arXiv subjects

Willy Benz

Publications and source records attributed to Willy Benz.

70 records · Page 4Linked to original sources

arXiv2005

New Jupiter and Saturn formation models meet observations

The wealth of observational data about Jupiter and Saturn provides strong constraints to guide our understanding of the formation of giant planets. The size of the core and the total amount of heavy elements in the envelope have been derived from internal structure studies by Saumon & Guillot (2004). The atmospheric abundance of some volatile elements has been measured {\it in situ} by the {\it Galileo} probe (Mahaffy et al. 2000, Wong et al. 2004) or by remote sensing (Briggs & Sackett 1989, Kerola et al. 1997). In this Letter, we show that, by extending the standard core accretion formation scenario of giant planets by Pollack et al. (1996) to include migration and protoplanetary disk evolution, it is possible to account for all of these constraints in a self-consistent manner.

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arXiv2005

On the volatile enrichments and composition of Jupiter

Using the clathrate hydrates trapping theory, we discuss the enrichments in volatiles in the atmosphere of Jupiter measured by the \textit{Galileo} probe in the framework of new extended core-accretion planet formation models including migration and disk evolution. We construct a self-consistent model in which the volatile content of planetesimals accreted during the formation of Jupiter is calculated from the thermodynamical evolution of the disk. Assuming CO2:CO:CH4 = 30:10:1 (ratios compatible with ISM measurements), we show that we can explain the enrichments in volatiles in a way compatible with the recent constraints set from internal structure modeling on the total amount of heavy elements present in the planet.

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arXiv2004

Models of Giant Planet formation with migration and disc evolution

We present a new model of giant planet formation that extends the core-accretion model of Pollack etal (1996) to include migration, disc evolution and gap formation. We show that taking into account these effects can lead to a much more rapid formation of giant planets, making it compatible with the typical disc lifetimes inferred from observations of young circumstellar discs. This speed up is due to the fact that migration prevents the severe depletion of the feeding zone as observed in in situ calculations. Hence, the growing planet is never isolated and it can reach cross-over mass on a much shorter timescale. To illustrate the range of planets that can form in our model, we describe a set of simulations in which we have varied some of the initial parameters and compare the final masses and semi-major axes with those inferred from observed extra-solar planets.

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arXiv2003

On the Early Evolution of Forming Jovian Planets I: Initial Conditions, Systematics and Qualitative Comparisons to Theory

(abridged) We analyze the formation and migration of a proto-Jovian companion in a circumstellar disk in 2d, during the period in which the companion makes its transition from `Type I' to `Type II' migration, using a PPM code. Spiral waves are generated by the gravitational torque of the planet on the disk. Their effects are to cause the planet to migrate inward and the disk to form a deep (low surface density) gap. Until a transition to slower Type II migration, the migration rate of the planet is of order 1 AU/10$^3$ yr, and varies by less than a factor of two with a factor twenty change in planet mass, but depends near linearly on the disk mass. Although the disk is stable to self gravitating perturbations (Toomre $Q>5$ everywhere), migration is faster by a factor of two or more when self gravity is suppressed. Migration is equally sensitive to the disk's mass distribution within 1--2 Hill radii of the planet, as demonstrated by our simulations' sensitivity to the planet's assumed gravitational softening parameter. Rapid migration can continue after gap formation. Gaps are typically several AU in width and display the \mplan$^{2/3}$ proportionality predicted by theory. Beginning from an initially unperturbed 0.05\msun disk, planets of mass $M_{\rm pl}> 0.3$\mj can open a gap deep and wide enough to complete the transition to slower \ttwo migration. Lower mass objects continue to migrate rapidly, eventually impacting the inner boundary of our grid. This transition mass is much larger than that predicted as the `Shiva mass' discussed in Ward and Hahn (2000), making the survival of forming planets even more precarious than they would predict.

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arXiv2003

On the Early Evolution of Forming Jovian Planets II: Analysis of Accretion and Gravitational Torques

(abridged) We find that a disk can supply a forming planet with mass at an essentially infinite rate ($\sim1$\mj/25 yr) so that a gap could form very quickly. We show that mass accretion rates faster than $\sim10^{-4}$\mj/yr are not physically reasonable in the limit of either a thin, circumplanetary disk or of a spherical envelope. Planet growth and ultimately survival are therefore limited to the planet's ability to accept additional matter, not by the disk in which it resides. We find that common analytic torque approximations predict values that are a factor $\sim10$ larger than those obtained from the simulations. Accounting for the disk's vertical structure (crudely modeled through a gravitational softening parameter), small shifts in resonance positions due to pressure gradients, to disk self gravity and to inclusion of non-WKB terms in the analysis (Artymowicz 1993) reduce the difference to a factor $\sim3-6$. Torques from the corotation resonances that are positive in sign contribute 20-30% or more of the net torque on the planet. The assumption of linearity underlying theoretical analyses is recovered in the simulations with planets with masses below 0.5\mj, but the assumption that interactions occur only at the resonances is more difficult to support. The detailed shape of the disk's response varies from pattern to pattern, making its true position less clear. We speculate that the finite width allows for overlap and mixing between resonances and may be responsible for the remainder of the differences between torques from theory and simulation, but whether accounting for such overlap in a theory will improve the agreement with the simulations is not clear.

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arXiv2002

Orbital migration and the frequency of giant planet formation

We present a statistical study of the post-formation migration of giant planets in a range of initial disk conditions. For given initial conditions we model the evolution of giant planet orbits under the influence of disk, stellar, and mass loss torques. We determine the mass and semi-major axis distribution of surviving planets after disk dissipation, for various disk masses, lifetimes, viscosities, and initial planet masses. The majority of planets migrate too fast and are destroyed via mass transfer onto the central star. Most surviving planets have relatively large orbital semi-major axes of several AU or larger. We conclude that the extrasolar planets observed to date, particularly those with small semi-major axes, represent only a small fraction (~25% to 33%) of a larger cohort of giant planets around solar-type stars, and many undetected giant planets must exist at large (>1-2 AU) distances from their parent stars. As sensitivity and completion of the observed sample increases with time, this distant majority population of giant planets should be revealed. We find that the current distribution of extrasolar giant planet masses implies that high mass (more than 1-2 Jupiter masses) giant planet formation must be relatively rare. Finally, our simulations imply that the efficiency of giant planet formation must be high: at least 10% and perhaps as many as 80% of solar-type stars possess giant planets during their pre-main sequence phase. These predictions, including those for pre-main sequence stars, are testable with the next generation of ground- and space-based planet detection techniques

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arXiv2002

A new Monte Carlo code for star cluster simulations: II. Central black hole and stellar collisions

We have recently written a new code to simulate the long term evolution of spherical clusters of stars. It is based on the pioneering Monte Carlo scheme proposed by Henon in the 70's. Our code has been devised in the specific goal to treat dense galactic nuclei. After having described how we treat relaxation in a first paper, we go on and include further physical ingredients that are mostly pertinent to galactic nuclei, namely the presence of a central (growing) black hole (BH) and collisions between MS stars. Stars that venture too close to the BH are destroyed by the tidal field. This process is a channel to feed the BH and a way to produce accretion flares. Collisions between stars have often been proposed as another mechanism to drive stellar matter into the central BH. To get the best handle on the role of this process in galactic nuclei, we include it with unpreceded realism through the use of a set of more than 10000 collision simulations carried out with a SPH (Smoothed Particle Hydrodynamics) code. Stellar evolution has also been introduced in a simple way, similar to what has been done in previous dynamical simulations of galactic nuclei. To ensure that this physics is correctly simulated, we realized a variety of tests whose results are reported here. This unique code, featuring most important physical processes, allows million particle simulations, spanning a Hubble time, in a few CPU days on standard personal computers and provides a wealth of data only rivalized by N-body simulations.

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arXiv2001

A new Monte Carlo code for star cluster simulations: I. Relaxation

We have developed a new simulation code aimed at studying the stellar dynamics of a galactic central star cluster surrounding a massive black hole. In order to include all the relevant physical ingredients (2-body relaxation, stellar mass spectrum, collisions, tidal disruption,...), we chose to revive a numerical scheme pioneered by Henon in the 70's. It is basically a Monte Carlo resolution of the Fokker-Planck equation. It can cope with any stellar mass spectrum or velocity distribution. Being a particle-based method, it also allows one to take stellar collisions into account in a very realistic way. This first paper covers the basic version of our code which treats the relaxation-driven evolution of stellar cluster without a central BH. A technical description of the code is presented, as well as the results of test computations. Thanks to the use of a binary tree to store potential and rank information and of variable time steps, cluster models with up to 2 million particles can be simulated on a standard personal computer and the CPU time required scales as N*ln(N) with the particle number N. Furthermore, the number of simulated stars needs not be equal to N but can be arbitrarily larger. A companion paper will treat further physical ingredients, mostly relevant to galactic nuclei.

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arXiv2001

Monte Carlo Simulations of Dense Galactic Nuclei

We have developed a new numerical code to simulate the joint evolution of a massive black hole (MBH) and a surrounding stellar cluster at the center of a galaxy. The physics treated in the simulations include: 2-body relaxation, stellar collisions (using a large set of "SPH" hydrodynamical simulations) and tidal disruption of stars by the MBH. In particular, we investigate the rates of star disruptive events that provide the MBH with gas to accrete.

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arXiv2001

A Monte Carlo Code to Investigate Stellar Collisions in Dense Galactic Nuclei

Stellar collisions have long been envisioned to be of great importance in the center of galaxies where densities of 1e6 stars per cubic pc or higher are attained. Not only can they play a unique dynamical role by modifying stellar masses and orbits, but high velocity disruptive encounters occurring in the vicinity of a massive black hole can also be an occasional source of fuel for the starved central engine. In the past few years, we have been building a comprehensive table of SPH (Smoothed Particle Hydrodynamics) collision simulations for main sequence stars. This database is now integrated as a module into our Henon-like Monte Carlo code. The combination of SPH collision simulations with a Monte Carlo cluster evolution code seems ideally suited to study the frequency, characteristics and effects of stellar collisions during the long term evolution of galactic nuclei.

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arXiv1999

Towards Understanding Jovian Planet Migration

We present 2D hydrodynamic simulations of circumstellar disks around protostars using a `Piecewise Parabolic Method' (PPM) code. We include a point mass embedded within the disk and follow the migration of that point mass through the disk. Companions with masses $M_c\ga 0.5M_J$ can open a gap in the disk sufficient to halt rapid migration through the disk. Lower mass companions open gaps, but migration continues because sufficient disk mass remains close to the disk to exert large tidal torques. We find that the torques which dominate the migration of low mass planets originate within a radial region within 1-2 Hill radii of the planet's orbit radius, a distance smaller than the thickness of the disk. We conclude that a very high resolution 3D treatment will be required to adequately describe the planet's migration.

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arXiv1999

Dynamics of Circumstellar Disks II: Heating and Cooling

We present a series of 2-d ($r,ϕ$) hydrodynamic simulations of marginally self gravitating disks around protostars using an SPH code. We implement simple dynamical heating and we cool each location as a black body, using a photosphere temperature obtained from the local vertical structure. We synthesize SEDs from our simulations and compare them to fiducial SEDs derived from observed systems. These simulations produce less distinct spiral structure than isothermally evolved systems, especially in the inner third of the disk. Pattern are similar further from the star but do not collapse into condensed objects. The photosphere temperature is well fit to a power law in radius with index $q\sim1.1$, which is very steep. Far from the star, internal heating ($PdV$ work and shocks) are not responsible for generating a large fraction of the thermal energy contained in the disk matter. Gravitational torques responsible for such shocks cannot transport mass and angular momentum efficiently in the outer disk. Within $\sim$5--10 AU of the star, rapid break up and reformation of spiral structure causes shocks, which provide sufficient dissipation to power a larger fraction of the near IR energy output. The spatial and size distribution of grains can have marked consequences on the observed near IR SED and can lead to increased emission and variability on $\lesssim 10$ year time scales. When grains are vaporized they do not reform into a size distribution similar to that from which most opacity calculations are based. With rapid grain reformation into the original size distribution, the disk does not emit near infrared photons. With a plausible modification to the opacity, it contributes much more.

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arXiv1998

Dynamics of Circumstellar Disks

We present a series of 2-dimensional hydrodynamic simulations of massive disks around protostars. We simulate the same physical problem using both a `Piecewise Parabolic Method' (PPM) code and a `Smoothed Particle Hydrodynamic' (SPH) code, and analyze their differences. The disks studied here range in mass from $0.05 M_*$ to $1.0 M_*$ and in initial minimum Toomre $Q$ value from 1.1 to 3.0. For this problem, the strengths of the codes overlap only in a limited fashion, but similarities exist in their predictions, including spiral arm pattern speeds and morphological features. Our results represent limiting cases (i.e. systems evolved isothermally) rather than true physical systems. Disks become active from the inner regions outward. From the earliest times, their evolution is a strongly dynamic process rather than a smooth progression toward eventual nonlinear behavior. We calculate approximate growth rates for the spiral patterns; the one-armed ($m=1$) spiral arm is not the fastest growing pattern of most disks. In our SPH simulations, disks with initial minimum $Q=1.5$ or lower break up into proto-binary or proto-planetary clumps. However, these simulations cannot follow the physics important for the flow and must be terminated before the system has completely evolved. At their termination, PPM simulations with similar initial conditions show uneven mass distributions within spiral arms, suggesting that clumping behavior might result if they were carried further. Concern that the point-like nature of SPH exaggerates clumping, that our representation of the gravitational potential in PPM is too coarse, and that our physics assumptions are too simple, suggest caution in interpretation of the clumping in both the disk and torus simulations.

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arXiv1997

Population Synthesis for Neutron Star Systems with Intrinsic Kicks

We use a Monte Carlo binary synthesis code to model the formation and evolution of neutron star systems including high-mass X-ray binaries, low-mass X-ray binaries, double neutron star systems and radio pulsars. Our focus is on the signature imprinted on such systems due to natal kicks to neutron stars over and above that imparted by orbital motions. The code incorporates the effect of the galactic potential (including rotation) on the velocities of these systems. A comparison between our models and the observations leads us to infer mean natal kicks between 400-500 km/s. Moreover, to be consistent with all the data, we require a bimodal kick distribution with one peak in the distribution near 0 km/s and the other above 600 km/s.

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arXiv1995

The Dynamics and Outcomes of Rapid Infall onto Neutron Stars

We present an extensive study of accretion onto neutron stars in which the velocity of the neutron star and structure of the surrounding medium is such that the Bondi-Hoyle accretion exceeds .001 Msun/y. For most cases, hypercritical accretion due to rapid neutrino cooling allows the neutron star to accrete above the Bondi-Hoyle rate as previously pointed out by Chevalier. However, for a subset of simulations which corresponds to evolutionarily common events, convection driven by neutrino heating can lead to explosions by a mechanism similar to that found in core-collapse supernovae. Armed with the results from our calculations, we are in a position to predict the fate of a range of rapid-infall neutron star accretors present in certain low-mass X-ray binaries, common envelope systems, supernova fallbacks and Thorne-Zytkow objects (TZOs). A majority of the common envelope systems that we considered led to explosions expelling the envelope, halting the neutron star's inward spiral, and allowing the formation of close binary systems. Smothered neutron stars produced in collisions also lead to explosions, preventing them from forming millisecond pulsars. For supernovae in which the fallback of material towards the neutron star is large, we find that a black hole is formed within a few seconds. Finally, we argue that the current set of TZO formation scenarios is inadequate and leads instead to hypercritical accretion and black hole formation. Moreover, it appears that many of the current TZ models have structures ill-suited for modeling by mixing length convection. This has prompted us to develop a simple test to determine the viability of this approximation for a variety of convective systems.

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arXiv1994

Inside the Supernova: A Powerful Convective Engine

Condensed Abstract: We present an extensive study of the inception of supernova explosions by following the evolution of the cores of two massive stars (15 Msun and 25 Msun) in two dimensions. Our calculations begin at the onset of core collapse and stop several 100 ms after the bounce, at which time successful explosions of the appropriate magnitude have been obtained. (...) Guided by our numerical results, we have developed a paradigm for the supernova explosion mechanism. We view a supernova as an open cycle thermodynamic engine in which a reservoir of low-entropy matter (the envelope) is thermally coupled and physically connected to a hot bath (the protoneutron star) by a neutrino flux, and by hydrodynamic instabilities. (...) In essence, a Carnot cycle is established in which convection allows out-of-equilibrium heat transfer mediated by neutrinos to drive low entropy matter to higher entropy and therefore extracts mechanical energy from the heat generated by gravitational collapse. We argue that supernova explosions are nearly guaranteed and self-regulated by the high efficiency of the thermodynamic engine. (...) Convection continues to accumulate energy exterior to the neutron star until a successful explosion has occurred. At this time, the envelope is expelled and therefore uncoupled from the heat source (the neutron star) and the energy input ceases. This paradigm does not invoke new or modified physics over previous treatments, but relies on compellingly straightforward thermodynamic arguments. It provides a robust and self-regulated explosion mechanism to power supernovae which is effective under a wide range of physical parameters.

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