Search

In this paper we present \texttt{SymOrb.jl}, a software which combines group representation theory and variational methods to provide numerical solutions of singular dynamical systems of paramount relevance in Celestial Mechanics and other interacting particles models. Among all, it prepares for large-scale search of symmetric periodic orbits for the classical $n$-body problem and their classification, paving the way towards a computational validation of Poincar\'e conjecture about the density of periodic orbits. Through the accessible language of Julia, \texttt{SymOrb.jl} offers a unified implementation of an earlier version. This paper provides theoretical and practical guidelines for the specific approach we adopt, complemented with examples.

The Ingot WFS belongs to a class of pupil-plane WFSs designed to address the challenges posed by Sodium Laser Guide Stars, and consists of a combination of refractive and reflective surfaces, arranged into a complex prismatic shape that extends in three dimensions. Specifically, it leverages the Scheimpflug principle to sense the full 3D volume of such elongated, time-varying sources, thus optimizing the performance of the next-generation AO-assisted giant telescopes. In this work we discuss the geometrical and optical motivations endorsing the development of this class of WFSs, showing the different configurations we propose to the AO community. We also provide a first order comparative analysis with other approaches and review the state-of-the-art of the Ingot project, including improvements made in the laboratory and future milestones., Comment: 6 pages, 3 figures, Proceedings of the SPIE 2024

The Ingot WFS was designed to overcome some of the challenges present in classical wavefront sensors when they deal with sodium LGSs. This innovative sensor works by sensing the full 3D volume of the elongated LGS and is suitable for use in very large telescopes. A test bench has been assembled at the INAF - Osservatorio Astronomico di Padova laboratories to test and characterize the functioning of the Ingot WFS. In this work, we summarize the main results of the tests performed on a new search algorithm. Then, we move towards a more accurate simulation of the sodium LGS by replicating real time-varying sodium layer profiles. The study of their impact on the ingot pupil signals is described in this work., Comment: 17 pages, 17 figures, Proceedings of SPIE 2024

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

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

Full sky coverage Adaptive Optics on Extremely Large Telescopes requires the adoption of several Laser Guide Stars as references.With such large apertures, the apparent elongation of the beacons is absolutely significant.With few exceptions,WaveFront Sensors designed for Natural Guide Stars are adapted and used in suboptimal mode in this context. We analyse and describe the geometrical properties of a class of WaveFront Sensors that are specifically designed to deal with Laser Guide Stars propagated from a location in the immediate vicinity of the telescope aperture. We describe in three dimensions the loci where the light of the Laser Guide Stars would focus in the focal volume located behind the focal plane (where astronomical objects are reimaged). We also describe the properties of several types of optomechanical devices that, through refraction and reflections, act as perturbers for this new class of pupil plane sensors, which we call ingot WaveFront Sensor. We give the recipes both for the most reasonable complex version of these WaveFront Sensors, with 6 pupils, and for the simplest one, with only 3 pupils. Both of them are referred to the ELT case. Elements to have a qualitative idea of how the sensitivity of such a new class of sensors compared to conventional ones are outlined. We present a new class of WaveFront Sensors, by carrying out the extension to the case of elongated sources at finite distance of the pyramid WaveFront Sensor and pointing out which advantages of the pyramid are retained and how it can be adopted to optimize the sensing., Comment: Accepted for publication in A&A; 11 pages, 9 figures

BACKGROUND: Radiology reports are typically written in a free-text format, making clinical information difficult to extract and use. Recently the adoption of structured reporting (SR) has been recommended by various medical societies thanks to the advantages it offers, e.g. standardization, completeness and information retrieval. We propose a pipeline to extract information from free-text radiology reports, that fits with the items of the reference SR registry proposed by a national society of interventional and medical radiology, focusing on CT staging of patients with lymphoma. METHODS: Our work aims to leverage the potential of Natural Language Processing (NLP) and Transformer-based models to deal with automatic SR registry filling. With the availability of 174 radiology reports, we investigate a rule-free generative Question Answering approach based on a domain-specific version of T5 (IT5). Two strategies (batch-truncation and ex-post combination) are implemented to comply with the model's context length limitations. Performance is evaluated in terms of strict accuracy, F1, and format accuracy, and compared with the widely used GPT-3.5 Large Language Model. A 5-point Likert scale questionnaire is used to collect human-expert feedback on the similarity between medical annotations and generated answers. RESULTS: The combination of fine-tuning and batch splitting allows IT5 to achieve notable results; it performs on par with GPT-3.5 albeit its size being a thousand times smaller in terms of parameters. Human-based assessment scores show a high correlation (Spearman's correlation coefficients>0.88, p-values<0.001) with AI performance metrics (F1) and confirm the superior ability of LLMs (i.e., GPT-3.5, 175B of parameters) in generating plausible human-like statements.

TOI-732 is an M dwarf hosting two transiting planets, which are located on the two opposite sides of the radius valley. By doubling the number of available space-based observations and increasing the number of radial velocity (RV) measurements, we aim at refining the parameters of TOI-732 b and c. We also aim at using the results to study the slope of both the radius valley and the density valley for a well characterised sample of M dwarf exoplanets. We performed a global MCMC analysis by jointly modelling ground-based light curves, CHEOPS and TESS observations, along with RV time series both taken from the literature and obtained with the MAROON-X spectrograph. The slopes of the M dwarf valleys were quantified via a Support Vector Machine (SVM) procedure. TOI-732 b is an ultra short period planet ($P\sim0.77$ d) with a radius $R_b=1.325_{-0.058}^{+0.057}$ $R_{\oplus}$ and a mass $M_b=2.46\pm0.19$ $M_{\oplus}$ (mean density $\rho_b=5.8_{-0.8}^{+1.0}$ g cm$^{-3}$), while the outer planet at $P\sim12.25$ d has $R_c=2.39_{-0.11}^{+0.10}$ $R_{\oplus}$, $M_c=8.04_{-0.48}^{+0.50}$ $M_{\oplus}$, and thus $\rho_c=3.24_{-0.43}^{+0.55}$ g cm$^{-3}$. Also considering our interior structure calculations TOI-732 b is a super-Earth and TOI-732 c is a mini-Neptune. Following the SVM approach, we quantified $\mathrm{d}\log{R_{p,{\mathrm{valley}}}}/\mathrm{d}\log{P}=-0.065_{-0.013}^{+0.024}$, which is flatter than for Sun-like stars. In line with former analyses, we noted a more filled radius valley for M-planets and we further quantified the density valley slope as $\mathrm{d}\log{\hat{\rho}_{\mathrm{valley}}}/\mathrm{d}\log{P}=-0.02_{-0.04}^{+0.12}$. Compared to FGK stars, the weaker dependence of the position of the radius valley with orbital period might indicate a heavier influence of formation relative to evolution mechanisms in shaping the radius valley around M-dwarfs., Comment: 28 pages (17 in the main text), 18 figures (9 in the main text), 11 tables (7 in the main text). Accepted for publication in A&A

Occultations are windows of opportunity to indirectly peek into the dayside atmosphere of exoplanets. High-precision transit events provide information on the spin-orbit alignment of exoplanets around fast-rotating hosts. We aim to precisely measure the planetary radius and geometric albedo of the ultra-hot Jupiter (UHJ) KELT-20 b as well as the system's spin-orbit alignment. We obtained optical high-precision transits and occultations of KELT-20 b using CHEOPS observations in conjunction with the simultaneous TESS observations. We interpret the occultation measurements together with archival infrared observations to measure the planetary geometric albedo and dayside temperatures. We further use the host star's gravity-darkened nature to measure the system's obliquity. We present time-averaged precise occultation depth of 82(6) ppm measured with seven CHEOPS visits and 131(+8/-7) ppm from the analysis of all available TESS photometry. Using these measurements, we precisely constrain the geometric albedo of KELT-20 b to 0.26(0.04) and the brightness temperature of the dayside hemisphere to 2566(+77/-80) K. Assuming Lambertian scattering law, we constrain the Bond albedo to 0.36(+0.04/-0.05) along with a minimal heat transfer to the nightside. Furthermore, using five transit observations we provide stricter constraints of 3.9(1.1) degrees on the sky-projected obliquity of the system. The aligned orbit of KELT-20 b is in contrast to previous CHEOPS studies that have found strongly inclined orbits for planets orbiting other A-type stars. KELT-20 b's comparably high planetary geometric albedo corroborates a known trend of strongly irradiated planets being more reflective. Finally, we tentatively detect signs of temporal variability in the occultation depths, which might indicate variable cloud cover advecting onto the planetary dayside., Comment: 27 pages, 15 figures, Accepted for publication in Astronomy & Astrophysics

MORFEO (Multi-conjugate adaptive Optics Relay For ELT Observations, formerly MAORY), the MCAO system for the ELT, will provide diffraction-limited optical quality to the large field camera MICADO. MORFEO has officially passed the Preliminary Design Review and it is entering the final design phase. We present the current status of the project, with a focus on the adaptive optics system aspects and expected milestones during the next project phase.

The planetary system around the naked-eye star $\nu^2$ Lupi (HD 136352; TOI-2011) is composed of three exoplanets with masses of 4.7, 11.2, and 8.6 Earth masses. The TESS and CHEOPS missions revealed that all three planets are transiting and have radii straddling the radius gap separating volatile-rich and volatile-poor super-earths. Only a partial transit of planet d had been covered so we re-observed an inferior conjunction of the long-period 8.6 Earth-mass exoplanet $\nu^2$ Lup d with the CHEOPS space telescope. We confirmed its transiting nature by covering its whole 9.1 h transit for the first time. We refined the planet transit ephemeris to P = 107.1361 (+0.0019/-0.0022) days and Tc = 2,459,009.7759 (+0.0101/-0.0096) BJD_TDB, improving by ~40 times on the previously reported transit timing uncertainty. This refined ephemeris will enable further follow-up of this outstanding long-period transiting planet to search for atmospheric signatures or explore the planet's Hill sphere in search for an exomoon. In fact, the CHEOPS observations also cover the transit of a large fraction of the planet's Hill sphere, which is as large as the Earth's, opening the tantalising possibility of catching transiting exomoons. We conducted a search for exomoon signals in this single-epoch light curve but found no conclusive photometric signature of additional transiting bodies larger than Mars. Yet, only a sustained follow-up of $\nu^2$ Lup d transits will warrant a comprehensive search for a moon around this outstanding exoplanet., Comment: 16 pages, 9 figures. Accepted for publication in Astronomy & Astrophysics

Among the hundreds of known hot Jupiters (HJs), only five have been found to have companions on short-period orbits. Within this rare class of multiple planetary systems, the architecture of WASP-47 is unique, hosting an HJ (planet -b) with both an inner and an outer sub-Neptunian mass companion (-e and -d, respectively) as well as an additional non-transiting, long-period giant (-c). The small period ratio between planets -b and -d boosts the transit time variation (TTV) signal, making it possible to reliably measure the masses of these planets in synergy with the radial velocity (RV) technique. In this paper, we present new space- and ground-based photometric data of WASP-47b and WASP-47-d, including 11 unpublished light curves from the ESA mission CHEOPS. We analyzed the light curves in a homogeneous way together with all the publicly available data to carry out a global $N$-body dynamical modeling of the TTV and RV signals. We retrieved, among other parameters, a mass and density for planet -d of $M_\mathrm{d}=15.5\pm 0.8$ $M_\oplus$ and $\rho_\mathrm{d}=1.69\pm 0.22$ g\,cm$^{-3}$, which is in good agreement with the literature and consistent with a Neptune-like composition. For the inner planet (-e), we found a mass and density of $M_\mathrm{e}=9.0\pm 0.5$ $M_\oplus$ and $\rho_\mathrm{e}=8.1\pm 0.5$ g\,cm$^{-3}$, suggesting an Earth-like composition close to other ultra-hot planets at similar irradiation levels. Though this result is in agreement with previous RV+TTV studies, it is not in agreement with the most recent RV analysis (at 2.8$\sigma$), which yielded a lower density compatible with a pure silicate composition. This discrepancy highlights the still unresolved issue of suspected systematic offsets between RV and TTV measurements. In this paper, we also significantly improve the orbital ephemerides of all transiting planets, which will be crucial for any future follow-up., Comment: 17 pages, 8 figures, 10 tables, A&A in press. Typos corrected

Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines fully aware of data constraints and symmetries. We introduce a class of persistence-based neural network layers. Persistence-based layers allow the users to easily inject knowledge about symmetries (equivariance) respected by the data, are equipped with learnable weights, and can be composed with state-of-the-art neural architectures.

The Ingot WFS represents an innovative and indispensable class of sensors conceived to overcome some limitations due to the LGSs geometry, which is significantly different from the point-object originated by a NGS. Here we overview the project, aiming at investigating the performance of an ELT-like telescope equipped with the Ingot WFS, facing different aspects of the program: the needs for numerical simulations and laboratory experiments, the prototype and, finally the future plan for the verification on sky., Comment: 7 pages, 5 figures; SPIE 2022 conference proceeding

The ingot WFS is a new kind of wavefront sensor specifically designed to deal with the elongation of LGS reference sources on ELT-class telescopes. Like the pyramid, it belongs to the family of pupil plane wavefront sensors and can be considered as a generalization of the pyramid WFS for extended, three-dimensional elongated sources. The current design uses a simple, reflective roof-shaped prism to split the light into three pupils that are used to retrieve the wavefront shape. A test-bench has been realized at the INAF-Padova laboratories to test the alignment and functioning of the ingot. The bench is equipped with a deformable lens, conjugated to the pupil plane, able to apply low-order aberrations and with a hexapod for the precise alignment of the ingot prism. In this work we present a robust and fully automated Python-code alignment procedure, which is able, by using the optical feedback from the I-WFS, to adjust its 6-degrees of freedom. Moreover, we report on the tests conducted with the deformable lens to characterize the ingot WFS response to low-order aberrations in terms of sensitivity and linearity. The results are used as a comparison for simulations to validate the ray-tracing modeling approach with the future goal of optimizing the procedure adopted for signal calculation and phase retrieval.

Observations of the phase curves and secondary eclipses of extrasolar planets provide a window on the composition and thermal structure of the planetary atmospheres. For example, the photometric observations of secondary eclipses lead to the measurement of the planetary geometric albedo $A_g$, which is an indicator of the presence of clouds in the atmosphere. In this work we aim to measure the $A_g$ in the optical domain of WASP-43b, a moderately irradiated giant planet with an equilibrium temperature of $\sim$1400~K. To this purpose, we analyze the secondary eclipse light curves collected by CHEOPS, together with TESS observations of the system and the publicly available photometry obtained with HST WFC3/UVIS. We also analyze the archival infrared observations of the eclipses and retrieve the thermal emission spectrum of the planet. By extrapolating the thermal spectrum to the optical bands, we correct the optical eclipses for thermal emission and derive the optical $A_g$. The fit of the optical data leads to a marginal detection of the phase curve signal, characterized by an amplitude of $160\pm60$~ppm and 80$^{+60}_{-50}$~ppm in the CHEOPS and TESS passband respectively, with an eastward phase shift of $\sim50^\circ$ (1.5$\sigma$ detection). The analysis of the infrared data suggests a non-inverted thermal profile and solar-like metallicity. The combination of optical and infrared analysis allows us to derive an upper limit for the optical albedo of $A_g<0.087$ with a confidence of 99.9\%. Our analysis of the atmosphere of WASP-43b places this planet in the sample of irradiated hot Jupiters, with monotonic temperature-pressure profile and no indication of condensation of reflective clouds on the planetary dayside.

Eclipsing binaries are important benchmark objects to test and calibrate stellar structure and evolution models. This is especially true for binaries with a fully convective M-dwarf component for which direct measurements of these stars' masses and radii are difficult using other techniques. Within the potential of M-dwarfs to be exoplanet host stars, the accuracy of theoretical predictions of their radius and effective temperature as a function of their mass is an active topic of discussion. Not only the parameters of transiting exoplanets but also the success of future atmospheric characterisation rely on accurate theoretical predictions. We present the analysis of five eclipsing binaries with low-mass stellar companions out of a sub-sample of 23, for which we obtained ultra high-precision light curves using the CHEOPS satellite. The observation of their primary and secondary eclipses are combined with spectroscopic measurements to precisely model the primary parameters and derive the M-dwarfs mass, radius, surface gravity, and effective temperature estimates using the PYCHEOPS data analysis software. Combining these results to the same set of parameters derived from TESS light curves, we find very good agreement (better than 1\% for radius and better than 0.2% for surface gravity). We also analyse the importance of precise orbits from radial velocity measurements and find them to be crucial to derive M-dwarf radii in a regime below 5% accuracy. These results add five valuable data points to the mass-radius diagram of fully-convective M-dwarfs., Comment: 19 pages, 12 figures, accepted for publication in MNRAS

Properties such as composability and automatic differentiation made artificial neural networks a pervasive tool in applications. Tackling more challenging problems caused neural networks to progressively become more complex and thus difficult to define from a mathematical perspective. We present a general definition of linear layer arising from a categorical framework based on the notions of integration theory and parametric spans. This definition generalizes and encompasses classical layers (e.g., dense, convolutional), while guaranteeing existence and computability of the layer's derivatives for backpropagation., Comment: 12 pages, submitted to SYCO 9

We provide a unifying framework where artificial neural networks and their architectures can be formally described as particular cases of a general mathematical construction--machines of finite depth. Unlike neural networks, machines have a precise definition, from which several properties follow naturally. Machines of finite depth are modular (they can be combined), efficiently computable and differentiable. The backward pass of a machine is again a machine and can be computed without overhead using the same procedure as the forward pass. We prove this statement theoretically and practically, via a unified implementation that generalizes several classical architectures--dense, convolutional, and recurrent neural networks with a rich shortcut structure--and their respective backpropagation rules., Comment: 30 pages, 3 figures

LINC-NIRVANA (LN) is one of the instruments on-board the Large Binocular Telescope (LBT). LN is a high-resolution, near-infrared imager equipped with an advanced adaptive optics module. LN implements layer-oriented Multi-Conjugate Adaptive Optics (MCAO) approach using two independent wavefront sensors per side of the binocular telescope measuring the turbulence volume above the telescope. The capability of acquiring up to 20 Natural Guide Stars simultaneously from two distinct fields of view, and using them for wavefront sensing with 20 separate pyramids per side of the telescope makes the LN MCAO system one of a kind. Commissioning of the left MCAO channel is almost complete, while that of the right arm is on-going. The Science Verification on the left side is expected to start soon after the MCAO performance is optimised for faint guide stars. In this article, we put together the lessons learned during the commissioning of the LN MCAO module. We hope and believe that this article will help the future MCAO instrument commissioning teams., Comment: AO$ELT6 Conference Proceeding (http://ao4elt6.copl.ulaval.ca/proceedings/401-GR5j-251.pdf)

55 Cnc e is a transiting super-Earth (radius $1.88\rm\,R_\oplus$ and mass $8\rm\, M_\oplus$) orbiting a G8V host star on a 17-hour orbit. Spitzer observations of the planet's phase curve at 4.5 $\mu$m revealed a time-varying occultation depth, and MOST optical observations are consistent with a time-varying phase curve amplitude and phase offset of maximum light. Both broadband and high-resolution spectroscopic analyses are consistent with either a high mean molecular weight atmosphere or no atmosphere for planet e. A long term photometric monitoring campaign on an independent optical telescope is needed to probe the variability in this system. We seek to measure the phase variations of 55 Cnc e with a broadband optical filter with the 30 cm effective aperture space telescope CHEOPS and explore how the precision photometry narrows down the range of possible scenarios. We observed 55 Cnc for 1.6 orbital phases in March of 2020. We designed a phase curve detrending toolkit for CHEOPS photometry which allows us to study the underlying flux variations of the 55 Cnc system. We detected a phase variation with a full-amplitude of $72 \pm 7$ ppm but do not detect a significant secondary eclipse of the planet. The shape of the phase variation resembles that of a piecewise-Lambertian, however the non-detection of the planetary secondary eclipse, and the large amplitude of the variations exclude reflection from the planetary surface as a possible origin of the observed phase variations. They are also likely incompatible with magnetospheric interactions between the star and planet but may imply that circumplanetary or circumstellar material modulate the flux of the system. Further precision photometry of 55 Cnc from CHEOPS will measure variations in the phase curve amplitude and shape over time this year., Comment: 15 pages, accepted by A&A

MAORY is the adaptive optics module for ELT providing two gravity invariant ports with the same optical quality for two different client instruments. It enable high angular resolution observations in the near infrared over a large field of view (~1 arcmin2 ) by real time compensation of the wavefront distortions due to atmospheric turbulence. Wavefront sensing is performed by laser and natural guide stars while the wavefront sensor compensation is performed by an adaptive deformable mirror in MAORY which works together with the telescope's adaptive and tip tilt mirrors M4 and M5 respectively., Comment: 4 pages, 4 figures

MAVIS (MCAO-Assisted Visible Imager and Spectrograph) is an instrument proposed for the VLT Adaptive Optics Facility (AOF), which is currently in the phase-A conceptual design study. It will be the first instrument performing Multi-conjugate adaptive optics at visible wavelengths, enabling a new set of science observations. MAVIS will be installed at the Nasmyth platform of VLT UT-4 taking advantage of the already operational Adaptive Optics Facility that consists of 4 LGS and an adaptive secondary mirror with 1170 actuators. In addition, two post-focal deformable mirrors and 3 Natural Guide Stars (NGS) are foreseen for the tomographic reconstruction and correction of atmospheric turbulence. The MAVIS AO module is intended to feed both an imager and a spectrograph that will take advantage of the increased resolution and depth with respect to current instrumentation. In this paper we present the trade-off study for the optical design of the MAVIS AO module, highlighting the peculiarities of the system and the requirements imposed by AO. We propose a set of possible optical solutions able to provide a compact and efficient implementation of the different subsystems and we compare them in terms of delivered optical quality, overall throughput, encumbrance, ease of alignment and residual distortion., Comment: 9 pages, 3 figures, AO4ELT6 conference proceedings, http://ao4elt6.copl.ulaval.ca/proceedings.html

The Ingot wavefront sensor is a novel pupil-plane wavefront sensor, specifically designed to cope with the elongation typical of the extended nature of the Laser Guide Star (LGS). In the framework of the ELT, we propose an optical solution suitable for a Laser launch telescope, located outside the telescope pupil. In this paper, we present the current optical design, based on a reflective roof-shaped prism, which, at the level of the focal plane, splits the light from an LGS producing three beams. The three images of the telescope pupils can be then used for the retrieval of the first derivative of the wavefront. The 3D nature of such a device requires new alignment techniques to be determined theoretically and verified in the real world. A possible fully automated procedure, relying solely on the illumination observed at the three pupils, to align the prism to the image of the LGS is discussed. Careful attention needs to be put both on the telecentricity of the system and on the reference systems of the Ingot adjustments in the 3D space. This is crucial in order to disentangle all the possible misalignment effects. In this context, we devised a test-bench able to reproduce, in a scaled manner, the 3D illumination that the Ingot will face at the ELT, in order to validate the design and to perform preliminary tests of phase retrieval., Comment: 6 pages, 8 figures, AO4ELT6 conference proceeding, http://ao4elt6.copl.ulaval.ca/proceedings.html

The detection of a super-Earth and three mini-Neptunes transiting the bright ($V$ = 9.2 mag) star HD 108236 (also known as TOI-1233) was recently reported on the basis of TESS and ground-based light curves. We perform a first characterisation of the HD 108236 planetary system through high-precision CHEOPS photometry and improve the transit ephemerides and system parameters. We characterise the host star through spectroscopic analysis and derive the radius with the infrared flux method. We constrain the stellar mass and age by combining the results obtained from two sets of stellar evolutionary tracks. We analyse the available TESS light curves and one CHEOPS transit light curve for each known planet in the system. We find that HD 108236 is a Sun-like star with $R_{\star}=0.877\pm0.008 R_{\odot}$, $M_{\star}=0.869^{+0.050}_{-0.048} M_{\odot}$, and an age of $6.7_{-5.1}^{+4.0}$ Gyr. We report the serendipitous detection of an additional planet, HD 108236 f, in one of the CHEOPS light curves. For this planet, the combined analysis of the TESS and CHEOPS light curves leads to a tentative orbital period of about 29.5 days. From the light curve analysis, we obtain radii of $1.615\pm0.051$, $2.071\pm0.052$, $2.539_{-0.065}^{+0.062}$, $3.083\pm0.052$, and $2.017_{-0.057}^{+0.052}$ $R_{\oplus}$ for planets HD 108236 b to HD 108236 f, respectively. These values are in agreement with previous TESS-based estimates, but with an improved precision of about a factor of two. We perform a stability analysis of the system, concluding that the planetary orbits most likely have eccentricities smaller than 0.1. We also employ a planetary atmospheric evolution framework to constrain the masses of the five planets, concluding that HD 108236 b and HD 108236 c should have an Earth-like density, while the outer planets should host a low mean molecular weight envelope., Comment: 20 pages, 14 figures, accepted for publication by A&A

The Ingot WFS, a Pyramid-like WFS, has been proposed as a relief to the LGS spot elongation. Actually, the artificial sources are confined in an excited cigar-shaped region in the sodium layer and portions of the telescope aperture have a corresponding different perspective. This diversity generates a variation of the WFS response depending on the illuminated sub-aperture position. The feasibility study of the INGOT WFS is developing within the MAORY project. In this work we present the numerical simulator built in order to investigate the performance of the IngotWFS in terms of Strehl Ratio, obtained reconstructing the incoming turbulent wavefront with a modal approach, in a closed-loop fashion. We also discuss the assumptions and tests we made in order to explore the range of parameters that play key roles in the game. Finally, we report on the overall results of the simulations of the performance expected by the Ingot WFS, under different conditions and input aberrations, with the aim to also compare the measured AO loop residuals with the Shack-Hartmann WFS ones, obtained working under the same assumptions., Comment: 8 pages, 9 figures, AO4ELT6 conference proceeding: http://ao4elt6.copl.ulaval.ca/proceedings.html

Deep observations of the Universe, usually as a part of sky surveys, are one of the symbols of the modern astronomy because they can allow big collaborations, exploiting multiple facilities and shared knowledge. The new generation of extremely large telescopes will play a key role because of their angular resolution and their capability in collecting the light of faint sources. Our simulations combine technical, tomographic and observational information, and benefit of the Global-Multi Conjugate Adaptive Optics (GMCAO) approach, a well demonstrated method that exploits only natural guide stars to correct the scientific field of view from the atmospheric turbulence. By simulating K-band observations of 6000 high redshift galaxies in the Chandra Deep Field South area, we have shown how an ELT can carry out photometric surveys successfully, recovering morphological and structural parameters. We present here a wide statistics of the expected performance of a GMCAO-equipped ELT in 22 well-known surveys in terms of SR., Comment: 6 pages, 4 figures, AO4ELT6 conference proceeding: http://ao4elt6.copl.ulaval.ca/proceedings.html

The basic outline of a pupil plane WaveFront Sensor is reviewed taking into account that the source to be sensed could be different from an unresolved source, i.e. it is extended, and that it could deploy also in a 3D fashion, enough to exceed the field's depth of the observing telescope. Under these conditions it is pointed out that the features of the reference are not invariant for different position on the pupil and it is shown that the INGOT WFS is the equivalent of the Pyramid for a Laser Guide Star. Under these conditions one can imagine to use a Dark WFS approach to improve the SNR of such a WFS, or to use a corrected upward beam in order to achieve a better use of the LGS photons with respect to an ideal Shack-Hartmann WFS., Comment: 6 pages, 4 figures, AO4ELT6 conference proceeding: http://ao4elt6.copl.ulaval.ca/proceedings.html

The ingot wavefront sensor (I-WFS) has been proposed, for ELT-like apertures, as a possible pupil plane WFS, to cope with the geometrical characteristics of a laser guide star (LGS). Within the study and development of such a WFS, on-going in the framework of the MAORY project, the final purpose of the I-WFS simulation is to estimate its performance in terms of wavefront aberration measurement capability. The first step of this analysis is to translate incoming wavefronts into the three pupil images, produced by the optical system. The intrinsic geometrical characteristics of the ingot optical element, designed to be coupled with the LGS elongated image, make the system conceptually different with respect to other pupil WFSs (like the Pyramid WFS, P-WFS) also in terms of the simulation technique to be selected, within the ones which can be found in literature. In this paper, we aim to report the considerations and derivations which led to the selection of a ray-tracing method for ingot pupil images simulation, and the geometrical assumptions and approach made to optimize the computing time., Comment: AO4ELT6 conference proceeding, http://ao4elt6.copl.ulaval.ca/proceedings.html

Several Extreme Adaptive Optics (XAO) systems dedicated to the detection and characterisation of the exoplanets are currently in operation for 8-10 meter class telescopes. Coronagraphs are commonly used in these facilities to reject the diffracted light of an observed star and enable direct imaging and spectroscopy of its circumstellar environment. SHARK-NIR is a coronagraphic camera that will be implemented at the Large Binocular Telescope (LBT). After an extensive simulation campaign, SHARK-NIR team selected a suite of coronagraphic techniques to be implemented in the instrument in order to fulfil the scientific requirements. In summary, the Gaussian Lyot coronagraph is the option to serve all those science cases requiring field-stabilization and moderate contrast. Observations in pupil-stabilized mode to search for exoplanets can take advantage of three Shaped Pupil masks (SPC) and a Four-Quadrant Phase Mask (FQPM) coronagraph. The SPC are designed for high contrast on a small field close to the star and are robust to image and pupil jitter. The FQPM allows to access the entire scientific FoV (18''x18'') and delivers excellent performance in ideal conditions (high Strehl ratios), but performance is still good, both close and further away from the star, even at lower Strehl and with moderate vibrations. After the procurement phase, the coronagraphic masks were delivered to our labs and we started to test their performance on the optical bench and define the alignment procedures that will be employed in the final integration of the instrument in our cleaning room. In this article, we describe the tests that we performed in the lab with SHARK-NIR coronagraphs. We measured the contrast achievable with each technique in very-high Strehl conditions and defined the alignment-integration procedures.

The CHEOPS space mission dedicated to exoplanet follow-up was launched in December 2019, equipped with the capacity to perform photometric measurements at the 20 ppm level. As CHEOPS carries out its observations in a broad optical passband, it can provide insights into the reflected light from exoplanets and constrain the short-wavelength thermal emission for the hottest of planets by observing occultations and phase curves. Here, we report the first CHEOPS observation of an occultation, namely, that of the hot Jupiter WASP-189b, a $M_P \approx 2 M_J$ planet orbiting an A-type star. We detected the occultation of WASP-189 b at high significance in individual measurements and derived an occultation depth of $dF = 87.9 \pm 4.3$ppm based on four occultations. We compared these measurements to model predictions and we find that they are consistent with an unreflective atmosphere heated to a temperature of $3435 \pm 27$K, when assuming inefficient heat redistribution. Furthermore, we present two transits of WASP-189b observed by CHEOPS. These transits have an asymmetric shape that we attribute to gravity darkening of the host star caused by its high rotation rate. We used these measurements to refine the planetary parameters, finding a $\sim25\%$ deeper transit compared to the discovery paper and updating the radius of WASP-189b to $1.619\pm0.021 R_J$. We further measured the projected orbital obliquity to be $\lambda = 86.4^{+2.9}_{-4.4}$deg, a value that is in good agreement with a previous measurement from spectroscopic observations, and derived a true obliquity of $\Psi = 85.4\pm4.3$deg. Finally, we provide reference values for the photometric precision attained by the CHEOPS satellite: for the V=6.6 mag star, and using a one-hour binning, we obtain a residual RMS between 10 and 17ppm on the individual light curves, and 5.7ppm when combining the four visits., Comment: In press at Astronomy and Astrophysics

The CHaracterising ExOPlanet Satellite (CHEOPS) was selected in 2012, as the first small mission in the ESA Science Programme and successfully launched in December 2019. CHEOPS is a partnership between ESA and Switzerland with important contributions by ten additional ESA Member States. CHEOPS is the first mission dedicated to search for transits of exoplanets using ultrahigh precision photometry on bright stars already known to host planets. As a follow-up mission, CHEOPS is mainly dedicated to improving, whenever possible, existing radii measurements or provide first accurate measurements for a subset of those planets for which the mass has already been estimated from ground-based spectroscopic surveys and to following phase curves. CHEOPS will provide prime targets for future spectroscopic atmospheric characterisation. Requirements on the photometric precision and stability have been derived for stars with magnitudes ranging from 6 to 12 in the V band. In particular, CHEOPS shall be able to detect Earth-size planets transiting G5 dwarf stars in the magnitude range between 6 and 9 by achieving a photometric precision of 20 ppm in 6 hours of integration. For K stars in the magnitude range between 9 and 12, CHEOPS shall be able to detect transiting Neptune-size planets achieving a photometric precision of 85 ppm in 3 hours of integration. This is achieved by using a single, frame-transfer, back-illuminated CCD detector at the focal plane assembly of a 33.5 cm diameter telescope. The 280 kg spacecraft has a pointing accuracy of about 1 arcsec rms and orbits on a sun-synchronous dusk-dawn orbit at 700 km altitude. The nominal mission lifetime is 3.5 years. During this period, 20% of the observing time is available to the community through a yearly call and a discretionary time programme managed by ESA., Comment: Submitted to Experimental Astronomy

Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplicial complexes. We introduce \textit{steady} and \textit{ranging} sets: two standardized ways of producing persistence diagrams directly from graph-theoretical features. The two constructions are framed in the context of \textit{indexing-aware persistence functions}. Furthermore, we introduce a sufficient condition for stability. Finally, we apply the steady- and ranging-based persistence constructions to toy examples and real-world applications.

Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how simple machines can be combined into more complex ones. We explore finite- and infinite-depth machines, which generalize neural networks and neural ordinary differential equations. Borrowing ideas from functional analysis and kernel methods, we build complete, normed, infinite-dimensional spaces of machines, and we discuss how to find optimal architectures and parameters -- within those spaces -- to solve a given computational problem. In our numerical experiments, these kernel-inspired networks can outperform classical neural networks when the training dataset is small., Comment: 28 pages, 4 figures

The Global-Multi Conjugated Adaptive Optics (GMCAO) approach offers an alternative way to correct an adequate scientific Field of View (FoV) using only natural guide stars (NGSs) to extremely large ground-based telescopes. Thus, even in the absence of laser guide stars, a GMCAO-equipped ELT-like telescope can achieve optimal performance in terms of Strehl Ratio (SR), retrieving impressive results in studying star-poor fields, as in the cases of the deep field observations. The benefits and usability of GMCAO have been demonstrated by studying 6000 mock high redshift galaxies in the Chandra Deep Field South region. However, a systematic study simulating observations in several portions of the sky is mandatory to have a robust statistic of the GMCAO performance. Technical, tomographic and astrophysical parameters, discussed here, are given as inputs to GIUSTO, an IDL-based code that estimates the SR over the considered field, and the results are analyzed with statistical considerations. The best performance is obtained using stars that are relatively close to the Scientific FoV; therefore, the SR correlates with the mean off-axis position of NGSs, as expected, while their magnitude plays a secondary role. This study concludes that the SRs correlate linearly with the galactic latitude, as also expected. Because of the lack of natural guide stars needed for low-order aberration sensing, the GMCAO confirms as a promising technique to observe regions that can not be studied without the use of laser beacons. It represents a robust alternative way or a risk mitigation strategy for laser approaches on the ELTs., Comment: 18 pages, 10 figures, accepted for publication on PASP

Persistence has proved to be a valuable tool to analyze real world data robustly. Several approaches to persistence have been attempted over time, some topological in flavor, based on the vector space-valued homology functor, other combinatorial, based on arbitrary set-valued functors. To unify the study of topological and combinatorial persistence in a common categorical framework, we give axioms for a generalized rank function on objects in a target category, so that functors to that category induce persistence functions. We port the interleaving and bottleneck distances to this novel framework and generalize classical equalities and inequalities. Unlike sets and vector spaces, in many categories the rank of an object does not identify it up to isomorphism: to preserve information about the structure of persistence modules, we define colorable ranks, persistence diagrams and prove the equality between multicolored bottleneck distance and interleaving distance in semisimple Abelian categories. To illustrate our framework in practice, we give examples of multicolored persistent homology on filtered topological spaces with a group action and labeled point cloud data., Comment: 24 pages, 3 figures