Search

We present new observations from CHEOPS and TESS to clarify the architecture of the planetary system hosted by the old Galactic thick disk star TOI-561. Our global analysis, which also includes previously published photometric and radial velocity data, incontrovertibly proves that TOI-561 is hosting at least four transiting planets with periods of 0.44 days (TOI-561 b), 10.8 days (TOI-561 c), 25.7 days (TOI-561 d), and 77.1 days (TOI-561 e) and a fifth non-transiting candidate, TOI-561f with a period of 433 days. The precise characterisation of TOI-561's orbital architecture is interesting since old and metal-poor thick disk stars are less likely to host ultra-short period Super-Earths like TOI-561 b. The new period of planet -e is consistent with the value obtained using radial velocity alone and is now known to be $77.14399\pm0.00025$ days, thanks to the new CHEOPS and TESS transits. The new data allowed us to improve its radius ($R_p = 2.517 \pm 0.045 R_{\oplus}$ from 5$\%$ to 2$\%$ precision) and mass ($M_p = 12.4 \pm 1.4 M_{\oplus}$) estimates, implying a density of $\rho_p = 0.778 \pm 0.097 \rho_{\oplus}$. Thanks to recent TESS observations and the focused CHEOPS visit of the transit of TOI-561 e, a good candidate for exomoon searches, the planet's period is finally constrained, allowing us to predict transit times through 2030 with 20-minute accuracy. We present an updated version of the internal structure of the four transiting planets. We finally performed a detailed stability analysis, which confirmed the long-term stability of the outer planet TOI-561 f., Comment: 13 pages, 10 Figures. Accepted on MNRAS. Updated the author list

Neutral sodium was the first atom detected in an exoplanetary atmosphere via transmission spectroscopy and remains the most frequently detected species due to its strong doublet in the optical. However, the center-to-limb variation (CLV) of these lines in the host star can bias the Na detection.When combined with the Rossiter-McLaughlin (RM) effect, the CLV can mimic or obscure planetary absorption features. This work investigates the impact of 3D radiation hydrodynamic stellar atmospheres and non-local thermodynamic equilibrium (NLTE) radiative transfer on the modeling of the CLV+RM effect in single-line transmission spectroscopy, to improve the characterization of exoplanet atmospheres. We produced a grid of 3D NLTE synthetic spectra for Na I for FGK stars within the following parameter space: Teff=4500-6500 K, log g=4.0-5.0 and [Fe/H]=-0.5, 0, 0.5.This grid was then interpolated to match the stellar parameters of four stars hosting giant exoplanets, to correct for the CLV+RM effect in their transmission spectra. We used ESPRESSO archival observations. Our work confirms the Na detections in three systems, namely WASP-52b, WASP-76b, and WASP-127b, improving the accuracy of the measured absorption depth. Furthermore, we find that 3D NLTE stellar models can explain the spectral features in HD 209458b without the need for any planetary absorption. In the grid of synthetic spectra, we observe that the CLV effect is stronger for stars with low Teff and high log g. However, the combined effect of CLV and RM is highly dependent on the orbital geometry of the planet-star system. With the continuous improvement of instrumentation, it is crucial to use the most accurate stellar models to correct for the CLV+RM effect in high-resolution transmission spectra, to achieve the best possible characterization of exoplanet atmospheres. We make our grid of 3D NLTE spectra for Na publicly available., Comment: Accepted for publication in A&A, 17 pages (23 with appendices)

The purpose of the present paper is to address multiple aspects of the Fuglede question dealing (Fourier spectra vs geometry) with a variety of $L^2$ contexts where we make precise the interplay between the three sides of the question: (i) existence of orthogonal families of Fourier basis functions (and associated spectra) on the one hand, (ii) extensions of partial derivative operators, and (iii) geometry of the corresponding domains, stressing systems of translation-tiles. We emphasize an account of old and new developments since the original 1974-paper by Bent Fuglede where the co-authors and Steen Pedersen have contributed.

Barnard's star is a primary target within the ESPRESSO guaranteed time observations (GTO) as it is the second closest neighbour to our Sun after the $\alpha$ Centauri stellar system. We present here a large set of 156 ESPRESSO observations of Barnard's star carried out over four years with the goal of exploring periods of shorter than 50 days, thus including the habitable zone (HZ). Our analysis of ESPRESSO data using Gaussian process (GP) to model stellar activity suggests a long-term activity cycle at 3200d and confirms stellar activity due to rotation at 140d as the dominant source of radial velocity (RV) variations. These results are in agreement with findings based on publicly available HARPS, HARPS-N, and CARMENES data. ESPRESSO RVs do not support the existence of the previously reported candidate planet at 233d. After subtracting the GP model, ESPRESSO RVs reveal several short-period candidate planet signals at periods of 3.15d, 4.12d, 2.34d, and 6.74d. We confirm the 3.15d signal as a sub-Earth mass planet, with a semi-amplitude of $55 \pm 7$cm/s, leading to a planet minimum mass $m_p \sin i$ of $0.37 \pm 0.05$Mearth, which is about three times the mass of Mars. ESPRESSO RVs suggest the possible existence of a candidate system with four sub-Earth mass planets in circular orbits with semi-amplitudes from 20 to 47cm/s, thus corresponding to minimum masses in the range of 0.17-0.32Mearth. The sub-Earth mass planet at $3.1533 \pm 0.0006$d is in a close-to circular orbit with a semi-major axis of $0.0229 \pm 0.0003$AU, thus located inwards from the HZ of Barnard's star, with an equilibrium temperature of 400K. Additional ESPRESSO observations would be required to confirm that the other three candidate signals originate from a compact short-period planet system orbiting Barnard's star inwards from its HZ., Comment: Accepted for publication in Astronomy and Astrophysics

Trans-Neptunian objects (TNOs) are considered to be among the most primitive objects in our Solar System. Knowledge of their primary physical properties is essential for understanding their origin and the evolution of the outer Solar System. We predicted a stellar occultation by this TNO for 2020 October 23 UT and ran a specific campaign to investigate this event. We derived the projected profile shape and size from the occultation observations by means of an elliptical fit to the occultation chords. We also performed photometric observations of (143707) 2003 UY117 to obtain the absolute magnitude and the rotational period from the observed rotational light curve. Finally, we combined these results to derive the three-dimensional shape, volume-equivalent diameter, and geometric albedo for this TNO. From the stellar occultation, we obtained a projected ellipse with axes of $(282 \pm 18) \times (184 \pm 32)$ km. The area-equivalent diameter for this ellipse is $D_\textrm{eq,A} = 228 \pm 21$ km. From our photometric $R$ band observations, we derived an absolute magnitude of $H_V = 5.97 \pm 0.07$ mag using $V-R = 0.46 \pm 0.07$ mag, which was derived from a $V$ band subset of these data. The rotational light curve has a peak-to-valley amplitude of $\Delta m = 0.36 \pm 0.13$ mag. We find the most likely rotation period to be $P = 12.376 \pm 0.0033$ hours. By combining the occultation with the rotational light curve results and assuming a triaxial ellipsoid, we derived axes of $a \times b \times c = (332 \pm 24)$ km $\times$ $(216 \pm 24)$ km $\times$ $(180\substack{+28\\-24})$ km for this ellipsoid, and therefore a volume-equivalent diameter of $D_\textrm{eq,V} = 235 \pm 25$ km. Finally, the values for the absolute magnitude and for the area-equivalent diameter yield a geometric albedo of $p_V = 0.139 \pm 0.027$., Comment: 9 pages, 7 figures, accepted for publication in Astronomy and Astrophysics on Sept 13, 2024

Thanks to their short orbital periods and hot extended atmospheres, hot Jupiters are ideal candidates for atmosphere studies with high-resolution spectroscopy. New stable spectrographs help improve our understanding of the evolution and composition of those types of planets. By analyzing two nights of observations using the ESPRESSO high-resolution spectrograph, we studied the architecture and atmosphere of hot Jupiter WASP-122b (KELT-14b). By analyzing the Rossiter-McLaughlin (RM) effect, we measured the spin-orbit angle of the system to be lambda = 0.09 +0.88/-0.90 deg. This result is in line with literature obliquity measurements of planetary systems around stars with effective temperatures cooler than 6500 K. Using the transmission spectroscopy, we studied the atmosphere of the planet. Applying both the single-line analysis and the cross-correlation method, we looked for Ca I, Cr I, FeH, Fe I, Fe II, H2O, Li I, Mg I, Na I, Ti I, TiO, V I, VO, and Y I. Our results show no evidence of any of these species in WASP-122b's atmosphere. The lack of significant detections can be explained by either the RM effect covering the regions where the atmospheric signal is expected and masking it, along with the low signal-to-noise ratio (S/N) of the observations or the absence of the relevant species in its atmosphere., Comment: Accepted for publication in A&A, 19 pages, 17 figures, 5 tables

Hot Jupiters are giant planets subject to intense stellar radiation. The physical and chemical properties of their atmosphere makes them the most amenable targets for the atmospheric characterization. In this paper we analyze the photometry collected during the secondary eclipses of the hot Jupiter WASP-3 b by CHEOPS, TESS and Spitzer. Our aim is to characterize the atmosphere of the planet by measuring the secondary eclipse depth in several passbands and constrain the planetary dayside spectrum. Our update of the stellar and planetary properties is consistent with previous works. The analysis of the occultations returns an eclipse depth of 92+-21 ppm in the CHEOPS passband, 83+-27 ppm for TESS and >2000 ppm in the IRAC 1-2-4 Spitzer passbands. Using the eclipse depths in the Spitzer bands we propose a set of likely emission spectra which constrain the emission contribution in the \cheops and TESS passbands to approximately a few dozens of parts per million. This allowed us to measure a geometric albedo of 0.21+-0.07 in the CHEOPS passband, while the TESS data lead to a 95\% upper limit of $\sim$0.2. WASP-3 b belongs to the group of ultra-hot Jupiters which are characterized by low Bond albedo (<0.3+-0.1), as predicted by different atmospheric models. On the other hand, it unexpectedly seems to efficiently recirculate the absorbed stellar energy, unlike similar highly irradiated planets. To explain this inconsistency, we propose that other energy recirculation mechanisms may be at play other than advection (for example, dissociation and recombination of H_2). Another possibility is that the observations in different bandpasses probe different atmospheric layers, making the atmospheric analysis difficult without an appropriate modeling of the thermal emission spectrum of WASP-3 b, which is not feasible with the limited spectroscopic data available to date.

SN 2023tsz is a Type Ibn supernova (SNe Ibn) discovered in an extremely low-mass host. SNe Ibn are an uncommon subtype of stripped-envelope core-collapse SNe. They are characterised by narrow helium emission lines in their spectra and are believed to originate from the collapse of massive Wolf-Rayet (WR) stars, though their progenitor systems still remain poorly understood. In terms of energetics and spectrophotometric evolution, SN 2023tsz is largely a typical example of the class, although line profile asymmetries in the nebular phase are seen, which may indicate the presence of dust formation or unshocked circumstellar material. Intriguingly, SN 2023tsz is located in an extraordinarily low-mass host galaxy that is in the 2nd percentile for SESN host masses and star formation rates (SFR). The host has a radius of 1.0 kpc, a $g$-band absolute magnitude of $-12.73$, and an estimated metallicity of $\log(Z_{*}/Z_{\odot}$) = $-1.56$. The SFR and metallicity of the host galaxy raise questions about the progenitor of SN 2023tsz. The low SFR suggests that a star with sufficient mass to evolve into a WR would be uncommon in this galaxy. Further, the very low-metallicity is a challenge for single stellar evolution to enable H and He stripping of the progenitor and produce a SN Ibn explosion. The host galaxy of SN 2023tsz adds another piece to the ongoing puzzle of SNe Ibn progenitors, and demonstrates that they can occur in hosts too faint to be observed in contemporary sky surveys at a more typical SN Ibn redshift., Comment: 14 pages, 10 figures, submitted to MNRAS

Ultra hot Jupiters (gas giants, Teq>2000 K) are intriguing exoplanets due to their extreme atmospheres. Their torrid daysides can be characterised using ground-based high-resolution emission spectroscopy. We search for signatures of neutral and singly ionised iron (Fe I and Fe II) in the dayside of the ultra hot Jupiter WASP-76 b, as these species were detected via transmission spectroscopy in this exoplanet. Furthermore, we aim to confirm the existence of a thermal inversion layer, which has been reported in previous studies, and attempt to constrain its properties. We observed WASP-76 b on four epochs with ESPRESSO at the VLT, at orbital phases shortly before and after the secondary transit, when the dayside is in view. We present the first analysis of high-resolution optical emission spectra for this exoplanet. We compare the data to synthetic templates from petitRADTRANS, using cross-correlation function techniques. We detect a blueshifted (-4.7+-0.3 km/s) Fe I emission signature on the dayside of WASP-76 b at 6.0-sigma. The signal is detected independently both before and after the eclipse, and blueshifted in both cases. The presence of iron emission features confirms the existence of a thermal inversion layer. Fe II was not detected, possibly because this species is located in the upper layers of the atmosphere, which are more optically thin. Thus the Fe II signature on the dayside of WASP-76 b is too weak to be detected with emission spectroscopy. We propose that the blueshifted Fe I signature is created by material rising from the hot spot to the upper layers of the atmosphere, and discuss possible scenarios related to the position of the hotspot. This work unveils some of the dynamic processes ongoing on the dayside of WASP-76 b through the analysis of the Fe I signature from its atmosphere, and complements previous knowledge obtained from transmission studies., Comment: 15 pages, 8 figures + 2 figures in appendix. Abstract slightly abridged. Published in Astronomy & Astrophysics

The exoplanet sub-Neptune population currently poses a conundrum. Are small-size planets volatile-rich cores without atmosphere, or are they rocky cores surrounded by H-He envelope? To test the different hypotheses from an observational point of view, a large sample of small-size planets with precise mass and radius measurements is the first necessary step. On top of that, much more information will likely be needed, including atmospheric characterisation and a demographic perspective on their bulk properties. We present the concept and strategy of THIRSTEE, a project which aims at shedding light on the composition of the sub-Neptune population across stellar types by increasing their number and improving the accuracy of bulk density measurements, as well as investigating their atmospheres and performing statistical, demographic analysis. We report the first results of the program, characterising a 2-planet system around the M dwarf TOI-406. We analyse TESS and ground-based photometry, together with ESPRESSO and NIRPS/HARPS RVs to derive the orbital parameters and investigate the internal composition of the 2 planets orbiting TOI-406, which have radii and masses of $R_b = 1.32 \pm 0.12 R_{\oplus}$, $M_b = 2.08_{-0.22}^{+0.23} M_{\oplus}$ and $R_c = 2.08_{-0.15}^{+0.16} R_{\oplus}$, $M_c = 6.57_{-0.90}^{+1.00} M_{\oplus}$, and periods of $3.3$ and $13.2$ days, respectively. Planet b is consistent with an Earth-like composition, while planet c is compatible with multiple internal composition models, including volatile-rich planets without H/He atmospheres. The 2 planets are located in 2 distinct regions in the mass-density diagram, supporting the existence of a density gap among small exoplanets around M dwarfs. With an equilibrium temperature of only 368 K, TOI-406 c stands up as a particularly interesting target for atmospheric characterisation with JWST in the low-temperature regime., Comment: 24 pages, 21 figures. SUBMITTED to A&A

Bratteli diagrams with countably infinite levels exhibit a new phenomenon: they can be horizontally stationary. The incidence matrices of these horizontally stationary Bratteli diagrams are infinite banded Toeplitz matrices. In this paper, we study the fundamental properties of horizontally stationary Bratteli diagrams. In these diagrams, we provide an explicit description of ergodic tail invariant probability measures. For a certain class of horizontally stationary Bratteli diagrams, we prove that all ergodic tail invariant probability measures are extensions of measures from odometers. Additionally, we establish conditions for the existence of a continuous Vershik map on the path space of a horizontally stationary Bratteli diagram., Comment: 25 pages, 2 figures

The TESS mission searches for transiting exoplanets by monitoring the brightness of hundreds of thousands of stars across the entire sky. M-type planet hosts are ideal targets for this mission due to their smaller size and cooler temperatures, which makes it easier to detect smaller planets near or within their habitable zones. Additionally, M~dwarfs have a smaller contrast ratio between the planet and the star, making it easier to measure the planet's properties accurately. Here, we report the validation analysis of 13 TESS exoplanet candidates orbiting around M dwarfs. We studied the nature of these candidates through a multi-colour transit photometry transit analysis using several ground-based instruments (MuSCAT2, MuSCAT3, and LCO-SINISTRO), high-spatial resolution observations, and TESS light curves. We present the validation of five new planetary systems: TOI-1883b, TOI-2274b, TOI2768b, TOI-4438b, and TOI-5319b, along with compelling evidence of a planetary nature for TOIs 2781b and 5486b. We also present an empirical definition for the Neptune desert boundaries. The remaining six systems could not be validated due to large true radius values overlapping with the brown dwarf regime or, alternatively, the presence of chromaticity in the MuSCAT2 light curves.

K2-24 is a planetary system composed of two transiting low-density Neptunians locked in an almost perfect 2:1 resonance and showing large TTVs, i.e., an excellent laboratory to search for signatures of planetary migration. Previous studies performed with K2, Spitzer and RV data tentatively claimed a significant non-zero eccentricity for one or both planets, possibly high enough to challenge the scenario of pure disk migration through resonant capture. With 13 new CHEOPS light curves (seven of planet -b, six of planet -c), we carried out a global photometric and dynamical re-analysis by including all the available literature data as well. We got the most accurate set of planetary parameters to date for the K2-24 system, including radii and masses at 1% and 5% precision (now essentially limited by the uncertainty on stellar parameters) and non-zero eccentricities $e_b=0.0498_{-0.0018}^{+0.0011}$, $e_c=0.0282_{-0.0007}^{+0.0003}$ detected at very high significance for both planets. Such relatively large values imply the need for an additional physical mechanism of eccentricity excitation during or after the migration stage. Also, while the accuracy of the previous TTV model had drifted by up to 0.5 days at the current time, we constrained the orbital solution firmly enough to predict the forthcoming transits for the next ~15 years, thus enabling an efficient follow-up with top-level facilities such as JWST or ESPRESSO., Comment: 19 pages, 11 figures, 8 tables. Accepted for publication in A&A on September 4, 2024. Typos corrected

We collected more than 300 high-resolution spectra of the 300 Myr old star BD+40 2790 (TOI-2076) over ~3 years. This star hosts three transiting planets discovered by TESS, with orbital periods ~10, 21, and 35 days. BD+40 2790 shows an activity-induced scatter larger than 30 m/s in the radial velocities. We employed different methods to measure the stellar radial velocities and several models to filter out the dominant stellar activity signal, in order to bring to light the planet-induced signals which are expected to have semi-amplitudes one order of magnitude lower. We evaluated the mass loss rate of the planetary atmospheres using photoionization hydrodynamic modeling. The dynamical analysis confirms that the three sub-Neptune-sized companions (our radius measurements are $R_b$=2.54$\pm$0.04, $R_c$=3.35$\pm$0.05, and $R_d$=3.29$\pm$0.06 $R_{\rm Earth}$) have masses in the planetary regime. We derive 3$\sigma$ upper limits below or close to the mass of Neptune for all the planets: 11--12, 12--13.5, and 14--19 $M_{\rm Earth}$ for planet $b$, $c$, and $d$ respectively. In the case of planet $d$, we found promising clues that the mass could be between ~7 and 8 $M_{\rm Earth}$, with a significance level between 2.3--2.5$\sigma$ (at best). This result must be further investigated using other analysis methods or using high-precision near-IR spectrographs to collect new radial velocities, which could be less affected by stellar activity. Atmospheric photo-evaporation simulations predict that BD+40~2790 b is currently losing its H-He gaseous envelope, which will be completely lost at an age within 0.5--3 Gyr if its current mass is lower than 12 $M_{\rm Earth}$. BD+40 2790 c could have a lower bulk density than $b$, and it could retain its atmosphere up to an age of 5 Gyr. For the outermost planet $d$, we predict almost negligible evolution of its mass and radius induced by photo-evaporation., Comment: Accepted for publication on A&A. Abstract abridged

Motivated by questions in quantum theory, we study Hilbert space valued Gaussian processes, and operator-valued kernels, i.e., kernels taking values in B(H) (= all bounded linear operators in a fixed Hilbert space H). We begin with a systematic study of p.d. B(H)-valued kernels and the associated of H-valued Gaussian processes, together with their correlation and transfer operators. In our consideration of B(H)-valued kernels, we drop the p.d. assumption. We show that input-output models can be computed for systems of signed kernels taking the precise form of realizability via associated transfer block matrices (of operators analogous to the realization transforms in systems theory), i.e., represented via 2\times2 operator valued block matrices. In the context of B(H)-valued kernels we present new results on regression with H-valued Gaussian processes.

We present the validation of two TESS super-Earth candidates transiting the mid-M dwarfs TOI-6002 and TOI-5713 every 10.90 and 10.44 days, respectively. The first star (TOI-6002) is located $32.038\pm0.019$ pc away, with a radius of $0.2409^{+0.0066}_{-0.0065}$ \rsun, a mass of $0.2105^{+0.0049}_{-0.0048}$ \msun, and an effective temperature of $3229^{+77}_{-57}$ K. The second star (TOI-5713) is located $40.946\pm0.032$ pc away, with a radius of $0.2985^{+0.0073}_{-0.0072}$ \rsun, a mass of $0.2653\pm0.0061$ \msun, and an effective temperature of $3225^{+41}_{-40}$ K. We validated the planets using TESS data, ground-based multi-wavelength photometry from many ground-based facilities, as well as high-resolution AO observations from Keck/NIRC2. TOI-6002 b has a radius of $1.65^{+0.22}_{-0.19}$ \re\ and receives $1.77^{+0.16}_{-0.11} S_\oplus$. TOI-5713 b has a radius of $1.77_{-0.11}^{+0.13} \re$ and receives $2.42\pm{0.11} S_\oplus$. Both planets are located near the radius valley and near the inner edge of the habitable zone of their host stars, which makes them intriguing targets for future studies to understand the formation and evolution of small planets around M-dwarf stars.

We report the spectroscopic confirmation and fundamental properties of TOI-757 b, a mini-Neptune on a 17.5-day orbit transiting a bright star ($V = 9.7$ mag) discovered by the TESS mission. We acquired high-precision radial velocity measurements with the HARPS, ESPRESSO, and PFS spectrographs to confirm the planet detection and determine its mass. We also acquired space-borne transit photometry with the CHEOPS space telescope to place stronger constraints on the planet radius, supported with ground-based LCOGT photometry. WASP and KELT photometry were used to help constrain the stellar rotation period. We also determined the fundamental parameters of the host star. We find that TOI-757 b has a radius of $R_{\mathrm{p}} = 2.5 \pm 0.1 R_{\oplus}$ and a mass of $M_{\mathrm{p}} = 10.5^{+2.2}_{-2.1} M_{\oplus}$, implying a bulk density of $\rho_{\text{p}} = 3.6 \pm 0.8$ g cm$^{-3}$. Our internal composition modeling was unable to constrain the composition of TOI-757 b, highlighting the importance of atmospheric observations for the system. We also find the planet to be highly eccentric with $e$ = 0.39$^{+0.08}_{-0.07}$, making it one of the very few highly eccentric planets among precisely characterized mini-Neptunes. Based on comparisons to other similar eccentric systems, we find a likely scenario for TOI-757 b's formation to be high eccentricity migration due to a distant outer companion. We additionally propose the possibility of a more intrinsic explanation for the high eccentricity due to star-star interactions during the earlier epoch of the Galactic disk formation, given the low metallicity and older age of TOI-757., Comment: Accepted for publication in MNRAS; 26 pages, 14 figures, 6 tables

Context: Rocky planets on ultra-short period orbits can have surface magma oceans and rock-vapour atmospheres in which dust can condense. Observations of that dust can inform about the composition surface conditions on these objects. Aims: We constrain the properties and long-term (decade) behaviour of the transiting dust cloud from the "evaporating" planet K2-22b. Methods: We observed K2-22b around 40 predicted transits with MuSCAT ground-based multi-optical channel imagers, and complemented these data with long-term monitoring by the ground-based ATLAS (2018-2024) and space-based TESS (2021-2023) surveys. Results: We detected signals during 7 transits, none of which showed significant wavelength dependence. The expected number of MuSCAT-detected transits is >=22, indicating a decline in mean transit depth since the K2 discovery observations in 2014. Conclusions: Lack of significant wavelength dependence indicates that dust grains are large or the cloud is optically thick. Long-term trends of depth could be due to a magnetic cycle on the host star or overturn of the planet's dayside surface magma ocean. The possibility that K2-22b is disappearing altogether is ruled out by the stability of the transit ephemeris against non-gravitational forces, which constrains the mass to be at least comparable to Ceres., Comment: accepted to Astronomy and Astrophysics Letters

The first generation of ELT instruments includes an optical-infrared high-resolution spectrograph, indicated as ELT-HIRES and recently christened ANDES (ArmazoNes high Dispersion Echelle Spectrograph). ANDES consists of three fibre-fed spectrographs ([U]BV, RIZ, YJH) providing a spectral resolution of $\sim$100,000 with a minimum simultaneous wavelength coverage of 0.4-1.8 $\mu$m with the goal of extending it to 0.35-2.4 $\mu$m with the addition of a U arm to the BV spectrograph and a separate K band spectrograph. It operates both in seeing- and diffraction-limited conditions and the fibre feeding allows several, interchangeable observing modes including a single conjugated adaptive optics module and a small diffraction-limited integral field unit in the NIR. Modularity and fibre-feeding allow ANDES to be placed partly on the ELT Nasmyth platform and partly in the Coud\'e room. ANDES has a wide range of groundbreaking science cases spanning nearly all areas of research in astrophysics and even fundamental physics. Among the top science cases, there are the detection of biosignatures from exoplanet atmospheres, finding the fingerprints of the first generation of stars, tests on the stability of Nature's fundamental couplings, and the direct detection of the cosmic acceleration. The ANDES project is carried forward by a large international consortium, composed of 35 Institutes from 13 countries, forming a team of almost 300 scientists and engineers which include the majority of the scientific and technical expertise in the field that can be found in ESO member states., Comment: SPIE astronomical telescope and instrumentation 2024, in press

We present a parallel between commutative and non-commutative polymorphisms. Our emphasis is the applications to conditional distributions from stochastic processes. In the classical case, both the measures and the positive definite kernels are scalar valued. But the non-commutative framework (as motivated by quantum theory) dictates a setting where instead now both the measures (in the form of quantum states), and the positive definite kernels, are operator valued. The non-commutative theory entails a systematic study of positive operator valued measures, abbreviated POVMs. And quantum states (normal states) are indexed by normalized positive trace-class operators. In the non-commutative theory, the parallel to the commutative/scalar valued theory helps us understand entanglement in quantum information. A further implication of our study of the non-commutative framework will entail an interplay between the two cases, scalar valued, vs operator valued.

Among the thousands of exoplanets discovered to date, approximately a few hundred gas giants on short-period orbits are classified as "lonely" and only a few are in a multi-planet system with a smaller companion on a close orbit. The processes that formed multi-planet systems hosting gas giants on close orbits are poorly understood, and only a few examples of this kind of system have been observed and well characterised. Within the contest of multi-planet system hosting gas-giant on short orbits, we characterise TOI-1130 system by measuring masses and orbital parameters. This is a 2-transiting planet system with a Jupiter-like planet (c) on a 8.35 days orbit and a Neptune-like planet (b) on an inner (4.07 days) orbit. Both planets show strong anti-correlated transit timing variations (TTVs). Furthermore, radial velocity (RV) analysis showed an additional linear trend, a possible hint of a non-transiting candidate planet on a far outer orbit. Since 2019, extensive transit and radial velocity observations of the TOI-1130 have been acquired using TESS and various ground-based facilities. We present a new photo-dynamical analysis of all available transit and RV data, with the addition of new CHEOPS and ASTEP+ data that achieve the best precision to date on the planetary radii and masses and on the timings of each transit. We were able to model interior structure of planet b constraining the presence of a gaseous envelope of H/He, while it was not possible to assess the possible water content. Furthermore, we analysed the resonant state of the two transiting planets, and we found that they lie just outside the resonant region. This could be the result of the tidal evolution that the system underwent. We obtained both masses of the planets with a precision less than 1.5%, and radii with a precision of about 1% and 3% for planet b and c, respectively., Comment: 22 pages, 10 figures, Accepted for publication by Astronomy and Astrophysics

Multiplanetary systems spanning the radius valley are ideal testing grounds for exploring the proposed explanations for the observed bimodality in the radius distribution of close-in exoplanets. One such system is HIP 29442 (TOI-469), an evolved K0V star hosting two super-Earths and a sub-Neptune. We observe HIP 29442 with CHEOPS for a total of 9.6 days, which we model jointly with 2 sectors of TESS data to derive planetary radii of $3.410\pm0.046$, $1.551\pm0.045$ and $1.538\pm0.049$ R$_\oplus$ for planets b, c and d, which orbit HIP 29442 with periods of 13.6, 3.5 and 6.4 days. For planet d, this value deviates by more than 3 sigma from the median value reported in the discovery paper, leading us to conclude that caution is required when using TESS photometry to determine the radii of small planets with low per-transit S/N and large gaps between observations. Given the high precision of these new radii, combining them with published RVs from ESPRESSO and HIRES provides us with ideal conditions to investigate the internal structure and formation pathways of the planets in the system. We introduce the publicly available code plaNETic, a fast and robust neural network-based Bayesian internal structure modelling framework. We then apply hydrodynamic models to explore the upper atmospheric properties of these inferred structures. Finally, we identify planetary system analogues in a synthetic population generated with the Bern model for planet formation and evolution. Based on this analysis, we find that the planets likely formed on opposing sides of the water iceline from a protoplanetary disk with an intermediate solid mass. We finally report that the observed parameters of the HIP 29442 system are compatible with both a scenario where the second peak in the bimodal radius distribution corresponds to sub-Neptunes with a pure H/He envelope as well as a scenario with water-rich sub-Neptunes., Comment: 30 pages, 17 figures, accepted for publication in A&A

We search for atmospheric constituents for the UHJ WASP-178 b with two ESPRESSO transits using the narrow-band and cross-correlation techniques, focusing on the detections of NaI, H$\alpha$, H$\beta$, H$\gamma$, MgI, FeI and FeII. Additionally, we show parallel photometry used to obtain updated and precise stellar, planetary and orbital parameters. We report the resolved line detections of NaI (5.5 and 5.4 $\sigma$), H$\alpha$ (13 $\sigma$), H$\beta$ (7.1 $\sigma$), and tentatively MgI (4.6 $\sigma$). In cross-correlation, we confirm the MgI detection (7.8 and 5.8 $\sigma$) and additionally report the detections of FeI (12 and 10 $\sigma$) and FeII (11 and 8.4 $\sigma$), on both nights separately. The detection of MgI remains tentative, however, due to the differing results between both nights, as well as compared with the narrow-band derived properties. None of our resolved spectral lines probing the mid- to upper atmosphere show significant shifts relative to the planetary rest frame, however H$\alpha$ and H$\beta$ exhibit line broadenings of 39.6 $\pm$ 2.1 km/s and 27.6 $\pm$ 4.6 km/s, respectively, indicating the onset of possible escape. WASP-178 b differs from similar UHJ with its lack of strong atmospheric dynamics in the upper atmosphere, however the broadening seen for FeI (15.66 $\pm$ 0.58 km/s) and FeII (11.32 $\pm$ 0.52 km/s) could indicate the presence of winds in the mid-atmosphere. Future studies on the impact of the flux variability caused by the host star activity might shed more light on the subject. Previous work indicated the presence of SiO cloud-precursors in the atmosphere of WASP-178 b and a lack of MgI and FeII. However, our results suggest that a scenario where the planetary atmosphere is dominated by MgI and FeII is more likely. In light of our results, we encourage future observations to further elucidate these atmospheric properties., Comment: 18 pages, 24 figures, accepted for publication in A&A

Since 2018, the ESPRESSO spectrograph at the VLT has been hunting for planets in the Southern skies via the RV method. One of its goals is to follow up candidate planets from transit surveys such as the TESS mission, particularly small planets. We analyzed photometry from TESS and ground-based facilities, high-resolution imaging, and RVs from ESPRESSO, HARPS, and HIRES, to confirm and characterize three new planets: TOI-260 b, transiting a late K-dwarf, and TOI-286 b and c, orbiting an early K-dwarf. We also update parameters for the known super-Earth TOI-134 b , hosted by an M-dwarf. TOI-260 b has a $13.475853^{+0.000013}_{-0.000011}$ d period, $4.23 \pm1.60 \mathrm{M_\oplus}$ mass and $1.71\pm0.08\mathrm{R_\oplus}$ radius. For TOI-286 b we find a $4.5117244^{+0.0000031}_{-0.0000027}$ d period, $4.53\pm0.78\mathrm{M_\oplus}$ mass and $1.42\pm0.10\mathrm{R_\oplus}$ radius; for TOI-286 c, a $39.361826^{+0.000070}_{-0.000081}$ d period, $3.72\pm2.22\mathrm{M_\oplus}$ mass and $1.88\pm 0.12\mathrm{R_\oplus}$ radius. For TOI-134 b we obtain a $1.40152604^{+0.00000074}_{-0.00000082}$ d period, $4.07\pm0.45\mathrm{M_\oplus}$ mass, and $1.63\pm0.14\mathrm{R_\oplus}$ radius. Circular models are preferred for all, although for TOI-260 b the eccentricity is not well-constrained. We compute bulk densities and place the planets in the context of composition models. TOI-260 b lies within the radius valley, and is most likely a rocky planet. However, the uncertainty on the eccentricity and thus on the mass renders its composition hard to determine. TOI-286 b and c span the radius valley, with TOI-286 b lying below it and having a likely rocky composition, while TOI-286 c is within the valley, close to the upper border, and probably has a significant water fraction. With our updated parameters for TOI-134 b, we obtain a lower density than previous findings, giving a rocky or Earth-like composition., Comment: 61 pages (of which pp. 24-61 are appendices), 20 figures (main text). Accepted for publication in A&A

Time-domain astrophysics continues to grow rapidly, with the inception of new surveys drastically increasing data volumes. Democratised, distributed approaches to training sets for machine learning classifiers are crucial to make the most of this torrent of discovery -- with citizen science approaches proving effective at meeting these requirements. In this paper, we describe the creation of and the initial results from the $\textit{Kilonova Seekers}$ citizen science project, built to find transient phenomena from the GOTO telescopes in near real-time. $\textit{Kilonova Seekers}$ launched in July 2023 and received over 600,000 classifications from approximately 2,000 volunteers over the course of the LIGO-Virgo-KAGRA O4a observing run. During this time, the project has yielded 20 discoveries, generated a `gold-standard' training set of 17,682 detections for augmenting deep-learned classifiers, and measured the performance and biases of Zooniverse volunteers on real-bogus classification. This project will continue throughout the lifetime of GOTO, pushing candidates at ever-greater cadence, and directly facilitate the next-generation classification algorithms currently in development., Comment: 20 pages, 15 figures. Accepted in MNRAS

CHEOPS is a space telescope specifically designed to monitor transiting exoplanets orbiting bright stars. In September 2023, CHEOPS completed its nominal mission and remains in excellent operational conditions. The mission has been extended until the end of 2026. Scientific and instrumental data have been collected throughout in-orbit commissioning and nominal operations, enabling a comprehensive analysis of the mission's performance. In this article, we present the results of this analysis with a twofold goal. First, we aim to inform the scientific community about the present status of the mission and what can be expected as the instrument ages. Secondly, we intend for this publication to serve as a legacy document for future missions, providing insights and lessons learned from the successful operation of CHEOPS. To evaluate the instrument performance in flight, we developed a comprehensive monitoring and characterisation programme. It consists of dedicated observations that allow us to characterise the instrument's response. In addition to the standard collection of nominal science and housekeeping data, these observations provide input for detecting, modelling, and correcting instrument systematics, discovering and addressing anomalies, and comparing the instrument's actual performance with expectations. The precision of the CHEOPS measurements has enabled the mission objectives to be met and exceeded. Careful modelling of the instrumental systematics allows the data quality to be significantly improved during the light curve analysis phase, resulting in more precise scientific measurements. CHEOPS is compliant with the driving scientific requirements of the mission. Although visible, the ageing of the instrument has not affected the mission's performance., Comment: Accepted for publication in Astronomy and Astrophysics

HIP 41378 d is a long-period planet that has only been observed to transit twice, three years apart, with K2. According to stability considerations and a partial detection of the Rossiter-McLaughlin effect, $P_\mathrm{d} = 278.36$ d has been determined to be the most likely orbital period. We targeted HIP 41378 d with CHEOPS at the predicted transit timing based on $P_\mathrm{d}= 278.36$ d, but the observations show no transit. We find that large ($>22.4$ hours) transit timing variations (TTVs) could explain this non-detection during the CHEOPS observation window. We also investigated the possibility of an incorrect orbital solution, which would have major implications for our knowledge of this system. If $P_\mathrm{d} \neq 278.36$ d, the periods that minimize the eccentricity would be $101.22$ d and $371.14$ d. The shortest orbital period will be tested by TESS, which will observe HIP 41378 in Sector 88 starting in January 2025. Our study shows the importance of a mission like CHEOPS, which today is the only mission able to make long observations (i.e., from space) to track the ephemeris of long-period planets possibly affected by large TTVs., Comment: Accepted for publication in Astronomy and Astrophysics

Recent discoveries of Earth-sized planets transiting nearby M dwarfs have made it possible to characterize the atmospheres of terrestrial planets via follow-up spectroscopic observations. However, the number of such planets receiving low insolation is still small, limiting our ability to understand the diversity of the atmospheric composition and climates of temperate terrestrial planets. We report the discovery of an Earth-sized planet transiting the nearby (12 pc) inactive M3.0 dwarf Gliese 12 (TOI-6251) with an orbital period ($P_{\rm{orb}}$) of 12.76 days. The planet, Gliese 12b, was initially identified as a candidate with an ambiguous $P_{\rm{orb}}$ from TESS data. We confirmed the transit signal and $P_{\rm{orb}}$ using ground-based photometry with MuSCAT2 and MuSCAT3, and validated the planetary nature of the signal using high-resolution images from Gemini/NIRI and Keck/NIRC2 as well as radial velocity (RV) measurements from the InfraRed Doppler instrument on the Subaru 8.2 m telescope and from CARMENES on the CAHA 3.5 m telescope. X-ray observations with XMM-Newton showed the host star is inactive, with an X-ray-to-bolometric luminosity ratio of $\log L_{\rm X}/L_{\rm bol} \approx -5.7$. Joint analysis of the light curves and RV measurements revealed that Gliese 12b has a radius of 0.96 $\pm$ 0.05 $R_\oplus$, a 3$\sigma$ mass upper limit of 3.9 $M_\oplus$, and an equilibrium temperature of 315 $\pm$ 6 K assuming zero albedo. The transmission spectroscopy metric (TSM) value of Gliese 12b is close to the TSM values of the TRAPPIST-1 planets, adding Gliese 12b to the small list of potentially terrestrial, temperate planets amenable to atmospheric characterization with JWST., Comment: 29 pages (20 pages in main body), 13 figures (10 figures in main body). Equal contributions from M. K. and A. F.. Accepted for Publication in ApJL at 2024 March 21

The TOI-178 system consists of a nearby late K-dwarf transited by six planets in the super-Earth to mini-Neptune regime, with radii ranging from 1.2 to 2.9 earth radius and orbital periods between 1.9 and 20.7 days. All planets but the innermost one form a chain of Laplace resonances. The fine-tuning and fragility of such orbital configurations ensure that no significant scattering or collision event has taken place since the formation and migration of the planets in the protoplanetary disc, hence providing important anchors for planet formation models. We aim to improve the characterisation of the architecture of this key system, and in particular the masses and radii of its planets. In addition, since this system is one of the few resonant chains that can be characterised by both photometry and radial velocities, we aim to use it as a test bench for the robustness of the planetary mass determination with each technique. We perform a global analysis of all available photometry and radial velocity. We also try different sets of priors on the masses and eccentricity, as well as different stellar activity models, to study their effects on the masses estimated by each method. We show how stellar activity is preventing us from obtaining a robust mass estimation for the three outer planets using radial velocity data alone. We also show that our joint photo-dynamical and radial velocity analysis resulted in a robust mass determination for planets c to g, with precision of 12% for the mass of planet c, and better than 10% for planets d to g. The new precisions on the radii range from 2 to 3%. The understanding of this synergy between photometric and radial velocity measurements will be valuable during the PLATO mission. We also show that TOI-178 is indeed currently locked in the resonant configuration, librating around an equilibrium of the chain.

Sub-Neptunes with $2-3R_\oplus$ are intermediate in size between rocky planets and Neptune-sized planets. The orbital properties and bulk compositions of transiting sub-Neptunes provide clues to the formation and evolution of close-in small planets. In this paper, we present the discovery and follow-up of four sub-Neptunes orbiting M dwarfs (TOI-782, TOI-1448, TOI-2120, and TOI-2406), three of which were newly validated by ground-based follow-up observations and statistical analyses. TOI-782 b, TOI-1448 b, TOI-2120 b, and TOI-2406 b have radii of $R_\mathrm{p} = 2.740^{+0.082}_{-0.079}\,R_\oplus$, $2.769^{+0.073}_{-0.068}\,R_\oplus$, $2.120\pm0.067\,R_\oplus$, and $2.830^{+0.068}_{-0.066}\,R_\oplus$ and orbital periods of $P = 8.02$, $8.11$, $5.80$, and $3.08$\,days, respectively. Doppler monitoring with Subaru/InfraRed Doppler instrument led to 2$\sigma$ upper limits on the masses of $<19.1\ M_\oplus$, $<19.5\ M_\oplus$, $<6.8\ M_\oplus$, and $<15.6\ M_\oplus$ for TOI-782 b, TOI-1448 b, TOI-2120 b, and TOI-2406 b, respectively. The mass-radius relationship of these four sub-Neptunes testifies to the existence of volatile material in their interiors. These four sub-Neptunes, which are located above the so-called ``radius valley'', are likely to retain a significant atmosphere and/or an icy mantle on the core, such as a water world. We find that at least three of the four sub-Neptunes (TOI-782 b, TOI-2120 b, and TOI-2406 b) orbiting M dwarfs older than 1 Gyr, are likely to have eccentricities of $e \sim 0.2-0.3$. The fact that tidal circularization of their orbits is not achieved over 1 Gyr suggests inefficient tidal dissipation in their interiors., Comment: Accepted for publication in AJ, 32 pages, 17 figures, 6 tables

Planetary systems in mean motion resonances hold a special place among the planetary population. They allow us to study planet formation in great detail as dissipative processes are thought to have played an important role in their existence. Additionally, planetary masses in bright resonant systems may be independently measured both by radial velocities (RVs) and transit timing variations (TTVs). In principle, they also allow us to quickly determine the inclination of all planets in the system, as for the system to be stable, they are likely all in coplanar orbits. To describe the full dynamical state of the system, we also need the stellar obliquity that provides the orbital alignment of a planet with respect to the spin of their host star and can be measured thanks to the Rossiter-McLaughlin effect. It was recently discovered that HD 110067 harbours a system of six sub-Neptunes in resonant chain orbits. We here analyze an ESPRESSO high-resolution spectroscopic time series of HD 110067 during the transit of planet c. We find the orbit of HD 110067 c to be well aligned with sky projected obliquity $\lambda =6^{+24}_{-26}$ deg. This result is indicative that the current architecture of the system has been reached through convergent migration without any major disruptive events. Finally, we report transit-timing variation in this system as we find a significant offset of 19 $\pm$ 4 minutes in the center of the transit compared to the published ephemeris., Comment: Accepted to A&A

In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued Gaussian processes, as they arise in applications to dynamics and to machine learning. Further applications are given in non-commutative probability theory, including a new non-commutative Radon--Nikodym theorem.

One of the main goals of the NASA's TESS (Transiting Exoplanet Survey Satellite) mission is the discovery of Earth-like planets around nearby M-dwarf stars. Here, we present the discovery and validation of three new short-period Earth-sized planets orbiting nearby M-dwarfs: TOI- 5720b, TOI-6008b and TOI-6086b. We combined TESS data, ground-based multi-color light curves, ground-based optical and near-infrared spectroscopy, and Subaru/IRD RVs data to validate the planetary candidates and constrain the physical parameters of the systems. In addition, we used archival images, high-resolution imaging, and statistical validation techniques to support the planetary validation. TOI-5720b is a planet with a radius of Rp=1.09 Re orbiting a nearby (23 pc) M2.5 host, with an orbital period of P=1.43 days. It has an equilibrium temperature of Teq=708 K and an incident flux of Sp=41.7 Se. TOI-6008b has a period of P=0.86 day, a radius of Rp=1.03 Re, an equilibrium temperature of Teq=707 K and an incident flux of Sp=41.5 Se. The host star (TOI-6008) is a nearby (36 pc) M5 with an effective temperature of Teff=3075 K. Based on the RV measurements collected with Subaru/IRD, we set a 3-sigma upper limit of Mp<4 M_Earth, thus ruling out a star or brown dwarf as the transiting companion. TOI-6086b orbits its nearby (31 pc) M3 host star (Teff=3200 K) every 1.39 days, and has a radius of Rp=1.18 Re, an equilibrium temperature of Teq=634 K and an incident flux of Sp=26.8 Se. Additional high precision radial velocity measurements are needed to derive the planetary masses and bulk densities, and to search for additional planets in the systems. Moreover, short-period earth-sized planets orbiting around nearby M-dwarfs are suitable targets for atmospheric characterization with the James Webb Space Telescope (JWST) through transmission and emission spectroscopy, and phase curve photometry., Comment: Accepted for publication in Astronomy & Astrophysics

We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as well as new applications. These include: (i) an explicit covariance analysis for Hilbert space-valued Gaussian processes, (ii) optimization results for quantum gates (from quantum information), (iii) new results for positive operator-valued measures (POVMs), and (iv) a new approach/result in inverse problems for quantum measurements.

Ultrahot Jupiters are a type of gaseous exoplanet that orbit extremely close to their host star, resulting in significantly high equilibrium temperatures. In recent years, high-resolution emission spectroscopy has been broadly employed in observing the atmospheres of ultrahot Jupiters. We used the CARMENES spectrograph to observe the high-resolution spectra of the dayside hemisphere of MASCARA-1b in both visible and near-infrared. Through cross-correlation analysis, we detected signals of \ion{Fe}{i} and \ion{Ti}{i}. Based on these detections, we conducted an atmospheric retrieval and discovered the presence of a strong inversion layer in the planet's atmosphere. The retrieved Ti and Fe abundances are broadly consistent with solar abundances. In particular, we obtained a relative abundance of [Ti/Fe] as $-1.0 \pm 0.8$ under the free retrieval and $-0.4^{+0.5}_{-0.8}$ under the chemical equilibrium retrieval, suggesting the absence of significant titanium depletion on this planet. Furthermore, we considered the influence of planetary rotation on spectral line profiles. The resulting equatorial rotation speed was determined to be $4.4^{+1.6}_{-2.0}\,\mathrm{km\,s^{-1}}$, which agrees with the rotation speed induced by tidal locking., Comment: 18 pages, 11 figures; accepted for publication in A&A

During the first Gyr of their life, exoplanet atmospheres suffer from different atmospheric escape phenomena that can strongly affect the shape and morphology of the exoplanet itself. These processes can be studied with Ly$\alpha$, H$\alpha$ and/or He I triplet observations. We present high-resolution spectroscopy observations from CARMENES and GIARPS checking for He I and H$\alpha$ signals in 20 exoplanetary atmospheres: V1298Tau c, K2-100b, HD63433b, HD63433c, HD73583b, HD73583c, K2-77b, TOI-2076b, TOI-2048b, HD235088b, TOI-1807b, TOI-1136d, TOI-1268b, TOI-1683b, TOI-2018b, MASCARA-2b, WASP-189b, TOI-2046b, TOI-1431b, and HAT-P-57b. We report two new high-resolution spectroscopy He I detections for TOI-1268b and TOI-2018b, and an H$\alpha$ detection for TOI-1136d. The MOPYS (Measuring Out-flows in Planets orbiting Young Stars) project aims to understand the evaporating phenomena and test their predictions from the current observations. We compiled a list of 70 exoplanets with He I and/or H$\alpha$ observations, from this work and the literature, and we considered the He I and H$\alpha$ results as proxy for atmospheric escape. Our principal results are that 0.1-1Gyr-old planets do not exhibit more He I or H$\alpha$ detections than older planets, and evaporation signals are more frequent for planets orbiting $\sim$1-3Gyr-old stars. We provide new constrains to the cosmic shoreline, the empirical division between rocky planets and planets with atmosphere, by using the evaporation detections and explore the capabilities of a new dimensionless parameter, $R_{\rm He}/R_{\rm Hill}$, to explain the He I triplet detections. Furthermore, we present a statistically significant upper boundary for the He I triplet detections in the $T_{\rm eq}$ vs $\rho_{\rm p}$ parameter space. Planets located above that boundary are unlikely to show He I absorption signals., Comment: Accepted in A&A. 64 pages, many figures. Supplementary material in Zenodo

Motivated by applications, we introduce a general and new framework for operator valued positive definite kernels. We further give applications both to operator theory and to stochastic processes. The first one yields several dilation constructions in operator theory, and the second to general classes of stochastic processes. For the latter, we apply our operator valued kernel-results in order to build new Hilbert space-valued Gaussian processes, and to analyze their structures of covariance configurations.

The TOI-421 planetary system contains two sub-Neptune-type planets and is a prime target to study the formation and evolution of planets and their atmospheres. The inner planet is especially interesting as the existence of a hydrogen-dominated atmosphere at its orbital separation cannot be explained by current formation models without previous orbital migration. We jointly analysed photometric data of three TESS sectors and six CHEOPS visits as well as 156 radial velocity data points to retrieve improved planetary parameters. We also searched for TTVs and modelled the interior structure of the planets. Finally, we simulated the evolution of the primordial H-He atmospheres of the planets using two different modelling frameworks. We determine the planetary radii and masses of TOI-421 b and c to be $R_{\rm b} = 2.64 \pm 0.08 \, R_{\oplus}$, $M_{\rm b} = 6.7 \pm 0.6 \, M_{\oplus}$, $R_{\rm c} = 5.09 \pm 0.07 \, R_{\oplus}$, and $M_{\rm c} = 14.1 \pm 1.4 \, M_{\oplus}$. We do not detect any statistically significant TTV signals. Assuming the presence of a hydrogen-dominated atmosphere, the interior structure modelling results in both planets having extensive envelopes. While the modelling of the atmospheric evolution predicts for TOI-421 b to have lost any primordial atmosphere that it could have accreted at its current orbital position, TOI-421 c could have started out with an initial atmospheric mass fraction somewhere between 10 and 35%. We conclude that the low observed mean density of TOI-421 b can only be explained by either a bias in the measured planetary parameters (e.g. driven by high-altitude clouds) and/or in the context of orbital migration. We also find that the results of atmospheric evolution models are strongly dependent on the employed planetary structure model., Comment: 21 pages, 12 figures, accepted for publication in A&A

This paper introduces the concept of Fractal Frenet equations, a set of differential equations used to describe the behavior of vectors along fractal curves. The study explores the analogue of arc length for fractal curves, providing a measure to quantify their length. It also discusses fundamental mathematical constructs, such as the analogue of the unit tangent vector, which indicates the curve's direction at different points, and the analogue of curvature vector or fractal curvature vector, which characterizes its curvature at various locations. The concept of torsion, describing the twisting and turning of fractal curves in three-dimensional space, is also explored. Specific examples, like the fractal helix and the fractal snowflake, illustrate the application and significance of the Fractal Frenet equations.

Context. White-light stellar flares are proxies for some of the most energetic types of flares, but their triggering mechanism is still poorly understood. As they are associated with strong X and UV emission, their study is particularly relevant to estimate the amount of high-energy irradiation onto the atmospheres of exoplanets, especially those in their stars' habitable zone. Aims. We used the high-cadence, high-photometric capabilities of the CHEOPS and TESS space telescopes to study the detailed morphology of white-light flares occurring in a sample of 130 late-K and M stars, and compared our findings with results obtained at a lower cadence. We developed dedicated software for this purpose. Results. Multi-peak flares represent a significant percentage ($\gtrsim 30$\%) of the detected outburst events. Our findings suggest that high-impulse flares are more frequent than suspected from lower-cadence data, so that the most impactful flux levels that hit close-in exoplanets might be more time-limited than expected. We found significant differences in the duration distributions of single-peak and complex flare components, but not in their peak luminosity. A statistical analysis of the flare parameter distributions provides marginal support for their description with a log-normal instead of a power-law function, leaving the door open to several flare formation scenarios. We tentatively confirmed previous results about quasi-periodic pulsations in high-cadence photometry, report the possible detection of a pre-flare dip, and did not find hints of photometric variability due to an undetected flare background. Conclusions. The high-cadence study of stellar hosts might be crucial to evaluate the impact of their flares on close-in exoplanets, as their impulsive phase emission might otherwise be incorrectly estimated. Future telescopes such as PLATO and Ariel will help in this respect., Comment: 28 pages, 25 figures, 4 tables, to be published in Astronomy & Astrophysics

We aim to constrain the internal structure and composition of HD 15337 b and c, two short-period planets situated on opposite sides of the radius valley, using new transit photometry and radial velocity data. We acquire 6 new transit visits with the CHaracterising ExOPlanet Satellite (CHEOPS) and 32 new radial velocity measurements from the High Accuracy Radial Velocity Planet Searcher (HARPS) to improve the accuracy of the mass and radius estimates for both planets. We reanalyse light curves from TESS sectors 3 and 4 and analyse new data from sector 30, correcting for long-term stellar activity. Subsequently, we perform a joint fit of the TESS and CHEOPS light curves, and all available RV data from HARPS and the Planet Finder Spectrograph (PFS). Our model fits the planetary signals, the stellar activity signal and the instrumental decorrelation model for the CHEOPS data simultaneously. The stellar activity was modelled using a Gaussian-process regression on both the RV and activity indicators. We finally employ a Bayesian retrieval code to determine the internal composition and structure of the planets. We derive updated and highly precise parameters for the HD 15337 system. Our improved precision on the planetary parameters makes HD 15337 b one of the most precisely characterised rocky exoplanets, with radius and mass measurements achieving a precision better than 2\% and 7\%, respectively. We are able to improve the precision of the radius measurement of HD 15337 c to 3\%. Our results imply that the composition of HD 15337 b is predominantly rocky, while HD 15337 c exhibits a gas envelope with a mass of at least $0.01\ M_\oplus$.Our results lay the groundwork for future studies, which can further unravel the atmospheric evolution of these exoplanets and give new insights into their composition and formation history and the causes behind the radius gap., Comment: 17 pages, including appendix

We report the confirmation and mass determination of a mini-Neptune transiting the M3.5 V star TOI-4438 (G 182-34) every 7.44 days. A transit signal was detected with NASA's TESS space mission in the sectors 40, 52, and 53. In order to validate the planet TOI-4438 b and to determine the system properties, we combined TESS data with high-precision radial velocity measurements from the CARMENES spectrograph, spanning almost one year, and ground-based transit photometry. We found that TOI-4438 b has a radius of Rb = 2.52 +/- 0.13 R_Earth (5% precision), which together with a mass of Mb=5.4 +/- 1.1 M_Earth (20% precision), results in a bulk density of rho = 1.85+0.51-0.44 g cm-3 (28% precision), aligning the discovery with a volatile-rich planet. Our interior structure retrieval with a pure water envelope yields a minimum water mass fraction of 46% (1-sigma). TOI-4438 b is a volatile-rich mini-Neptune with likely H/He mixed with molecules, such as water, CO_2, and CH_4. The primary star has a J-band magnitude of 9.7, and the planet has a high transmission spectroscopy metric (TSM) of 136 +/- 13. Taking into account the relatively warm equilibrium temperature of T_eq = 435 +/- 15 K, and the low activity level of its host star, TOI-4438 b is one of the most promising mini-Neptunes around an M dwarf for transmission spectroscopy studies., Comment: Accepted for publication on Astronomy & Astrophysics

For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal $L^2$ Fourier expansions. Our results hold for probability measures $\mu$ with finite support in $\mathbb{R}^d$ that satisfy a certain disintegration condition that we refer to as ``slice-singular''. In this general framework, we present explicit $L^{2}(\mu)$-Fourier expansions, with Fourier exponentials having positive Fourier frequencies in each of the d coordinates. Our Fourier representations apply to every $f \in L^2(\mu)$, are based on an extended Kaczmarz algorithm, and use a new recursive $\mu$ Rokhlin disintegration representation. In detail, our Fourier series expansion for $f$ is in terms of the multivariate Fourier exponentials $\{e_n\}$, but the associated Fourier coefficients for $f$ are now computed from a Kaczmarz system $\{g_n\}$ in $L^{2}(\mu)$ which is dual to the Fourier exponentials. The $\{g_n\}$ system is shown to be a Parseval frame for $L^{2}(\mu)$. Explicit computations for our new Fourier expansions entail a detailed analysis of subspaces of the Hardy space on the polydisk, dual to $L^{2}(\mu)$, and an associated d-variable Normalized Cauchy Transform. Our results extend earlier work for measures $\mu$ in one and two dimensions, i.e., $d=1 (\mu $ singular), and $d=2 (\mu$ assumed slice-singular). Here our focus is the extension to the cases of measures $\mu$ in dimensions $d >2$. Our results are illustrated with the use of explicit iterated function systems (IFSs), including the IFS generated Menger sponge for $d=3$.

Ultra-hot Jupiters present a unique opportunity to understand the physics and chemistry of planets at extreme conditions. WASP-12b stands out as an archetype of this class of exoplanets. We performed comprehensive analyses of the transits, occultations, and phase curves of WASP-12b by combining new CHEOPS observations with previous TESS and Spitzer data to measure the planet's tidal deformation, atmospheric properties, and orbital decay rate. The planet was modeled as a triaxial ellipsoid parameterized by the second-order fluid Love number, $h_2$, which quantifies its radial deformation and provides insight into the interior structure. We measured the tidal deformation of WASP-12b and estimated a Love number of $h_2=1.55_{-0.49}^{+0.45}$ (at 3.2$\sigma$) from its phase curve. We measured occultation depths of $333\pm24$ppm and $493\pm29$ppm in the CHEOPS and TESS bands, respectively, while the dayside emission spectrum indicates that CHEOPS and TESS probe similar pressure levels in the atmosphere at a temperature of 2900K. We also estimated low geometric albedos of $0.086\pm0.017$ and $0.01\pm0.023$ in the CHEOPS and TESS passbands, respectively, suggesting the absence of reflective clouds in the dayside of the WASP-12b. The CHEOPS occultations do not show strong evidence for variability in the dayside atmosphere of the planet. Finally, we refine the orbital decay rate by 12% to a value of -30.23$\pm$0.82 ms/yr. WASP-12b becomes the second exoplanet, after WASP-103b, for which the Love number has been measured (at 3$sigma$) from the effect of tidal deformation in the light curve. However, constraining the core mass fraction of the planet requires measuring $h_2$ with a higher precision. This can be achieved with high signal-to-noise observations with JWST since the phase curve amplitude, and consequently the induced tidal deformation effect, is higher in the infrared., Comment: accepted for publication in A&A

We report the characterization of two planet candidates detected by the Transiting Exoplanet Survey Satellite (TESS), TOI-1199 b and TOI-1273 b, with periods of 3.7 and 4.6 days, respectively. Follow-up observations for both targets, which include several ground-based light curves, confirmed the transit events. High-precision radial velocities from the SOPHIE spectrograph revealed signals at the expected frequencies and phases of the transiting candidates and allowed mass determinations with a precision of $8.4\%$ and $6.7\%$ for TOI-1199 b and TOI-1273 b, respectively. The planetary and orbital parameters were derived from a joint analysis of the radial velocities and photometric data. We find that the planets have masses of $0.239\,\pm\,0.020\,M_{\mathrm{J}}$ and $0.222\,\pm\,0.015\,M_{\mathrm{J}}$ and radii of $0.938\,\pm\,0.025\,R_{\mathrm{J}}$ and $0.99\,\pm\,0.22\,R_{\mathrm{J}}$, respectively. The grazing transit of TOI-1273 b translates to a larger uncertainty in its radius, and hence also in its bulk density, compared to TOI-1199 b. The inferred bulk densities of $0.358\,\pm\,0.041\,\mathrm{g}\,\mathrm{cm}^{-3}$ and $0.28\,\pm\,0.11\,\mathrm{g}\,\mathrm{cm}^{-3}$ are among the lowest known for exoplanets in this mass range, which, considering the brightness of the host stars ($V \approx 11\,\mathrm{mag}$), render them particularly amenable to atmospheric characterization via the transit spectroscopy technique. The better constraints on the parameters of TOI-1199 b provide a transmission spectroscopy metric of $134\,\pm\,17$, making it the better suited of the two planets for atmospheric studies., Comment: Accepted for publication in A&A. 20 pages, 7 tables, and 15 figures

The number of super-Earth and mini-Neptune planet discoveries has increased significantly in the last two decades thanks to transit and radial velocity surveys. When it is possible to apply both techniques, we can characterise the internal composition of exoplanets, which in turn provides unique insights on their architecture, formation and evolution. We performed a combined photometric and radial velocity analysis of TOI-238 (TYC 6398-132-1), which has one short-orbit super-Earth planet candidate announced by NASA's TESS team. We aim to confirm its planetary nature using radial velocities taken with the ESPRESSO and HARPS spectrographs, to measure its mass and to detect the presence of other possible planetary companions. We carried out a joint analysis by including Gaussian processes and Keplerian orbits to account for the stellar activity and planetary signals simultaneously. We detected the signal induced by TOI-238 b in the radial velocity time-series, and the presence of a second transiting planet, TOI-238 c, whose signal appears in RV and TESS data. TOI-238 b is a planet with a radius of 1.402$^{+0.084}_{-0.086}$ R$_{\oplus}$ and a mass of 3.40$^{+0.46}_{-0.45}$ M$_{\oplus}$. It orbits at a separation of 0.02118 $\pm$ 0.00038 AU of its host star, with an orbital period of 1.2730988 $\pm$ 0.0000029 days, and has an equilibrium temperature of 1311 $\pm$ 28 K. TOI-238 c has a radius of 2.18$\pm$ 0.18 R$_{\oplus}$ and a mass of 6.7 $\pm$ 1.1 M$_{\oplus}$. It orbits at a separation of 0.0749 $\pm$ 0.0013 AU of its host star, with an orbital period of 8.465652 $\pm$ 0.000031 days, and has an equilibrium temperature of 696 $\pm$ 15 K. The mass and radius of planet b are fully consistent with an Earth-like composition, making it likely a rocky super-Earth. Planet c could be a water-rich planet or a rocky planet with a small H-He atmosphere., Comment: 33 pages, 31 figures, 5 tables. Accepted for publication at A&A

The two known planets in the planetary system of Teegarden's Star are among the most Earth-like exoplanets currently known. Revisiting this nearby planetary system with two planets in the habitable zone aims at a more complete census of planets around very low-mass stars. A significant number of new radial velocity measurements from CARMENES, ESPRESSO, MAROON-X, and HPF, as well as photometry from TESS motivated a deeper search for additional planets. We confirm and refine the orbital parameters of the two know planets Teegarden's Star b and c. We also report the detection of a third planet d with an orbital period of 26.13+-0.04 d and a minimum mass of 0.82+-0.17 M_Earth. A signal at 96 d is attributed to the stellar rotation period. The interpretation of a signal at 172 d remains open. The TESS data exclude transiting short-period planets down to about half an Earth radius. We compare the planetary system architecture of very low-mass stars. In the currently known configuration, the planetary system of Teegarden's star is dynamically quite different from that of TRAPPIST-1, which is more compact, but dynamically similar to others such as GJ 1002., Comment: Astronomy & Astrophysics, accepted; 21 pages, 18 figures

The Transiting Exoplanet Survey Satellite (TESS) provides a continuous suite of new planet candidates that need confirmation and precise mass determination from ground-based observatories. This is the case for the G-type star TOI-1710, which is known to host a transiting sub-Saturn planet ($\mathrm{M_p}=$28.3$\pm$4.7$\mathrm{M}_\oplus$) in a long-period orbit (P=24.28\,d). Here we combine archival SOPHIE and new and archival HARPS-N radial velocity data with newly available TESS data to refine the planetary parameters of the system and derive a new mass measurement for the transiting planet, taking into account the impact of the stellar activity on the mass measurement. We report for TOI-1710b a radius of $\mathrm{R_p}$$=$5.15$\pm$0.12$\mathrm{R}_\oplus$, a mass of $\mathrm{M_p}$$=$18.4$\pm$4.5$\mathrm{M}_\oplus$, and a mean bulk density of $\rho_{\rm p}$$=$0.73$\pm$0.18$\mathrm{g \, cm^{-3}}$, which are consistent at 1.2$\sigma$, 1.5$\sigma$, and 0.7$\sigma$, respectively, with previous measurements. Although there is not a significant difference in the final mass measurement, we needed to add a Gaussian process component to successfully fit the radial velocity dataset. This work illustrates that adding more measurements does not necessarily imply a better mass determination in terms of precision, even though they contribute to increasing our full understanding of the system. Furthermore, TOI-1710b joins an intriguing class of planets with radii in the range 4-8 $\mathrm{R}_\oplus$ that have no counterparts in the Solar System. A large gaseous envelope and a bright host star make TOI-1710b a very suitable candidate for follow-up atmospheric characterization., Comment: Accepted for publication in A&A. 21 pages, 14 figures

Planets with orbital periods shorter than 1 day are rare and have formation histories that are not completely understood. Small ($R_\mathrm{p} < 2\; R_\oplus$) ultra-short-period (USP) planets are highly irradiated, probably have rocky compositions with high bulk densities, and are often found in multi-planet systems. Additionally, USP planets found around small stars are excellent candidates for characterization using present-day instrumentation. Of the current full sample of approximately 5500 confirmed exoplanets, only 130 are USP planets and around 40 have mass and radius measurements. Wolf 327 (TOI-5747) is an M dwarf ($R_\star = 0.406 \pm 0.015 \; R_\odot$, $M_\star = 0.405 \pm 0.019 \; M_\odot$, $T_{\mathrm{eff}}=3542 \pm 70$ K, and $V = 13$ mag) located at a distance $d = 28.5$ pc. NASA's planet hunter satellite, TESS, detected transits in this star with a period of 0.573 d (13.7 h) and with a transit depth of 818 ppm. Ground-based follow-up photometry, high resolution imaging, and radial velocity (RV) measurements taken with the CARMENES spectrograph confirm the presence of this new USP planet. Wolf 327b is a super-Earth with a radius of $R_\mathrm{p} = 1.24 \pm 0.06 \; R_\oplus$ and a mass of $M_\mathrm{p} = 2.53 \pm 0.46 \; M_\oplus$, yielding a bulk density of $7.24 \pm 1.66 $\,g cm$^{-3}$ and thus suggesting a rocky composition. Owing to its close proximity to its host star ($a = 0.01$ au), Wolf 327b has an equilibrium temperature of $996 \pm 22$ K. This planet has a mass and radius similar to K2-229b, a planet with an inferred Mercury-like internal composition. Planet interior models suggest that Wolf 327b has a large iron core, a small rocky mantle, and a negligible (if any) H/He atmosphere., Comment: 26 pages, 19 figures. Accepted for publication in A&A