are pinched and radially accelerated in the reconnection region, eventually become supersonic at around r ∼ 5 R∗. The latitudinal angle dependence of the wind at the outer boundary is illustrated in Fig. 2, where the gray shaded regions represent the dynamical range of radial velocity (top-left), luminosity (top-right), torque (bottom-left), and mass loss rate (bottom-right). As described in the previous paragraphs, radial velocities in the near-equatorial direction can reach and transiently exceed the Michel velocity (represented by the horizontal dotted line) during eruptions caused by reconnection at the Y-point. Consequently, the wind luminosity, dominated by the radial kinetic term, also exhibits a sharp peak in the equatorial direction. On the other hand, the torque is primarily exerted by corotation with the magnetic fields and reaches its peak slightly off the equatorial plane (θ ∼ 85◦), corresponding to the edge of the concave shape of the Alfven radius. 3.2. Time variability Time variability The acceleration of the rotating magnetic wind in the equatorial direction occurs in a time-variable manner, associated with magnetic reconnection at the Y-point. Consequently, the overall flux of mass, energy, and angular momentum from the central WD can also vary with time. Fig. 3 displays the time evolution of the mass loss rate (M˙ ), luminosity (L), and torque (T) in our fiducial model. All quantities are normalized by their time-averaged values. The lower panel of Fig. 3, which provides a long-term perspective, reveals a recurrent eruptive behavior. A recurrent cycle consists of pre-eruption, reconnection, post-eruption phases: In the pre-eruption phase, gases injected into the near-equatorial plane become trapped within the closed field lines. Due to the centrifugal force, the gases accumulate at the tip of the last closed loop, resulting in a continuous decrease in plasma beta in that region. When the centrifugal force acting on the accumulated gases exceeds the tension of the closed magnetic fields, the tip of the closed zone starts expanding radially and is subsequently ejected as a plasmoid through reconnection. Such a plasmoid can be observed at r ∼ 4 - 5 R∗ in Fig. 1. Afterwards, the cycle returns to the pre-eruption phase and restores the gases within the closed magnetic field lines. This type of recurrent eruptions has been known as slingshot prominence in the context of magnetically-active rapidly-rotating stars (e.g., Ferreira 2000; Townsend & Owocki 2005; Jardine & Collier Cameron 2019). The upper panel of Fig. 3 focuses on the fluxes during a rotation period (t = 15-16 [2π/Ω∗]), as also depicted in Fig. 2. In comparison to the pre- and post-eruption phases, represented by the purple and red lines, respectively, the observed fluxes of mass, energy, and angular momentum consistently increase as the erupted plasmoids reach the outer boundary, indicated by the green lines. Notably, the magnetic torque significantly contributes to the overall torque increase during the eruption phase and plays a dominant role in the central WD’s spin-down. We note that the specifics of reconnection dynamics, such as the frequency of recurrent eruptions and the resulting time evolution of mass, energy, and angular momentum fluxes, may be influenced by our numerical parameters, including spatial resolution (which governs numerical resistivity) and the width of the wind launching region. However, we have verified that the time-averaged values of wind velocities, mass loss rate, luminosity, and torque have all reached convergence concerning the spatial resolution in our simulations and the width of the wind launching region (see Appendix B). 3.3. Scaling relation of the spin-down torque Scaling relation of the spin-down torque Here we consider how the spin-down torque of rotating magnetic wind depends on the system parameters based on our numerical results. As we show in the previous sub-sections, the time-averaged torque is essentially determined by the magnetic torque exerted on the gases at the tip of the last closed field lines, or the Y-point, where the field configuration is still roughly compatible with the rotating dipole. In this case, the (electro)magnetic torque at the Y point can be estimated as [3] In relativistic MHD regime, speed of light c is conventionally used as the characteristic speed of the system (e.g., see the definition of σ0 in Bucciantini et al. 2006).

Magnetic Wind From a Massive White Dwarf Merger: Result

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Konstantin V. Getman, Department of Astronomy & Astrophysics, Pennsylvania State University;
(2) Agnes Kospal, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, E¨otv¨os Lor´and Research Network (ELKH), MTA Centre of Excellence, Max Planck Institute for Astronomy, and ELTE E¨otv¨os Lor´and University, Institute of Physics;
(3) Nicole Arulanantham, Space Telescope Science Institute;
(4) Dmitry A. Semenov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences;
(5) Grigorii V. Smirnov-Pinchukov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences;
(6) Sierk E. van Terwisga, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences. Table of Links Abstract and Intro
X-ray Observations and Data Extraction
Flare Analyses
Comparison with X-ray Flares from Young Stars
Discussion
Conclusions
Acknowledgments and References 2. X-RAY OBSERVATIONS AND DATA EXTRACTION 2.1. NuSTAR Data We conducted a single observation (ObsID 30801011002; PI K. Getman) of this system with NuSTAR (Harrison et al. 2013) from 04:51:09 UTC on July 28, 2022, to 19:36:09 UTC on July 31, 2022. This time window covers the orbital phase range of Φ = (0.9 − 1.13) around the periastron passage on July 30, 2022 (Φ = 1.0). The science exposure of the observation, taking into account Earth occultations, is 156 ksec. The data obtained from focal plane modules A and B (FPMA and FPMB), covering similar energy ranges, were processed using tools from the NuSTAR Data Analysis Software package NuSTARDAS (v. 2.1.2), which is incorporated into HEASOFT (v. 6.31.1) as detailed in (Nasa High Energy Astrophysics Science Archive Research Center (Heasarc) 2014). NuSTAR’s calibration database (CALDB) v. 20221229 was utilized. The data went through calibration and screening using the nupipeline tool. Parameters saamode=OPTIMIZED and tentacle=yes were employed to screen the data for elevated count rates resulting from the spacecraft’s passages through the South Atlantic Anomaly. Subsequently, the nuproducts tool was utilized to generate various outputs, including the source and background lightcurves and spectra, as well as response and response matrix files. Figures 1(a,b) present images of the combined FPMA and FPMB event lists for the (3 − 10) keV and (10 − 50) keV energy bands, respectively. The source counts were obtained from a circular region with a radius of 40′′ (indicated by the green circle in Figure 1), representing 60% of the energy within the point spread function. The background measurement was performed locally in an area devoid of sources. Within the source extraction circle, there are 771 X-ray events with energies ranging from 3 to 10 keV, approximately one third of which are background events. The source is not detected in the (10 − 20) keV band (not shown) or the (10 − 50) keV band (Figure 1b), nor at higher energies. 2.2. Swift Data Using the Neil Gehrels Swift observatory (Gehrels et al. 2004), we conducted 16 short observations of DQ Tau near periastron over a time period of July 28 to August 2, 2022. These observations are part of our joint NuSTAR/Swift program. The observations were spaced several hours apart, with durations ranging from 1 to 1.7 ksec, totaling 22.5 ksec. The target ID for these observations is 14857. The X-ray Telescope (XRT) operated in the PC mode, while the Ultraviolet/Optical Telescope (UVOT) operated in the 0x30ed standard sixfilter blue-weighted mode. The Swift-XRT data product generator (Evans et al. 2007, 2009) was utilized to construct X-ray light curves and source/background spectra, along with the relevant calibration files. The generator employed HEASOFT package (v. 6.29) and CALDB (v. 20230109). Figure 1c presents the XRT image obtained from merging the event lists of all 16 observations. Within the circular source extraction region of a 30′′ radius (indicated by the green circle in the image), we identified 249 X-ray counts with energies ranging from 0.2 to 10 keV, of which only a few percent represented background counts. For each of the 16 observations, UVOT magnitudes for the six filters (V:B:U:W1:M2:W2) were measured by applying the fappend (Blackburn et al. 1999) and uvotmaghist tools from HEASOFT (v. 6.31.1). 2.3. Chandra Data To investigate the soft X-ray emission throughout the entire orbital phase of DQ Tau and complement the observations made by NuSTAR and Swift at periastron, additional X-ray data were obtained utilizing the Chandra X-ray Observatory (Weisskopf et al. 2002). The investigation involved 12 short Chandra imaging observations of DQ Tau away from periastron, with each observation lasting approximately 1.5 ksec. These observations were part of the Director’s Discretionary Time (DDT) program, with corresponding observation IDs ranging from 26464 to 26475. Data were obtained between August 1 and August 14, 2022, covering an orbital phase range of 1.1 to 1.9. To mitigate potential pileup effects during anticipated Xray flares, a 1/8 sub-array of a single ACIS-I3 chip was employed (Garmire et al. 2003). For the Chandra data reduction and analysis, CIAO v4.15(Fruscione et al. 2006) and CALDB v4.10.4 were utilized. The CIAO tools chandra repro and reproject obs were used to reprocess the data and merge the event images. Figure 1d displays the cutout of the merged Chandra-ACIS-I3 image of DQ Tau. Count rates and apparent fluxes were measured, and spectra and response files were generated using the srcflux tool. Within the circular source extraction region, with a radius of 2′′ (indicated by the green circle in the image), and within the energy band of (0.5 − 8) keV, net X-ray events were observed between 30 and 50 per observation in 8 instances. However, the remaining 4 consecutive observations (ObsIDs 26471, 26472, 26473, and 26474) exhibited higher net count levels, ranging from 61 to 781 counts per observation. This paper is available on arxiv under CC 4.0 license. Authors: (1) Konstantin V. Getman, Department of Astronomy & Astrophysics, Pennsylvania State University; (2) Agnes Kospal, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, E¨otv¨os Lor´and Research Network (ELKH), MTA Centre of Excellence, Max Planck Institute for Astronomy, and ELTE E¨otv¨os Lor´and University, Institute of Physics; (3) Nicole Arulanantham, Space Telescope Science Institute; (4) Dmitry A. Semenov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences; (5) Grigorii V. Smirnov-Pinchukov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences; (6) Sierk E. van Terwisga, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Konstantin V. Getman, Department of Astronomy & Astrophysics, Pennsylvania State University; (2) Agnes Kospal, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, E¨otv¨os Lor´and Research Network (ELKH), MTA Centre of Excellence, Max Planck Institute for Astronomy, and ELTE E¨otv¨os Lor´and University, Institute of Physics; (3) Nicole Arulanantham, Space Telescope Science Institute; (4) Dmitry A. Semenov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences; (5) Grigorii V. Smirnov-Pinchukov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences; (6) Sierk E. van Terwisga, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences. Table of Links Abstract and Intro X-ray Observations and Data Extraction Flare Analyses Comparison with X-ray Flares from Young Stars Discussion Conclusions Acknowledgments and References Abstract and Intro Abstract and Intro X-ray Observations and Data Extraction X-ray Observations and Data Extraction Flare Analyses Flare Analyses Comparison with X-ray Flares from Young Stars Comparison with X-ray Flares from Young Stars Discussion Discussion Conclusions Conclusions Acknowledgments and References Acknowledgments and References 2. X-RAY OBSERVATIONS AND DATA EXTRACTION 2.1. NuSTAR Data We conducted a single observation (ObsID 30801011002; PI K. Getman) of this system with NuSTAR (Harrison et al. 2013) from 04:51:09 UTC on July 28, 2022, to 19:36:09 UTC on July 31, 2022. This time window covers the orbital phase range of Φ = (0.9 − 1.13) around the periastron passage on July 30, 2022 (Φ = 1.0). The science exposure of the observation, taking into account Earth occultations, is 156 ksec. The data obtained from focal plane modules A and B (FPMA and FPMB), covering similar energy ranges, were processed using tools from the NuSTAR Data Analysis Software package NuSTARDAS (v. 2.1.2), which is incorporated into HEASOFT (v. 6.31.1) as detailed in (Nasa High Energy Astrophysics Science Archive Research Center (Heasarc) 2014). NuSTAR’s calibration database (CALDB) v. 20221229 was utilized. The data went through calibration and screening using the nupipeline tool. Parameters saamode=OPTIMIZED and tentacle=yes were employed to screen the data for elevated count rates resulting from the spacecraft’s passages through the South Atlantic Anomaly. Subsequently, the nuproducts tool was utilized to generate various outputs, including the source and background lightcurves and spectra, as well as response and response matrix files. Figures 1(a,b) present images of the combined FPMA and FPMB event lists for the (3 − 10) keV and (10 − 50) keV energy bands, respectively. The source counts were obtained from a circular region with a radius of 40′′ (indicated by the green circle in Figure 1), representing 60% of the energy within the point spread function. The background measurement was performed locally in an area devoid of sources. Within the source extraction circle, there are 771 X-ray events with energies ranging from 3 to 10 keV, approximately one third of which are background events. The source is not detected in the (10 − 20) keV band (not shown) or the (10 − 50) keV band (Figure 1b), nor at higher energies. 2.2. Swift Data Using the Neil Gehrels Swift observatory (Gehrels et al. 2004), we conducted 16 short observations of DQ Tau near periastron over a time period of July 28 to August 2, 2022. These observations are part of our joint NuSTAR/Swift program. The observations were spaced several hours apart, with durations ranging from 1 to 1.7 ksec, totaling 22.5 ksec. The target ID for these observations is 14857. The X-ray Telescope (XRT) operated in the PC mode, while the Ultraviolet/Optical Telescope (UVOT) operated in the 0x30ed standard sixfilter blue-weighted mode. The Swift-XRT data product generator (Evans et al. 2007, 2009) was utilized to construct X-ray light curves and source/background spectra, along with the relevant calibration files. The generator employed HEASOFT package (v. 6.29) and CALDB (v. 20230109). Figure 1c presents the XRT image obtained from merging the event lists of all 16 observations. Within the circular source extraction region of a 30′′ radius (indicated by the green circle in the image), we identified 249 X-ray counts with energies ranging from 0.2 to 10 keV, of which only a few percent represented background counts. For each of the 16 observations, UVOT magnitudes for the six filters (V:B:U:W1:M2:W2) were measured by applying the fappend (Blackburn et al. 1999) and uvotmaghist tools from HEASOFT (v. 6.31.1). 2.3. Chandra Data To investigate the soft X-ray emission throughout the entire orbital phase of DQ Tau and complement the observations made by NuSTAR and Swift at periastron, additional X-ray data were obtained utilizing the Chandra X-ray Observatory (Weisskopf et al. 2002). The investigation involved 12 short Chandra imaging observations of DQ Tau away from periastron, with each observation lasting approximately 1.5 ksec. These observations were part of the Director’s Discretionary Time (DDT) program, with corresponding observation IDs ranging from 26464 to 26475. Data were obtained between August 1 and August 14, 2022, covering an orbital phase range of 1.1 to 1.9. To mitigate potential pileup effects during anticipated Xray flares, a 1/8 sub-array of a single ACIS-I3 chip was employed (Garmire et al. 2003). For the Chandra data reduction and analysis, CIAO v4.15(Fruscione et al. 2006) and CALDB v4.10.4 were utilized. The CIAO tools chandra repro and reproject obs were used to reprocess the data and merge the event images. Figure 1d displays the cutout of the merged Chandra-ACIS-I3 image of DQ Tau. Count rates and apparent fluxes were measured, and spectra and response files were generated using the srcflux tool. Within the circular source extraction region, with a radius of 2′′ (indicated by the green circle in the image), and within the energy band of (0.5 − 8) keV, net X-ray events were observed between 30 and 50 per observation in 8 instances. However, the remaining 4 consecutive observations (ObsIDs 26471, 26472, 26473, and 26474) exhibited higher net count levels, ranging from 61 to 781 counts per observation.

Colliding Magnetospheres: X-ray Observations and Data Extraction

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Konstantin V. Getman, Department of Astronomy & Astrophysics, Pennsylvania State University;
(2) Agnes Kospal, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, E¨otv¨os Lor´and Research Network (ELKH), MTA Centre of
Excellence, Max Planck Institute for Astronomy, and ELTE E¨otv¨os Lor´and University, Institute of Physics;
(3) Nicole Arulanantham, Space Telescope Science Institute;
(4) Dmitry A. Semenov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences;
(5) Grigorii V. Smirnov-Pinchukov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences;
(6) Sierk E. van Terwisga, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences. Table of Links Abstract and Intro
X-ray Observations and Data Extraction
Flare Analyses
Comparison with X-ray Flares from Young Stars
Discussion
Conclusions
Acknowledgments and References ABSTRACT DQ Tau is a unique young high-eccentricity binary system that exhibits regular magnetic reconnection flares and pulsed accretion near periastron. We conducted NuSTAR, Swift, and Chandra observations during the July 30, 2022 periastron to characterize X-ray, near-ultraviolet (NUV), and optical flaring emissions. Our findings confirm the presence of X-ray super-flares accompanied by substantial NUV and optical flares, consistent with previous discoveries of periastron flares in 2010 and 2021. These observations, supported by new evidence, strongly establish the magnetosphere collision mechanism as the primary driver of magnetic energy release during DQ Tau’s periastron flares. The energetics of the observed X-ray super-flares remain consistent across the three periastrons, indicating recurring energy sources during each passage, surpassing the capabilities of single stars. The observed flaring across multiple bands supports the Adams et al. model for magnetosphere interaction in eccentric binaries. Evidence from modeling and past and current observations suggests that both the mm/X-ray periastron flares and tentatively, the magnetic reconnection-related components of the optical/NUV emissions, conform to the classical solar/stellar non-thermal thick-target model, except for the distinctive magnetic energy source. However, our NuSTAR observations suffered from high background levels, hindering the detection of anticipated non-thermal hard X-rays. Furthermore, we report serendipitous discovery of X-ray super-flares occurring away from periastron, potentially associated with interacting magnetospheres. The current study is part of a broader multi-wavelength campaign, which is planned to investigate the influence of DQ Tau’s stellar radiation on gas-phase ion chemistry within its circumbinary disk. Keywords: Pre-main sequence stars (1290) — Spectroscopic binary stars (1557) — X-ray stars (1823) — Stellar magnetic fields (1610) — Optical flares (1166) — Ultraviolet transient sources (1854) —- Stellar x-ray flares (1637) — Solar x-ray flares (1816) — Solar flares (1496) — Stellar flares (1603) — Protoplanetary disks (1300) 1. INTRODUCTION DQ Tau is a nearby (D = 195 pc; Gaia Collaboration et al. 2023), non-eclipsing, double-lined spectro scopic binary system, consisting of two pre-main sequence (PMS) stars of equal mass (0.6 M⊙) and equal radius (2 R⊙) (Mathieu et al. 1997; Czekala et al. 2016; Pouilly et al. 2023). These stars exhibit spectral types within the range of M0 to K7. The rotational periods of the primary and secondary components are 3 days (K´osp´al et al. 2018) and 4.5 days (Pouilly et al. in prep.), respectively. The orbital period measures 15.8 days. DQ Tau boasts a highly eccentric orbit (e ∼ 0.6) and displays an exceptionally small periastron separation, measuring only about 8 −10 stellar radii (Mathieu et al. 1997; Czekala et al. 2016; Pouilly et al. 2023). Furthermore, the binary components of DQ Tau harbor relatively strong surface magnetic fields, estimated at around 2.5 kG, which give rise to formidable magnetospheres (Pouilly et al. 2023, Pouilly et al. in prep.). Surrounding DQ Tau is a protoplanetary disk of average size (≤ 100 au), complete with a small 0.3 au cavity (Czekala et al. 2016; K´osp´al et al. 2018; Ballering & Eisner 2019). Large optical and UV brightenings primarily occur at orbital phase (Φ = 0.8 − 1.2), and they are mainly attributed to the pulsed accretion of disk material onto the binary components (Tofflemire et al. 2017; K´osp´al et al. 2018; Muzerolle et al. 2019; Fiorellino et al. 2022). However, far-UV (FUV) observations of DQ Tau with the Cosmic Origins Spectrograph onboard HST (HST-COS) showed no correlation between the orbital phase of the binary and the C IV flux, a tracer of mass accretion rate, indicating that some component of the behavior is stochastic (Ardila et al. 2015). The system exhibits powerful mm/X-ray flares coinciding with periastron passage, attributed to collisions between the magnetospheres of the binary components. The evidence supporting the magnetsophere collision hypothesis includes the recurrence of synchrotron mmband flaring during 4 periastron encounters (Salter et al. 2008, 2010), the recurrence of soft X-ray flaring in 2 periastron encounters (Getman et al. 2011, 2022a), the timing and energy relationships between the mm and X-ray flares, and the consistency observed between the flare loop size and binary separation (Salter et al. 2010; Getman et al. 2011). Several other young binary systems with high eccentricities have been reported to exhibit enhanced levels of either X-ray, optical/mm, or radio emissions near their periastron passages. Notable examples include ϵ Lupi (Das et al. 2023), a collective study of four binaries (Parenago 523, RX J1622.7-2325 Nw, UZ Tau E, and HD 152404) conducted by Getman et al. (2016), UZ Tau E (K´osp´al et al. 2011), and V773 Tau A (Massi et al. 2008; Adams et al. 2011). In these systems, magnetosphere collision has been proposed as a primary mechanism responsible for generating the magnetic reconnection energy that drives these events. Modelling studies have shown that PMS X-rays have strong impact on disk ionization and chemistry (Glassgold et al. 2000; Alexander et al. 2014). But most studies assume continuous irradiation without considering the high-amplitude variations in flux and spectrum due to super-flares. A few time-dependent calculations show that disk ionization may respond to sudden large Xray flares (Rab et al. 2017; Waggoner & Cleeves 2022). This may already have been seen. One empirical report of ionization variability has emerged: the H13CO+ abundance of IM Lup’s disk jumped up and down by a factor of 2.5 over months (Cleeves et al. 2017). However, since no concurrent X-ray observations were conducted, the exact cause cannot be definitively ascribed to X-ray flaring. The occurrence of large X-ray flares in young stars is relatively rare and unpredictable, displaying a stochastic nature (Getman & Feigelson 2021). However, the presence of predictable X-ray super-flares and accretion outbursts in close proximity to periastron passage makes DQ Tau an extraordinary laboratory for investigating the influence of stellar radiation on the gas-phase ion chemistry within its disk. To achieve this, we conducted a single X-ray observation using the NuSTAR telescope, along with multiple short-duration observations using the Swift telescope in the X-ray, UV, and optical wavelengths. These observations were strategically timed near a specific periastron passage of DQ Tau, taking place in July-August 2022. Additionally, we captured multiple snapshots of the non-periastron portion of DQ Tau’s orbit using the Chandra X-ray telescope. However, we encountered unfavorable weather conditions that limited our ALMA observations to a single short session near periastron. The results from this ALMA observation will be presented in a forthcoming paper. Meanwhile, building upon the X-ray/UV/optical data acquired in 2022 and the previously obtained X-ray/mm data (Salter et al. 2010; Getman et al. 2011, 2022a), our current study is dedicated to further investigating the origins and energetic properties of X-ray flares, along with their corresponding near-ultraviolet (NUV) and optical flare counterparts, observed within the remarkable young binary system DQ Tau. The structure of the paper is outlined as follows: Section 2 provides a detailed description of the data reduction and reduction procedures employed for X-ray, UV, and optical analyses. In Section 3, we present the detection of flares and examine their spectral properties. Section 4 offers a comparison between the X-ray periastron flares observed in DQ Tau and super-flares observed in numerous other PMS stars. Finally, Section 5 delves into a discussion surrounding the origin and energetics of the X-ray flares, as well as their associated NUV and optical counterparts. This paper is available on arxiv under CC 4.0 license. Authors: (1) Konstantin V. Getman, Department of Astronomy & Astrophysics, Pennsylvania State University; (2) Agnes Kospal, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, E¨otv¨os Lor´and Research Network (ELKH), MTA Centre of Excellence, Max Planck Institute for Astronomy, and ELTE E¨otv¨os Lor´and University, Institute of Physics; (3) Nicole Arulanantham, Space Telescope Science Institute; (4) Dmitry A. Semenov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences; (5) Grigorii V. Smirnov-Pinchukov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences; (6) Sierk E. van Terwisga, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Konstantin V. Getman, Department of Astronomy & Astrophysics, Pennsylvania State University; (2) Agnes Kospal, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, E¨otv¨os Lor´and Research Network (ELKH), MTA Centre of Excellence, Max Planck Institute for Astronomy, and ELTE E¨otv¨os Lor´and University, Institute of Physics; (3) Nicole Arulanantham, Space Telescope Science Institute; (4) Dmitry A. Semenov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences; (5) Grigorii V. Smirnov-Pinchukov, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences; (6) Sierk E. van Terwisga, Konkoly Observatory, Research Centre for Astronomy and Earth Sciences. Table of Links Abstract and Intro X-ray Observations and Data Extraction Flare Analyses Comparison with X-ray Flares from Young Stars Discussion Conclusions Acknowledgments and References Abstract and Intro Abstract and Intro X-ray Observations and Data Extraction X-ray Observations and Data Extraction Flare Analyses Flare Analyses Comparison with X-ray Flares from Young Stars Comparison with X-ray Flares from Young Stars Discussion Discussion Conclusions Conclusions Acknowledgments and References Acknowledgments and References ABSTRACT DQ Tau is a unique young high-eccentricity binary system that exhibits regular magnetic reconnection flares and pulsed accretion near periastron. We conducted NuSTAR, Swift, and Chandra observations during the July 30, 2022 periastron to characterize X-ray, near-ultraviolet (NUV), and optical flaring emissions. Our findings confirm the presence of X-ray super-flares accompanied by substantial NUV and optical flares, consistent with previous discoveries of periastron flares in 2010 and 2021. These observations, supported by new evidence, strongly establish the magnetosphere collision mechanism as the primary driver of magnetic energy release during DQ Tau’s periastron flares. The energetics of the observed X-ray super-flares remain consistent across the three periastrons, indicating recurring energy sources during each passage, surpassing the capabilities of single stars. The observed flaring across multiple bands supports the Adams et al. model for magnetosphere interaction in eccentric binaries. Evidence from modeling and past and current observations suggests that both the mm/X-ray periastron flares and tentatively, the magnetic reconnection-related components of the optical/NUV emissions, conform to the classical solar/stellar non-thermal thick-target model, except for the distinctive magnetic energy source. However, our N u STAR observations suffered from high background levels, hindering the detection of anticipated non-thermal hard X-rays. Furthermore, we report serendipitous discovery of X-ray super-flares occurring away from periastron, potentially associated with interacting magnetospheres. The current study is part of a broader multi-wavelength campaign, which is planned to investigate the influence of DQ Tau’s stellar radiation on gas-phase ion chemistry within its circumbinary disk. u Keywords : Pre-main sequence stars (1290) — Spectroscopic binary stars (1557) — X-ray stars (1823) — Stellar magnetic fields (1610) — Optical flares (1166) — Ultraviolet transient sources (1854) —- Stellar x-ray flares (1637) — Solar x-ray flares (1816) — Solar flares (1496) — Stellar flares (1603) — Protoplanetary disks (1300) Keywords 1. INTRODUCTION DQ Tau is a nearby (D = 195 pc; Gaia Collaboration et al. 2023), non-eclipsing, double-lined spectro scopic binary system, consisting of two pre-main sequence (PMS) stars of equal mass (0.6 M⊙) and equal radius (2 R⊙) (Mathieu et al. 1997; Czekala et al. 2016; Pouilly et al. 2023). These stars exhibit spectral types within the range of M0 to K7. The rotational periods of the primary and secondary components are 3 days (K´osp´al et al. 2018) and 4.5 days (Pouilly et al. in prep.), respectively. The orbital period measures 15.8 days. DQ Tau boasts a highly eccentric orbit (e ∼ 0.6) and displays an exceptionally small periastron separation, measuring only about 8 −10 stellar radii (Mathieu et al. 1997; Czekala et al. 2016; Pouilly et al. 2023). Furthermore, the binary components of DQ Tau harbor relatively strong surface magnetic fields, estimated at around 2.5 kG, which give rise to formidable magnetospheres (Pouilly et al. 2023, Pouilly et al. in prep.). Surrounding DQ Tau is a protoplanetary disk of average size (≤ 100 au), complete with a small 0.3 au cavity (Czekala et al. 2016; K´osp´al et al. 2018; Ballering & Eisner 2019). Large optical and UV brightenings primarily occur at orbital phase (Φ = 0.8 − 1.2), and they are mainly attributed to the pulsed accretion of disk material onto the binary components (Tofflemire et al. 2017; K´osp´al et al. 2018; Muzerolle et al. 2019; Fiorellino et al. 2022). However, far-UV (FUV) observations of DQ Tau with the Cosmic Origins Spectrograph onboard HST (HST-COS) showed no correlation between the orbital phase of the binary and the C IV flux, a tracer of mass accretion rate, indicating that some component of the behavior is stochastic (Ardila et al. 2015). The system exhibits powerful mm/X-ray flares coinciding with periastron passage, attributed to collisions between the magnetospheres of the binary components. The evidence supporting the magnetsophere collision hypothesis includes the recurrence of synchrotron mmband flaring during 4 periastron encounters (Salter et al. 2008, 2010), the recurrence of soft X-ray flaring in 2 periastron encounters (Getman et al. 2011, 2022a), the timing and energy relationships between the mm and X-ray flares, and the consistency observed between the flare loop size and binary separation (Salter et al. 2010; Getman et al. 2011). Several other young binary systems with high eccentricities have been reported to exhibit enhanced levels of either X-ray, optical/mm, or radio emissions near their periastron passages. Notable examples include ϵ Lupi (Das et al. 2023), a collective study of four binaries (Parenago 523, RX J1622.7-2325 Nw, UZ Tau E, and HD 152404) conducted by Getman et al. (2016), UZ Tau E (K´osp´al et al. 2011), and V773 Tau A (Massi et al. 2008; Adams et al. 2011). In these systems, magnetosphere collision has been proposed as a primary mechanism responsible for generating the magnetic reconnection energy that drives these events. Modelling studies have shown that PMS X-rays have strong impact on disk ionization and chemistry (Glassgold et al. 2000; Alexander et al. 2014). But most studies assume continuous irradiation without considering the high-amplitude variations in flux and spectrum due to super-flares. A few time-dependent calculations show that disk ionization may respond to sudden large Xray flares (Rab et al. 2017; Waggoner & Cleeves 2022). This may already have been seen. One empirical report of ionization variability has emerged: the H13CO+ abundance of IM Lup’s disk jumped up and down by a factor of 2.5 over months (Cleeves et al. 2017). However, since no concurrent X-ray observations were conducted, the exact cause cannot be definitively ascribed to X-ray flaring. The occurrence of large X-ray flares in young stars is relatively rare and unpredictable, displaying a stochastic nature (Getman & Feigelson 2021). However, the presence of predictable X-ray super-flares and accretion outbursts in close proximity to periastron passage makes DQ Tau an extraordinary laboratory for investigating the influence of stellar radiation on the gas-phase ion chemistry within its disk. To achieve this, we conducted a single X-ray observation using the N u STAR telescope, along with multiple short-duration observations using the Swift telescope in the X-ray, UV, and optical wavelengths. These observations were strategically timed near a specific periastron passage of DQ Tau, taking place in July-August 2022. Additionally, we captured multiple snapshots of the non-periastron portion of DQ Tau’s orbit using the Chandra X-ray telescope. However, we encountered unfavorable weather conditions that limited our ALMA observations to a single short session near periastron. The results from this ALMA observation will be presented in a forthcoming paper. u Meanwhile, building upon the X-ray/UV/optical data acquired in 2022 and the previously obtained X-ray/mm data (Salter et al. 2010; Getman et al. 2011, 2022a), our current study is dedicated to further investigating the origins and energetic properties of X-ray flares, along with their corresponding near-ultraviolet (NUV) and optical flare counterparts, observed within the remarkable young binary system DQ Tau. The structure of the paper is outlined as follows: Section 2 provides a detailed description of the data reduction and reduction procedures employed for X-ray, UV, and optical analyses. In Section 3, we present the detection of flares and examine their spectral properties. Section 4 offers a comparison between the X-ray periastron flares observed in DQ Tau and super-flares observed in numerous other PMS stars. Finally, Section 5 delves into a discussion surrounding the origin and energetics of the X-ray flares, as well as their associated NUV and optical counterparts.

Colliding Magnetospheres in The Young High-Eccentricity Binary DQ Tau: Abstract and Intro

How to Create a Steel Base Plate Design Web App Using Python and Viktor

পাইথন এবং ভিক্টর ব্যবহার করে কীভাবে একটি স্টিল বেস প্লেট ডিজাইন ওয়েব অ্যাপ তৈরি করবেন

So erstellen Sie mit Python und Viktor eine Web-App zum Entwerfen von Stahlgrundplatten

Cómo crear una aplicación web de diseño de placa base de acero usando Python y Viktor

Comment créer une application Web de conception de plaques de base en acier à l'aide de Python et Viktor

पायथन और विक्टर का उपयोग करके स्टील बेस प्लेट डिज़ाइन वेब ऐप कैसे बनाएं

Python と Viktor を使用してスチールベースプレート設計 Web アプリを作成する方法

Python과 Viktor를 사용하여 강철 베이스 플레이트 디자인 웹 앱을 만드는 방법

Como criar um aplicativo Web de design de placa de base de aço usando Python e Viktor

Как создать веб-приложение для проектирования стальной опорной пластины с помощью Python и Viktor

Python ve Viktor'u Kullanarak Çelik Taban Plaka Tasarımı Web Uygulaması Nasıl Oluşturulur

Cách tạo ứng dụng web thiết kế tấm đế thép bằng Python và Viktor

如何使用 Python 和 Viktor 创建钢底板设计 Web 应用程序

This paper is available on arxiv under CC BY-SA 4.0 DEED license.
Authors:
(1) Lana L. Blaschke, Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, Potsdam Institute for Climate Impact Research, Potsdam, Germany and lana.blaschke@pik-potsdam.de;
(2) Da Nian, Potsdam Institute for Climate Impact Research, Potsdam, Germany;
(3) Sebastian Bathiany,  Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, and Potsdam Institute for Climate Impact Research, Potsdam, Germany;
(4)  Maya Ben-Yami,  Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, and Potsdam Institute for Climate Impact Research, Potsdam, Germany;
(5) Taylor Smith, Institute of Geosciences, University of Potsdam, 14476 Potsdam, Germany;
(6)  Chris A. Boulton, Global Systems Institute, University of Exeter, EX4 4QE Exeter, UK ;
(7) Niklas Boers, Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, Potsdam Institute for Climate Impact Research, Potsdam, Germany, Global Systems Institute, University of Exeter, EX4 4QE Exeter, UK, and Department of Mathematics, University of Exeter, EX4 4QF Exeter, UK. Table of Links Abstract and Introduction
Materials and Methods
Data
Results
Conclusions, Open Research Section and Conflict of Interest/Competing Interests
Author Contributions, Supplementary Information, Acknowledgments and References
Additional Insight from the Conceptual Model 
AMSR2 until 2022 Excluded Due to Missing Human Land Use Data
Investigation of Resilience Loss in AMSR2’s X-Band
Results Proving Robustness
Potential Driving Forces and Sources of Bias RESULTS PROVING ROBUSTNESS Text S8. Robustness with respect to the parameterization of the STL algorithm The results in Figures 5 and 6 are based on the residual found by the STL algorithm with default parameterization. Yet, Figure S9 and S10 prove that the analysis is not influenced by this choice as the results are almost identical when the length of the seasonal smoother equals 13 (instead of 7). Text S9. Robustness with respect to the size of the sliding windows The choice of the sliding window size is difficult for short time series as that of AMSR-E’s and AMSR2’s VOD. Yet, the results are robust w.r.t it, as Figure S11 based on sliding windows of 3 years is almost identical to Figure 5 with windows of 5 years. This also holds for the summarizing Figure S12 when compared to Figure 6. It is to note that the spatially averaged time series of the three indicators are more noisy for the choice of smaller windows, which is due to the fact the the calculation of the indicators becomes more unstable when calculated on only 36 data points, corresponding to the 3 years. The right choice of the window size in an approach to resilience analysis like the one shown here is challenging, as the increase can only be determined reliably based on enough indicator time steps either. The fact that the results are robust with respect to the window size gives confidence in the choice of 5 years as default. Text S10. Robustness with respect to the measure of change In the main text, any change in indicators is measured in terms of linear trends. Yet, another option would be the Kendall’s τ as a measure of steadiness of increase. Figure S13 is the analogue of Figure 5 but with increase in time series quantified in terms of Kendall’s τ . In Figure 6, increase in the indicators is quantified in terms of linear trends. The results are almost identical when measuring the indicators’ increase by the Kendall τ rank coefficient. Text S11. Robustness with respect to the distance defining neighboring cells The definition of the spatial correlation depends on the distance taken into account when taking the average correlation with neighboring cells. Figure S15 shows the trends of the spatial correlation for the different VIs comparing different radii defining the set of neighboring cells. As expected, a greater number of neighbors spatially smooths the results, but does not influence the general spatial pattern of the trends of spatial correlation. The turquoise circle on the bottom of the map shows an exemplary circular band of neighboring cells. In the main text, all results are based on a radius of 100 km. This paper is available on arxiv under CC BY-SA 4.0 DEED license. Authors: (1) Lana L. Blaschke, Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, Potsdam Institute for Climate Impact Research, Potsdam, Germany and lana.blaschke@pik-potsdam.de; (2) Da Nian, Potsdam Institute for Climate Impact Research, Potsdam, Germany; (3) Sebastian Bathiany,  Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, and Potsdam Institute for Climate Impact Research, Potsdam, Germany; (4)  Maya Ben-Yami,  Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, and Potsdam Institute for Climate Impact Research, Potsdam, Germany; (5) Taylor Smith, Institute of Geosciences, University of Potsdam, 14476 Potsdam, Germany; (6)  Chris A. Boulton, Global Systems Institute, University of Exeter, EX4 4QE Exeter, UK ; (7) Niklas Boers, Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, Potsdam Institute for Climate Impact Research, Potsdam, Germany, Global Systems Institute, University of Exeter, EX4 4QE Exeter, UK, and Department of Mathematics, University of Exeter, EX4 4QF Exeter, UK. This paper is available on arxiv under CC BY-SA 4.0 DEED license. Authors: Authors: (1) Lana L. Blaschke, Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, Potsdam Institute for Climate Impact Research, Potsdam, Germany and lana.blaschke@pik-potsdam.de; (2) Da Nian, Potsdam Institute for Climate Impact Research, Potsdam, Germany; (3) Sebastian Bathiany,  Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, and Potsdam Institute for Climate Impact Research, Potsdam, Germany; (4)  Maya Ben-Yami,  Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, and Potsdam Institute for Climate Impact Research, Potsdam, Germany; (5) Taylor Smith, Institute of Geosciences, University of Potsdam, 14476 Potsdam, Germany; (6)  Chris A. Boulton, Global Systems Institute, University of Exeter, EX4 4QE Exeter, UK ; (7) Niklas Boers, Earth System Modelling, School of Engineering and Design, Technical University of Munich, Munich, Germany, Potsdam Institute for Climate Impact Research, Potsdam, Germany, Global Systems Institute, University of Exeter, EX4 4QE Exeter, UK, and Department of Mathematics, University of Exeter, EX4 4QF Exeter, UK. Table of Links Abstract and Introduction Materials and Methods Data Results Conclusions, Open Research Section and Conflict of Interest/Competing Interests Author Contributions, Supplementary Information, Acknowledgments and References Additional Insight from the Conceptual Model AMSR2 until 2022 Excluded Due to Missing Human Land Use Data Investigation of Resilience Loss in AMSR2’s X-Band Results Proving Robustness Potential Driving Forces and Sources of Bias Abstract and Introduction Abstract and Introduction Materials and Methods Materials and Methods Data Data Results Results Conclusions, Open Research Section and Conflict of Interest/Competing Interests Conclusions, Open Research Section and Conflict of Interest/Competing Interests Author Contributions, Supplementary Information, Acknowledgments and References Author Contributions, Supplementary Information, Acknowledgments and References Additional Insight from the Conceptual Model Additional Insight from the Conceptual Model AMSR2 until 2022 Excluded Due to Missing Human Land Use Data AMSR2 until 2022 Excluded Due to Missing Human Land Use Data Investigation of Resilience Loss in AMSR2’s X-Band Investigation of Resilience Loss in AMSR2’s X-Band Results Proving Robustness Results Proving Robustness Potential Driving Forces and Sources of Bias Potential Driving Forces and Sources of Bias RESULTS PROVING ROBUSTNESS Text S8. Robustness with respect to the parameterization of the STL algorithm The results in Figures 5 and 6 are based on the residual found by the STL algorithm with default parameterization. Yet, Figure S9 and S10 prove that the analysis is not influenced by this choice as the results are almost identical when the length of the seasonal smoother equals 13 (instead of 7). Text S9. Robustness with respect to the size of the sliding windows The choice of the sliding window size is difficult for short time series as that of AMSR-E’s and AMSR2’s VOD. Yet, the results are robust w.r.t it, as Figure S11 based on sliding windows of 3 years is almost identical to Figure 5 with windows of 5 years. This also holds for the summarizing Figure S12 when compared to Figure 6. It is to note that the spatially averaged time series of the three indicators are more noisy for the choice of smaller windows, which is due to the fact the the calculation of the indicators becomes more unstable when calculated on only 36 data points, corresponding to the 3 years. The right choice of the window size in an approach to resilience analysis like the one shown here is challenging, as the increase can only be determined reliably based on enough indicator time steps either. The fact that the results are robust with respect to the window size gives confidence in the choice of 5 years as default. Text S10. Robustness with respect to the measure of change In the main text, any change in indicators is measured in terms of linear trends. Yet, another option would be the Kendall’s τ as a measure of steadiness of increase. Figure S13 is the analogue of Figure 5 but with increase in time series quantified in terms of Kendall’s τ . In Figure 6, increase in the indicators is quantified in terms of linear trends. The results are almost identical when measuring the indicators’ increase by the Kendall τ rank coefficient. Text S11. Robustness with respect to the distance defining neighboring cells The definition of the spatial correlation depends on the distance taken into account when taking the average correlation with neighboring cells. Figure S15 shows the trends of the spatial correlation for the different VIs comparing different radii defining the set of neighboring cells. As expected, a greater number of neighbors spatially smooths the results, but does not influence the general spatial pattern of the trends of spatial correlation. The turquoise circle on the bottom of the map shows an exemplary circular band of neighboring cells. In the main text, all results are based on a radius of 100 km.

Loss of Amazon Rainforest Resilience: Results Proving Robustness

Design Systems: A Front-End Engineer's Guide to Efficient Atomic Design

Mission Generation Using Classic Machine Learning and Recurrent Neural Networks in Zombie State

জম্বি রাজ্যে ক্লাসিক মেশিন লার্নিং এবং পুনরাবৃত্ত নিউরাল নেটওয়ার্ক ব্যবহার করে মিশন জেনারেশন

Missionsgenerierung mit klassischem maschinellem Lernen und rekurrierenden neuronalen Netzwerken im Zombie-Zustand

Generación de misiones utilizando aprendizaje automático clásico y redes neuronales recurrentes en estado zombie

Génération de mission à l'aide de l'apprentissage automatique classique et des réseaux de neurones récurrents dans un état zombie

ज़ोंबी स्टेट में क्लासिक मशीन लर्निंग और रीकरंट न्यूरल नेटवर्क का उपयोग करके मिशन जनरेशन

ゾンビ状態での古典的な機械学習とリカレントニューラルネットワークを使用したミッション生成

좀비 상태에서 고전적인 기계 학습과 순환 신경망을 사용한 미션 생성

Geração de missão usando aprendizado de máquina clássico e redes neurais recorrentes no estado zumbi

Генерация миссий с использованием классического машинного обучения и рекуррентных нейронных сетей в состоянии зомби

Zombie State'te Klasik Makine Öğrenimi ve Tekrarlayan Sinir Ağlarını Kullanarak Görev Oluşturma

Tạo nhiệm vụ bằng cách sử dụng mạng lưới thần kinh định kỳ và học máy cổ điển ở trạng thái Zombie

在僵尸状态下使用经典机器学习和循环神经网络生成任务

"How Many Colors Can the Human Eye See?": The Application

This Javascript Code Generates Random Quotes

এই জাভাস্ক্রিপ্ট কোড এলোমেলো উদ্ধৃতি তৈরি করে

Dieser Javascript-Code generiert zufällige Zitate

Este código Javascript genera citas aleatorias

Ce code Javascript génère des citations aléatoires

यह जावास्क्रिप्ट कोड यादृच्छिक उद्धरण उत्पन्न करता है

このJavascriptコードはランダムな引用を生成します

이 자바스크립트 코드는 무작위 인용문을 생성합니다

Este código Javascript gera citações aleatórias

Этот код Javascript генерирует случайные цитаты

Bu Javascript Kodu Rastgele Alıntılar Oluşturuyor

Mã Javascript này tạo ra các trích dẫn ngẫu nhiên

这段 JavaScript 代码可生成随机引号

Python Bokeh is one of the best Python packages for data visualization. Today, we are going to see some Python Bokeh Examples. I have also provided the Python Bokeh project source code on GitHub. Learn this easy visualization tool and add it to your Python stack. What is Python Bokeh? Python is a data visualization tool, or we can also say Python Bokeh is used to plot various types of graphs. There are various other graph plotting libraries like matplotlib, but Python Bokeh graphs are dynamic in nature, which means you can interact with the generated graph. See the below examples… Bokeh Installation 💻: Python Bokeh can be easily installed using PIP. You can install the Python Bokeh easily by running the command: pip install bokeh Now everything is ready, let’s go through the examples 🏃‍♂️… 1. LinePlot from bokeh.plotting import figure, show, output_notebook
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="{LinePlot Python Bokeh Example")
p.line(x, y, line_width=2)
output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 2. Scatter Plot from bokeh.plotting import figure, show, output_notebook
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="Scatter Plot Python Bokeh Example by PratikPathak.com")
p.circle(x, y, size=10, color="navy", alpha=0.5)
output_notebook()
show(p) 3. Bar Chart from bokeh.plotting import figure, show, output_notebook
categories = ["A", "B", "C", "D", "E"]
values = [10, 15, 8, 12, 6]
p = figure(x_range=categories, title="Bar Chart Python Bokeh Example by PratikPathak.com")
p.vbar(x=categories, top=values, width=0.9)
output_notebook()
show(p) 4. Histogram from bokeh.plotting import figure, show, output_notebook
import numpy as np
data = np.random.normal(0, 1, 1000)
p = figure(title="Histogram Python Bokeh Example by PratikPathak.com")
p.hist(data, bins=30, color="navy", alpha=0.5)
output_notebook()
show(p) 5. Pie Chart from bokeh.plotting import figure, show, output_notebook
labels = ["A", "B", "C", "D"]
values = [10, 15, 8, 12]
p = figure(title="Pie Chart Python Bokeh Example by PratikPathak.com")
p.wedge(x=0, y=0, radius=0.4, start_angle=0.6, end_angle=2.6, color=["red", "green", "blue", "yellow"], legend_label=labels)
output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 6. Time Series Plot from bokeh.plotting import figure, show, output_notebook
from datetime import datetime, timedelta
start = datetime(2023, 1, 1)
end = start + timedelta(days=30)
x = [start + timedelta(days=i) for i in range((end-start).days)]
y = [10, 15, 8, 12, 6, 18, 9, 14, 7, 11, 5, 16, 8, 13, 6]
p = figure(x_axis_type="datetime", title="Time Series Plot Python Bokeh Example by PratikPathak.com")
p.line(x, y, line_width=2)
output_notebook()
show(p) 7. Linked Brushing from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource
x1 = [1, 2, 3, 4, 5]
y1 = [4, 5, 5, 7, 3]
x2 = [2, 3, 4, 5, 6]
y2 = [2, 4, 6, 8, 4]
source = ColumnDataSource(data=dict(x1=x1, y1=y1, x2=x2, y2=y2))
p1 = figure(title="Scatter Plot 1")
p1.circle('x1', 'y1', source=source)
p2 = figure(title="Scatter Plot 2 Python Bokeh Example by PratikPathak.com")
p2.circle('x2', 'y2', source=source)
output_notebook()
show(p1, p2) 8. Hover Tooltips from bokeh.plotting import figure, show, output_notebook
from bokeh.models import HoverTool
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="Hover Tooltips Python Bokeh Example by PratikPathak.com")
p.circle(x, y, size=15, fill_color="navy", line_color="white", alpha=0.5)
hover = HoverTool(tooltips=[("(x,y)", "(@x, @y)")])
p.add_tools(hover)
output_notebook()
show(p) 9. Annotations from bokeh.plotting import figure, show, output_notebook
from bokeh.models import Arrow, VectorRenderer, Label
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="Annotations Python Bokeh Example by PratikPathak.com")
p.circle(x, y, size=15, fill_color="navy", line_color="white", alpha=0.5)
arrow = Arrow(x_start=2, y_start=4, x_end=3, y_end=5, line_width=2, line_color="red")
label = Label(x=3, y=6, text="This is a label", render_mode='css', border_line_color='black', border_line_alpha=1.0, background_fill_color='white', background_fill_alpha=0.5)
p.add_layout(arrow)
p.add_layout(label)
output_notebook()
show(p) 10. Custom Glyphs from bokeh.plotting import figure, show, output_notebook
from bokeh.models.glyphs import Asterisk
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="Custom Glyphs Python Bokeh Example by PratikPathak.com")
p.add_glyph(x, y, Asterisk(size=20, line_color="red", fill_color="yellow"))
output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 11. Gridlines and Axes from bokeh.plotting import figure, show, output_notebook
x = [1, 2, 3, 4, 5]
y = [4, 5, 5, 7, 3]
p = figure(title="Gridlines and Axes Python Bokeh Example by PratikPathak.com", x_range=(0, 6), y_range=(0, 8))
p.grid.grid_line_color = "grey"
p.grid.grid_line_dash = [6, 4]
p.xaxis.axis_label = "X-axis"
p.yaxis.axis_label = "Y-axis"
p.line(x, y, line_width=2)
output_notebook()
show(p) 12. Legend from bokeh.plotting import figure, show, output_notebook
x1 = [1, 2, 3, 4, 5]
y1 = [4, 5, 5, 7, 3]
x2 = [2, 3, 4, 5, 6]
y2 = [2, 4, 6, 8, 4]
p = figure(title="Legend Python Bokeh Example by PratikPathak.com")
p.line(x1, y1, line_width=2, color="red", legend_label="Line 1")
p.line(x2, y2, line_width=2, color="blue", legend_label="Line 2")
p.legend.location = "top_left"
output_notebook()
show(p) 13. Categorical Plots from bokeh.plotting import figure, show, output_notebook
fruits = ["Apples", "Pears", "Nectarines", "Plums", "Grapes", "Strawberries"]
counts = [5, 3, 4, 2, 4, 6]
p = figure(x_range=fruits, title="Categorical Plots Python Bokeh Example by PratikPathak.com")
p.vbar(x=fruits, top=counts, width=0.9)
p.xaxis.axis_label = "Fruit"
p.yaxis.axis_label = "Count"
p.xaxis.axis_label_text_font_size = "12pt"
p.yaxis.axis_label_text_font_size = "12pt"
output_notebook()
show(p) 14. Subplots from bokeh.plotting import figure, show, output_notebook
from bokeh.layouts import gridplot
x1 = [1, 2, 3, 4, 5]
y1 = [4, 5, 5, 7, 3]
x2 = [2, 3, 4, 5, 6]
y2 = [2, 4, 6, 8, 4]
p1 = figure(title="Scatter Plot 1 Python Bokeh Example by PratikPathak.com")
p1.circle(x1, y1, size=10, color="navy", alpha=0.5)
p2 = figure(title="Scatter Plot 2 Python Bokeh Example by PratikPathak.com")
p2.circle(x2, y2, size=10, color="red", alpha=0.5)
grid = gridplot([[p1, p2]], plot_width=400, plot_height=400)
output_notebook()
show(grid) 15. Interactive Plots from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource, HoverTool, BoxSelectTool
import numpy as np
x = np.random.random(1000)
y = np.random.random(1000)
source = ColumnDataSource(data=dict(x=x, y=y))
p = figure(title="Interactive Plots Python Bokeh Example by PratikPathak.com", tools="hover,box_select")
p.circle('x', 'y', source=source, size=3, color="navy", alpha=0.5)
hover = HoverTool(tooltips=[("(x,y)", "(@x, @y)")])
p.add_tools(hover)
output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 16. Linked Panning and Zooming from bokeh.plotting import figure, show, output_notebook
from bokeh.models import Range1d
x1 = [1, 2, 3, 4, 5]
y1 = [4, 5, 5, 7, 3]
x2 = [2, 3, 4, 5, 6]
y2 = [2, 4, 6, 8, 4]
p1 = figure(title="Scatter Plot 1 Python Bokeh Example by PratikPathak.com", x_range=Range1d(0, 6), y_range=Range1d(0, 8))
p1.circle(x1, y1, size=10, color="navy", alpha=0.5)
p2 = figure(title="Scatter Plot 2 Python Bokeh Example by PratikPathak.com", x_range=p1.x_range, y_range=p1.y_range)
p2.circle(x2, y2, size=10, color="red", alpha=0.5)
output_notebook()
show(p1, p2) 17. Linked Axis Ranges from bokeh.plotting import figure, show, output_notebook
from bokeh.models import Range1d
x1 = [1, 2, 3, 4, 5]
y1 = [4, 5, 5, 7, 3]
x2 = [2, 3, 4, 5, 6]
y2 = [2, 4, 6, 8, 4]
p1 = figure(title="Scatter Plot 1", x_range=(0, 6), y_range=(0, 8))
p1.circle(x1, y1, size=10, color="navy", alpha=0.5)
p2 = figure(title="Scatter Plot 2", x_range=p1.x_range, y_range=p1.y_range)
p2.circle(x2, y2, size=10, color="red", alpha=0.5)
output_notebook()
show(p1, p2) 18. DateTime Axis from bokeh.plotting import figure, show, output_notebook
from datetime import datetime, timedelta
start = datetime(2023, 1, 1)
end = start + timedelta(days=30)
x = [start + timedelta(days=i) for i in range((end-start).days)]
y = [10, 15, 8, 12, 6, 18, 9, 14, 7, 11, 5, 16, 8, 13, 6]
p = figure(x_axis_type="datetime", title="Datetime Axis Python Bokeh Example by PratikPathak.com")
p.line(x, y, line_width=2)
output_notebook()
show(p) 19. Heatmap from bokeh.plotting import figure, show, output_notebook
import numpy as np
data = np.random.rand(10, 10)
p = figure(title="Heatmap Python Bokeh Example by PratikPathak.com")
p.image(image=[data], x=0, y=0, dw=10, dh=10, palette="Viridis256")
output_notebook()
show(p) 20. Streamgraph from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource
import numpy as np
# Generate some sample data
x = np.linspace(0, 10, 100)
y1 = np.cumsum(np.random.randn(100))
y2 = np.cumsum(np.random.randn(100))
y3 = np.cumsum(np.random.randn(100))
y4 = np.cumsum(np.random.randn(100))
y5 = np.cumsum(np.random.randn(100))
source = ColumnDataSource(data=dict(x=x, y1=y1, y2=y2, y3=y3, y4=y4, y5=y5))
p = figure(title="Streamgraph Python Bokeh Example by PratikPathak.com")
p.area(x='x', y1='y1', y2='y2', y3='y3', y4='y4', y5='y5', source=source, line_color=None)
output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 21. Polar Plot from bokeh.plotting import figure, show, output_notebook
import numpy as np
r = np.linspace(0.1, 1, 10)
theta = np.linspace(0, 2*np.pi, 10)
p = figure(title="Polar Plot Python Bokeh Example by PratikPathak.com", plot_width=600, plot_height=600, x_range=(-1.2, 1.2), y_range=(-1.2, 1.2), toolbar_location=None)
p.polar(r, theta, color="navy", alpha=0.5, line_width=2)
output_notebook()
show(p) 22. Donut Chart from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource
labels = ["A", "B", "C", "D"]
values = [10, 15, 8, 12]
source = ColumnDataSource(data=dict(labels=labels, values=values))
p = figure(title="Donut Chart Python Bokeh Example by PratikPathak.com", x_range=labels)
p.wedge(x=0, y=1, radius=0.4, start_angle=0.6, end_angle=2.6, color=["red", "green", "blue", "yellow"], legend_field="labels")
p.wedge(x=0, y=1, inner_radius=0.3, outer_radius=0.4, start_angle=0.6, end_angle=2.6, color="white")
p.axis.visible = False
p.grid.grid_line_color = None
output_notebook()
show(p) 23. Treemap from bokeh.plotting import figure, show, output_notebook
from bokeh.models import TreemapRenderer, ColumnDataSource
import pandas as pd

# Sample data
data = pd.DataFrame({
    'label': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'],
    'parent': ['', 'A', 'A', 'B', 'B', 'C', 'C', 'D'],
    'value': [10, 5, 4, 3, 2, 1, 1, 1]
})

source = ColumnDataSource(data)
p = figure(title="Treemap Python Bokeh Example by PratikPathak.com")
treemap = TreemapRenderer(
    source=source,
    label='label',
    parent='parent',
    value='value',
    color_discrete_sequence=["#e6550d", "#3182bd", "#31a354", "#756bb1", "#636363", "#9e9ac8", "#de2d26", "#fd8d3c"],
)
p.add_layout(treemap)
output_notebook()
show(p) If you get any error, make sure you have installed Python pandas by using the “pip install pandas” command 24. Network Plot from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource, HoverTool, NodesAndLinkedEdges
import networkx as nx

# Sample data
nodes = ['A', 'B', 'C', 'D', 'E', 'F']
edges = [('A', 'B'), ('A', 'C'), ('B', 'D'), ('B', 'E'), ('C', 'F')]
G = nx.Graph()
G.add_nodes_from(nodes)
G.add_edges_from(edges)

node_positions = nx.spring_layout(G)
node_x = [node_positions[node][0] for node in G.nodes()]
node_y = [node_positions[node][1] for node in G.nodes()]
node_color = ['red', 'green', 'blue', 'yellow', 'purple', 'orange']

source = ColumnDataSource(data=dict(
    x=node_x,
    y=node_y,
    color=node_color,
    node=nodes
))

p = figure(title="Network Plot Python Bokeh Example by PratikPathak.com", x_range=(-1.1, 1.1), y_range=(-1.1, 1.1))
p.add_tools(HoverTool(tooltips=[("Node", "@node")]))
p.circle('x', 'y', size=15, color='color', source=source)

edge_x = []
edge_y = []
for start, end in edges:
    x0, y0 = node_positions[start]
    x1, y1 = node_positions[end]
    edge_x.append(x0)
    edge_x.append(x1)
    edge_x.append(None)
    edge_y.append(y0)
    edge_y.append(y1)
    edge_y.append(None)

p.multi_line(edge_x, edge_y, color="black", alpha=0.5, line_width=1)

output_notebook()
show(p) 25. Sankey Diagram from bokeh.plotting import figure, show, output_notebook
from bokeh.models import Sankey, ColumnDataSource

# Sample data
flows = [
    ('A', 'X', 5),
    ('B', 'X', 3),
    ('A', 'Y', 2),
    ('B', 'Y', 4),
    ('X', 'C', 4),
    ('X', 'D', 3),
    ('Y', 'C', 2),
    ('Y', 'D', 4)
]

source = ColumnDataSource(data=dict(
    source=[flow[0] for flow in flows],
    target=[flow[1] for flow in flows],
    value=[flow[2] for flow in flows]
))

p = figure(plot_width=800, plot_height=400, title="Sankey Diagram Python Bokeh Example by PratikPathak.com")
sankey = Sankey(source=source, label_text_color="white", label_text_font_size="8pt")
p.renderers.append(sankey)

output_notebook()
show(p) | | Live Preview Source Code 🌿 Contribute 26. Chord Diagram from bokeh.plotting import figure, show, output_notebook
from bokeh.models import ColumnDataSource, CategoricalColorMapper
import numpy as np

# Sample data
nodes = ['A', 'B', 'C', 'D', 'E', 'F']
connections = [
    ('A', 'B', 0.5), ('A', 'C', 0.3), ('A', 'D', 0.2),
    ('B', 'C', 0.4), ('B', 'D', 0.3), ('B', 'E', 0.3),
    ('C', 'D', 0.2), ('C', 'E', 0.3), ('C', 'F', 0.5),
    ('D', 'E', 0.2), ('D', 'F', 0.3), ('E', 'F', 0.4)
]

source = ColumnDataSource(data=dict(
    start=np.array([con[0] for con in connections]),
    end=np.array([con[1] for con in connections]),
    value=np.array([con[2] for con in connections])
))

p = figure(title="Chord Diagram Python Bokeh Example by PratikPathak.com", plot_width=800, plot_height=800)
chord = p.chord(
    source=source, 
    start_angle=np.pi / 2,
    direction="clockwise",
    colors=CategoricalColorMapper(factors=nodes, palette="Spectral11")
)

output_notebook()
show(p) How to Contribute? Feel free to open a PR request on our GitHub repo. Steps to contribute: Fork the repo Make changes in the Forked repo and save Open a Pull Request That’s it 😄! 🌿 Contribute Conclusion In this Repo, I have shared 25+ Python Bokeh examples that can help you learn Python Bokeh. Feel free to contribute to our GitHub repo and keep it updated. Also published . here

Getting Started With Python Bokeh: 25+ Data Visualization Examples With Source Code

I was recently inspired by some interesting performance characteristics for collection initializers and collection expressions in C#, and I wanted to put together an introductory article. This article will be part of a small series where I first introduce you to the syntax we have to work with for both collection expressions and collection initializers in C#. We’ll see the difference in style and readability — which the dotnet team has been progressing to make the language feel less heavy-handed while still maintaining expressiveness. Once you’ve got a feel for how collection initializers and collection expressions in C# work, you’ll be geared up to check out some of the performance benchmarks on them. There’s no point in hyper-optimizing for this stuff unless you understand the basics! Using List<T> with Collection Initializers in C# Collection initializers in C# allow for a concise and readable way to populate collections like upon instantiation. This feature simplifies code by enabling the initialization of a collection with a set of predefined elements without the need for multiple calls to the method. List<T> Add These next subsections will show examples of collection initializers with the type. Keep in mind that the entire point of these initializers is to define collections with elements in them to start with, which would save us from doing something like the following: List<T> List<string> devLeaderCoolList = new List<string>();
devLeaderCoolList.Add("Hello");
devLeaderCoolList.Add(", ");
devLeaderCoolList.Add("World!"); So, with this as a starting point, consider that the upcoming examples will make this feel more streamlined and concise. Example 1: Initializing a List of Integers List<int> primeNumbers = new List<int> { 2, 3, 5, 7, 11, 13, 17 }; This example demonstrates initializing a with a collection of prime numbers. The numbers are enclosed in braces and separated by commas, directly following the instantiation of the list. List<int> {} We can also use a slightly more short-hand syntax to drop the entire duplicated type definition from the right side of the equal sign: List<int> primeNumbers = new() { 2, 3, 5, 7, 11, 13, 17 }; Example 2: Combining Object and Collection Initializers public class Student
{
    public string Name { get; set; }
    public int Age { get; set; }
}

List<Student> students = new List<Student>
{
    new Student { Name = "Alice", Age = 22 },
    new Student { Name = "Bob", Age = 24 }
}; Here, we combine object and collection initializers to create a where each object is initialized with and properties. This approach streamlines the process of filling a collection with fully initialized objects. The important thing to pay attention to here is that the object initializer syntax is very much like the collection initializer syntax, but we are indeed doing two things: List<Student> Student Name Age Assigning values to properties of new objects Assigning the collection elements upon collection creation Example 3: Using Complex Expressions List<double> areas = new List<double>
{
    Math.PI * Math.Pow(3, 2),
    Math.PI * Math.Pow(5, 2)
}; This example initializes a with areas of circles (using ), where is the radius. It illustrates that expressions, including method calls, can be used within collection initializers — that is, there is no restriction on constants or pre-evaluated values. List<double> πr² r Example 4: Nested Collection Initializers public class Classroom
{
    public List<Student> Students { get; set; }
}

List<Classroom> classrooms = new List<Classroom>
{
    new Classroom
    {
        Students = new List<Student>
        {
            new Student { Name = "Alice", Age = 22 }
        }
    },
    new Classroom
    {
        Students = new List<Student>
        {
            new Student { Name = "Bob", Age = 24 }
        }
    }
}; This example shows how to use nested collection initializers to initialize a list of objects, each containing a list of objects. It is very much like Example 2, which we have already looked at, but this takes things up one more notch, showing multiple collection initializers and object initialization. Classroom Student Example 5: Simple List Initialization with Collection Expressions . This was a step forward in reducing the verbosity of collection declarations using more shorthand, similar to other languages. Microsoft says in its documentation: In C# 11, we start to get some new fancier syntax for collection expressions You can use a to create common collection values. A is a terse syntax that, when evaluated, can be assigned to many different collection types. A collection expression contains a sequence of elements between and brackets. collection expression collection expression [ ] Microsoft Let’s check out an example: List<int> evenNumbers = [2, 4, 6, 8, 10]; This example demonstrates the straightforward initialization of a using the new collection expressions syntax, making the code more concise and readable. List<int> Example 6: Combining Collections with Spread Operator And there are even more goodies in : C# 12 — we get the spread operator for collection initialization List<int> firstBatch = [1, 2, 3];
List<int> combinedList = [0, ..firstBatch, 4]; Here, the spread operator is used to include elements from an existing collection ( ) into a new list, showcasing the flexibility of the new syntax in combining collections seamlessly. .. firstBatch Where Are We Headed With These? As you read through the various code examples, you can decide for yourself which ones offer you the readability that you prefer. There’s not necessarily a right or wrong answer here, but with variety and choice, we are likely going to need to make decisions within our teams about how to stay consistent. Try to strike a balance between minimizing redundancy without hiding too much type information! But what’s next? Do we care THAT much about readability? I mean, I do. Honestly, I think it’s incredibly important to prioritize readability in code. But if you’re curious like me, you might see a post like this from on the interwebs and get very curious: Dave Callan And since this is what sparked my interest and caused me to write this article as a primer, you’ll perhaps be interested in the performance characteristics that I investigated! Wrapping Up C# Collection Initializers and Collection Expressions Now that you’ve seen various examples of the syntax that we have access to, you can make your own informed decisions about which are most readable to you. I think it’s always important to spend some time looking at alternatives so that you can understand different perspectives, even if it seems like the differences might be minor. Odds are you’re going to read and write collection initializers and collection expressions MANY times in your software engineering career, so why not optimize your choice? Speaking of optimizations… wait until you see ! the next article on the performance of collection initializers If you found this useful and you’re looking for more learning opportunities, consider and check out my ! subscribing to my free weekly software engineering newsletter free videos on YouTube Also published . here

C# Collection Expressions and Collection Initializers

The Bitcoin halving is slated for sometime around April 19th, 2024. As you might have heard, it follows the Bitcoin supply equation; which is a geometric series terminating after 32 divisions or halvings. In April 2024, we shall have the 4th halving, taking us from 6.25 to 3.125 mined per 10 minutes. BTC The last satoshi shall be mined 32 * 4 years from 2009, which shall be the year 2137. Below is a curve I made in MS Excel modeling the Bitcoin supply equation; Interestingly, however, 3 other equations look like the Bitcoin halving. One equation is behind the most profitable options trading algorithm in the world, one is behind the most powerful energy resource in the world, and one is behind the ability to find the energy in any physical system. More on these below: 1. The Black-Scholes equation The Black-Scholes equation is behind most of the profitable options trading in the world, including Exchange Traded Funds (ETFs) which can be traded like regular options. Multinational companies like BlackRock, which manages trillions of dollars in assets, recently launched a successful product for its investors. Bitcoin ETF Notice the term at the end, Assume an equilibrium situation with: Let the constant number be 5. Thus, we have: Let r be 2 and model as, When graphed, this behaves like the Bitcoin halving, as seen below. Here are similar graphs from other people’s research. 2. The Radioactive Decay equation Radioactivity is the spontaneous decay of heavy, unstable atomic nuclei to form stable nuclei. It is the power behind nuclear fission, the most powerful energy resource on the planet. Interestingly, while radioactivity is so good at releasing gargantuan amounts of energy, Bitcoin is good at absorbing it. But even more, both the Bitcoin halving and the radioactive decay process are exponential functions whose graphs grow in the same way. Consider the radioactive decay equation; The formula is easy enough to be taught to 17-year-olds studying A-level mathematics in High Schools. Now, represents the amount left. If this was Bitcoin, would be the bitcoins left to be mined. A A How about if we track the amount decayed, just like the bitcoins already mined? Easy enough. Subtract from thus; A A_0, Which we can see is similar to what we had before with the Black-Scholes equation. Taking A_0 = 5 and λ = 2, it is the same deal with us modelling y = 5 (1 - e^(-2x) ), hence a similar graph. 3. The Hamiltonian The Hamiltonian, of a mechanical system is defined as the amount of energy contained in the system. H While Bitcoin might be a digital computational system, from what Alan Turing describes in his thesis on a Universal Turing Machine, we can represent any computational system as a mechanical system. Therefore, Bitcoin can be represented as a mechanical computational system. Not that we have the resources to do it on earth. By further extension, classical mechanics can be described in terms of quantum mechanics, hence Bitcoin is a quantum-mechanical computational system. Thus, Bitcoin has a Hamiltonian unknown to us, that can describe its minimum workings absent external complexities and fluctuations in the number of users and miners joining and leaving the network. At the nanoscale, where Bitcoin’s digital dance of the halving resides, the simplest Hamiltonian is the quantum Hamiltonian, represented by hat{H} below. We can see this Hamiltonian operator is part of Schrödinger’s wave equation, fundamental to relating the Hamiltonian with the state of a quantum system at time ; t Notice the term: which is similar to: above. Using Euler’s formula, The introduction of the imaginary component has thrown us off the beaten path of a nice exponential leveling off like the Bitcoin supply equation.  We instead get a circle  with an angle given by and radius R = 1. i Ht Now let radius R = 1, and take |r| e^(-iθ) to be the common ratio of a geometric series with r being a complex number, |r| < 1 and first term a = 1. The resulting geometric series; can be modeled as a Fourier series hence the graphic below with r = 0.5,  a = 1 forming a circle of radius R = 4/3. https://en.wikipedia.org/wiki/File:Complex_geometric_series_animation.ogv?embedable=true#filelinks But what if radius R = 1, as we want? What would common ratio r be? First, we need to know that for the general form of a geometric progression; + + + + + … a ar ar^2 ar^3 ar^4 the sum to n terms, for |r| < 1. The sum to n terms then converges to a unique value as n to infinity. This is because r^n to 0. tends tends Hence, we can summarise as below; Note: Because Bitcoin's supply is capped at 21,000,000 it moves in a circle! This via circularity leveraging its monetary transactions velocity, V, in Irving Fischer's equation → MV = PT *** More wonders From the following are related to the Bitcoin halving; https://en.wikipedia.org/wiki/Geometric_series The expansion of the universe, where the common ratio r is defined by Hubble's constant. The decay of radioactive carbon-14 atoms, where the common ratio r is defined by the half-life of carbon-14. Last but not least, One of my Hackernoon post’s viewership statistics.

The Mathematical Mysteries of Bitcoin's Halving

বিটকয়েনের অর্ধেক হওয়ার গাণিতিক রহস্য

Die mathematischen Geheimnisse der Bitcoin-Halbierung

Los misterios matemáticos de la reducción a la mitad de Bitcoin

Les mystères mathématiques de la réduction de moitié du Bitcoin

बिटकॉइन को आधा करने का गणितीय रहस्य

ビットコインの半減期の数学的謎

비트코인 반감기의 수학적 미스터리

Os mistérios matemáticos da redução do Bitcoin pela metade

Математические тайны халвинга биткойна

Bitcoin Yarılanmasının Matematiksel Gizemleri

Những bí ẩn toán học về việc giảm một nửa Bitcoin

比特币减半的数学之谜

Affiliate marketing is a real powerhouse in the digital marketing realm and in recent years has gone through significant growth and transformation. Chances are, you’ve been on the receiving end of it yourself! Now, it is not the time to ignore this approach, since the power of social media, increased device usage, and the boom of creator-led media are all here to help your business thrive. According to _ __, the affiliate marketing industry is experiencing robust growth and there are approximately 9,600 global services and companies related to affiliate marketing in 2023 including agencies, platforms, and various other organizations or apps providing affiliate services. Additionally, forecasts that affiliate marketing spending will reach a staggering US$ 39,805.4 Mn by 2031. Influencer Marketing Hub Astute Analytica For context, reported that global affiliate revenue for affiliate networks amounted to $6.5 billion in 2006. MoreNiche Exciting numbers, huh? Here are some more. According to Performance marketing association survey data: 84% of businesses find affiliate marketing to be more profitable than other marketing methods. In 2021, affiliate marketing contributed to around $71 billion in ecommerce revenue in the United States. On average, every $1 spent on the affiliate channel resulted in $12 in ecommerce revenue across all industries. 84% of media publishers and bloggers create content for affiliate marketing. Retail brands were responsible for 76% of affiliate channel spending, with about one-third going to clothing affiliate programs. Again, number-heavy facts, but you and I know that marketing is nothing without numbers. The explosive growth of the affiliate marketing industry in the 21st century can be credited to a few key factors. First off, the surge in digital operations and the widespread use of mobile devices. Then, the subsequent digitalization of services, the advancements in digital marketing, and the increased volume of online purchases, fueled by a shift in consumer behavior, have all contributed to the flourishing landscape of affiliate marketing. Affiliate marketing's widespread appeal also stems from its affordability, and the high return on investment in terms of both time and cost when compared to alternative marketing approaches. Businesses caught on the wave, adapting their operations and creating affiliate marketing programs to drive their revenue. Then, the social media boom was exactly what gave affiliate marketing the kick in needed, coupled with the rise of influencer marketing and brand partnerships. Thanks to the significant increase of social media usage (from 5% in 2005 to 79% in 2019 according to ), platforms like Facebook and Instagram became key to affiliate marketing campaigns. Our World In Data That’s kind of how we got here. Now, it's not just something companies do on the side; it's a real way to make money. As we navigate the landscape, it's evident that the rise of Cost-Per-Action models is not just a trend but an exciting narrative for sellers on the global stage. So, what’s in plan? In this article I’d like to introduce to you current trends in affiliate marketing and most recent market breakthroughs, seen through the lens of a founder. Choose your fighter A growing market is nothing without innovation, and the very expected emergence of newer tools is a great indicator for market relevance. Just as with any increasing complexity, humans start to seek (and make) tools for dealing with the tools we already have. The rapidly growing affiliate marketing industry is no exception to the rool. Here are the purposes, and some of the tools we’ve got so far: This is software offered by Impact Radius, Awin, and Post Affiliate Pro and it provides advanced tracking and analytics for affiliate marketing campaigns, letting brands and their affiliates optimize their strategies based on performance data. Affiliate Tracking: Companies like AspireIQ, Upfluence, and CreatorIQ can help brands connect with influencers (including micro-influencers), streamlining the process of finding the right partners for affiliate marketing. Influencer Marketing Platforms: If you need a little help creating the visuals, tools like Canva and Adobe Spark let affiliates and marketers easily create high-quality, engaging content for promoting products across almost any channel of choice. Content Creation Tools: For managing affiliate marketing content across multiple social media platforms, doing things like scheduling posts, or analyzing engagement metrics – Hootsuite, Buffer, and Later are the way to go! Social Media Management Tools: Big-time players like Mailchimp and ConvertKit are well-known powerful tools for creating email lists and launching outreach email campaigns with personalized affiliate offers and content. You can also track opens, clicks, and conversions. Email Marketing Services: SEO-helpers such as SEMrush, Ahrefs, Moz and similar services provide affiliates with critical insights into keywords, competition, and performance, helping you optimize content and improve visibility in search engine results. SEO Tools: To conclude In recent years affiliate marketing has become not only a useful tool, but a robust solution for sales, bound to be a prominent player in the future of marketing as a whole. And for that, there are many reasons. Its low-risk nature provides a secure avenue for both businesses and marketers and the potential for high rewards and a scalable income adds an enticing element to the affiliate marketing landscape. With affiliate marketing you simultaneously build brand awareness and drive traffic, presenting itself as a holistic marketing solution and an attractive choice in the evolving landscape of digital marketing, making it a pivotal player in shaping the future of promotional strategies. So, are you in?

Inside the Affiliate Marketing Product Boom: A Founder's Perspective on Market Trends

Coding Patterns Revealed 

Authors: (1) Sha-Bo Lin, Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi’an Jiaotong University; (2) Xingping Sun, Department of Mathematics, Missouri State University; (3) Di Wang, §Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi’an Jiaotong University. Content Overview Abstract & Introduction Uncertainty Relation of Kernel Interpolation on Spheres Distributed Kernel Interpolation Operator Differences via Quadrature Rules Proofs Numerical Verifications References Abstract For radial basis function (RBF) kernel interpolation of scattered data, Schaback [30] in 1995 proved that the attainable approximation error and the condition number of the underlying interpolation matrix cannot be made small simultaneously. He referred to this finding as an “uncertainty relation”, an undesirable consequence of which is that RBF kernel interpolation is susceptible to noisy data. In this paper, we propose and study a distributed interpolation method to manage and quantify the uncertainty brought on by interpolating noisy spherical data of non-negligible magnitude. We also present numerical simulation results showing that our method is practical and robust in terms of handling noisy data from challenging computing environments. Kernel interpolation, distributed uncertainty mitigation, scattered spherical data Key words. Uncertainty Relation of Kernel Interpolation on Spheres 3. Distributed Kernel Interpolation. Corollary 2.2 shows that kernel interpolation performs poorly while confronting noisy data of non-negligible magnitude. To overcome this major drawback, we propose and study in this section a distributed kernel interpolation (DKI) method, which is motivated by the “distributed learning” in the literature [37, 19]. Figuratively speaking, this is a divide-and-conquer strategy for uncertainty quantification. To elaborate, we describe the method in three steps. 4. Operator Differences via Quadrature Rules. In this section, we first briefly exposit an integral-operator approach initiated in [8] and then derive tight upper bounds for differences of operators of our interest, obtaining a certain type of Sobolev sampling inequalities [12] as a byproduct. Highlights of the section include Proposition 4.5) and Lemma 4.8. 6. Numerical Verifications Four simulations are carried out in this section to verify the excellent performance of DKI. The first one shows that DKI succeeds in circumventing the uncertainty of kernel interpolation. The second one exhibits the role of m in DKI. The third one focuses on the role of the division strategy in DKI. The last one compares DKI with several popular spherical data fitting schemes including the distributed filtered hyperinterpolation (DFH) [21], sketching with s ∗ -designs [20], and distributed kernel ridge regression (DKRR) [8]. In this simulation, we show the role of the parameter m in DKI. We generate 10014 training samples (with 141-designs as inputs). The number of divisions, m, ranges from {5, 10, · · · , 200}. Figure 6.2 shows the relation between RMSE of DKI and the number of local machines under different levels of Gaussian noise, provided that the total number of training samples is given. From Figure 6.2, we can conclude the following assertions: 1) For training samples with higher levels of noise, the testing RMSE generally decreases at first and then increases slowly as the number of local machines increases. Moderate values of m are more conductive to good approximation property for DKI. The reason is that too small m does not successfully address the uncertainty issue in kernel interpolation; too large m increases the fitting error, resulting in slightly worse generalization performance. 2) The optimal number m with the lowest RMSE grows with increasing Gaussian noise. This verifies the equation (3.3) of Theorem 3.2, in which the approximation error is primarily concerned with the sample error for large noise (i.e., large M) and can be reduced using a large m. Simulation 2: REFERENCES [1] R. Bhatia, Matrix Analysis, vol. 169, Springer Science & Business Media, 2013. [2] J. S. Brauchart and K. Hesse, Numerical integration over spheres of arbitrary dimension, Constructive Approximation, 25 (2007), pp. 41–71. [3] G. Brown and F. Dai, Approximation of smooth functions on compact two-point homogeneous spaces, Journal of Functional Analysis, 220 (2005), pp. 401–423. [4] A. Chernih, I. H. Sloan, and R. S. Womersley, Wendland functions with increasing smoothness converge to a gaussian, Advances in Computational Mathematics, 40 (2014), pp. 185– 200. [5] F. Dai, Multivariate polynomial inequalities with respect to doubling weights and a∞ weights, Journal of Functional Analysis, 235 (2006), pp. 137–170. [6] F. 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Phillips, Potential anomalies on a sphere: Applications to the thickness of the lunar crust, Journal of Geophysical Research: Planets, 103 (1998), pp. 1715–1724. [36] R. S. Womersley, Efficient spherical designs with good geometric properties, in Contemporary computational mathematics-A celebration of the 80th birthday of Ian Sloan, Springer, 2018, pp. 1243–1285. [37] Y. Zhang, J. Duchi, and M. Wainwright, Divide and conquer kernel ridge regression: A distributed algorithm with minimax optimal rates, The Journal of Machine Learning Research, 16 (2015), pp. 3299–3340. In this Appendix, we present the detailed implementation of the select-and-judge (SAJ) strategy. Our aim is to derive a series of subsets of similar Cardinality with separation radius not smaller than a given tolerance c0. There are two stages for SAJ. SM1. Appendix A: Select-and-Judge Strategy for Data Division. This paper is under CC0 1.0 DEED license. available on arxiv

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