arXiv subjects

S. Charnoz

Publications and source records attributed to S. Charnoz.

At least 55 records · Page 3Linked to original sources

arXiv2022

CHEOPS geometric albedo of the hot Jupiter HD 209458b

We report the detection of the secondary eclipse of the hot Jupiter HD 209458b in optical/visible light using the CHEOPS space telescope. Our measurement of 20.4 +/- 3.3 ppm translates into a geometric albedo of A_g = 0.096 +/- 0.016. The previously estimated dayside temperature of about 1500 K implies that our geometric albedo measurement consists predominantly of reflected starlight and is largely uncontaminated by thermal emission. This makes the present result one of the most robust measurements of A_g for any exoplanet. Our calculations of the bandpass-integrated geometric albedo demonstrate that the measured value of A_g is consistent with a cloud-free atmosphere, where starlight is reflected via Rayleigh scattering by hydrogen molecules, and the water and sodium abundances are consistent with stellar metallicity. We predict that the bandpass-integrated TESS geometric albedo is too faint to detect and that a phase curve of HD 209458b observed by CHEOPS would have a distinct shape associated with Rayleigh scattering if the atmosphere is indeed cloud free.

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arXiv2022

Transit timing variations of AU Microscopii b and c

Here we report large-amplitude transit timing variations (TTVs) for AU\,Microcopii b and c as detected in combined TESS (2018, 2020) and CHEOPS (2020, 2021) transit observations. AU Mic is a young planetary system with a debris disk and two transiting warm Neptunes. A TTV on the order of several minutes was previously reported for AU Mic b, which was suggested to be an outcome of mutual perturbations between the planets in the system. In 2021, we observed AU Mic b (five transits) and c (three transits) with the CHEOPS space telescope to follow-up the TTV of AU Mic b and possibly detect a TTV for AU Mic c. When analyzing TESS and CHEOPS 2020--2021 measurements together, we find that a prominent TTV emerges with a full span of ~23 minutes between the two TTV extrema. Assuming that the period change results from a periodic process - such as mutual perturbations - we demonstrate that the times of transits in the summer of 2022 are expected to be 30--85 minutes later than predicted by the available linear ephemeris.

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arXiv2022

Spi-OPS: Spitzer and CHEOPS confirm the near-polar orbit of MASCARA-1 b and reveal a hint of dayside reflection

The light curves of tidally locked hot Jupiters transiting fast-rotating, early-type stars are a rich source of information about both the planet and star, with full-phase coverage enabling a detailed atmospheric characterisation of the planet. Although it is possible to determine the true spin-orbit angle $Ψ$, a notoriously difficult parameter to measure, from any transit asymmetry resulting from gravity darkening induced by the stellar rotation, the correlations that exist between the transit parameters have led to large disagreements in published values of $Ψ$ for some systems. We aimed to study these phenomena in the light curves of the ultra-hot Jupiter MASCARA-1 b. We obtained optical CHEOPS transit and occultation light curves of MASCARA-1 b, and analysed them jointly with a Spitzer/IRAC 4.5 $μ$m full-phase curve. When fitting the CHEOPS and Spitzer transits together, the degeneracies are greatly diminished and return results consistent with previously published Doppler tomography. Placing priors informed by the tomography achieves even better precision, allowing a determination of $Ψ=72.1^{+2.5}_{-2.4}$ deg. From the occultations and phase variations, we derived dayside and nightside temperatures of $3062^{+66}_{-68}$ K and $1720\pm330$ K, respectively. In addition, we could separately derive geometric albedo $A_g=0.171^{+0.066}_{-0.068}$ and spherical albedo $A_s=0.266^{+0.097}_{-0.100}$ from the CHEOPS data, and Bond albedo $A_B=0.057^{+0.083}_{-0.101}$ from the Spitzer phase curve. Where possible, priors informed by Doppler tomography should be used when fitting transits of fast-rotating stars, though multi-colour photometry may also unlock an accurate measurement of $Ψ$. Our approach to modelling the phase variations at different wavelengths provides a template for how to separate thermal emission from reflected light in spectrally resolved JWST phase curves.

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arXiv2022

Investigating the architecture and internal structure of the TOI-561 system planets with CHEOPS, HARPS-N and TESS

We present a precise characterization of the TOI-561 planetary system obtained by combining previously published data with TESS and CHEOPS photometry, and a new set of $62$ HARPS-N radial velocities (RVs). Our joint analysis confirms the presence of four transiting planets, namely TOI-561 b ($P = 0.45$ d, $R = 1.42$ R$_\oplus$, $M = 2.0$ M$_\oplus$), c ($P = 10.78$ d, $R = 2.91$ R$_\oplus$, $M = 5.4$ M$_\oplus$), d ($P = 25.7$ d, $R = 2.82$ R$_\oplus$, $M = 13.2$ M$_\oplus$) and e ($P = 77$ d, $R = 2.55$ R$_\oplus$, $M = 12.6$ M$_\oplus$). Moreover, we identify an additional, long-period signal ($>450$ d) in the RVs, which could be due to either an external planetary companion or to stellar magnetic activity. The precise masses and radii obtained for the four planets allowed us to conduct interior structure and atmospheric escape modelling. TOI-561 b is confirmed to be the lowest density ($ρ_{\rm b} = 3.8 \pm 0.5$ g cm$^{-3}$) ultra-short period (USP) planet known to date, and the low metallicity of the host star makes it consistent with the general bulk density-stellar metallicity trend. According to our interior structure modelling, planet b has basically no gas envelope, and it could host a certain amount of water. In contrast, TOI-561 c, d, and e likely retained an H/He envelope, in addition to a possibly large water layer. The inferred planetary compositions suggest different atmospheric evolutionary paths, with planets b and c having experienced significant gas loss, and planets d and e showing an atmospheric content consistent with the original one. The uniqueness of the USP planet, the presence of the long-period planet TOI-561 e, and the complex architecture make this system an appealing target for follow-up studies.

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arXiv2021

The changing face of AU Mic b: stellar spots, spin-orbit commensurability, and Transit Timing Variations as seen by CHEOPS and TESS

AU Mic is a young planetary system with a resolved debris disc showing signs of planet formation and two transiting warm Neptunes near mean-motion resonances. Here we analyse three transits of AU Mic b observed with the CHaracterising ExOPlanet Satellite (CHEOPS), supplemented with sector 1 and 27 Transiting Exoplanet Survey Satellite (TESS) photometry, and the All-Sky Automated Survey (ASAS) from the ground. The refined orbital period of AU Mic b is 8.462995 \pm 0.000003 d, whereas the stellar rotational period is P_{rot}=4.8367 \pm 0.0006 d. The two periods indicate a 7:4 spin--orbit commensurability at a precision of 0.1%. Therefore, all transits are observed in front of one of the four possible stellar central longitudes. This is strongly supported by the observation that the same complex star-spot pattern is seen in the second and third CHEOPS visits that were separated by four orbits (and seven stellar rotations). Using a bootstrap analysis we find that flares and star spots reduce the accuracy of transit parameters by up to 10% in the planet-to-star radius ratio and the accuracy on transit time by 3-4 minutes. Nevertheless, occulted stellar spot features independently confirm the presence of transit timing variations (TTVs) with an amplitude of at least 4 minutes. We find that the outer companion, AU Mic c may cause the observed TTVs.

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arXiv2021

CHEOPS Precision Phase Curve of the Super-Earth 55 Cnc e

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

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arXiv2021

The EBLM project -- VIII. First results for M-dwarf mass, radius and effective temperature measurements using CHEOPS light curves

The accuracy of theoretical mass, radius and effective temperature values for M-dwarf stars is an active topic of debate. Differences between observed and theoretical values have raised the possibility that current theoretical stellar structure and evolution models are inaccurate towards the low-mass end of the main sequence. To explore this issue we use the CHEOPS satellite to obtain high-precision light curves of eclipsing binaries with low mass stellar companions. We use these light curves combined with the spectroscopic orbit for the solar-type companion to measure the mass, radius and effective temperature of the M-dwarf star. Here we present the analysis of three eclipsing binaries. We use the pycheops data analysis software to fit the observed transit and eclipse events of each system. Two of our systems were also observed by the TESS satellite -- we similarly analyse these light curves for comparison. We find consistent results between CHEOPS and TESS, presenting three stellar radii and two stellar effective temperature values of low-mass stellar objects. These initial results from our on-going observing programme with CHEOPS show that we can expect to have ~24 new mass, radius and effective temperature measurements for very low mass stars within the next few years.

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arXiv2021

Survival of exomoons around exoplanets

Despite numerous attempts, no exomoon has firmly been confirmed to date. New missions like CHEOPS aim to characterize previously detected exoplanets, and potentially to discover exomoons. In order to optimize search strategies, we need to determine those planets which are the most likely to host moons. We investigate the tidal evolution of hypothetical moon orbits in systems consisting of a star, one planet and one test moon. We study a few specific cases with ten billion years integration time where the evolution of moon orbits follows one of these three scenarios: (1) "locking", in which the moon has a stable orbit on a long time scale ($\gtrsim$ 10$^9$ years); (2) "escape scenario" where the moon leaves the planet's gravitational domain; and (3) "disruption scenario", in which the moon migrates inwards until it reaches the Roche lobe and becomes disrupted by strong tidal forces. Applying the model to real cases from an exoplanet catalogue, we study the long-term stability of moon orbits around known exoplanets. We calculate the survival rate which is the fraction of the investigated cases when the moon survived around the planet for the full integration time (which is the age of the star, or if not known, then the age of the Sun).The most important factor determining the long term survival of an exomoon is the orbital period of the planet. For the majority of the close-in planets (<10 days orbital periods) there is no stable orbit for moons. Between 10 and 300 days we find a transition in survival rate from about zero to 70\%. Our results give a possible explanation to the lack of successful exomoon discoveries for close-in planets. Tidal instability causes moons to escape or being tidally disrupted around close-in planets which are mostly favoured by current detection techniques.

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arXiv2021

Tidal pull of the Earth strips the proto-Moon of its volatiles

Prevailing models for the formation of the Moon invoke a giant impact between a planetary embryo and the proto-Earth \citep{Canup_2004, Cuk_Stewart_2012}. Despite similarities in the isotopic and chemical abundances of refractory elements compared to Earth's mantle, the Moon is depleted in volatiles \citep{Wolf_Anders_1980}. Current models favour devolatilisation via incomplete condensation of the proto-Moon in an Earth-Moon debris-disk \citep{Charnoz_Michaut_2015,Canup_2015,Lock_2018}. However the physics of this protolunar disk is poorly understood and thermal escape of gas is inhibited by the Earth's strong gravitational field \citep{Nakajima_Stevenson_2014}. Here we investigate a simple process, wherein the Earth's tidal pull promotes intense hydrodynamic escape from the liquid surface of a molten proto-Moon assembling at 3-6 Earth radii. Such tidally-driven atmospheric escape persisting for less than 1 Kyr at temperatures $\sim 1600-1700$ K reproduces the measured lunar depletion in K and Na.

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arXiv2021

A transit survey to search for planets around hot subdwarfs: I. methods and performance tests on light curves from Kepler, K2, TESS, and CHEOPS

Context. Hot subdwarfs experienced strong mass loss on the Red Giant Branch (RGB) and are now hot and small He-burning objects. Aims. In this project we aim to perform a transit survey in all available light curves of hot subdwarfs from space-based telescopes (Kepler, K2, TESS, and CHEOPS), with our custom-made pipeline SHERLOCK, in order to determine the occurrence rate of planets around these stars, as a function of orbital period and planetary radius. Methods. In this first paper, we perform injection-and-recovery tests of synthetic transits for a selection of representative Kepler, K2 and TESS light curves, to determine which transiting bodies, in terms of object radius and orbital period, we will be able to detect with our tools. We also provide such estimates for CHEOPS data, which we analyze with the pycheops package. Results. Transiting objects with a radius $\lesssim$ 1.0 $R_{\Earth}$ can be detected in most of Kepler, K2 and CHEOPS targets for the shortest orbital periods (1 d and below), reaching values as small as $\sim$0.3 $R_{\Earth}$ in the best cases. Reaching sub-Earth-sized bodies is achieved only for the brightest TESS targets, and the ones observed during a significant number of sectors. We also give a series of representative results for farther and bigger planets, for which the performances strongly depend on the target magnitude, the length and the quality of the data. Conclusions. The TESS sample will provide the most important statistics for the global aim of measuring the planet occurrence rate around hot subdwarfs. The Kepler, K2 and CHEOPS data will allow us to search for planetary remnants, i.e. very close and small (possibly disintegrating) objects, which would have partly survived the engulfment in their red giant host.

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arXiv2021

CHEOPS observations of the HD 108236 planetary system: A fifth planet, improved ephemerides, and planetary radii

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

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arXiv2021

Six transiting planets and a chain of Laplace resonances in TOI-178

Determining the architecture of multi-planetary systems is one of the cornerstones of understanding planet formation and evolution. Resonant systems are especially important as the fragility of their orbital configuration ensures that no significant scattering or collisional event has taken place since the earliest formation phase when the parent protoplanetary disc was still present. In this context, TOI-178 has been the subject of particular attention since the first TESS observations hinted at a 2:3:3 resonant chain. Here we report the results of observations from CHEOPS, ESPRESSO, NGTS, and SPECULOOS with the aim of deciphering the peculiar orbital architecture of the system. We show that TOI-178 harbours at least six planets in the super-Earth to mini-Neptune regimes, with radii ranging from 1.152(-0.070/+0.073) to 2.87(-0.13/+0.14) Earth radii and periods of 1.91, 3.24, 6.56, 9.96, 15.23, and 20.71 days. All planets but the innermost one form a 2:4:6:9:12 chain of Laplace resonances, and the planetary densities show important variations from planet to planet, jumping from 1.02(+0.28/-0.23) to 0.177(+0.055/-0.061) times the Earth's density between planets c and d. Using Bayesian interior structure retrieval models, we show that the amount of gas in the planets does not vary in a monotonous way, contrary to what one would expect from simple formation and evolution models and unlike other known systems in a chain of Laplace resonances. The brightness of TOI-178 allows for a precise characterisation of its orbital architecture as well as of the physical nature of the six presently known transiting planets it harbours. The peculiar orbital configuration and the diversity in average density among the planets in the system will enable the study of interior planetary structures and atmospheric evolution, providing important clues on the formation of super-Earths and mini-Neptunes.

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arXiv2020

The hot dayside and asymmetric transit of WASP-189b seen by CHEOPS

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

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arXiv2020

Can planetary rings explain the extremely low density of HIP 41378f?

The presence of rings around a transiting planet can cause its radius to be overestimated and lead to an underestimation of its density if the mass is known. We employ a Bayesian framework to show that the anomalously low density ($\sim$0.09 g cm${^{-3}}$) of the transiting long-period planet HIP$\,$41378$\,f$ might be due to the presence of opaque circum-planetary rings. Given our adopted model priors and data from the K2 mission, we find the statistical evidence for the ringed planet scenario to be comparable to that of the planet-only scenario. The ringed planet solution suggests a larger planetary density of $\sim$1.23$\,$g$\,$cm$^{-3}$ similar to Uranus. The associated ring extends from 1.05 to 2.59 times the planetary radius and is inclined away from the sky-plane by $\sim$25$^\mathrm{o}$. Future high-precision transit observations of HIP$\,$41378$\,f$ would be necessary to confirm/dismiss the presence of planetary rings.

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arXiv2017

Scientific rationale for Uranus and Neptune in situ explorations

The ice giants Uranus and Neptune are the least understood class of planets in our solar system but the most frequently observed type of exoplanets. Presumed to have a small rocky core, a deep interior comprising ~70% heavy elements surrounded by a more dilute outer envelope of H2 and He, Uranus and Neptune are fundamentally different from the better-explored gas giants Jupiter and Saturn. Because of the lack of dedicated exploration missions, our knowledge of the composition and atmospheric processes of these distant worlds is primarily derived from remote sensing from Earth-based observatories and space telescopes. As a result, Uranus's and Neptune's physical and atmospheric properties remain poorly constrained and their roles in the evolution of the Solar System not well understood. Exploration of an ice giant system is therefore a high-priority science objective as these systems (including the magnetosphere, satellites, rings, atmosphere, and interior) challenge our understanding of planetary formation and evolution. Here we describe the main scientific goals to be addressed by a future in situ exploration of an ice giant. An atmospheric entry probe targeting the 10-bar level, about 5 scale heights beneath the tropopause, would yield insight into two broad themes: i) the formation history of the ice giants and, in a broader extent, that of the Solar System, and ii) the processes at play in planetary atmospheres. The probe would descend under parachute to measure composition, structure, and dynamics, with data returned to Earth using a Carrier Relay Spacecraft as a relay station. In addition, possible mission concepts and partnerships are presented, and a strawman ice-giant probe payload is described. An ice-giant atmospheric probe could represent a significant ESA contribution to a future NASA ice-giant flagship mission.

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arXiv2017

The Origin of Planetary Ring Systems

This chapter of the book Planetary Ring Systems addresses the origin of planetary rings, one of the least understood processes related to planet formation and evolution. Whereas rings seem ubiquitous around giant planets, their great diversity of mass, structure and composition is a challenge for any formation scenario. Recent advances in our understanding of ring and satellite formation and destruction suggest that these processes are interconnected, so that rings and satellites may be two aspects of the same geological system. However, no single theory seems able to explain the origin of the different planetary rings known in our Solar System, and it now seems evident that rings may result from a variety of processes like giant collisions, tidal stripping of comets or satellites, as well as planet formation itself. In order to build any theory of ring formation it is important to specify physical processes that affect the long-term evolution of rings, as well as to describe the different observations that any ring formation model should explain. This is the topic of section 2. In section 3, we focus our attention on Saturn's rings and their main properties, and then discuss the pros and cons of a series of ring formation models. We also discuss the link between rings and satellites. In section 4, we extend the discussion to the other giant planets (Jupiter, Uranus, and Neptune). Section 5 is devoted to new types of rings -- the recent discovery of rings orbiting small outer Solar System bodies (Centaurs), and the possible rings around extrasolar planets. In section 6, we conclude and try to identify critical observations and theoretical advances needed to better understand the origin of rings and their significance in the global evolution of planets.

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arXiv2015

Growth of calcium-aluminum-rich inclusions by coagulation and fragmentation in a turbulent protoplanetary disk: observations and modelisation

Whereas it is generally accepted that calcium-aluminum-rich inclusions (CAIs) from chondritic meteorites formed in a hot environment in the solar protoplanetary disk, the conditions of their formation remain debated. Recent laboratory studies of CAIs have provided new kind of data: their size distributions. We show that size distributions of CAIs measured in laboratory from sections of carbonaceous chondrites have a power law size distribution with cumulative size exponent between -1.7 and -1.9, which translates into cumulative size exponent between -2.5 and -2.8 after correction for sectioning. To explain these observations, numerical simulations were run to explore the growth of CAIs from micrometer to centimeter sizes, in a hot and turbulent protoplanetary disk through the competition of coagulation and fragmentation. We show that the size distributions obtained in growth simulations are in agreement with CAIs size distributions in meteorites. We explain the CAI sharp cut-off of their size distribution at centimeter sizes as the direct result from the famous fragmentation barrier, provided that CAI fragment for impact velocities larger than 10 m/s. The growth/destruction timescales of millimeter- and centimeter-sized CAIs is inversely proportional to the local dust/gas ratio and is about 10 years at 1300 K and up to 104 years at 1670K. This implies that the most refractory CAIs are expected to be smaller in size owing to their long growth timescale compared to less refractory CAIs. Conversely, the least refractory CAIs could have been recycled many times during the CAI production era which may have profound consequences for their radiometric age.

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arXiv2013

LIDT-DD: A new self-consistent debris disc model including radiation pressure and coupling dynamical and collisional evolution

The first attempt at developing a fully self-consistent code coupling dynamics and collisions to study debris discs (Kral, Thebault, Charnoz, 2013) is presented. So far, these two crucial mechanisms were studied separately, with N-body and statistical collisional codes respectively, because of stringent computational constraints. In particular, incorporating collisional effects (especially destructive collisions) into an N-body scheme was deemed an impossible task because of the exponential increase of particles it would imply. We present here a new model named LIDT-DD which is able to follow over long timescales the coupled evolution of dynamics (including radiation pressure) and collisions in a self-consistent way.

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