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NEW YORK, New York, March 26th, 2024/Chainwire/--**Syntax takes natural language and converts it into Solidity code, enabling individuals and enterprises to ship production grade smart contracts, arbitrage agents, NFTs, rollups, and more. Syntax marks the manifestation of the Agent Economy in Web3. Today, has launched Syntax, a new LLM enabling people to ship agents that automate onchain projects and tasks, thereby manifesting their Web3 product ideas. While still in beta, Syntax’s vision is to create an open onchain Agent Economy, where developers, individuals, and enterprises can for the first time select the agents they would want to delegate their Web3 tasks, projects, and product development to. These projects and products include production grade smart contracts, arbitrage agents, NFTs, rollups, and more. Spectral Labs Scaling web3 engineering efforts and shipping new onchain products is limited by the number of solidity developers, as well as enterprises’ ability to test and ship smart contract code in a fast and effective way without burning through engineering resources. Spectral has set out to solve this with its new LLM, Syntax, a development environment designed to manifest Web3 product ideas by converting natural language into Solidity code that can be deployed instantly onchain. For professional developers, Syntax can accelerate and optimize bandwidth by writing large libraries and components. Syntax provides an Agentic experience, where users tell Syntax what they want to build, and Syntax writes and deploys the code onchain at the click of a button. Spectral defines an Onchain Agent as a set of instructions and code capable of deploying itself onchain and possessing a dedicated provisioned wallet for doing so. Loosely similar to custom instructions in ChatGPT, Syntax Agents also have their own identity and can autonomously figure out ways to interact with deployment infrastructure. With Syntax, users can compile, debug, and deploy AI-generated solidity code. Syntax gives users and the industry the ability to quickly test, ship and scale new products, as well as determining the usability and functional relevance of the code generated while also giving them control to quickly edit code snippets. Initially, Spectral’s Onchain Agents will be curated and built by Spectral, but soon every user will be able to create their own Agent and monetize it in future Syntax releases. "At Spectral, we're pioneering a future where autonomous Agents redefine what's possible onchain. With Spectral Syntax, we empower these agents to operate independently, making it simpler for everyone to bring their blockchain ideas to life." Sishir Varghese, Founder. What truly sets Syntax apart is its capability to deploy code directly onchain, executing deployments through Foundry by writing instructions that Foundry can process, including code compilation, onchain deployment, and signing transactions. Syntax is pioneering an accessible onchain Agent Economy, inviting users to select agents tailored for their specific Web3 tasks. Users can either interact with the foundational agent or opt for one of the specialized agents, each adept in distinct tasks and operations—like the Code Forker assistant, ideal for those aiming to fork and customize a codebase. Additionally, users can discern an agent's expertise and trustworthiness by reviewing its category listing and the popularity reflected through its user engagement. "Syntax by Spectral is at the forefront of merging AI with web3, pioneering the onchain agent economy and making it easier and more accessible for users to create their own blockchain products," said Josh Rosenthal, Partner, Polychain Syntax produces accurate and gas-optimized Solidity code for a variety of prompts ranging from low to medium complexity, and it outperforms baseline models on Spectral’s Solidity evaluation dataset. As Spectral’s modeling efforts continue to evolve, the company expects Syntax to deliver optimized code for increasingly complex problems. These Solidity models are explicitly designed to assist developers in writing optimized, modern, well-tested, and secure code. About Spectral , a pioneer of the agent economy behind Syntax, is at the forefront of integrating AI with blockchain to democratize development in Web3. Our mission is to simplify the creation and deployment of decentralized applications through autonomous Onchain Agents. Syntax, Spectral’s flagship product, translates natural language into Solidity code, enabling both novices and experts to build on the blockchain effortlessly. Spectral With a commitment to transparency and user empowerment, Spectral is shaping a future where anyone can participate in the blockchain revolution. Join us in making this vision a reality and explore the potential of autonomous agents with Spectral. For more information, visit /. For more information, users can follow Spectral on and . https://spectrallabs.xyz Twitter Discord Contact Spectral Labs Spectral info@spectrallabs.xyz This story was distributed as a release by Chainwire under HackerNoon’s Business Blogging Program. Learn more about the program here.

Spectral Launches Syntax Enabling Web3 Users To Build Autonomous Agents And Deploy Onchain Products

Authors: (1) Michael Sorochan Armstrong, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (2) Jose Carlos P´erez-Gir´on, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada; (3) Jos´e Camacho, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (4) Regino Zamora, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada. Table of Links Abstract & Introduction Optimization of the Optical Interpolation Materials and Methods Results and Discussion Conclusion Appendix A: Proof of Hermitian Self-Adjoint product identity for Equidistant Time-Domain Measurements Appendix B: AAH ̸= MIN I in the Non-Equidistant Case Acknowledgments & References 5 CONCLUSION A convenient mathematical expression to solve for the spectrum of irregularly sampled time-domain data has been demonstrated in a way that satisfies the conditions for an inverse non-uniform Fourier transform. This methodology has been derived from cost function proposed in the original study, and via its idealised quadratic form strongly suggests that its minimum is unique and convex. Using a randomly sample time series from data with few missing values, the observed relative error is on the same order of magnitude as the most current solution to this problem [10]. Upon cross-validation with contiguous blocks, we report a relative error that is much higher, and suggest this is a more critical, but informative lens through which to view interpolation problems. he proposed formula will find use in a variety of signal processing applications, where the use of an FFT is impractical given its assumption of a consistent time-domain density. The software package used in this work is available online: https://github.com/CoDaSLab/intrp infft 1d This paper is under CC 4.0 license. available on arxiv

Novel Mathematical Expression for Spectrum Determination of Irregularly Sampled Data

Authors: (1) Michael Sorochan Armstrong, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (2) Jose Carlos P´erez-Gir´on, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada; (3) Jos´e Camacho, Computational Data Science (CoDaS) Lab in the Department of Signal Theory, Telematics, and Communications at the University of Granada; (4) Regino Zamora, part of the Interuniversity Institute for Research on the Earth System in Andalucia through the University of Granada. Table of Links Abstract & Introduction Optimization of the Optical Interpolation Materials and Methods Results and Discussion Conclusion Appendix A: Proof of Hermitian Self-Adjoint product identity for Equidistant Time-Domain Measurements Appendix B: AAH ̸= MIN I in the Non-Equidistant Case Acknowledgments & References Abstract A simple least-squares optimization enables the determination of the spectrum for irregularly sampled data that is readily reconstructed using an adjoint transformation of the Non-Uniform Fast Fourier Transform (NFFT). This is an improvement upon previously reported iterative methods for such problems and is competitive in terms of time complexity with more recently proposed direct NFFT inversions when considering comparable matrix pre-computation steps. The software is highly portable, and available as a convenient Python package using standard libraries. Given its mathematical simplicity, however, it can be conveniently implemented on any platform. —Sensors, Digital processing, Non-uniformity correction, Remote monitor Index Terms 1 INTRODUCTION Remote sensor data is streamed from regions that are difficult to access for conventional measurements. Due to interruptions in either network connectivity, power or other environmental conditions there may be significant periods of time during which data acquisition is interrupted. This may not pose problems for ”binned” time-series analysis of the data, if the acquisition rate of the data is relatively high compared with the expected duration of a typical outage. Binning data does partially resolve the spatio-temporal lag of phenomena measured across different points for the same event which is assumed to take place within a predefined period of time. However regardless of whether or not missing data is present, this does not make use of the full acquisition rate of the instrument, which negates some benefits of remote measurement. Instead, it is possible to perform an analysis of the spectrum or frequency domain information of the remote measurements and reconstruct the original data based on parallel analysis of similar remote stations. Spectral analysis of irregularly sampled data is an active area of research, and is often referenced broadly as a leastsquares analysis, owing to a need for numerical estimation. This type of analysis commonly finds applications wherever there is an interruption in measurement - as is commonly seen in climate applications [1], and other environmental monitoring [2]. 1.1 Fourier transforms of irregularly sampled data A full spectrum of Fourier coefficients in can be calculated up to where the maximum frequency of is the Nyquist frequency; beyond which the sampling rate is not sufficient to warrant calculation of further coefficients. N M = N N/2 1.2 Non-Uniform Fast Fourier Transforms Equations 5, 6, and 7 refer to non-uniform transforms of types: (irregularly-sampled time-series data; equispaced frequency-domain data), (equispaced time-series data, discontinuous frequency-domain data), and (discontinuous time and frequency-domain data) which are equivalent to the transform: I II III 1.3 Inverse NFFTs Inverting A directly via a pseudo-inverse is computationally inefficient, relative to the standard set by an inverse Fourier transform in the equidistant case. Rather, it is more convenient to find a series of Fourier coefficients such that the original time series data is recoverable via the adjoint transform. This can be done in the least squares sense by minimising: A number of proposals to solve this optimisation problem, and others have been put forward, but the method varies depending on the condition of the inverse problem, especially for direct solutions [9]. Tables 1.3 and 1.3 are provided to clear any potential confusion, for transformations of types I & II. For the purposes of this work and to explicate the far more common scenario where irregularly sampled time-series data are provided, the focus will be exclusively on type-I transforms, although it would be relatively straightforward to apply the same thinking to type-II transforms. 1.4 Optimal interpolation problem The optimal interpolation problem has been solved earlier using the Conjugate Gradient Method that minimises the successive error at each iteration, rather than the residuals relative to the original data [10]. This work demonstrates the quadratic form of Equation 12, and offers a convenient method for solving the interpolative iNFFT without the need to iterate. In addition, it avoids problems with dimensionality by inverting the AAH matrix, which sacrifices time complexity for simplicity; this is an acceptable trade-off for small values of N and competitive with faster algorithms for the direct inversion of non-uniform fast Fourier transforms which require similar O(N2 ) matrix pre-computations [9]. can be used to define the Sobolev kernel, first as an intermediate and generalisable weight function: This paper is under CC 4.0 license. available on arxiv

Solving the Interpolative Inverse Non-Uniform Fast Fourier Transform Problem for Spectral Analysis

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 6. RESULTS 6.1. Cross-correlation search We cross-correlated the models described in Section 4 with the processed data and searched for peaks in the phase-folded cross-correlation function at the expected KP and vsys of GJ 486b. Figs. 2 − 8 show the results of our search for H2O, CO2, HCN, NH3, CH4, Na, and the 700 K solar abundance model with condensation, respectively. These figures show the 1D cross-correlation functions phase-folded using GJ 486b’s expected value of KP as well as its negative value. We show the result of using −KP as we later use it to inject model spectra into the data in Section 6.2. We find no evidence for robust correlations between any of our models[9] and the data. The most promising feature is of H2O in the IGRINS data set (see Fig. 2), which is at the 3σ level[10] in the expected position in KP and vsys. However, it is likely that this feature is produced by imperfectly removed water lines in the spectrum of GJ 486b’s M-dwarf host star, given that it is present after applying only one iteration of SYSREM, as shown in Fig. 9. We do not understand why these residuals were not removed by SYSREM and only appear in the IGRINS data set. However, we note that they appear to be qualitatively similar to those reported by Brogi et al. (2013). In their case, Brogi et al. (2013) detected molecular absorption in the dayside emission spectrum of 51 Pegasi b on two separate occasions, but not a third occasion when strong stellar residuals were present in the data. Chiavassa & Brogi (2019) revisited this data and used 3D simulations of stellar convection to remove the stellar spectrum. This method better suppressed the stellar residuals in the third observation and allowed the planetary signal to be detected. In a future study, it may be beneficial to investigate whether the method of Chiavassa & Brogi (2019) can better suppress the stellar residuals in our IGRINS data. Regarding our nondetection of Na, Caballero et al. (2022) suggest that if GJ 486b were to have a tenuous atmosphere with a surface pressure of 10−6 bar, nonthermal processes such as surface sputtering by ions may heat its atmosphere to temperatures on the order of 10,000 K. They show that a Na abundance of 10−9 in such an atmosphere would produce transit depths of approximately 1% in the cores of the Na D lines (5889.95 and 5895.92 ˚A), which could be detected by observing only a few transits with the Calar Alto high-Resolution search for M dwarfs with Exoearths with Near-infrared and optical Echelle Spectrographs (CARMENES; Quirrenbach et al. 2014). The spectral ranges of our observations do not include the Na D lines, but our IRD and SPIRou data sets do include the Na lines at 1.138 and 1.141 µm, which are much weaker and more difficult to detect. Therefore, while we found no evidence for a nonthermal Na atmosphere, we do not consider this to be evidence for its absence. We recommend further investigation of this scenario with additional observations targeting the Na D lines. 6.2. Constraining GJ 486b’s Atmospheric Composition As we did not detect the atmosphere of GJ 486b, here we determine the abundances that our data can rule out under the assumption that GJ 486b’s atmosphere is clear. We do this by injecting cloud-free model spectra into the reduced data before processing and crosscorrelating as in Sections 3 and 5. For each in-transit frame, we injected the model transmission spectrum at the velocity given by Equation 2 if KP were replaced by its negative value. We injected the signals at −KP so that they would not be affected by any weak real planet signals that may be present in the data. To optimally combine the different data sets, we summed the log-likelihoods. Our cross-correlation to log-likelihood mapping produced an array with dimensions KP, vsys, and α. Examples of the recovered conditional (2D) and marginalized (1D) likelihood distributions after injecting a water model into the data are shown in Fig. 10. We used the marginalized distributions of KP, vsys, and α (as shown in Fig. 10) to find their most likely values and their associated 1σ errors. With this approach, the significance to which an injected signal was recovered is well approximated by how well α is constrained (Gibson et al. 2020, 2022). This method works because we assume that marginalized distributions of α that are constant at α = 0, or unconstrained, correspond to a nondetection. Therefore, we are essentially measuring how significantly α differs from zero. However, in practice, our recovered values of α were slightly less than the true values, leading to a slight underestimate of the true recovered detection significances. This is because we did not explicitly account for how SYSREM distorts an underlying planet signal when removing the stellar and telluric lines. Gibson et al. (2022) showed that this can be corrected by pre-processing the models in an analogous way to how SYSREM processes the planet signal in the data. We investigated the feasibility of using this approach by trying it for a single model spectrum and a typical grid covering ±60 km s−1 around the expected KP and vsys with step sizes of 1 km s −1 . The run time of this trial on a reasonably capable workstation[11] was 80 minutes. Our full analysis uses about 640 different model spectra, which would therefore require a total run time of about 36 days. We consider this to be infeasible for this study, so we instead report our upper limits with the caveat that they likely underestimate the true upper limits. We were able to recover some injected models for H2O, CH4, NH3, HCN, CO2, and CO, indicating that our high-resolution observations can constrain the abundances of these chemical species under the assumption of GJ 486b having a clear atmosphere. As these species have different molecular weights, line strengths, and numbers of lines, they are each sensitive to different regions of VMR-MMW parameter space. These constraints are shown in Fig 11 for H2O, CH4, NH3, HCN, CO2, and CO, respectively. Each figure shows the VMRMMW constraints for the individual data sets (SPIRou, IRD, IGRINS) and all data sets combined. Models with higher MMWs have smaller atmospheric scale heights, making them more difficult to recover. Injected models that were recovered to significances of ≥5σ and 3≤σ<5 are colored in black and gray, respectively. Injected models that were recovered to significances of 0≤σ<3 are considered to have not been recovered and are shown in light blue. This means that we can rule out model atmospheres to 5σ and 3σ in the VMR-MMW regions colored black and gray, respectively. Conversely, the light blue regions represent atmospheric compositions that are allowed by our data. We obtain strong constraints on the presence of H2O in GJ 486b’s atmosphere. Assuming a clear atmosphere, our observations rule out log10(VMR) ≥ −3 for atmospheric MMWs ≤ 5 and log10(VMR) ≥ −4 for MMWs ≤2.5 to 5σ. Therefore, our observations are inconsistent with a clear H2/He-dominated atmosphere with solar (or somewhat subsolar) H2O abundances. We can also, less confidently, rule out a clear atmosphere of log10(VMR) ≥ −2 for MMWs ≤ 16 and a clear 100% H2O atmosphere to 3σ. Our results, therefore, suggest that GJ 486b does not have a clear H2O-dominated atmosphere. This could have important implications for planetary interior models, which often predict H2O-dominated atmospheres as the most likely possibility for 3 M⊕ planets like GJ 486b (e.g., Ortenzi et al. 2020). Our derived constraints on the abundances of CH4, NH3, HCN, CO2, and CO are summarized in Table 2. These constraints show that our observations are inconsistent with a clear H2/He-dominated atmosphere with a solar CH4 abundance. However, solar abundances of NH3, HCN, CO2, and CO are consistent with our data. For cloud-free models including all the above species at solar abundances, we rule out to 5σ those with temperatures > 500 K, as shown in Fig. 12. We were not able to recover any of our injected models for C2H2, FeH, H2S, Na, K, PH3, SiO, TiO, or VO. This indicates that, regardless of their VMR or the background atmosphere MMW, our observations are not sensitive to these chemical species. For all the species considered here, the data from IGRINS on Gemini-S offers the strongest limits. This likely results from Gemini-S having a larger collecting area than SPIRou’s CFHT and the wavelength coverage (1.45-2.45 µm) of IGRINS extending further into the infrared than that of IRD (0.97-1.75 µm). Overall, these upper limits indicate that GJ 486b lacks a clear H/He-dominated atmosphere with solar abundances. However, some possible cloudy atmospheres or high-MMW secondary atmospheres are allowed by our data. [9] Including both the Exomol (Yurchenko & Tennyson 2014) and HITEMP 2020 (Hargreaves et al. 2020) opacity data for CH4. [10] Approximated as the amplitude of the cross-correlation function at the expected velocity divided by the standard deviation of the surrounding regions. [11] With the following specifications: Ryzen 5900X (12 core) CPU, 128 GB of DDR 3200 RAM, and a PCIe 4.0 M.2 SSD.

High-Resolution Transmission Spectroscopy of the Terrestrial Exoplanet GJ 486b: Results

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 3. DATA REDUCTION AND PROCESSING The IRD transit data were reduced following the approach of Hirano et al. (2020), which uses a custom code to correct for a known count bias that depends on the readout channel (Kuzuhara et al. 2018). Subsequent reduction steps were performed using the echelle package of IRAF. As these observations did not use the laser frequency comb, the wavelength calibration was based on the Th-Ar lamp. The wavelength solution was stable to within approximately 0.04 km s−1 over the course of the observations. This stability was determined by first cross-correlating every frame with a model telluric spectrum produced using SkyCalc (Noll et al. 2012; Jones et al. 2013) to find the telluric radial velocity of each frame. We then calculated the standard deviation of all telluric radial velocities during the night (after applying a barycentric correction). The model produced by SkyCalc is highly customizable, but the most important parameters are target elevation or airmass and the precipitable water vapor. The IGRINS transit data were reduced by the IGRINS Pipeline Package (PLP; Sim et al. 2014; Mace et al. 2018). Though this pipeline provides wavelengthcalibrated data, the PLP wavelength calibration drifted by about 1 kms−1 through the course of the observations. To fit and correct this drift, we first crosscorrelated SkyCalc telluric models (as above) with every frame in spectral orders that had no saturated telluric lines. The spectral orders used for these crosscorrelations are shown in Table 3. For each frame, we then summed the cross-correlation functions (CCFs) from all our considered orders to produce a master CCF. Next, we fit a Gaussian to the master CCF of each frame and adopted the Gaussian center as the radial velocity of the observed telluric spectrum. Finally, we fit the telluric radial velocities with a third-degree polynomial as a function of time and used this to shift the data onto a common wavelength grid using linear interpolation. The amplitudes of the corrective shifts were approximately 0.5−1 km s−1 . The SPIRou transit data were reduced by the observatory using the SPIRou Data Reduction Software (DRS) [4] . This pipeline provides data with and without a telluric correction, and we opted to use the telluric-corrected data. For all data sets, after the above procedures, we normalized the spectra on a per-order basis to have a continuum flux of 1. We then masked all spectral regions with a normalized flux less than 0.3. For the IGRINS data, we also masked telluric emission lines, as in Rousselot et al. (2000) and Oliva et al. (2015). We then applied the SYSREM algorithm (Tamuz et al. 2005) to all data sets to remove remaining telluric features and other systematic trends. We applied SYSREM to our data in fluxes (without first converting to magnitudes), as in Gibson et al. (2020) and Nugroho et al. (2021). Because SYSREM incorporates uncertainties, we estimated the uncertainties of the normalized data as where σt and σλ are the standard deviations in the time and wavelength dimensions, respectively, σt,λ is the standard deviation in both the time and wavelength dimensions, and ⊗ is the outer product operator. To determine an effective number of SYSREM iterations to use, we followed a well-established approach and examined how each order’s variance decreased as a function of the number of applied SYSREM iterations (e.g., Deibert et al. 2021a; Herman et al. 2022). For each order, we examined plots of the variance as a function of the number of SYSREM iterations and identified by eye the number of iterations where the decrease in data variance began to plateau. We noted the number of SYSREM iterations determined for each order and then used the most common number of iterations as a constant for each data set. This resulted in us applying five SYSREM iterations to all orders of the SPIRou and IRD data and 10 SYSREM iterations to all orders of the IGRINS data. While our chosen values are likely not the formal optimal values, they are a close approximation, as telluric features and other systematic trends were removed effectively. In general, previous studies have found that the exact number of SYSREM iterations has little to no effect on the final results (e.g., Deibert et al. 2021b). Some IGRINS orders, as indicated in Table 3, had near-total telluric extinction across most of their spectral range. Such severe contamination cannot be corrected by SYSREM, so we excluded these orders from the analysis. Finally, for all data sets, we removed any outlying points more than three standard deviations away from the mean. Barycentric corrections for the IRD and IGRINS data were calculated with the radial velocity correction function in Astropy. The same corrections for the SPIRou data were provided by the DRS. [4] http://www.cfht.hawaii.edu/Instruments/SPIRou/SPIRou pipeline.php

High-Resolution Transmission Spectroscopy: Data Reduction and Processing

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 2. OBSERVATIONS We used three different instruments to observe three separate transit events of GJ 486b. The first transit was observed with the Infrared Doppler (IRD) instrument on the 8.2 m Subaru telescope, providing a wavelength coverage of 0.97-1.75 µm at a resolving power of R = 70k (Tamura et al. 2012; Kotani et al. 2018). The second transit was observed with the Immersion GRating INfrared Spectrometer (IGRINS) on the 8.1 m GeminiSouth telescope (program ID: GS-2021A-DD-105), providing a wavelength coverage of 1.45-2.45 µm at a resolving power of R = 45k (Park et al. 2014; Lee & Gullikson 2016; Mace et al. 2018). The third transit was observed with the SPectropolarim`etre InfraROUge (SPIRou) on the 3.6 m Canada-France-Hawai’i Telescope (CFHT) in queue mode (run ID: 21BC34), providing a wavelength coverage of 0.98-2.35 µm at a resolving power of R = 75k (Artigau et al. 2014). The observation start time, duration, integration time, cadence, total number of frames, number of frames in transit, number of frames out of transit, and average signal-to-noise (S/N) ratio per pixel for these observations are shown in Table 1.

High-Resolution Transmission Spectroscopy of the Terrestrial Exoplanet GJ 486b: Observation

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 4. MODEL SPECTRA We searched for chemical species in GJ 486b’s atmosphere through a cross-correlation analysis with model transmission spectra. We generated a grid of template spectra using the open-source radiative transfer code petitRADTRANS[5] (Molli`ere et al. 2019). Each template contains one or more absorbing chemical species embedded in a background of spectrally inactive gas. Specifically, we searched for a wide range of gaseous absorbers: C2H2, CH4, CO, CO2, FeH, H2O, HCN, H2S, K, Na, NH3, PH3, SiO, TiO, and VO. We used the default opacity data included with petitRADTRANS (see Molli`ere et al. 2019) for all species. However, for CH4 we used both the default opacity data from Exomol (Yurchenko & Tennyson 2014) and our custom-made opacity grid based on a line list adopted from HITEMP 2020 (Hargreaves et al. 2020). We produced the custom opacity grid following the pressure-temperature grid in the petitRADTRANS website (e.g., PTgrid.dat). We calculated the cross section using HELIOS-K 2.0 (Grimm & Heng 2015; Grimm et al. 2021) with a line wing cutoff of 100 cm−1 at a resolution of 0.001 cm−1 which was later resampled at a constant resolution of R = 106 . Our templates include two chemical models: (i) single chemical species models and (ii) multispecies chemical equilibrium models. Our single-species models span a range of volume mixing ratios (VMRs) and MMWs. The VMRs range from log10(VMR) = −7 to 0 (assumed constant with altitude). We varied the MMWs independently of the VMRs, subject to the following boundary conditions: (i) the minimum MMW corresponds to a H2-dominated atmosphere with the template species (i.e. MMWmin ≈ 2 · (1 − VMRi) + VMRi · MMWi); and (ii) the maximum MMW corresponds to an N2-dominated atmosphere with the template species (i.e. MMWmax ≈ 28 · (1 − VMRi) + VMRi · MMWi). These boundary conditions ensure the MMWs are physically consistent with the presence of a spectrally inactive gas mixture with unknown ratios of H2, He, or N2. These models assumed an isothermal pressure-temperature (P-T) profile at GJ 486b’s equilibrium temperature: 700 K (Trifonov et al. 2021). Our second set of models included all the above mentioned spectrally active species with thermochemical equilibrium abundances. We computed equilibrium abundances for a solar composition atmosphere using the open-source code GGchem[6] (Woitke et al. 2018), assuming isothermal P-T profiles at 400, 500, 600, and 700 K. We considered three different approaches for modeling condensation in GGchem: (1) no condensation, (2) condensation included, and (3) condensation included, but condensates removed (e.g., rain out). These abundance profiles are shown in Fig. 1. Although condensation would likely result in the production of aerosols such as clouds or hazes, we do not attempt to account for the effect of such aerosols on the resulting transmission spectrum. Our petitRADTRANS models were computed line by line at R = 106 using 130 layers spaced evenly in logpressure from 10−11 to 102 bar. We then resampled the model spectra to the resolution of the data (R = 45 k, 70 k, and 75 k for IGRINS, IRD, and SPIRou, respectively) using the SpectRes package[7] (Carnall 2017) which preserves the integrated flux. Because cross-correlations are not sensitive to continua, we subtracted the continuum from our model spectra (after binning to the data resolution) to produce our final cross-correlation templates. [5] https://petitradtrans.readthedocs.io/en/latest/ [6] https://github.com/pw31/GGchem [7] https://spectres.readthedocs.io/en/latest/

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