Analytical determination of orbital elements using Fourier analysis. I. The radial velocity case

We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of the orbital parameters. The accuracy is mainly limited by the accuracy of the computation of the Fourier decomposition of the signal which is sensitive to sampling and noise. Our method is complementary with more accurate (and more expensive in computer time) numerical algorithms (e.g. Levenberg-Marquardt, Markov chain Monte Carlo, genetic algorithms). Indeed, the analytical approximation can be used as an initial condition to accelerate the convergence of these numerical methods. Our method can be applied iteratively to search for multiple planets in the same system.Comment: accepted to A&

The Hot Neptune WASP-166 b with ESPRESSO II: Confirmation of atmospheric sodium

The hot Neptune desert, a distinct lack of highly irradiated planets in the size range of Neptune, remains one of the most intriguing results of exoplanet population studies. A deeper understanding of the atmosphere of exoplanets sitting at the edge or even within the Neptune desert will allow us to better understand if planetary formation or evolution processes are at the origin of the desert. A detection of sodium in WASP-166b was presented previously with tentative line broadening at the 3.4 sigma with the HARPS spectrograph. We update this result with two transits observed with the ESPRESSO spectrograph, confirming the detection in each night and the broadened character of the line. This result marks the first confirmed resolved sodium detection within the Neptune desert. In this work, we additionally highlight the importance of treating low-SNR spectral regions, particularly where absorption lines of stellar sodium and planetary sodium overlap at mid-transit - an important caveat for future observations of the system.Comment: Letter, re-submitted to MNRAS after minor referee report; comments welcom

Multi-band high resolution spectroscopy rules out the hot Jupiter BD+20 1790b - First data from the GIARPS Commissioning

Context. Stellar activity is currently challenging the detection of young planets via the radial velocity (RV) technique. Aims. We attempt to definitively discriminate the nature of the RV variations for the young active K5 star BD+20 1790, for which visible (VIS) RV measurements show divergent results on the existence of a substellar companion. Methods. We compare VIS data with high precision RVs in the near infrared (NIR) range by using the GIANO - B and IGRINS spectrographs. In addition, we present for the first time simultaneous VIS-NIR observations obtained with GIARPS (GIANO - B and HARPS - N) at Telescopio Nazionale Galileo (TNG). Orbital RVs are achromatic, so the RV amplitude does not change at different wavelengths, while stellar activity induces wavelength-dependent RV variations, which are significantly reduced in the NIR range with respect to the VIS. Results. The NIR radial velocity measurements from GIANO - B and IGRINS show an average amplitude of about one quarter with respect to previously published VIS data, as expected when the RV jitter is due to stellar activity. Coeval multi-band photometry surprisingly shows larger amplitudes in the NIR range, explainable with a mixture of cool and hot spots in the same active region. Conclusions. In this work, the claimed massive planet around BD+20 1790 is ruled out by our data. We exploited the crucial role of multi- wavelength spectroscopy when observing young active stars: thanks to facilities like GIARPS that provide simultaneous observations, this method can reach its maximum potential.Comment: 12 pages, 7 figure

HELIOS-K 2.0 Opacity Calculator and Open-source Opacity Database for Exoplanetary Atmospheres

Computing and using opacities is a key part of modeling and interpreting data of exoplanetary atmospheres. Since the underlying spectroscopic line lists are constantly expanding and currently include up to ∼1010–1011 transition lines, the opacity calculator codes need to become more powerful. Here we present major upgrades to the HELIOS-K GPU-accelerated opacity calculator and describe the necessary steps to process large line lists within a reasonable amount of time. Besides performance improvements, we include more capabilities and present a toolbox for handling different atomic and molecular data sets, from downloading and preprocessing the data to performing the opacity calculations in a user-friendly way. HELIOS-K supports line lists from ExoMol, HITRAN, HITEMP, NIST, Kurucz, and VALD3. By matching the resolution of 0.1 cm−1 and cutting length of 25 cm−1 used by the ExoCross code for timing performance (251 s excluding data read-in time), HELIOS-K can process the ExoMol BT2 water line list in 12.5 s. Using a resolution of 0.01 cm−1, it takes 45 s, equivalent to about 107 lines s−1. As a wavenumber resolution of 0.01 cm−1 suffices for most exoplanetary atmosphere spectroscopic calculations, we adopt this resolution in calculating opacity functions for several hundred atomic and molecular species and make them freely available on the open-access DACE database. For the opacity calculations of the database, we use a cutting length of 100 cm−1 for molecules and no cutting length for atoms. Our opacities are available for downloading from https://dace.unige.ch/opacityDatabase and may be visualized using https://dace.unige.ch/opacity

Exploring the stellar surface phenomena of WASP-52 and HAT-P-30 with ESPRESSO

We analyse spectroscopic and photometric transits of the hot Jupiters WASP-52b and HAT-P30b obtained with ESPRESSO, Eulercam and NGTS for both targets, and additional TESS data for HAT-P-30. Our goal is to update the system parameters and refine our knowledge of the host star surfaces. For WASP-52, the companion planet has occulted starspots in the past, and as such our aim was to use the reloaded Rossiter-McLaughlin technique to directly probe its starspot properties. Unfortunately, we find no evidence for starspot occultations in the datasets herein. Additionally, we searched for stellar surface differential rotation (DR) and any centre-to-limb variation (CLV) due to convection, but return a null detection of both. This is unsurprising for WASP-52, given its relatively cool temperature, high magnetic activity (which leads to lower CLV), and projected obliquity near 0 degrees (meaning the transit chord is less likely to cross several stellar latitudes). For HAT-P-30, this result was more surprising given its hotter effective temperature, lower magnetic field, and high projected obliquity (near 70 degrees). To explore the reasons behind the null DR and CLV detection for HAT-P-30, we simulated a variety of scenarios. We find that either the CLV present on HAT-P-30 is below the solar level or the presence of DR prevents a CLV detection given the precision of the data herein. A careful treatment of both DR and CLV is required, especially for systems with high impact factors, due to potential degeneracies between the two. Future observations and/or a sophisticated treatment of the red noise present in the data (likely due to granulation) is required to refine the DR and CLV for these particular systems; such observations would also present another opportunity to try to examine starspots on WASP-52.Comment: 11 pages main text, 8 figures; accepted for publication in A&

Exploring the stellar surface phenomena of WASP-52 and HAT-P-30 with ESPRESSO

We analyse spectroscopic and photometric transits of the hot Jupiters WASP-52 b and HAT-P30 b obtained with ESPRESSO, Eulercam and NGTS for both targets, and additional TESS data for HAT-P-30. Our goal is to update the system parameters and refine our knowledge of the host star surfaces. For WASP-52, the companion planet has occulted starspots in the past, and as such our aim was to use the reloaded Rossiter-McLaughlin technique to directly probe its starspot properties. Unfortunately, we find no evidence for starspot occultations in the datasets herein. Additionally, we searched for stellar surface differential rotation (DR) and any centre-to-limb variation (CLV) due to convection, but return a null detection of both. This is unsurprising for WASP-52, given its relatively cool temperature, high magnetic activity (which leads to lower CLV), and projected obliquity near 0° (meaning the transit chord is less likely to cross several stellar latitudes). For HAT-P-30, this result was more surprising given its hotter effective temperature, lower magnetic field, and high projected obliquity (near 70°). To explore the reasons behind the null DR and CLV detection for HAT-P-30, we simulated a variety of scenarios. We find that either the CLV present on HAT-P-30 is below the solar level or the presence of DR prevents a CLV detection given the precision of the data herein. A careful treatment of both DR and CLV is required, especially for systems with high impact factors, due to potential degeneracies between the two. Future observations and/or a sophisticated treatment of the red noise present in the data (likely due to granulation) is required to refine the DR and CLV for these particular systems; such observations would also present another opportunity to try to examine starspots on WASP-52

The hot Neptune WASP-166 b with ESPRESSO III: A blue-shifted tentative water signal constrains the presence of clouds

With high-resolution spectroscopy we can study exoplanet atmospheres and learn about their chemical composition, temperature profiles, and presence of clouds and winds, mainly in hot, giant planets. State-of-the-art instrumentation is pushing these studies towards smaller exoplanets. Of special interest are the few planets in the ‘Neptune desert’, a lack of Neptune-size planets in close orbits around their hosts. Here, we assess the presence of water in one such planet, the bloated super-Neptune WASP-166 b, which orbits an F9-type star in a short orbit of 5.4 days. Despite its close-in orbit, WASP-166 b preserved its atmosphere, making it a benchmark target for exoplanet atmosphere studies in the desert. We analyse two transits observed in the visible with ESPRESSO. We clean the spectra from the Earth’s telluric absorption via principal component analysis, which is crucial to the search for water in exoplanets. We use a cross-correlation-to-likelihood mapping to simultaneously estimate limits on the abundance of water and the altitude of a cloud layer, which points towards a low water abundance and/or high clouds. We tentatively detect a water signal blue-shifted ∼5 km s−1 from the planetary rest frame. Injection and retrieval of model spectra show that a solar-composition, cloud-free atmosphere would be detected at high significance. This is only possible in the visible due to the capabilities of ESPRESSO and the collecting power of the VLT. This work provides further insight on the Neptune desert planet WASP-166 b, which will be observed with JWST

Detection Limits of Low-mass, Long-period Exoplanets Using Gaussian Processes Applied to HARPS-N Solar Radial Velocities

Radial velocity (RV) searches for Earth-mass exoplanets in the habitable zone around Sun-like stars are limited by the effects of stellar variability on the host star. In particular, suppression of convective blueshift and brightness inhomogeneities due to photospheric faculae/plage and starspots are the dominant contribution to the variability of such stellar RVs. Gaussian process (GP) regression is a powerful tool for statistically modeling these quasi-periodic variations. We investigate the limits of this technique using 800 days of RVs from the solar telescope on the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) spectrograph. These data provide a well-sampled time series of stellar RV variations. Into this data set, we inject Keplerian signals with periods between 100 and 500 days and amplitudes between 0.6 and 2.4 ms−1. We use GP regression to fit the resulting RVs and determine the statistical significance of recovered periods and amplitudes. We then generate synthetic RVs with the same covariance properties as the solar data to determine a lower bound on the observational baseline necessary to detect low-mass planets in Venus-like orbits around a Sun-like star. Our simulations show that discovering planets with a larger mass (∼0.5 ms−1) using current-generation spectrographs and GP regression will require more than 12 yr of densely sampled RV observations. Furthermore, even with a perfect model of stellar variability, discovering a true exo-Venus (∼0.1 m s −1 ) with current instruments would take over 15 yr. Therefore, next-generation spectrographs and better models of stellar variability are required for detection of such planets

Detection Limits of Low-mass, Long-period Exoplanets Using Gaussian Processes Applied to HARPS-N Solar Radial Velocities

Radial velocity (RV) searches for Earth-mass exoplanets in the habitable zone around Sun-like stars are limited by the effects of stellar variability on the host star. In particular, suppression of convective blueshift and brightness inhomogeneities due to photospheric faculae/plage and starspots are the dominant contribution to the variability of such stellar RVs. Gaussian process (GP) regression is a powerful tool for statistically modeling these quasi-periodic variations. We investigate the limits of this technique using 800 days of RVs from the solar telescope on the High Accuracy Radial velocity Planet Searcher for the Northern hemisphere (HARPS-N) spectrograph. These data provide a well-sampled time series of stellar RV variations. Into this data set, we inject Keplerian signals with periods between 100 and 500 days and amplitudes between 0.6 and 2.4 m s$^{-1}$. We use GP regression to fit the resulting RVs and determine the statistical significance of recovered periods and amplitudes. We then generate synthetic RVs with the same covariance properties as the solar data to determine a lower bound on the observational baseline necessary to detect low-mass planets in Venus-like orbits around a Sun-like star. Our simulations show that discovering planets with a larger mass ($\sim$ 0.5 m s$^{-1}$) using current-generation spectrographs and GP regression will require more than 12 yr of densely sampled RV observations. Furthermore, even with a perfect model of stellar variability, discovering a true exo-Venus ($\sim$ 0.1 m s$^{-1}$) with current instruments would take over 15 yr. Therefore, next-generation spectrographs and better models of stellar variability are required for detection of such planets