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Solana Projects Attract Investments as the Ecosystem Grows Before its January 28 Mainnet launch, , a decentralized finance (DeFi) application on the Solana network, has raised $10 million. Hubble was able to accomplish this considerable rise with the help of some of crypto’s most powerful and well-known figures. Marius Ciubotariu, the project lead at Hubble Protocol, in an exclusive interview with Hackernoon, Hubble Protocol discussed the advantages of the Solana ecosystem, such as its scalability, composability, and latency. Three Arrows / DeFiance Capital, , , , ParaFi, Jump Capital, , CMS, Spartan, DeFi Alliance, and Mechanism Capital were among the investors in Hubble’s funding rounds. Delphi Digital Digital Currency Group Crypto.com Capital Decentral Park Capital Hubble will use this funding to grow its workforce and DeFi products throughout 2022. Hubble will commence the first phase of its development on January 28, a zero-interest lending platform that will produce USDH, a censorship-resistant crypto-backed stablecoin. USDH is primed to become a “building block” for additional protocols on Solana, as stated in Decentral Park Capital’s investment thesis. The protocol aims to improve the future of DeFi and Web3 continually. Hubble’s native token, HBB, allows users to earn the bulk of the protocol’s fees by minting USDH. The revenue streams contributing to this fee-share may expand in the future. HBB will be available on three launchpads at the end of January: SolRazr, Solanium, and DAO Maker. As the ecosystem for Solana is still at its nascent stage, building the initial infrastructure such as a decentralized stablecoin to a novel borrowing marketplace and undercollateralized lending is the key to building DeFi primitives for the Solana ecosystem. These are essential components of the Web3 financial stack on the most well-known cryptocurrency infrastructure. Solana Eats the Market Share of Ethereum In a research note, informed clients that the Solana blockchain might become the “Visa of the digital asset ecosystem” since it focuses on scalability, cheap transaction costs, and simplicity of use. Due to the success of Solana as a high throughput blockchain, projects such as Hubble Protocol are building DeFi infrastructure on the blockchain. Bank of America Since its premiere in 2020, Solana has seen rapid acceptance and has settled more than 50 billion transactions and has more than $11 billion in total value locked, and has been used to mint more than 5.7 million non-fungible tokens (NFTs). For comparison, Visa, the payment processing giant, handled 164.7 billion transactions in the year ended September 30. According to the bank, Solana is designed for consumer use cases like micropayments and gaming. While Solana promotes scalability, a less decentralized and secure blockchain comes with trade-offs, as seen by multiple network performance concerns since its launch. Ethereum values decentralization and security above scalability, resulting in periods of network congestion and transaction fees that are often more than the value of the transaction being transmitted. According to Bank of America, Solana and other blockchains might eat into Ethereum’s market share over time and will begin to differentiate themselves via user acceptance and developer engagement. Catch all the breaking news, and Don’t forget to like the story!

Hubble Protocol, a DeFi project on Solana Raises $10 Million Led By Crypto.com Capital, DCG and CMS 

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

This paper is available on arxiv under CC 4.0 license. Authors: (1) Andrew Ridden-Harper, Department of Astronomy and Carl Sagan Institute, Cornell University & Las Cumbres Observatory; (2) Stevanus K. Nugroho, Astrobiology Center & Japan & National Astronomical Observatory of Japan; (3) Laura Flagg, Department of Astronomy and Carl Sagan Institute, Cornell University; (4) Ray Jayawardhana, Department of Astronomy, Cornell University; (5) Jake D. Turner, Department of Astronomy and Carl Sagan Institute, Cornell University & NHFP Sagan Fellow; (6) Ernst de Mooij, Astrophysics Research Centre, School of Mathematics and Physics & Queen’s University Belfast; (7) Ryan MacDonald, Department of Astronomy and Carl Sagan Institute; (8) Emily Deibert, David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto & Gemini Observatory, NSF’s NOIRLab; (9) Motohide Tamura, Dunlap Institute for Astronomy & Astrophysics, University of Toronto (10) Takayuki Kotani, Department of Astronomy, Graduate School of Science, The University of Tokyo, Astrobiology Center & National Astronomical Observatory of Japan; (11) Teruyuki Hirano, Astrobiology Center, National Astronomical Observatory of Japan & Department of Astronomical Science, The Graduate University for Advanced Studies; (12) Masayuki Kuzuhara, Las Cumbres Observatory & Astrobiology Center; (13) Masashi Omiya, Las Cumbres Observatory & Astrobiology Center; (14) Nobuhiko Kusakabe, Las Cumbres Observatory & Astrobiology Center. Table of Links Abstract & Introduction Observation Data Reduction and Processing Model Spectra Cross-Correlation Method Results Clouds and Hazes Implications for JWST Conclusion and Acknowledgement Appendix & References ABSTRACT Terrestrial exoplanets orbiting M-dwarf stars are promising targets for transmission spectroscopy with existing or near-future instrumentation. The atmospheric composition of such rocky planets remains an open question, especially given the high X-ray and ultraviolet flux from their host M dwarfs that can drive atmospheric escape. The 1.3 R⊕ exoplanet GJ 486b (Teq ∼ 700 K), orbiting an M3.5 star, is expected to have one of the strongest transmission spectroscopy signals among known terrestrial exoplanets. We observed three transits of GJ 486b using three different high-resolution spectrographs: IRD on Subaru, IGRINS on Gemini-South, and SPIRou on the Canada-France-Hawai’i Telescope. We searched for atmospheric absorption from a wide variety of molecular species via the cross-correlation method, but did not detect any robust atmospheric signals. Nevertheless, our observations are sufficiently sensitive to rule out several clear atmospheric scenarios via injection and recovery tests, and extend comparative exoplanetology into the terrestrial regime. Our results suggest that GJ 486b does not possess a clear H2/He-dominated atmosphere, nor a clear 100% water-vapor atmosphere. Other secondary atmospheres with high mean molecular weights or H2/He-dominated atmospheres with clouds remain possible. Our findings provide further evidence suggesting that terrestrial planets orbiting M-dwarf stars may experience significant atmospheric loss. : Exoplanet atmospheres (487) — Planetary atmospheres (1244) — Exoplanets (498) — Exoplanet atmospheric composition (2021) Keywords 1. INTRODUCTION Exoplanets that transit M-dwarf stars produce relatively deep transits due to their high planet-star radius ratios. Consequently, it may be possible to detect biosignatures in the atmospheres of terrestrial exoplanets with existing or near-future instrumentation (e.g., Snellen et al. 2013; Wunderlich et al. 2019). However, the long-term habitability of such planets depends crucially on the stability of their atmospheres, which are subject to high X-ray + extreme UV (XUV) emissions during the pre-main-sequence phase of their M-dwarf hosts (e.g., Shkolnik & Barman 2014; Peacock et al. 2020) as well as flare events (e.g., Neves Ribeiro do Amaral et al. 2022) that can drive atmospheric escape (e.g., Vidal-Madjar et al. 2003; Bourrier et al. 2017a; Airapetian et al. 2017). Terrestrial exoplanets are expected to exhibit a rich diversity in atmospheric compositions. Exoplanets with Rp < 1.4 R⊕ and orbital periods < 100 days likely form as gas-rich sub-Neptunes that subsequently lose their primordial atmospheres due to photoevaporation (Rogers & Owen 2021). The amount of primordial atmosphere retained depends on several factors, such as their host star’s spectral energy distribution and activity levels, along with how much gas they accrete during formation (e.g., Bolmont et al. 2017; Owen et al. 2020). Should the primordial hydrogen-dominated atmosphere be lost, a secondary atmosphere may be retained. The composition of secondary atmospheres depends on a variety of processes, including interior outgassing, impact delivery, erosion, atmosphere-surface exchange, weathering, and volatile sequestration (e.g., Rogers et al. 2011). Driven by these processes, hot terrestrial planets (T & 1500 K) are predicted to have atmospheres containing atoms and ions, such as Na or Ca+, produced by surface vaporization (Schaefer & Fegley 2009) — though other hydrogen- or nitrogen-rich compositions are possible (Miguel 2019). However, cooler terrestrial planets are likely rich in molecular species, such as H2O, CO2, CO, O2, C2H2, and CH4 (e.g., Ramirez & Kaltenegger 2014; Madhusudhan et al. 2016; Kite & Schaefer 2021). Given the range of theoretical possibilities, observational constraints on the composition of terrestrial exoplanet atmospheres are crucially needed. While there have been several attempts to detect the atmospheres of a few terrestrial exoplanets, these have only yielded constraints from nondetections. For example, 55 Cancri e is a 1.9 R⊕ exoplanet with a temperature of approximately 2400 K due to its 17 hr orbit around its G8V host star (Morris et al. 2021). Hubble Space Telescope observations suggest that 55 Cancri e may possess a thick atmosphere (Tsiaras et al. 2016). However, phase curve observations with the Spitzer space telescope (Demory et al. 2016) and ground-based high-resolution transmission spectroscopy point toward 55 Cancri e not possessing a thick atmosphere or having no atmosphere at all (Ridden-Harper et al. 2016; Esteves et al. 2017; Jindal et al. 2020; Deibert et al. 2021a; Zhang et al. 2021). A similar result was found for the cooler 1.3 R⊕ exoplanet LHS 3844 b, which has an equilibrium temperature of 800 K and orbits an M5 host star (Vanderspek et al. 2019). Kreidberg et al. (2019) observed the phase curve of LHS 3844 b with the Spitzer space telescope and found that thick atmospheres with surface pressures greater than 10 bar could be ruled out, while less massive atmospheres would be susceptible to erosion by the stellar wind. Additionally, they found that a bare rock model fit their data well. Another candidate for atmospheric characterization that orbits an M-dwarf is GJ 1132b, which has a radius, mass, and equilibrium temperature of 1.1 R⊕, 1.7 M⊕, and 580 K, respectively (Berta-Thompson et al. 2015). Using transit observations from the Hubble Space Telescope (HST), Swain et al. (2021) inferred that GJ 1132b possesses a H/He-rich atmosphere with large-amplitude spectral features. However, using the same HST data, Libby-Roberts et al. (2022) and Mugnai et al. (2021) independently found a featureless transmission spectrum, possibly indicating an atmosphere with a high mean molecular weight (MMW), a high-altitude aerosol layer, or a near-total lack of an atmosphere. These contrasting results highlight the difficulty of characterizing the atmospheres of small planets, even with space-based instrumentation. Comprehensive searches for the atmospheres of the seven approximately Earth-sized planets that transit the M8V star TRAPPIST-1 have also been carried out. These transit observations with the Hubble and Spitzer space telescopes all point toward the absence of extended hydrogen-dominated atmospheres. However, denser, potentially habitable atmospheres are consistent with the observational limits for some TRAPPIST-1 planets (de Wit et al. 2016; Bourrier et al. 2017b,a; de Wit et al. 2018; Zhang et al. 2018; Wakeford et al. 2019; Gressier et al. 2022). GJ 486b[1] is a 1.3 R⊕ and 2.8 M⊕ exoplanet with an equilibrium temperature of about 700 K, an M3.5 V host star of J-band magnitude 7.2, and an orbital period of 1.5 days (Trifonov et al. 2021). These system properties make GJ 486b well suited to atmospheric characterization with transmission spectroscopy, as reflected by it having one of the largest transmission spectroscopy metrics (as defined by Kempton et al. 2018) of all known terrestrial planets (Trifonov et al. 2021). Therefore, GJ 486b is an ideal observational target to inform our understanding of terrestrial planets around M-dwarf stars. Previous studies have surmised that a wide range of atmospheric compositions are possible for GJ 486b. Caballero et al. (2022) refined GJ 486b’s mass and radius, and presented a suite of interior and atmospheric models. They showed that possible atmospheres include: (i) a H/He-dominated atmosphere with solar abundances; (ii) a H/He atmosphere with enhanced metallicity (e.g., 100x solar abundances); (iii) a H2O-dominated atmosphere; (iv) a CO2-dominated atmosphere; or (v) bare rock with a tenuous atmosphere, possibly containing Na. Geochemical models based on initial conditions representative of a range of possible planets suggest that a H2O-dominated atmosphere is the most likely outcome for a 3 M⊕ planet like GJ 486b (Ortenzi et al. 2020). However, carbonaceous chondrite outgassing measurements suggest that CO2-dominated atmospheres could also evolve on terrestrial planets (Thompson et al. 2021). Differentiating between these scenarios requires spectroscopic observations. Molecular species such as those expected to be in GJ 486b’s atmosphere produce dense forests of spectral lines that can be individually resolved with high-resolution spectroscopy. The signals from these lines can be combined, even if they are individually hidden in the noise, by cross-correlating the data with a template containing the molecular lines (e.g., Snellen et al. 2010; Birkby 2018). This powerful technique has facilitated the detection of species such as H2O, CO, HCN, CH4, NH3, and C2H2 in the transmission spectra of hot Jupiters (e.g., Giacobbe et al. 2021). As high-resolution spectroscopy probes line cores, which contain information about the upper (low-pressure) regions of exoplanet atmospheres, it is highly complementary to low-resolution observations from telescopes such as the JWST, which probe higher pressures (Brogi & Line 2019). JWST is scheduled to observe two transits and eclipses of GJ 486b in programs GO 1981[2] (P.I.: K. Stevenson) and GO 1743[3] (P. I.: M. Mansfield), respectively. Here, we present the first high-resolution transmission spectroscopy observations of GJ 486b. We use three transits to constrain GJ 486b’s atmospheric composition. In what follows, in Sections 2 and 3 we describe our observations and data reduction approach. Section 4 describes our model spectra, while Section 5 describes our cross-correlation methodology. Section 6 presents our results, while Section 8 discusses the implications of our results for the upcoming JWST observations. Finally, Section 9 offers concluding remarks. [1] Alternative names include Wolf 437b and TOI 1827b. [2] program-information.html?id=1981 https://www.stsci.edu/jwst/science-execution/ [3] program-information.html?id=1743 https://www.stsci.edu/jwst/science-execution/

High-Resolution Transmission Spectroscopy of the Terrestrial Exoplanet GJ 486b: Abstract & Intro

This paper is available on arxiv under CC 4.0 license. Authors: (1) Andrew Ridden-Harper, Department of Astronomy and Carl Sagan Institute, Cornell University & Las Cumbres Observatory; (2) Stevanus K. Nugroho, Astrobiology Center & Japan & National Astronomical Observatory of Japan; (3) Laura Flagg, Department of Astronomy and Carl Sagan Institute, Cornell University; (4) Ray Jayawardhana, Department of Astronomy, Cornell University; (5) Jake D. Turner, Department of Astronomy and Carl Sagan Institute, Cornell University & NHFP Sagan Fellow; (6) Ernst de Mooij, Astrophysics Research Centre, School of Mathematics and Physics & Queen’s University Belfast; (7) Ryan MacDonald, Department of Astronomy and Carl Sagan Institute; (8) Emily Deibert, David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto & Gemini Observatory, NSF’s NOIRLab; (9) Motohide Tamura, Dunlap Institute for Astronomy & Astrophysics, University of Toronto (10) Takayuki Kotani, Department of Astronomy, Graduate School of Science, The University of Tokyo, Astrobiology Center & National Astronomical Observatory of Japan; (11) Teruyuki Hirano, Astrobiology Center, National Astronomical Observatory of Japan & Department of Astronomical Science, The Graduate University for Advanced Studies; (12) Masayuki Kuzuhara, Las Cumbres Observatory & Astrobiology Center; (13) Masashi Omiya, Las Cumbres Observatory & Astrobiology Center; (14) Nobuhiko Kusakabe, Las Cumbres Observatory & Astrobiology Center. Table of Links Abstract & Introduction Observation Data Reduction and Processing Model Spectra Cross-Correlation Method Results Clouds and Hazes Implications for JWST Conclusion and Acknowledgement Appendix & References 9. CONCLUSION In this study, we searched for the atmosphere of the 1.3 R⊕ exoplanet GJ 486b using high-resolution transmission spectroscopy. Our resultant atmospheric constraints additionally offer an improved understanding of the possible atmospheres for terrestrial planets orbiting M-dwarf stars. We observed three transits of GJ 486b with the spectrographs IRD, IGRINS, and SPIRou, and searched for absorption by its atmosphere with the high-resolution cross-correlation method. We searched for C2H2, CH4, CO, CO2, FeH, H2O, HCN, H2S, K, Na, NH3, PH3, SiO, TiO, and VO, but did not detect any robust atmospheric signals. Our best potential detection was H2O at the 3σ level, seen only in the IGRINS data set. However, this potential signal is likely an artifact of imperfectly removed H2O lines in the stellar spectrum. We suggest that it may be possible to improve the suppression of these stellar lines by using 3D models of stellar convection, as shown by Chiavassa & Brogi (2019). Nevertheless, we derived informative upper limits on the abundances of many chemical species by performing signal injection and recovery tests. Our recovery tests allow us to rule out a clear H2/He-dominated atmosphere with solar molecular abundances to a confidence of >5σ, while also ruling out a clear 100% water atmosphere to a confidence of 3σ. Since a water-dominated atmosphere is often considered to be the most likely possibility for 3 M⊕ planets like GJ 486b (e.g., Ortenzi et al. 2020), our results could have important implications for planetary interior models. We also investigated the implications of our findings for the upcoming JWST transit observations of GJ 486b. We found that these observations will be especially sensitive to the presence of CO2, but with weaker sensitivity to H2O, highlighting the complementary capabilities of high-resolution and JWST observations. In summary, our results indicate that GJ 486b does not possess a cloud-free H/He-dominated atmosphere that has solar abundances. However, it may possess a secondary atmosphere with high mean molecular weight or a H2/He-dominated atmosphere with clouds. Our findings provide further evidence suggesting that terrestrial planets orbiting M-dwarf stars experience significant atmospheric loss. ACKNOWLEDGMENTS We thank the anonymous reviewer for constructive comments. We are also grateful to Hajime Kawahara for helpful suggestions. This research is based [in part] on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. We are honored and grateful for the opportunity of observing the Universe from Maunakea, which has cultural, historical, and natural significance in Hawaii. This work used the Immersion Grating Infrared Spectrometer (IGRINS) that was developed under a collaboration between the University of Texas at Austin and the Korea Astronomy and Space Science Institute (KASI) with the financial support of the Mt. Cuba Astronomical Foundation, of the US National Science Foundation under grants AST-1229522 and AST-1702267, of the McDonald Observatory of the University of Texas at Austin, of the Korean GMT Project of KASI, and of the Gemini Observatory. Based on observations obtained at the international Gemini Observatory, a program of NSF’s NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation on behalf of the Gemini Observatory partnership: the National Science Foundation (United States), the National Research Council (Canada), Agencia Nacional de Investigaci´on y Desarrollo (Chile), Ministerio de Ciencia, Tecnolog´ıa e Innovaci´on (Argentina), Minist´erio da Ciˆencia, Tecnologia, Inova¸c˜oes e Comunica¸c˜oes (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). Based on observations obtained at the CanadaFrance-Hawaii Telescope (CFHT), which is operated from the summit of Maunakea by the National Research Council of Canada, the Institut National des Sciences de l’Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii. The observations at the Canada-France-Hawaii Telescope were performed with care and respect from the summit of Maunakea which is a significant cultural and historic site. Based on observations obtained with SPIRou, an international project led by Institut de Recherche en Astrophysique et Plan´etologie, Toulouse, France. This research has made use of the Extrasolar Planet Encyclopaedia, NASA’s Astrophysics Data System Bibliographic Services, and the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. M.T. is supported by JSPS KAKENHI grant Nos. 18H05442, 15H02063, and 22000005. S. K. N. is supported by JSPS KAKENHI grant No. 22K14092. J.D.T’s support for this work was provided by NASA through the NASA Hubble Fellowship grant #HSTHF2-51495.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5- 26555. : 8.2 m Subaru telescope (IRD), 8.1 m Gemini-South telescope (IGRINS), 3.6 m Canada France Hawai’i Telescope (SPIRou) Facilities : Astropy (Astropy Collaboration et al. 2013, 2018); SciPy (Virtanen et al. 2020); NumPy (Harris et al. 2020); petitRADTRANS (Molli`ere et al. 2019); SpectRes (Carnall 2017). Software

High-Resolution Transmission Spectroscopy: Conclusion and Acknowledgement

This paper is under CC 4.0 license. available on arxiv Authors: (1) Prajwal Niraula, Department of Earth, Atmospheric and Planetary Sciences; (2) Julien de Wit, Department of Earth, Atmospheric and Planetary Sciences; (3) Benjamin V. Rackham, Department of Earth, Atmospheric and Planetary Sciences; (4) Elsa Ducrot, Astrobiology Research Unit, University of Li`ege; (5) Artem Burdanov, Department of Earth, Atmospheric and Planetary Sciences; (6) Ian J. M. Crossfield, Kansas University Department of Physics and Astronomy; (7) Valerie Van Grootel´, Space Sciences, Technologies and Astrophysics Research (STAR) Institute, University of Li`ege; (8) Catriona Murray, 5Cavendish Laboratory; (9) Lionel J. Garcia, Astrobiology Research Unit, University of Li`ege; (10) Roi Alonso, Instituto de Astrof´ısica de Canarias & Dpto. de Astrof´ısica, Universidad de La Laguna; (11) Corey Beard, Department of Physics & Astronomy, The University of California; (12) Yilen Gomez Maqueo Chew, Instituto de Astronom´ıa, Universidad Nacional Aut´onoma de M´exico, Ciudad Universitaria; (13) Laetitia Delrez, Astrobiology Research Unit, University of Li`ege, Space Sciences, Technologies and Astrophysics Research (STAR) Institute, University of Li`ege & 0Observatoire de lUniversit´e de Gen`eve; (14) Brice-Olivier Demory, University of Bern, Center for Space and Habitability; (15) Benjamin J. Fulton, NASA Exoplanet Science Institute/Caltech-IPAC; (16) Michael Gillon, Astrobiology Research Unit, University of Li`ege; (17) Maximilian N. Gunther, Department of Physics, and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology; (18) Andrew W. Howard, California Institute of Technology; (19) Howard Issacson, Department of Astronomy, University of California Berkeley; (20) Emmanuel Jehin, Space Sciences, Technologies and Astrophysics Research (STAR) Institute, University of Li`ege; (21) Peter P. Pedersen, Cavendish Laboratory; (22) Francisco J. Pozuelos, Astrobiology Research Unit, University of Li`ege & Space Sciences, Technologies and Astrophysics Research (STAR) Institute, University of Li`ege; (23) Didier Queloz, Cavendish Laboratory; (24) Rafael Rebolo-Lopez, Instituto de Astrof´ısica de Canarias & Dpto. de Astrof´ısica, Universidad de La Laguna'; (25) Sairam Lalitha, School of Physics & Astronomy, University of Birmingham; (26) Daniel Sebastian, Astrobiology Research Unit, University of Li`ege (27) Samantha Thompson, Cavendish Laboratory; (28) Amaury H.M.J. Triaud, School of Physics & Astronomy, University of Birmingham. Table of Links Abstract & Introduction Observation Analysis and Validation Future Prospects & References 3. ANALYSIS AND VALIDATION 3.1. Stellar Host Characterization 3.1.1. Semi-empirical Stellar Parameters We constructed the spectral energy distribution (SED) of EPIC 249631677 using photometric magnitudes from Gaia (GBP and GRP ; Gaia Collaboration et al. 2018) and the AllWISE source catalog (J, H, Ks, W1, W2, and W3; Cutri et al. 2013). The corresponding fluxes for these magnitudes are tabulated on VizieR (Ochsenbein et al. 2000) and shown in Figure 5 and Table 1. The parallax of EPIC 249631677 is π = 17.61 ± 0.09 mas, which yields a distance of 56.8 ± 0.3 pc (Gaia Collaboration et al. 2018; Stassun & Torres 2018). We then derived the stellar luminosity L∗ by integrating over the SED, which yielded L∗ = 0.0041 ± 0.0001L . Two independent methods were applied to obtain stellar mass. First, we used the empirical M∗−MKs relation (applying the metallicity obtained in Section 3.1.2) from Mann et al. (2019) to obtain M∗ = 0.1721 ± 0.0044M . We also applied stellar evolution modeling, using the models presented in Fernandes et al. (2019), using as a constraint the luminosity inferred above and the metallicity derived in Sect. 3.1.2). We considered the stellar age to be >1 Gyr in the absence of signs of youth, such as presence of prominent flares (Ilin et al. 2019, see Section 3.1.3). We obtained with this method M∗ = 0.176 ± 0.004 M . This uncertainty reflects the error propagation on the stellar luminosity and metallicity, but also the uncertainty associated with the input physics of the stellar models. We combined these two mass estimates as in Van Grootel et al. (2018) to obtain M∗ = 0.174±0.004M as our best estimate for the stellar mass of EPIC 249631677. Given its proximity, we expect minimal extinction (Av) for the target; the SED fitting analysis described in Section 3.2.1 similarly constrains it to be 0.02 at 3σ confidence and we adopt that upper limit here. Finally, we note that given its luminosity, mass, and Gaia colors this star is likely to be fully convective (Jao et al. 2018; Rabus et al. 2019). Due to the absence of a strong constraint on the stellar density from the transits, we further obtained stellar radius, surface gravity, effective temperature and density from our evolutionary models. Table 1 summarizes the results from this analysis, along with other properties of the star. Our values are consistent with those listed in the TESS Input Catalog (Stassun et al. 2019), and we adopt them for the remainder of this analysis. 3.1.2. Reconaissance Spectroscopy To confirm EPIC 249631677’s stellar properties and better characterize the system, we acquired an optical spectrum using Keck/HIRES (Vogt et al. 1994) on UT 30 May 2020. The observation took place in 0.6 00 effective seeing and using the C2 decker without the HIRES iodine gas cell, giving an effective resolution of λ/∆λ ≈ 55, 000 from 3600 ˚A to 7990 ˚A. We exposed for 1800 s and obtained SNR of roughly 23 per pixel. Data reduction followed the standard approach of the California Planet Search consortium (Howard et al. 2010). We used our Keck/HIRES radial velocity and Gaia DR2 data to estimate the 3D galactic (UV W) space velocity using the online kinematics calculator[2] of Rodriguez (2016). Following Chubak et al. (2012), our Keck/HIRES spectrum gives a barycentric radial velocity of 6.25±0.17 km s−1 . With the Gaia-derived coordinates, proper motion, and distance listed in Table 1, we find (U, V, W) values of (−17.02, −9.06, +33.66) km s−1 , indicating a likely membership in the Milky Way’s thin disk (Bensby et al. 2014). Using the SpecMatch-Empirical algorithm (Yee et al. 2017), we derive from our HIRES spectrum stellar parameters of Teff = 3195 ± 70 K, R∗ = 0.23 ± 0.10R , and [Fe/H]= −0.24 ± 0.09, consistent with the values tabulated in Table 1. The three best-matching stars in the SpecMatch-Empirical template library are GJ 15B, GJ 447, and GJ 725B, which have spectral types of M3.5V, M4V, and M3.5V, respectively. Given the close match between the spectra of these stars and our target (see Fig. 4), we therefore classify EPIC 249631677 as an M dwarf with subclass 3.5±0.5. We see no evidence of emission line cores at Hα, consistent with our determination that our target is not a young star. We see no evidence of spectral broadening compared to these three stars (which all have v sin i < 2.5 km s−1 ; Reiners et al. 2012), so we set an upper limit on EPIC 249631677’s projected rotational velocity of < 5 km s−1 , comparable to the spectral resolution of HIRES. 3.1.3. Stellar Variability The long-term variations apparent in the everest light curve (Figure 1) are not evident in light curves from other reduction pipelines (e.g., K2SFF). These variations likely arise from systematics and are not reliable for estimating the stellar rotation period (Esselstein et al. 2018). Similarly, no flares are apparent either in the K2 or SPECULOOS data. Flare rates peak for ∼M3.5 stars in TESS data (G¨unther et al. 2020). However, given the long integration time of 29.4 minutes as well as a need for data processing which corrects for the saw-tooth pattern, flare signals, unless very prominent, are expected to be difficult to detect in K2 long cadence data. 3.2. Vetting In order to produce a transit depth on the level of 0.2% in the light curve of the primary target, a background eclipsing binary producing eclipses with depths of 25% to 50% would have to be 5.25 to 6.0 mag fainter than the target, respectively. Qualitatively, the odds of EPIC 249631677 hosting a planet are higher than the odds of such magnitude contrast eclipsing binary being present within the SPECULOOS aperture, given occurrence rates of M-dwarf planets (Dressing & Charbonneau 2013; Mulders et al. 2015; Hardegree-Ullman et al. 2019). A stringent quantitative constraint can be placed using the ingress/egress duration (T12/T34) compared to the total transit duration (T14) (Seager & Mall´enOrnelas 2003, Equation 21). Such a test yields an upper limit on the relative radius of the transiting body. By assuming equal effective surface temperatures, the lower magnitude limit ∆m (corresponding to a flux difference ∆F) for a blended binary mimicking a signal of depth δ is given by: Using the posterior for the transit fit (See Section 3.3), we find for EPIC 249631677 that such a background object can be fainter at most by 1.73 mag at the 3σ level. Fortunately, EPIC 249631677 has a significant proper motion, ∼140 mas yr−1 , which allows us to investigate the presence of background sources at its current sky position. We looked at archival imaging of EPIC 246331677 going back to 1953[3] . A POSS I plate from 1953 is the publicly available oldest image of EPIC 249631677, and it does not show any background source at the current position of the target as shown in Figure 6. The plate is sensitive to objects at least 3.5 magnitudes fainter than the target. Similarly, the Hubble Guide Star Catalogue (GSC), with a limiting magnitude of 20 (Lasker et al. 1990), does not show any background source. While POSS II would go the deepest in terms of limiting magnitude (20.8, Reid et al. 1991), the star has moved appreciably closer to its current location, precluding a definitive measurement from this image. Overall, using archival images we can rule out the possibility of the transit signal originating from background star at a high level of confidence. 3.2.1. Binarity of the Host Star Despite the lack of background sources, the host star could produce a false-positive transit signal if it were a grazing eclipsing binary or a hierarchical eclipsing binary. We investigated the evidence for host star binarity using the isochrones software package (Morton 2015), which performs isochrone fitting in the context of the MESA (Paxton et al. 2011, 2013, 2015) Isochrones and Stellar Tracks database (Dotter 2016; Choi et al. 2016). Single-star and binary evolutionary models are available within isochrones, and the inference is performed via the nested sampling algorithm MULTINEST (Feroz et al. 2009) (as implemented in the PyMultiNest software package (Buchner et al. 2014)), which allows for direct comparisons of the Bayesian evidence ln Z. We tested both single-star and binary models using the priors on photometric magnitudes and stellar distance described in Section 3.1.1. The inferred properties from the single-star model fit are consistent with those given in Table 1 at the 2σ level. The ln Z for the single-star model is −213.86±0.04, whereas the ln Z for the binary model is −229.6 ± 0.2. According to Kass & Raftery (1995), the corresponding Bayes factor of 16 indicates “decisive” evidence in favor of the single-star model. We also examined our Keck/HIRES spectrum for secondary lines that would indicate the presence of another star following the approach of Kolbl et al. (2015). We found no evidence of additional lines down to the method’s standard sensitivity limit of ∆V = 5 mag for ∆v > 10 km s−1 , consistent with EPIC 249631677 being a single, isolated star. We therefore conclude that the available data strongly support EPIC 246331677 being a single star. 3.2.2. Photometric Tests We performed a series of tests on the photometric data to rule out false-positive scenarios. First, we performed an even-odd test on the target using K2 photometry. The even and odd transits are consistent with one another in transit depth to within 1σ. We also looked for secondary eclipses in the phase-folded light curve and found none to be present. Note that since we observe consistent signals in both the K2 and SPECULOOS data sets, we can rule out the signal originating from systematics. The transit depth in SPECULOOS observations with I+z filter, which is redder than Kepler bandpass, are consistent to K2 transit depths within 1σ level, keeping up with the expectation of the achromatic nature of planetary transit. Furthermore, a massive companion, such as a faint white dwarf, can be ruled out using the ellipsoidal variation, which puts a 3σ upper limit on the mass of any companions at the given orbital period of the transit signal as ∼100 MJup (Morris 1985; Niraula et al. 2018). From the transit fit, we can rule out a grazing eclipse originating from a larger transiting object (i.e. ≥ 2R⊕) at >3σ confidence. Together, these tests rule out the object at 3.14 days being a massive companion. 3.3. Transit Fitting We used the refined estimates of the host properties together with a joint analysis of the K2 and SPECULOOS light curves to derive the planetary properties. In order to calculate the transit model, we used batman (Kreidberg 2015). We simultaneously model both the K2 observation as well as the ground-based observations with 21 parameters in a Monte Carlo Markov Chain (MCMC) framework using the emcee package (ForemanMackey et al. 2013). We use a Gaussian prior on the scaled semi-major axis of the orbit a/R∗ of N (25.72, 0.27), derived using Eq. 30 from Winn (2010) along with the stellar density of 32.6 ± 1.0 g cm−3 (see Section 3.1.1) and orbital period of 3.1443 days from the TLS search. As for the limb darkening, we use the non-informative q1, q2 parameterization of the quadratic limb-darkening law as suggested by Kipping (2013). We fixed the eccentricity to 0, given that the expected time of circularization is 50 Myr (assuming a quality factor Qp ∼ 500, Goldreich & Soter 1966; Patra et al. 2017), which is at least an order of magnitude smaller than the estimated age of the system. For K2 data, we supersample the transits by a factor of 15 in batman to take into account the effect of non-negligible integration time. As for the ground-based data, we use second-order polynomials to detrend against the observables airmass and FWHM. We ran the MCMC for 50,000 steps with 150 walkers performing a combined fit of K2 and SPECULOOS — (1) This work. (2) Huber et al. (2016). (3) Stassun et al. (2019). (4) Cutri et al. (2003). (5) Gaia Collaboration et al. (2018). (6) Cutri et al. (2013). (7) This work, evolutionary model analysis. (8) This work, Keck/HIRES analysis. (9) This work, SED analysis. References data, and use the last half of the run to build the parameter posteriors. We assessed the convergence of walkers using the suggested autocorrelation test for emcee. The resulting median values from the fit with 1σ deviation are reported in Table 2, while the best-fit transit models are shown in Figure 2 and Figure 3. [2] http://kinematics.bdnyc.org/query [3] http://stdatu.stsci.edu/cgi-bin/dss form

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Let's learn about via these 63 free stories. They are ordered by most time reading created on HackerNoon. Visit the to find the most read stories about any technology. Space /Learn Repo 1. Exodus from Mars Mother Earth, the womb of the solar system. Every other place, foster homes for her unwanted children. What is next? 2. The Impact of Web3 and Blockchain on the Space Industry How can Web3 and Blockchain, two new technologies that are more associated with grifting and scams have anything to do with the space race? 3. Lets Go Beyond Nuclear Fusion and Extract Energy from Blackholes I actually have been thinking about this for many years, and up until recently it has been confirmed. This is nothing new, as cosmologist and thermonuclear physicist Yakov Zeldovich have discussed this nearly half a century ago. 4. The Westall UFO Incident Explained In Under 5 Minutes The Westall UFO [incident] occurred on April 6, 1966, in the Melbourne suburb of Westall, Victoria, Australia. The incident involved multiple reports of... 5. DIY Tutorial: Building a System to Track and Communicate with Satellites in Orbit The purpose of my project is to build a system for tracking satellites in orbit and will make it possible to communicate with the satellites 6. Why Every Company Will Eventually Become a Space Company At some point, every company will become a space company. Sounds stupid at the moment but soon all companies will want to be part of the industry. Here's how. 7. How Twilio Sent Code to Space In a first of its kind mission, Twilio invited participants to launch their code into the stratosphere, and have it run in space. 8. “A robot army isn’t an ideal opponent, but I would have a water gun” Naturally, another good portion of the population would be trying to destroy everything around them for stupidity’s sake. 9. I'll pick up the check - from space! Everyone is all like, don't come back from space Jeff, but let me you tell you something, I am single and ready to mingle. 10. Can Mankind Survive as an Interplanetary Species? Humanity is well on the way to becoming an interplanetary species, but can we overcome the challenges of survival on another planet? 11. With Close to $100 million in Total Sales in Metaverses, NFTs Are Boosting Commerce in Metaverses Space is a 3D virtual world experience which provides its citizens powerful tools to create content, build businesses, interact collaboratively, and own and mon 12. Nominee Paul Bailey is Building the Future of Automated Space Systems Paul Bailey from the United States has been nominated for a 2020 Noonie in the Software Development category. He is a System Architect at CognitiveSpace, a company performing R&D in the field of aerospace engineering. 13. 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Spacetex: Clothes Made for Space, the Fiber Behind Gravity Spacetex textile is changing the game in fashion introducing subcategories such as Dystopian Fashion and Techwear. 50. Latin America Seeks its Riches in Space by Reaching Jupiter in 30 Days JOVE is a novel solar-powered mission that will use the solar wind's momentum, speed, and direction as the propulsive thrust to reach Jupiter in 30 days 51. The REAL Life of Pi: Ethereal, Romantic, Mysterious And Completely Memorizing “Probably no symbol in mathematics has evoked as much mystery, romanticism, misconception and human interest as the number Pi” ~William L. Schaaf, Nature and History of Pi. π 52. Space Exploration: New Frontier For Technological Innovations From the earliest known periods of human history, people have always been fascinated by the big yellow ball that provided light and heat, the tiny light dots shimmering in and regularly recurring tailed streaks dashing across the night sky. We wanted to know more about those objects, but the crippling limitations in our knowledge and technology didn’t allow that. 53. Starhopper: The Prototype Of Starship By SpaceX SpaceX is a space exploration company owned by a genius and a visionary Elon Musk who’s also the CEO of Tesla Inc. The main goal of SpaceX is to make space travel and exploration easy and efficient. Throughout the years, Elon Musk has done a lot of amazing things and has stayed completely open to the questions of the people. I think that Elon Musk’s transparency is his best quality. Anyways, let’s take a closer look at the latest advancement of SpaceX. 54. Can Satellites Help Combat Global Warming? In this slogging thread, our technology channel took the chance to discuss this news about the possibility of satellites helping fight global warming. 55. The Ongoing Mars Missions: Are We Ready to Live on the Red Planet? 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Celebrate this Intentional Holiday with Girls that Rule the World! 59. The Space Tech Startup Making Our Internet A Better Place With Lasers🖖 Greetings, humans. I remote chat this afternoon with Rohit Jha, the CEO & Co-Founder of Transcelestial Technologies, a startup building light speed communications infrastructure for the next 100 years. 60. Visualizing Asteroids in Python with Bokeh and NASA APIs A GET request to the Astronomy Picture of the Day (APOD) web service on September 18, 2020, returned the above photo of the spiral galaxy Arp 78.  APOD is one of many APIs available through NASA Open APIs.  Like APOD, some include imagery, such as the Earth Polychromatic Imaging Camera (EPIC) API, which returns images like this: 61. Into Space MANY of my readers will remember the mysterious radio messages which were heard by both amateur and professional short wave operators during the night 62. NexOS, Internet of Things (IoT), And Beyond: Part I Understanding the inspiration and history behind Nexus helps convey the current vision. This is the first of three articles covering pertinent aspects of Nexus’ history in which the context is set for the burgeoning NexOS (Nexus Operating System), and its innovative security principles are introduced. 63. Argentina’s Steady And Visionary Path To Space Is An Inspiring Tale Which path is required for us to reach new worlds? Argentina’s history in the space industry shows an unwavering course of perseverance and resilience. Thank you for checking out the 63 most read stories about Space on HackerNoon. to find the most read stories about any technology. Visit the /Learn Repo

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