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 B. CONVERGENCE OF RESULTS The convergence of our rotating magnetic wind solutions against both mesh resolution and the size of wind launching region have been confirmed. We show the results for our fiducial model (B1.5e6Ω0.23) in Fig. 5. In the top panel we increase the spatial resolution for 4 times both along the radial and latitudinal direction, while in the bottom panel we change the thickness of wind launching region from D = 0.6 R∗ (fiducial value we are using, corresponding to 9 cells) to D = 0.3 R∗ (which corresponds to 5 cells). We check the time evolution of the spindown torque T for both changes, and zoom into the first few eruptive peaks to show the difference clearly. We find that the time-averaged value as well as the power-law trend converge with respect to both the spatial resolution and the size of the wind launching region, but the time variability vary. This is due to the fact that the reconnections in our simulations are mainly modulated by numerical resistivities. 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 B. CONVERGENCE OF RESULTS The convergence of our rotating magnetic wind solutions against both mesh resolution and the size of wind launching region have been confirmed. We show the results for our fiducial model (B1.5e6Ω0.23) in Fig. 5. In the top panel we increase the spatial resolution for 4 times both along the radial and latitudinal direction, while in the bottom panel we change the thickness of wind launching region from D = 0.6 R∗ (fiducial value we are using, corresponding to 9 cells) to D = 0.3 R∗ (which corresponds to 5 cells). We check the time evolution of the spindown torque T for both changes, and zoom into the first few eruptive peaks to show the difference clearly. We find that the time-averaged value as well as the power-law trend converge with respect to both the spatial resolution and the size of the wind launching region, but the time variability vary. This is due to the fact that the reconnections in our simulations are mainly modulated by numerical resistivities.

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