arXiv subjects

M. Brož

Publications and source records attributed to M. Brož.

At least 37 records · Page 2Linked to original sources

arXiv2022

Towards a consistent model of the hot quadruple system HD 93206 = QZ Carinae - I. Observations and their initial analyses

The hot nine-component system HD 93206, which contains a gravitationally bounded eclipsing Ac1+Ac2 binary ($P=5.9987$~d) and a spectroscopic Aa1+Aa2 ($P=20.734$~d) binary can provide~important insights into the origin and evolution of massive stars. Using archival and new spectra, and a~rich collection of ground-based and space photometric observations, we carried out a detailed study of this object. We provide a much improved description of both short orbits and a good estimate of the mutual period of both binaries of about 14500~d (i.e. 40 years). For the first time, we detected weak lines of the fainter component of the 6.0~d eclipsing binary in the optical region of the spectrum, measured their radial velocities, and derived a mass ratio of $M_{\rm Ac2}/M_{\rm Ac1}=1.29$, which is the opposite of what was estimated from the International Ultraviolet explorer (IUE) spectra. We confirm that the eclipsing subsystem Ac is semi-detached and is therefore in a phase of large-scale mass transfer between its components. The Roche-lobe filling and spectroscopically brighter component Ac1 is the less massive of the two and is eclipsed in the secondary minimum. We show that the bulk of the \ha emission, so far believed to be associated with the eclipsing system, moves with the primary O9.7I component Aa1 of the 20.73~d spectroscopic binary. However, the weak emission in the higher Balmer lines seems to be associated with the accretion disc around component Ac2. We demonstrate that accurate masses and other basic physical properties including the distance of this unique system can be obtained but require a more sophisticated modelling. A~first step in this direction is presented in the accompanying Paper~II (Brož et al.).

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arXiv2021

Observed tidal evolution of Kleopatra's outer satellite

The orbit of the outer satellite Alexhelios of (216) Kleopatra is already constrained by adaptive-optics astrometry, obtained with the VLT/SPHERE instrument. However, there is also a preceding occultation event in 1980 attributed to this satellite. Hereinafter, we try to link all observations, spanning 1980--2018. We find the nominal orbit exhibits an unexplained shift by $+60^\circ$ in the true longitude. Using both periodogram analysis and an $\ell = 10$ multipole model suitable for the motion of mutually interacting moons about the irregular body, we confirmed that it is not possible to adjust the respective osculating period $P_2$. Instead, we were forced to use a model with tidal dissipation (and increasing orbital periods) to explain the shift. We also analyzed light curves, spanning 1977--2021, and searched for the expected spin deceleration of Kleopatra. According to our best-fit model, the observed period rate is $\dot P_2 = (1.8\pm 0.1)\cdot 10^{-8}\,{\rm d}\,{\rm d}^{-1}$ and the corresponding time lag $Δt_2 = 42\,{\rm s}$ of tides, for the assumed value of the Love number $k_2 = 0.3$. It is the first detection of tidal evolution for moons orbiting 100-km asteroids. The corresponding dissipation factor $Q$ is comparable with other terrestrial bodies, albeit at a higher loading frequency $2|ω-n|$. We also predict a secular evolution of the inner moon, $\dot P_1 = 5.0\cdot 10^{-8}$, as well as a spin deceleration of Kleopatra, $\dot P_0 = 1.9\cdot 10^{-12}$. In alternative models, with moons captured in the 3:2 mean-motion resonance or more massive moons, the respective values of $Δt_2$ are a factor of 2--3 lower. Future astrometric observations by direct imaging or occultations should allow to distinguish between these models, which is important for the internal structure and mechanical properties of (216) Kleopatra.

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arXiv2021

Terrestrial planet formation by torque-driven convergent migration of planetary embryos

Massive cores of the giant planets are thought to have formed in a gas disk by accretion of pebble-size particles whose accretional cross-section is enhanced by aerodynamic gas drag [1][2]. A commonly held view is that the terrestrial planet system formed later (30-200 Myr after the dispersal of the gas disk) by giant collisions of tens of roughly Mars-size protoplanets [3]. Here we propose, instead, that the terrestrial planets formed earlier by gas-driven convergent migration of protoplanets toward $\sim\!1\,{\rm au}$ (related ref. [4] invoked a different process to concentrate planetesimals). To investigate situations in which convergent migration occurs, we developed a radiation-hydrodynamic model with realistic opacities [5][6] to determine the thermal structure of the gas and pebble disks in the terrestrial planet zone. We find that protoplanets rapidly grow by mutual collisions and pebble accretion, and gain orbital eccentricities by gravitational scattering and the hot-trail effect [7][8]. The orbital structure of the terrestrial planet system is well reproduced in our simulations, including its tight mass concentration at 0.7-1 au and the small sizes of Mercury and Mars. The early-stage protosolar disk temperature exceeds 1500 K inside 0.4 au implying that Mercury grew in a highly reducing environment, next to the evaporation lines of iron and silicates, influencing Mercury's bulk composition [9]. In a late-stage cold gas disk, accretion of icy/hydrated pebbles would contribute to Earth's water budget.

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arXiv2021

(216) Kleopatra, a low density critically rotating M-type asteroid

Context. The recent estimates of the 3D shape of the M/Xe-type triple asteroid system (216) Kleopatra indicated a density of 5 g.cm$^{-3}$. Such a high density implies a high metal content and a low porosity which is not easy to reconcile with its peculiar dumbbell shape. Aims. Given the unprecedented angular resolution of the VLT/SPHERE/ZIMPOL camera, we aim to constrain the mass and the shape of Kleopatra with high accuracy, hence its density. Methods. We combined our new VLT/SPHERE observations of Kleopatra recorded in 2017 and 2018 with archival data, as well as lightcurve, occultation, and delay-Doppler images, to derive its 3D shape model using two different algorithms (ADAM, MPCD). Furthermore, an N-body dynamical model allowed us to retrieve the orbital elements of the two moons as explained in the accompanying paper. Results. The shape of Kleopatra is very close to an equilibrium dumbbell figure with two lobes and a thick neck. Its volume equivalent diameter (118.75$\pm$1.40) km and mass (2.97$\pm$0.32) 10$^{18}$ kg imply a bulk density of (3.38$\pm$0.50) g cm$^{-3}$. Such a low density for a supposedly metal-rich body indicates a substantial porosity within the primary. This porous structure along with its near-equilibrium shape is compatible with a formation scenario including a giant impact followed by reaccumulation. Kleopatra's current rotation period and dumbbell shape imply that it is in a critically rotating state. The low effective gravity along the equator of the body, together with the equatorial orbits of the moons and possibly rubble-pile structure, opens the possibility that the moons formed via mass shedding. Conclusions. Kleopatra is a puzzling multiple system due to the unique characteristics of the primary. It deserves particular attention in the future, with the Extremely Large Telescopes and possibly a dedicated space mission.

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arXiv2021

An advanced multipole model for (216) Kleopatra triple system

To interpret adaptive-optics observations of (216) Kleopatra, we need to describe an evolution of multiple moons, orbiting an extremely irregular body and including their mutual interactions. Such orbits are generally non-Keplerian and orbital elements are not constants. Consequently, we use a modified $N$-body integrator, which was significantly extended to include the multipole expansion of the gravitational field up to the order $\ell = 10$. Its convergence was verified against the `brute-force' algorithm. We computed the coefficients $C_{\ell m},S_{\!\ell m}$ for Kleopatra's shape, assuming a~constant bulk density. For solar-system applications, it was also necessary to implement a variable distance and geometry of observations. Our $χ^2$ metric then accounts for the absolute astrometry, the relative astrometry (2nd moon with respect to 1st), angular velocities, and also silhouettes, constraining the pole orientation. This allowed us to derive the orbital elements of Kleopatra's two moons. Using both archival astrometric data and new VLT/SPHERE observations (ESO LP 199.C-0074), we were able to identify the true periods of the moons, $P_1 = (1.822359\pm0.004156)\,{\rm d}$, $P_2 = (2.745820\pm0.004820)\,{\rm d}$. They orbit very close to the 3:2 mean-motion resonance, but their osculating eccentricities are too small compared to other perturbations (multipole, mutual), so that regular librations of the critical argument are not present. The resulting mass of Kleopatra, $m_1 = (1.49\pm0.16)\cdot10^{-12}\,M_\odot$ or $2.97\cdot10^{18}\,{\rm kg}$, is significantly lower than previously thought. An implication explained in the accompanying paper (Marchis et al.) is that (216) Kleopatra is a critically rotating body.

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arXiv2020

Optically thin circumstellar medium in $β$ Lyr A system

beta Lyr A is a complex binary system with an extensive observational dataset: light curves (from FUV to FIR), interferometric squared visibility, closure phase, triple product measurements, spectral-energy distribution (SED), high-resolution spectroscopy, differential visibility amplitude, and also differential phase. In particular, we use spectra from Ondrejov 2m telescope from 2013 to 2015, to measure the emission in Halpha, HeI, SiII, NeI, or CII lines, and differential interferometry by CHARA/VEGA from the 2013 campaign to measure wavelength-dependent sizes across Halpha and HeI 6678. This allows us to constrain not only optically thick objects (primary, secondary, accretion disk), but also optically thin objects (disk atmosphere, jets, shell). We extended our modelling tool Pyshellspec (based on Shellspec; a 1D LTE radiative transfer code) to include all new observables, to compute differential visibilities/phases, to perform a Doppler tomography, and to determine a joint chi^2 metric. After an optimisation of 38 free parameters, we derive a robust model of the beta Lyr A system. According to the model, the emission is formed in an extended atmosphere of the disk, two perpendicular jets expanding at ~700 km s^-1, and a symmetric shell with the radius ~70 R_S. The spectroscopy indicates a low abundance of carbon, 10^-2 of the solar value. We also quantify systematic differences between datasets and discuss alternative models, with higher resolution, additional asymmetries, or He-rich abundance.

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arXiv2019

Impacts into rotating targets: angular momentum draining and efficient formation of synthetic families

About 10% of the observed asteroids have rotational periods lower than P = 3 h and they seem to be relatively close to the spin barrier. Yet, the rotation has often been neglected in simulations of asteroid collisions. To determine the effect of rotation, we perform a large number of SPH/N-body impact simulations with rotating targets. We developed a new unified SPH/N-body code with self-gravity, suitable for simulations of both fragmentation phase and gravitational reaccumulation. The code has been verified against previous ones (Benz and Asphaug 1994), but we also tested new features, e.g. rotational stability, tensile stability, etc. Using the new code, we ran simulations with D_pb = 10 km and 100 km monolithic targets and compared synthetic asteroid families created by these impacts with families corresponding to non-rotating targets. The rotation affects mostly cratering events at oblique impact angles. The total mass ejected by these collision can be up to five times larger for rotating targets. We further compute the transfer of the angular momentum and determine conditions under which impacts accelerate or decelerate the target. While individual cratering collisions can cause both acceleration and deceleration, the deceleration prevails on average, collisions thus cause a systematic spin-down of asteroid population.

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arXiv2019

Properties and nature of Be stars 31. The binary nature, light variability, physical elements, and emission-line changes of HD~81357

Reliable determination of the basic physical properties of hot emission-line binaries with Roche-lobe filling secondaries is important for developing the theory of mass exchange in binaries. It is not easy, however, due to the presence of circumstellar matter. Here, we report the first detailed investigation of a new representative of this class of binaries, HD~81357, based on the analysis of spectra and photometry from several observatories. HD~81357 was found to be a double-lined spectroscopic binary and an ellipsoidal variable seen under an intermediate orbital inclination of $\sim(63\pm5)^\circ$, having an orbital period of 33\fd77445(41) and a~circular orbit. From an automated comparison of the observed and synthetic spectra, we estimate the component's effective temperatures to be 12930(540)~K and 4260(24)~K. The combined light-curve and orbital solutions, also constrained by a very accurate Gaia Data Release 2 parallax, give the following values of the basic physical properties: masses $3.36\pm0.15$ and $0.34\pm0.04$~\Mnom, radii $3.9\pm0.2$ and 13.97\pm0.05$~\Rnom, and a~mass ratio $10.0\pm0.5$. Evolutionary modelling of the system including the phase of mass transfer between the components indicated that HD~81357 is a~system observed in the final slow phase of the mass exchange after the mass-ratio reversal. Contrary to what has been seen for similar binaries like AU~Mon, no cyclic light variations were found on a~time scale an~order of magnitude longer than the orbital period. 243,1 15%

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arXiv2019

The shape of (7) Iris as evidence of an ancient large impact?

Asteroid (7) Iris is an ideal target for disk-resolved imaging owing to its brightness (V$\sim$7-8) and large angular size of 0.33 arcsec during its apparitions. Iris is believed to belong to the category of large unfragmented asteroids that avoided internal differentiation, implying that its current shape and topography may record the first few 100 Myr of the solar system's collisional evolution. We recovered information about the shape and surface topography of Iris from disk-resolved VLT/SPHERE/ZIMPOL images acquired in the frame of our ESO large program. We used the All-Data Asteroid Modeling (ADAM) shape reconstruction algorithm to model the 3D shape of Iris, using optical disk-integrated data and disk-resolved images from SPHERE as inputs. We analyzed the SPHERE images to infer the asteroid's global shape and the morphology of its main craters. We present the volume-equivalent diameter D$_{\rm eq}$=214$\pm$5 km, and bulk density $ρ$=2.7$\pm$0.3 g cm$^{-3}$ of Iris. Its shape appears to be consistent with that of an oblate spheroid with a large equatorial excavation. We identified eight putative surface features 20--40 km in diameter detected at several epochs, which we interpret as impact craters. Craters on Iris have depth-to-diameter ratios that are similar to those of analogous 10 km craters on Vesta. The bulk density of Iris is consistent with that of its meteoritic analog, namely LL ordinary chondrites. Considering the absence of a collisional family related to Iris and the number of large craters on its surface, we suggest that its equatorial depression may be the remnant of an ancient (at least 3 Gyr) impact. Iris's shape further opens the possibility that large planetesimals formed as almost perfect oblate spheroids. Finally, we attribute the difference in crater morphology between Iris and Vesta to their different surface gravities.

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arXiv2018

SPH/N-body simulations of small (D = 10 km) asteroidal breakups and improved parametric relations for Monte-Carlo collisional models

We report on our study of asteroidal breakups, i.e. fragmentations of targets, subsequent gravitational reaccumulation and formation of small asteroid families. We focused on parent bodies with diameters $D_{\rm pb} = 10$ km. Simulations were performed with a smoothed-particle hydrodynamics (SPH) code combined with an efficient N-body integrator. We assumed various projectile sizes, impact velocities and impact angles (125 runs in total). Resulting size-frequency distributions are significantly different from scaled-down simulations with $D_{\rm pb} = 100$ km targets (Durda et al., 2007). We derive new parametric relations describing fragment distributions, suitable for Monte-Carlo collisional models. We also characterize velocity fields and angular distributions of fragments, which can be used as initial conditions for N-body simulations of small asteroid families. Finally, we discuss a number of uncertainties related to SPH simulations.

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arXiv2017

Improved model of the triple system V746 Cas that has a bipolar magnetic field associated with the tertiary

V746 Cas is known to be a triple system composed of a close binary with an alternatively reported period of either 25.4d or 27.8d and a third component in a 62000d orbit. The object was also reported to exhibit multiperiodic light variations with periods from 0.83d to 2.50d, on the basis of which it was classified as a slowly pulsating B star. Interest in further investigation of this system was raised by the detection of a variable magnetic field. Analysing spectra from four instruments, earlier published radial velocities, and several sets of photometric observations, we arrived at the following conclusions: (1) The optical spectrum is dominated by the lines of the B-type primary (Teff1~16500(100) K), contributing 70% of the light in the optical region, and a slightly cooler B tertiary (Teff3~13620(150) K). The lines of the low-mass secondary are below our detection threshold; we estimate that it could be a normal A or F star. (2) We resolved the ambiguity in the value of the inner binary period and arrived at a linear ephemeris of T_super.conj.=HJD 2443838.78(81)+25.41569(42)xE. (3) The intensity of the magnetic field undergoes a~sinusoidal variation in phase with one of the known photometric periods, namely 2.503867(19)d, which we identify with the rotational period of the tertiary. (4) The second photometric 1.0649524(40)d period is identified with the rotational period of the B-type primary, but this interpretation is much less certain and needs further verification. (5) If our interpretation of photometric periods is confirmed, the classification of the object as a slowly pulsating B star should be revised. (6) Applying an N-body model to different types of available observational data, we constrain the orbital inclination of the inner orbit to ~60 deg to 85 deg even in the absence of eclipses, and estimate the probable properties of the triple system and its components.

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arXiv2017

An advanced N-body model for interacting multiple stellar systems

We construct an advanced model for interacting multiple stellar systems in which we compute all trajectories with a numerical N-body integrator, namely the Bulirsch--Stoer from the SWIFT package. We can then derive various observables: astrometric positions, radial velocities, minima timings (TTVs), eclipse durations, interferometric visibilities, closure phases, synthetic spectra, spectral-energy distribution, and even complete light curves. We use a modified version of the Wilson--Devinney code for the latter, in which the instantaneous true phase and inclination of the eclipsing binary are governed by the N-body integration. If one has all kinds of observations at disposal, a joint $χ^2$ metric and an optimisation algorithm (a~simplex or simulated annealing) allows to search for a global minimum and construct very robust models of stellar systems. At the same time, our N-body model is free from artefacts which may arise if mutual gravitational interactions among all components are not self-consistently accounted for. Finally, we present a number of examples showing dynamical effects that can be studied with our code and we discuss how systematic errors may affect the results (and how to prevent this from happening).

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arXiv2015

The origin of long-lived asteroids in the 2:1 mean-motion resonance with Jupiter

The 2:1 mean-motion resonance with Jupiter harbours two distinct groups of asteroids. The short-lived population is known to be a transient group sustained in steady state by the Yarkovsky semimajor axis drift. The long-lived asteroids, however, can exhibit dynamical lifetimes comparable to $4\,\mathrm{Gyr}$. They reside near two isolated islands of the phase space denoted $\mathrm{A}$ and $\mathrm{B}$, with an uneven population ratio $\mathrm{B}/\mathrm{A} \simeq 10$. The orbits of $\mathrm{A}$-island asteroids are predominantly highly inclined, compared to island $\mathrm{B}$. The size-frequency distribution is steep but the orbital distribution lacks any evidence of a collisional cluster. These observational constraints are somewhat puzzling and therefore the origin of the long-lived asteroids has not been explained so far. With the aim to provide a viable explanation, we first update the resonant population and revisit its physical properties. Using an $N$-body model with seven planets and the Yarkovsky effect included, we demonstrate that the dynamical depletion of island $\mathrm{A}$ is faster, in comparison with island $\mathrm{B}$. Then we investigate (i) the survivability of primordial resonant asteroids and (ii) capture of the population during planetary migration, following a recently described scenario with an escaping fifth giant planet and a jumping-Jupiter instability. We also model the collisional evolution of the resonant population over past $4\,\mathrm{Gyr}$. Our conclusion is that the long-lived group was created by resonant capture from a narrow part of hypothetical outer main-belt family during planetary migration. Primordial asteroids surviving the migration were probably not numerous enough to substantially contribute to the observed population.

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arXiv2015

The thermal emission from boulders on (25143) Itokawa and general implications for the YORP effect

Infrared radiation emitted from an asteroid surface causes a torque that can significantly affect rotational state of the asteroid. The influence of small topographic features on this phenomenon, called the YORP effect, seems to be of utmost importance. In this work, we show that a lateral heat diffusion in boulders of suitable sizes leads to an emergence of a local YORP effect which magnitude is comparable to the YORP effect due to the global shape. We solve a three-dimensional heat diffusion equation in a boulder and its surroundings by the finite element method, using the FreeFem++ code. The contribution to the total torque is inferred from the computed temperature distribution. Our general approach allows us to compute the torque induced by a realistic irregular boulder. For an idealized boulder, our result is consistent with an existing one-dimensional model. We also estimated (and extrapolated) a size distribution of boulders on (25143) Itokawa from close-up images of its surface. We realized that topographic features on Itokawa can potentially induce a torque corresponding to a rotational acceleration of the order 10^-7 rad day^-2 and can therefore explain the observed phase shift in light curves.

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arXiv2013

An anisotropic distribution of spin vectors in asteroid families

Current amount of ~500 asteroid models derived from the disk-integrated photometry by the lightcurve inversion method allows us to study not only the spin-vector properties of the whole population of MBAs, but also of several individual collisional families. We create a data set of 152 asteroids that were identified by the HCM method as members of ten collisional families, among them are 31 newly derived unique models and 24 new models with well-constrained pole-ecliptic latitudes of the spin axes. The remaining models are adopted from the DAMIT database or the literature. We revise the preliminary family membership identification by the HCM method according to several additional criteria - taxonomic type, color, albedo, maximum Yarkovsky semi-major axis drift and the consistency with the size-frequency distribution of each family, and consequently we remove interlopers. We then present the spin-vector distributions for eight asteroidal families. We use a combined orbital- and spin-evolution model to explain the observed spin-vector properties of objects among collisional families. In general, we observe for studied families similar trends in the (a_p, β) space: (i) larger asteroids are situated in the proximity of the center of the family; (ii) asteroids with β>0° are usually found to the right from the family center; (iii) on the other hand, asteroids with β<0° to the left from the center; (iv) majority of asteroids have large pole-ecliptic latitudes (|β|\gtrsim 30°); and finally (v) some families have a statistically significant excess of asteroids with β>0° or β<0°. Our numerical simulation of the long-term evolution of a collisional family is capable of reproducing well the observed spin-vector properties. Using this simulation, we also independently constrain the age of families Flora (1.0\pm0.5 Gyr) and Koronis (2.5-4 Gyr).

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arXiv2013

Asteroids' physical models from combined dense and sparse photometry and scaling of the YORP effect by the observed obliquity distribution

The larger number of models of asteroid shapes and their rotational states derived by the lightcurve inversion give us better insight into both the nature of individual objects and the whole asteroid population. With a larger statistical sample we can study the physical properties of asteroid populations, such as main-belt asteroids or individual asteroid families, in more detail. Shape models can also be used in combination with other types of observational data (IR, adaptive optics images, stellar occultations), e.g., to determine sizes and thermal properties. We use all available photometric data of asteroids to derive their physical models by the lightcurve inversion method and compare the observed pole latitude distributions of all asteroids with known convex shape models with the simulated pole latitude distributions. We used classical dense photometric lightcurves from several sources and sparse-in-time photometry from the U.S. Naval Observatory in Flagstaff, Catalina Sky Survey, and La Palma surveys (IAU codes 689, 703, 950) in the lightcurve inversion method to determine asteroid convex models and their rotational states. We also extended a simple dynamical model for the spin evolution of asteroids used in our previous paper. We present 119 new asteroid models derived from combined dense and sparse-in-time photometry. We discuss the reliability of asteroid shape models derived only from Catalina Sky Survey data (IAU code 703) and present 20 such models. By using different values for a scaling parameter cYORP (corresponds to the magnitude of the YORP momentum) in the dynamical model for the spin evolution and by comparing synthetics and observed pole-latitude distributions, we were able to constrain the typical values of the cYORP parameter as between 0.05 and 0.6.

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arXiv2013

Constraining the cometary flux through the asteroid belt during the late heavy bombardment

In the Nice model, the late heavy bombardment (LHB) is related to an orbital instability of giant planets which causes a fast dynamical dispersion of a transneptunian cometary disk. We study effects produced by these hypothetical cometary projectiles on main-belt asteroids. In particular, we want to check whether the observed collisional families provide a lower or an upper limit for the cometary flux during the LHB. We present an updated list of observed asteroid families as identified in the space of synthetic proper elements by the hierarchical clustering method, colour data, albedo data and dynamical considerations and we estimate their physical parameters. We selected 12 families which may be related to the LHB according to their dynamical ages. We then used collisional models and N-body orbital simulations to gain insight into the long-term dynamical evolution of synthetic LHB families over 4 Gyr. We account for the mutual collisions, the physical disruptions of comets, the Yarkovsky/YORP drift, chaotic diffusion, or possible perturbations by the giant-planet migration. Assuming a "standard" size-frequency distribution of primordial comets, we predict the number of families with parent-body sizes D_PB >= 200 km which seems consistent with observations. However, more than 100 asteroid families with D_PB >= 100 km should be created at the same time which are not observed. This discrepancy can be nevertheless explained by the following processes: i) asteroid families are efficiently destroyed by comminution (via collisional cascade), ii) disruptions of comets below some critical perihelion distance (q <~ 1.5 AU) are common. Given the freedom in the cometary-disruption law, we cannot provide stringent limits on the cometary flux, but we can conclude that the observed distribution of asteroid families does not contradict with a cometary LHB.

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arXiv2011

Did the Hilda collisional family form during the late heavy bombardment?

We model the long-term evolution of the Hilda collisional family located in the 3/2 mean-motion resonance with Jupiter. Its eccentricity distribution evolves mostly due to the Yarkovsky/YORP effect and assuming that: (i) impact disruption was isotropic, and (ii) albedo distribution of small asteroids is the same as for large ones, we can estimate the age of the Hilda family to be $4_{-1}^{+0}\,{\rm Gyr}$. We also calculate collisional activity in the J3/2 region. Our results indicate that current collisional rates are very low for a 200\,km parent body such that the number of expected events over Gyrs is much smaller than one. The large age and the low probability of the collisional disruption lead us to the conclusion that the Hilda family might have been created during the Late Heavy Bombardment when the collisions were much more frequent. The Hilda family may thus serve as a test of orbital behavior of planets during the LHB. We tested the influence of the giant-planet migration on the distribution of the family members. The scenarios that are consistent with the observed Hilda family are those with fast migration time scales $\simeq 0.3\,{\rm Myr}$ to $3\,{\rm Myr}$, because longer time scales produce a family that is depleted and too much spread in eccentricity. Moreover, there is an indication that Jupiter and Saturn were no longer in a compact configuration (with period ratio $P_{\rm S}/P_{\rm J} > 2.09$) at the time when the Hilda family was created.

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