arXiv subjects

R. Alonso

Publications and source records attributed to R. Alonso.

At least 37 records · Page 2Linked to original sources

arXiv2024

CHEOPS observations confirm nodal precession in the WASP-33 system

Aims: We aim to observe the transits and occultations of WASP-33b, which orbits a rapidly-rotating $δ$ Scuti pulsator, with the goal of measuring the orbital obliquity via the gravity-darkening effect, and constraining the geometric albedo via the occultation depth. Methods: We observed four transits and four occultations with CHEOPS, and employ a variety of techniques to remove the effects of the stellar pulsations from the light curves, as well as the usual CHEOPS systematic effects. We also performed a comprehensive analysis of low-resolution spectral and Gaia data to re-determine the stellar properties of WASP-33. Results: We measure an orbital obliquity 111.3 +0.2 -0.7 degrees, which is consistent with previous measurements made via Doppler tomography. We also measure the planetary impact parameter, and confirm that this parameter is undergoing rapid secular evolution as a result of nodal precession of the planetary orbit. This precession allows us to determine the second-order fluid Love number of the star, which we find agrees well with the predictions of theoretical stellar models. We are unable to robustly measure a unique value of the occultation depth, and emphasise the need for long-baseline observations to better measure the pulsation periods.

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arXiv2024

A joint effort to discover and characterize two resonant mini Neptunes around TOI-1803 with TESS, HARPS-N and CHEOPS

We present the discovery of two mini Neptunes near a 2:1 orbital resonance configuration orbiting the K0 star TOI-1803. We describe their orbital architecture in detail and suggest some possible formation and evolution scenarios. Using CHEOPS, TESS, and HARPS-N datasets we can estimate the radius and the mass of both planets. We used a multidimensional Gaussian Process with a quasi-periodic kernel to disentangle the planetary components from the stellar activity in the HARPS-N dataset. We performed dynamical modeling to explain the orbital configuration and performed planetary formation and evolution simulations. For the least dense planet, we define possible atmospheric characterization scenarios with simulated JWST observations. TOI-1803 b and TOI-1803 c have orbital periods of $\sim$6.3 and $\sim$12.9 days, respectively, residing in close proximity to a 2:1 orbital resonance. Ground-based photometric follow-up observations revealed significant transit timing variations (TTV) with an amplitude of $\sim$10 min and $\sim$40 min, respectively, for planet -b and -c. With the masses computed from the radial velocities data set, we obtained a density of (0.39$\pm$0.10) $ρ_{earth}$ and (0.076$\pm$0.038) $ρ_{earth}$ for planet -b and -c, respectively. TOI-1803 c is among the least dense mini Neptunes currently known, and due to its inflated atmosphere, it is a suitable target for transmission spectroscopy with JWST. We report the discovery of two mini Neptunes close to a 2:1 orbital resonance. The detection of significant TTVs from ground-based photometry opens scenarios for a more precise mass determination. TOI-1803 c is one of the least dense mini Neptune known so far, and it is of great interest among the scientific community since it could constrain our formation scenarios.

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arXiv2024

A close outer companion to the ultra-hot Jupiter TOI-2109 b?

Hot Jupiters with close-by planetary companions are rare, with only a handful of them having been discovered so far. This could be due to their suggested dynamical histories, leading to the possible ejection of other planets. TOI-2109 b is special in this regard because it is the hot Jupiter with the closest relative separation from its host star, being separated by less than 2.3 stellar radii. Unexpectedly, transit timing measurements from recently obtained CHEOPS observations show low amplitude transit-timing variations (TTVs). We aim to search for signs of orbital decay and to characterise the apparent TTVs, trying to gain information about a possible companion. We fit the newly obtained CHEOPS light curves using TLCM and extract the resulting mid-transit timings. Successively, we use these measurements in combination with TESS and archival photometric data and radial velocity data to estimate the rate of tidal orbital decay of TOI-2109 b, as well as characterise the TTVs using the N-body code TRADES and the photodynamical approach of PyTTV. We find tentative evidence at $3σ$ for orbital decay in the TOI-2109 system, when we correct the mid-transit timings using the best-fitting sinusoidal model of the TTVs. We do not detect additional transits in the available photometric data, but find evidence towards the authenticity of the apparent TTVs, indicating a close-by, outer companion with $P_\mathrm{c} > 1.125\,$d. Due to the fast rotation of the star, the new planetary candidate cannot be detected in the available radial velocity (RV) measurements, and its parameters can only be loosely constrained by our joint TTV and RV modelling. TOI-2109 could join a small group of rare hot Jupiter systems that host close-by planetary companions, only one of which (WASP-47 b) has an outer companion. More high-precision photometric measurements are necessary to confirm the planetary companion.

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arXiv2024

Architecture of TOI-561 planetary system

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 $ρ_p = 0.778 \pm 0.097 ρ_{\oplus}$. 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.

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arXiv2024

The CHEOPS view on the climate of WASP-3 b

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.

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arXiv2024

The K2-24 planetary system revisited by CHEOPS

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.

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arXiv2024

One-dimensional inelastic Boltzmann equation: Stability and uniqueness of self-similar $L^{1}$-profiles for moderately hard potentials

We prove the stability of $L^{1}$ self-similar profiles under the hard-to-Maxwell potential limit for the one-dimensional inelastic Boltzmann equation with moderately hard potentials which, in turn, leads to the uniqueness of such profiles for hard potentials collision kernels of the form $|\cdot|^γ$ with $γ>0$ sufficiently small (explicitly quantified). Our result provides the first uniqueness statement for self-similar profiles of inelastic Boltzmann models allowing for strong inelasticity besides the explicitly solvable case of Maxwell interactions (corresponding to $γ=0$). Our approach relies on a perturbation argument from the corresponding Maxwell model and a careful study of the associated linearized operator recently derived in the companion paper \cite{maxwel}. The results can be seen as a first step towards a complete proof, in the one-dimensional setting, of a conjecture in \cite{ernst} regarding the determination of the long-time behaviour of solutions to inelastic Boltzmann equation, at least, in a regime of moderately hard potentials.

math.AP↗

arXiv2024

TOI-757 b: an eccentric transiting mini-Neptune on a 17.5-d orbit

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 $ρ_{\text{p}} = 3.6 \pm 0.8$ 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.

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arXiv2024

Characterisation of the Warm-Jupiter TOI-1130 system with CHEOPS and photo-dynamical approach

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.

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arXiv2024

Relaxation in Sobolev spaces and $L^1$ spectral gap of the 1D dissipative Boltzmann equation with Maxwell interactions

We study the dynamic relaxation to equilibrium of the 1D dissipative Boltzmann equation with Maxwell interactions in classical $H^s$ Sobolev spaces. In addition, we present a spectral shrinkage analysis and spectral gap estimates for the linearised 1D dissipative Boltzmann operator with such interactions. Based on this study, we explore the convergence in $H^s$ and $L^{1}$ spaces for the linear and nonlinear models. This study extends classical results found in the literature given for spaces with weak topologies.

math.AP↗

arXiv2024

Unveiling the internal structure and formation history of the three planets transiting HIP 29442 (TOI-469) with CHEOPS

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.

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arXiv2024

CHEOPS in-flight performance: A comprehensive look at the first 3.5 years of operations

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.

astro-ph.IM↗

arXiv2024

HIP 41378 observed by CHEOPS: Where is planet d?

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.

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arXiv2024

Photo-dynamical characterisation of the TOI-178 resonant chain

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.

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arXiv2024

Characterisation of the TOI-421 planetary system using CHEOPS, TESS, and archival radial velocity data

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.

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arXiv2024

Detailed cool star flare morphology with CHEOPS and TESS

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.

astro-ph.SR↗

arXiv2024

Precise characterisation of HD 15337 with CHEOPS: a laboratory for planet formation and evolution

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.

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arXiv2024

The tidal deformation and atmosphere of WASP-12b from its phase curve

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$σ$) 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.

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