Search

The Fewster-Verch (FV) framework was introduced as a prescription to define local operations within a quantum field theory (QFT) that are free from Sorkin-like causal paradoxes. In this framework the measurement device is modeled via a probe QFT that, after interacting with the target QFT, is subject to an arbitrary local measurement. While the FV framework is rich enough to carry out quantum state tomography, it has two drawbacks. First, it is unclear if the FV framework allows conducting arbitrary local measurements. Second, if the probe field is interpreted as physical and the FV framework as fundamental, then one must demand the probe measurement to be itself implementable within the framework. That would involve a new probe, which should also be subject to an FV measurement, and so on. It is unknown if there exist non-trivial FV measurements for which such an "FV-Heisenberg cut" can be moved arbitrarily far away. In this work, we advance the first problem by proving that measurements of locally smeared fields fit within the FV framework. We solve the second problem by showing that any such field measurement admits a movable FV-Heisenberg cut., Comment: 21 pages

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 $3\sigma$ 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., Comment: Accepted for publication in A&A. 21 pages, 21 figures

We show that the dynamics of the Di\'osi-Penrose (DP) model of classical gravity can entangle the mechanical degrees of freedom of two separate particles. For standard experiments of gravitationally induced entanglement (GIE), we find that entanglement can be generated iff the particles are separated by a distance smaller than some limiting value $d_c$, proportional to the only free parameter of the DP model. Greater distances can be achieved through new experimental configurations, where the initial wave-function of the particles is allowed to spread perpendicularly (as opposed to parallely) to the spatial axis separating them. Although the DP dynamics asymptotically drives the system to a separable state, we observe that, for reasonable experimental parameters, GIE can survive for more than a day. In the context of the debate on the nature of gravity, our results prove that experimental demonstrations of GIE are insufficient to conclude that gravity is fundamentally quantum., Comment: 8 pages, 3 figures, comments welcome

Increasing complications due to bacterial and viral infections require novel antimicrobial approaches. One emerging strategy is that based on catalysts able to selectively deliver reactive oxygen species (ROS) without leaching of other substances. In particular, metal oxide thin films activated by daylight can produce ROS by simply catalyzing oxygen and water molecules. This study examines plasma technology, combining deposition and oxidation processes, as well as plasma polymerization, to obtain functionalized AgOx-doped titanium oxide (TiOx) catalytic materials. The high-energy conditions in the reactive, ionized gas enable the intrinsic formation of a large number of reactive sites at defects and interfaces between the metal oxide nanostructures. Furthermore, plasma functionalization with nanoporous SiOx films (up to 100 nm thick) allows to precisely control the ROS delivery as well as unravel ROS formation mechanism at the metal oxide interface. Combining fluorescence spectroscopy and electron paramagnetic resonance, the controlled delivery of superoxide anion and singlet oxygen has been tuned based on the thickness of the nanoporous functional layer. ROS delivery by functionalized catalytic plasma coating has been related to excellent antimicrobial activity against E. coli bacteria as well as murine hepatitis virus, while avoiding cytotoxic and sensitization effects., Comment: 23 pages, 7 figures

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

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.

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

Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where those might be defined. Many of these problems are known to admit a complete hierarchy of semidefinite programming (SDP) relaxations. NPO theory has found application in quantum information theory, quantum chemistry and statistical physics. In this work, we consider a variant of NPO problems where a subset of the operator variables satisfies a system of ordinary differential equations. We find that, under mild conditions of operator boundedness, for every such problem one can construct a standard NPO problem with the same solution. This allows us to define a complete hierarchy of SDPs to tackle the original differential problem. We apply this method to extrapolate quantum time series in a semi-device-independent way and sketch how one can use it to model Hamiltonian time evolution in many-body quantum systems.

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

Investigations into Hawking radiation often assume a black hole model featuring an event horizon, despite the growing consensus that such causal structures may not exist in nature. While this assumption is not crucial for deriving the local properties of radiation at future null infinity, it plays a significant role in discussions about Hawking partners -- the field modes that purify Hawking radiation. This article aims to explore the definition and fate of Hawking partners in black hole scenarios where semiclassical mass loss due to Hawking radiation is considered. Our analysis avoids the assumption of event horizons and instead focuses on collapse processes that feature a trapped region bounded by a dynamical horizon. We derive the form of the partners, accounting for the effects of back-scattering. Furthermore, using these results and mild assumptions, we find that Hawking partners cannot "leak" out of the dynamical horizon to partially purify the Hawking radiation in the regime where general relativity coexists semiclassically with quantum field theory. This finding emphasizes the necessity for new physics, such as quantum gravity, to resolve the final fate of information., Comment: 31 pages, 5 figures, 3 appendices, matches published version

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

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

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.

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

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 study what can or cannot be certified in communication scenarios where the assumption of independence and identical distribution (iid) between experimental rounds fails. In this respect, we prove that membership tests for non-convex sets of correlations cannot be formulated in the non-iid regime. Similarly, it is impossible to self-test non-extreme quantum operations, such as mixed states, or noisy quantum measurements, unless one allows more than a single use thereof within the same experimental round. One consequence of our results is that non-classicality in causal networks without inputs cannot be experimentally demonstrated. By analyzing optimal non-iid strategies in the triangle scenario, we raise the need to take into account the prior communication required to set up a causal network.

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 investigate the long-term motion of Saturn's North-Pole Hexagon and the structure of its associated eastward jet, using Cassini ISS and ground-based images from 2008 to 2014. We show that both are persistent features that have survived the long polar night, the jet profile remaining essentially unchanged. During those years the hexagon vertices showed a steady rotation period of 10 hr 39 min 23.01 $\pm$ 0.01 s. Analysis of Voyager 1 and 2 (1980-1981) and HST and ground-based (1990-91) images shows a period shorter by 3.5s, due to the presence at the time of a large anticyclone. We interpret the hexagon as a manifestation of a vertically trapped Rossby wave on the polar jet and, because of their survival and unchanged properties under the strong seasonal variations in insolation, we propose that both hexagon and jet are deep-rooted atmospheric features that could reveal the true rotation of the planet Saturn.

Observations of low-mass stars have frequently shown a disagreement between observed stellar radii and radii predicted by theoretical stellar structure models. This ``radius inflation'' problem could have an impact on both stellar and exoplanetary science. We present the final results of our observation programme with the CHEOPS satellite to obtain high-precision light curves of eclipsing binaries with low mass stellar companions (EBLMs). Combined with the spectroscopic orbits of the solar-type companion, we can derive the masses, radii and effective temperatures of 23 M-dwarf stars. We use the PYCHEOPS data analysis software to analyse their primary and secondary occultations. For all but one target, we also perform analyses with TESS light curves for comparison. We have assessed the impact of starspot-induced variation on our derived parameters and account for this in our radius and effective temperature uncertainties using simulated light curves. We observe trends for inflation with both metallicity and orbital separation. We also observe a strong trend in the difference between theoretical and observational effective temperatures with metallicity. There is no such trend with orbital separation. These results are not consistent with the idea that observed inflation in stellar radius combines with lower effective temperature to preserve the luminosity predicted by low-mass stellar models. Our EBLM systems are high-quality and homogeneous measurements that can be used in further studies into radius inflation., Comment: 21 pages, 10 figures, accepted for publication in MNRAS, Supplementary material provided as ancillary files

We consider the problem of optimizing the state average of a polynomial of non-commuting variables, over all states and operators satisfying a number of polynomial constraints, and over all Hilbert spaces where such states and operators are defined. Such non-commutative polynomial optimization (NPO) problems are routinely solved through hierarchies of semidefinite programming (SDP) relaxations. By formulating the general NPO problem in Lagrangian terms, we heuristically derive first-order optimality conditions via small variations in the problem variables. Although the derivation is not rigorous, it gives rise to two types of optimality conditions - state and operator - which are rigorously analyzed in the paper. Both types of conditions can be enforced through additional positive semidefinite constraints in the SDP hierarchies. State optimality conditions are shown to be satisfied by all NPO problems. For NPO problems with optimal solutions (such as, e.g., Archimedean ones) they allow enforcing a new type of constraints: namely, restricting the optimization over states to the set of common ground states of an arbitrary number of operators. Operator optimality conditions are the non-commutative analogs of the Karush-Kuhn-Tucker (KKT) conditions, which are known to hold in many classical optimization problems. In this regard, we prove that a weak form of operator optimality holds for all NPO problems; stronger versions require the problem constraints to satisfy some qualification criterion, just like in the classical case (e.g. Mangasarian-Fromovitz constraint qualification). We test the power of the new optimality conditions by computing local properties of ground states of many-body spin systems and the maximum quantum violation of Bell inequalities., Comment: v4: cleaner and more rigorous version from referee feedback

The dynamics of the expectation value of the volume is one of the key ingredients behind the replacement of the Big Bang singularity by a bounce in Loop Quantum Cosmology. As such, it is of great importance that this quantity is mathematically well-defined in the space of physical states of the theory. A number of caveats have been raised about such a definition entering in conflict with the quantum evolution of states, motivated by the situation found in quantum geometrodynamics. We show that there are ways around these caveats, all of which are related to the existence of quantization prescriptions leading to a nondegenerate curvature operator in Loop Quantum Cosmology. Interestingly, the properties of the curvature operator that may allow for a good behavior of the volume are only possible thanks to the discreteness of the geometry characteristic of the loop quantization procedure., Comment: 11 pages, revised version

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

In this paper, based on the results from [On the localization of Hutchinson-Barnsley fractals, Chaos Solitons Fractals, 173 (2023), 113674], we generate coverings (consisting of finite families of rhombi) of the graph of fractal interpolation functions. As a by-product we obtain estimations for the range of such functions. Some concrete examples and graphical representations are provided., Comment: 24 pages, 15 figures

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

HD 139139 (a.k.a. 'The Random Transiter') is a star that exhibited enigmatic transit-like features with no apparent periodicity in K2 data. The shallow depth of the events ($\sim$200 ppm -- equivalent to transiting objects with radii of $\sim$1.5 R$_\oplus$ in front of a Sun-like star), and their non-periodicity, constitutes a challenge for the photometric follow-up of this star. The goal of this study is to confirm with independent measurements the presence of shallow, non-periodic transit-like features on this object. We performed observations with CHEOPS, for a total accumulated time of 12.75 d, distributed in visits of roughly 20 h in two observing campaigns in years 2021 and 2022. The precision of the data is sufficient to detect 150 ppm features with durations longer than 1.5 h. We use the duration and times of the events seen in the K2 curve to estimate how many should have been detected in our campaigns, under the assumption that their behaviour during the CHEOPS observations would be the same as in the K2 data of 2017. We do not detect events with depths larger than 150 ppm in our data set. If the frequency, depth, and duration of the events were the same as in the K2 campaign, we estimate the probability of having missed all events due to our limited observing window would be 4.8 %. We suggest three different scenarios to explain our results: 1) Our observing window was not long enough, and the events were missed with the estimated 4.8 % probability. 2) The events recorded in the K2 observations were time critical, and the mechanism producing them was either not active in the 2021 and 2022 campaigns or created shallower events under our detectability level. 3) The enigmatic events in the K2 data are the result of an unidentified and infrequent instrumental noise in the original data set or its data treatment., Comment: 7 pages, 3 figures, accepted for publication in A&A. Language-corrected version

Multiwavelength photometry of the secondary eclipses of extrasolar planets is able to disentangle the reflected and thermally emitted light radiated from the planetary dayside. This leads to the measurement of the planetary geometric albedo $A_g$, which is an indicator of the presence of clouds in the atmosphere, and the recirculation efficiency $\epsilon$, which quantifies the energy transport within the atmosphere. In this work we aim to measure $A_g$ and $\epsilon$ for the planet WASP-178 b, a highly irradiated giant planet with an estimated equilibrium temperature of 2450 K.} We analyzed archival spectra and the light curves collected by Cheops and Tess to characterize the host WASP-178, refine the ephemeris of the system and measure the eclipse depth in the passbands of the two respective telescopes. We measured a marginally significant eclipse depth of 70$\pm$40 ppm in the Tess passband and statistically significant depth of 70$\pm$20 ppm in the Cheops passband. Combining the eclipse depth measurement in the Cheops (lambda_eff=6300 AA) and Tess (lambda_eff=8000 AA) passbands we constrained the dayside brightness temperature of WASP-178 b in the 2250-2800 K interval. The geometric albedo 0.1<$\rm A_g$<0.35 is in general agreement with the picture of poorly reflective giant planets, while the recirculation efficiency $\epsilon>$0.7 makes WASP-178 b an interesting laboratory to test the current heat recirculation models., Comment: Accepted by Astronomy and Astrophysics on 31/08/2023

The TOI-178 system consists of a nearby late K-dwarf transited by six planets in the super-Earth to mini-Neptune regime, with orbital periods between 1.9 and 20.7 days. All planets but the innermost one form a chain of Laplace resonances. Mass estimates derived from a preliminary radial velocity (RV) dataset suggest that the planetary densities do not decrease in a monotonic way with the orbital distance to the star, contrary to what one would expect based on simple formation and evolution models. To improve the characterisation of this key system and prepare for future studies (in particular with JWST), we perform a detailed photometric study based on 40 new CHEOPS visits, one new TESS sector, as well as previously published CHEOPS, TESS, and NGTS data. First we perform a global analysis of the 100 transits contained in our data to refine the transit parameters of the six planets and study their transit timing variations (TTVs). We then use our extensive dataset to place constraints on the radii and orbital periods of potential additional transiting planets in the system. Our analysis significantly refines the transit parameters of the six planets, most notably their radii, for which we now obtain relative precisions $\lesssim$3%, with the exception of the smallest planet $b$ for which the precision is 5.1%. Combined with the RV mass estimates, the measured TTVs allow us to constrain the eccentricities of planets $c$ to $g$, which are found to be all below 0.02, as expected from stability requirements. Taken alone, the TTVs also suggest a higher mass for planet $d$ than the one estimated from the RVs, which had been found to yield a surprisingly low density for this planet. However, the masses derived from the current TTV dataset are very prior-dependent and further observations, over a longer temporal baseline, are needed to deepen our understanding of this iconic planetary system., Comment: 20 pages, 5 figures, 9 tables. Accepted for publication in A&A

In scenarios of physical interest in Loop Quantum Cosmology, with a preinflationary epoch where the kinetic energy of the inflaton dominates, the analytic study of the dynamics of the primordial fluctuations has been carried out by neglecting the inflaton potential in those stages of the evolution. In this work we develop approximations to investigate the influence of the potential as the period of kinetic dominance gives way to the inflationary regime, treating the potential as a perturbation. Specifically, we study how the potential modifies the effective mass that dictates the dynamics of the scalar perturbations in the preinflationary epochs, within the framework of the so-called hybrid prescription for Loop Quantum Cosmology. Moreover, we motivate and model a transition period that connects the kinetically dominated regime with inflation, allowing us to study the interval of times where the contribution of the potential is no longer negligible but an inflationary description is not yet valid. Finally, we include the main modifications coming from a slow-roll correction to a purely de Sitter evolution of the perturbations during inflation. We analytically solve the dynamics of the perturbations in each of these different epochs of cosmological evolution, starting from initial conditions fixed by the criterion of asymptotic Hamiltonian diagonalization. This enables us to compute and quantitatively analyze the primordial power spectrum in a specific case, using a quadratic inflaton potential., Comment: 17 pages, 3 figures

55 Cnc e is an ultra-short period super-Earth transiting a Sun-like star. Previous observations in the optical range detected a time-variable flux modulation that is phased with the planetary orbital period, whose amplitude is too large to be explained by reflected light and thermal emission alone. The goal of the study is to investigate the origin of the variability and timescale of the phase-curve modulation in 55 Cnc e. To this end, we used the CHaracterising ExOPlanet Satellite (CHEOPS), whose exquisite photometric precision provides an opportunity to characterise minute changes in the phase curve from one orbit to the next. CHEOPS observed 29 individual visits of 55 Cnc e between March 2020 and February 2022. Based on these observations, we investigated the different processes that could be at the origin of the observed modulation. In particular, we built a toy model to assess whether a circumstellar torus of dust driven by radiation pressure and gravity might match the observed flux variability timescale. We find that the phase-curve amplitude and peak offset of 55 Cnc e do vary between visits. The sublimation timescales of selected dust species reveal that silicates expected in an Earth-like mantle would not survive long enough to explain the observed phase-curve modulation. We find that silicon carbide, quartz, and graphite are plausible candidates for the circumstellar torus composition because their sublimation timescales are long. The extensive CHEOPS observations confirm that the phase-curve amplitude and offset vary in time.We find that dust could provide the grey opacity source required to match the observations. However, the data at hand do not provide evidence that circumstellar material with a variable grain mass per unit area causes the observed variability. Future observations with the James Webb Space Telescope promise exciting insights into this iconic super-Earth., Comment: 27 pages, 22 figures. Accepted for publication on A&A

We study the canonical quantization of a scalar field in a Kantowski-Sachs spacetime. For simplicity, we consider compactified spatial sections, since this does not affect the ultraviolet behavior. A time-dependent canonical transformation is performed prior to quantization. As in previously studied cases, the purpose of this canonical transformation is to identify and extract the background contribution to the field evolution which is obstructing a unitary implementation of the field dynamics at the quantum level. This splitting of the time dependence into a background piece and the part to be seen as true quantum evolution is to a large extent determined by the unitarity requirement itself. The quantization is performed in the usual setup of Fock representations, demanding the preservation of the spatial symmetries. Under the joint requirements of quantum unitary dynamics and compatibility with those classical symmetries, the quantization is shown to be unique, in the sense that any two representations with these properties are unitarily equivalent. This confirms the validity of our conditions as criteria to discriminate among possibly inequivalent quantum descriptions. The interest of this analysis goes beyond cosmological applications since the interior of a nonrotating black hole has a geometry of the Kantowski-Sachs type., Comment: 13 pages

Considerable attention has been paid to the study of the quantum geometry of nonrotating black holes within the framework of Loop Quantum Cosmology. This interest has been reinvigorated since the introduction of a novel effective model by Ashtekar, Olmedo, and Singh. Despite recent advances in its foundation, there are certain questions about its quantization that still remain open. Here we complete this quantization taking as starting point an extended phase space formalism suggested by several authors, including the proposers of the model. Adopting a prescription that has proven successful in Loop Quantum Cosmology, we construct an operator representation of the Hamiltonian constraint. By searching for solutions to this constraint operator in a sufficiently large set of dual states, we show that it can be solved for a continuous range of the black hole mass. This fact seems in favour of a conventional classical limit (at least for large masses) and contrasts with recent works that advocate a discrete spectrum. We present an algorithm that determines the solutions in closed form. To build the corresponding physical Hilbert space and conclude the quantization, we carry out an asymptotic analysis of those solutions, which allows us to introduce a suitable inner product on them., Comment: 16 pages

We report the discovery of two warm sub-Neptunes transiting the bright (G = 9.5 mag) K-dwarf HD 15906 (TOI 461, TIC 4646810). This star was observed by the Transiting Exoplanet Survey Satellite (TESS) in sectors 4 and 31, revealing two small transiting planets. The inner planet, HD 15906 b, was detected with an unambiguous period but the outer planet, HD 15906 c, showed only two transits separated by $\sim$ 734 days, leading to 36 possible values of its period. We performed follow-up observations with the CHaracterising ExOPlanet Satellite (CHEOPS) to confirm the true period of HD 15906 c and improve the radius precision of the two planets. From TESS, CHEOPS and additional ground-based photometry, we find that HD 15906 b has a radius of 2.24 $\pm$ 0.08 R$_\oplus$ and a period of 10.924709 $\pm$ 0.000032 days, whilst HD 15906 c has a radius of 2.93$^{+0.07}_{-0.06}$ R$_\oplus$ and a period of 21.583298$^{+0.000052}_{-0.000055}$ days. Assuming zero bond albedo and full day-night heat redistribution, the inner and outer planet have equilibrium temperatures of 668 $\pm$ 13 K and 532 $\pm$ 10 K, respectively. The HD 15906 system has become one of only six multiplanet systems with two warm ($\lesssim$ 700 K) sub-Neptune sized planets transiting a bright star (G $\leq$ 10 mag). It is an excellent target for detailed characterisation studies to constrain the composition of sub-Neptune planets and test theories of planet formation and evolution., Comment: 30 pages, 20 figures, 11 tables (including appendix). Published in MNRAS

Multi-planet systems are important sources of information regarding the evolution of planets. However, the long-period planets in these systems often escape detection. HD 22946 is a bright star around which 3 transiting planets were identified via TESS photometry, but the true orbital period of the outermost planet d was unknown until now. We aim to use CHEOPS to uncover the true orbital period of HD 22946d and to refine the orbital and planetary properties of the system, especially the radii of the planets. We used the available TESS photometry of HD 22946 and observed several transits of the planets b, c, and d using CHEOPS. We identified 2 transits of planet d in the TESS photometry, calculated the most probable period aliases based on these data, and then scheduled CHEOPS observations. The photometric data were supplemented with ESPRESSO radial velocity data. Finally, a combined model was fitted to the entire dataset. We successfully determined the true orbital period of the planet d to be 47.42489 $\pm$ 0.00011 d, and derived precise radii of the planets in the system, namely 1.362 $\pm$ 0.040 R$_\oplus$, 2.328 $\pm$ 0.039 R$_\oplus$, and 2.607 $\pm$ 0.060 R$_\oplus$ for planets b, c, and d, respectively. Due to the low number of radial velocities, we were only able to determine 3$\sigma$ upper limits for these respective planet masses, which are 13.71 M$_\oplus$, 9.72 M$_\oplus$, and 26.57 M$_\oplus$. We estimated that another 48 ESPRESSO radial velocities are needed to measure the predicted masses of all planets in HD 22946. Planet c appears to be a promising target for future atmospheric characterisation. We can also conclude that planet d, as a warm sub-Neptune, is very interesting because there are only a few similar confirmed exoplanets to date. Such objects are worth investigating in the near future, for example in terms of their composition and internal structure.

HIP 9618 (HD 12572, TOI-1471, TIC 306263608) is a bright ($G=9.0$ mag) solar analogue. TESS photometry revealed the star to have two candidate planets with radii of $3.9 \pm 0.044$ $R_\oplus$ (HIP 9618 b) and $3.343 \pm 0.039$ $R_\oplus$ (HIP 9618 c). While the 20.77291 day period of HIP 9618 b was measured unambiguously, HIP 9618 c showed only two transits separated by a 680-day gap in the time series, leaving many possibilities for the period. To solve this issue, CHEOPS performed targeted photometry of period aliases to attempt to recover the true period of planet c, and successfully determined the true period to be 52.56349 d. High-resolution spectroscopy with HARPS-N, SOPHIE and CAFE revealed a mass of $10.0 \pm 3.1 M_\oplus$ for HIP 9618 b, which, according to our interior structure models, corresponds to a $6.8\pm1.4\%$ gas fraction. HIP 9618 c appears to have a lower mass than HIP 9618 b, with a 3-sigma upper limit of $< 18M_\oplus$. Follow-up and archival RV measurements also reveal a clear long-term trend which, when combined with imaging and astrometric information, reveal a low-mass companion ($0.08^{+0.12}_{-0.05} M_\odot$) orbiting at $26^{+19}_{-11}$ au. This detection makes HIP 9618 one of only five bright ($K<8$ mag) transiting multi-planet systems known to host a planet with $P>50$ d, opening the door for the atmospheric characterisation of warm ($T_{\rm eq}<750$ K) sub-Neptunes., Comment: 19 pages, 16 figures, 9 tables. Accepted at MNRAS. CHEOPS, RV and ground-based photometric data is available on CDS at https://cdsarc.cds.unistra.fr/viz-bin/cat/J/MNRAS/523/3069

A large sample of long-period giant planets has been discovered thanks to long-term radial velocity surveys, but only a few dozen of these planets have a precise radius measurement. Transiting gas giants are crucial targets for the study of atmospheric composition across a wide range of equilibrium temperatures and for shedding light on the formation and evolution of planetary systems. Indeed, compared to hot Jupiters, the atmospheric properties and orbital parameters of cooler gas giants are unaltered by intense stellar irradiation and tidal effects. We identify long-period planets in the Transiting Exoplanet Survey Satellite (TESS) data as duo-transit events. To solve the orbital periods of TESS duo-transit candidates, we use the CHaracterising ExOPlanet Satellite (CHEOPS) to observe the highest-probability period aliases in order to discard or confirm a transit event at a given period. We also collect spectroscopic observations with CORALIE and HARPS in order to confirm the planetary nature and measure the mass of the candidates. We report the discovery of a warm transiting Neptune-mass planet orbiting TOI-5678. After four non-detections corresponding to possible periods, CHEOPS detected a transit event matching a unique period alias. Joint modeling reveals that TOI-5678 hosts a 47.73 day period planet. TOI-5678 b has a mass of 20 (+-4) Me and a radius of 4.91 (+-0.08 Re) . Using interior structure modeling, we find that TOI-5678 b is composed of a low-mass core surrounded by a large H/He layer with a mass of 3.2 (+1.7, -1.3) Me. TOI-5678 b is part of a growing sample of well-characterized transiting gas giants receiving moderate amounts of stellar insolation (11 Se). Precise density measurement gives us insight into their interior composition, and the objects orbiting bright stars are suitable targets to study the atmospheric composition of cooler gas giants., Comment: 17 pages, 10 figures, accepted to A&A

We consider communication scenarios where one party sends quantum states of known dimensionality $D$, prepared with an untrusted apparatus, to another, distant party, who probes them with uncharacterized measurement devices. We prove that, for any ensemble of reference pure quantum states, there exists one such prepare-and-measure scenario and a linear functional $W$ on its observed measurement probabilities, such that $W$ can only be maximized if the preparations coincide with the reference states, modulo a unitary or an anti-unitary transformation. In other words, prepare-and-measure scenarios allow one to "self-test" arbitrary ensembles of pure quantum states. Arbitrary extreme $D$-dimensional quantum measurements, or sets thereof, can be similarly self-tested. Our results rely on a robust generalization of Wigner's theorem, a well-known result in particle physics that characterizes physical symmetries., Comment: Close to published version

Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then we consider an iterated function system giving rise to a fractal interpolation function of a set of data., Comment: Numerical Algorithms (Accepted)

TOI-1055 is a Sun-like star known to host a transiting Neptune-sized planet on a 17.5-day orbit (TOI-1055 b). Radial velocity (RV) analyses carried out by two independent groups using nearly the same set of HARPS spectra have provided measurements of planetary masses that differ by $\sim$ 2$\sigma$. Our aim in this work is to solve the inconsistency in the published planetary masses by significantly extending the set of HARPS RV measurements and employing a new analysis tool that is able to account and correct for stellar activity. Our further aim was to improve the precision on measurements of the planetary radius by observing two transits of the planet with the CHEOPS space telescope. We fit a skew normal (SN) function to each cross correlation function extracted from the HARPS spectra to obtain RV measurements and hyperparameters to be used for the detrending. We evaluated the correlation changes of the hyperparameters along the RV time series using the breakpoint technique. We performed a joint photometric and RV analysis using a Markov chain Monte Carlo (MCMC) scheme to simultaneously detrend the light curves and the RV time series. We firmly detected the Keplerian signal of TOI-1055 b, deriving a planetary mass of $M_b=20.4_{-2.5}^{+2.6} M_{\oplus}$ ($\sim$12%). This value is in agreement with one of the two estimates in the literature, but it is significantly more precise. Thanks to the TESS transit light curves combined with exquisite CHEOPS photometry, we also derived a planetary radius of $R_b=3.490_{-0.064}^{+0.070} R_{\oplus}$ ($\sim$1.9%). Our mass and radius measurements imply a mean density of $\rho_b=2.65_{-0.35}^{+0.37}$ g cm$^{-3}$ ($\sim$14%). We further inferred the planetary structure and found that TOI-1055 b is very likely to host a substantial gas envelope with a mass of $0.41^{+0.34}_{-0.20}$ M$_\oplus$ and a thickness of $1.05^{+0.30}_{-0.29}$ R$_\oplus$., Comment: 13 pages, 6 figures, 5 tables. Accepted for publication in A&A

Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through adaptive measurements, computing the maximum average score of a preparation game over a continuous set of target states and limiting the behavior of a (quantum) finite-state automaton. In this work, we introduce tractable relaxations of this class of optimization problems. To illustrate their performance, we use them to: (a) compute the probability that a finite-state automaton outputs a given sequence of bits; (b) develop a new many-body entanglement detection protocol; (c) let the computer invent an adaptive protocol for magic state detection. As we further show, the maximum score of a sequential problem in the limit of infinitely many time steps is in general incomputable. Nonetheless, we provide general heuristics to bound this quantity and show that they provide useful estimates in relevant scenarios., Comment: Close to published version

Context. Measurements of the occultation of an exoplanet at visible wavelengths allow us to determine the reflective properties of a planetary atmosphere. The observed occultation depth can be translated into a geometric albedo. This in turn aids in characterising the structure and composition of an atmosphere by providing additional information on the wavelength-dependent reflective qualities of the aerosols in the atmosphere. Aims. Our aim is to provide a precise measurement of the geometric albedo of the gas giant HD 189733b by measuring the occultation depth in the broad optical bandpass of CHEOPS (350 - 1100 nm). Methods. We analysed 13 observations of the occultation of HD 189733b performed by CHEOPS utilising the Python package PyCHEOPS. The resulting occultation depth is then used to infer the geometric albedo accounting for the contribution of thermal emission from the planet. We also aid the analysis by refining the transit parameters combining observations made by the TESS and CHEOPS space telescopes. Results. We report the detection of an $24.7 \pm 4.5$ ppm occultation in the CHEOPS observations. This occultation depth corresponds to a geometric albedo of $0.076 \pm 0.016$. Our measurement is consistent with models assuming the atmosphere of the planet to be cloud-free at the scattering level and absorption in the CHEOPS band to be dominated by the resonant Na doublet. Taking into account previous optical-light occultation observations obtained with the Hubble Space Telescope, both measurements combined are consistent with a super-stellar Na elemental abundance in the dayside atmosphere of HD 189733b. We further constrain the planetary Bond albedo to between 0.013 and 0.42 at 3$\sigma$ confidence., Comment: 17 pages, 10 figures, accepted for publication in A&A

Given a renormalization scheme, we show how to formulate a tractable convex relaxation of the set of feasible local density matrices of a many-body quantum system. The relaxation is obtained by introducing a hierarchy of constraints between the reduced states of ever-growing sets of lattice sites. The coarse-graining maps of the underlying renormalization procedure serve to eliminate a vast number of those constraints, such that the remaining ones can be enforced with reasonable computational means. This can be used to obtain rigorous lower bounds on the ground state energy of arbitrary local Hamiltonians, by performing a linear optimization over the resulting convex relaxation of reduced quantum states. The quality of the bounds crucially depends on the particular renormalization scheme, which must be tailored to the target Hamiltonian. We apply our method to 1D translation-invariant spin models, obtaining energy bounds comparable to those attained by optimizing over locally translation-invariant states of $n\gtrsim 100$ spins. Beyond this demonstration, the general method can be applied to a wide range of other problems, such as spin systems in higher spatial dimensions, electronic structure problems, and various other many-body optimization problems, such as entanglement and nonlocality detection., Comment: Section III, that presents the general framework, was revised