arXiv subjects

Joachim Stadel

Publications and source records attributed to Joachim Stadel.

At least 55 records · Page 3Linked to original sources

arXiv2016

Cold Dark Matter Substructures in Early-Type Galaxy Halos

We present initial results from the "Ponos" zoom-in numerical simulations of dark matter substructures in massive ellipticals. Two very highly resolved dark matter halos with $M_{\rm vir}=1.2\times 10^{13}$ $M_{\odot}$ and $M_{\rm vir}=6.5\times 10^{12}$ $M_{\odot}$ and different ("violent" vs. "quiescent") assembly histories have been simulated down to $z=0$ in a $Λ$CDM cosmology with a total of 921,651,914 and 408,377,544 particles, respectively. Within the virial radius, the total mass fraction in self-bound $M_{\rm sub}>10^6$ $M_{\odot}$ subhalos at the present epoch is 15% for the violent host and 16.5% for the quiescent one. At $z=0.7$, these fractions increase to 19 and 33%, respectively, as more recently accreted satellites are less prone to tidal destruction. In projection, the average fraction of surface mass density in substructure at a distance of $R/R_{\rm vir}=0.02$ ($\sim 5-10$ kpc) from the two halo centers ranges from 0.6% to $\gtrsim 2$%, significantly higher than measured in simulations of Milky Way-sized halos. The contribution of subhalos with $M_{\rm sub} < 10^9$ $M_{\odot}$ to the projected mass fraction is between one fifth and one third of the total, with the smallest share found in the quiescent host. We assess the impact of baryonic effects via twin, lower-resolution hydrodynamical simulations that include metallicity-dependent gas cooling, star formation, and a delayed-radiative-cooling scheme for supernova feedback. Baryonic contraction produces a super-isothermal total density profile and increases the number of massive subhalos in the inner regions of the main host. The host density profiles and projected subhalo mass fractions appear to be broadly consistent with observations of gravitational lenses.

astro-ph.GA↗

arXiv2016

Matter power spectrum and the challenge of percent accuracy

Future galaxy surveys require one percent precision in the theoretical knowledge of the power spectrum over a large range including very nonlinear scales. While this level of accuracy is easily obtained in the linear regime with perturbation theory, it represents a serious challenge for small scales where numerical simulations are required. In this paper we quantify the precision of present-day $N$-body methods, identifying main potential error sources from the set-up of initial conditions to the measurement of the final power spectrum. We directly compare three widely used $N$-body codes, Ramses, Pkdgrav3, and Gadget3 which represent three main discretisation techniques: the particle-mesh method, the tree method, and a hybrid combination of the two. For standard run parameters, the codes agree to within one percent at $k\leq1$ $h\,\rm Mpc^{-1}$ and to within three percent at $k\leq10$ $h\,\rm Mpc^{-1}$. We also consider the bispectrum and show that the reduced bispectra agree at the sub-percent level for $k\leq 2$ $h\,\rm Mpc^{-1}$. In a second step, we quantify potential errors due to initial conditions, box size, and resolution using an extended suite of simulations performed with our fastest code Pkdgrav3. We demonstrate that the simulation box size should not be smaller than $L=0.5$ $h^{-1}\rm Gpc$ to avoid systematic finite-volume effects (while much larger boxes are required to beat down the statistical sample variance). Furthermore, a maximum particle mass of $M_{\rm p}=10^{9}$ $h^{-1}\rm M_{\odot}$ is required to conservatively obtain one percent precision of the matter power spectrum. As a consequence, numerical simulations covering large survey volumes of upcoming missions such as DES, LSST, and Euclid will need more than a trillion particles to reproduce clustering properties at the targeted accuracy.

astro-ph.CO↗

arXiv2015

The same with less: The cosmic web of warm versus cold dark matter dwarf galaxies

We explore fundamental properties of the distribution of low mass dark matter halos within the cosmic web using warm dark matter (WDM) and cold dark matter (CDM) cosmological simulations. Using self abundance-matched mock galaxy catalogs, we show that the distribution of dwarf galaxies in a WDM universe, wherein low mass halo formation is heavily suppressed, is nearly indistinguishable to that of a CDM universe whose low mass halos are not seen because galaxy formation is suppressed below some threshold halo mass. However, if the scatter between dwarf galaxy luminosity and halo properties is large enough, low mass CDM halos would sometimes host relatively bright galaxies thereby populating CDM voids with the occasional isolated galaxy and reducing the numbers of completely empty voids. Otherwise, without high mass to light scatter, all mock galaxy clustering statistics that we consider--the auto-correlation function, the numbers and radial profiles of satellites, the numbers of isolated galaxies, and the PDF of small voids--are nearly identical in CDM and WDM. WDM voids are neither larger nor emptier than CDM voids, when constructed from abundance-matched halo catalogs. It is thus a challenge to determine whether the CDM problem of the over-abundance of small halos with respect to the number density of observed dwarf galaxies has a cosmological solution or an astrophysical solution. However, some clues about the dark matter particle and the scatter between the properties of dwarf galaxies and their dark matter halo hosts might be found in the cosmic web of galaxies in future surveys of the local volume.

astro-ph.CO↗

arXiv2013

Structure Finding in Cosmological Simulations: The State of Affairs

The ever increasing size and complexity of data coming from simulations of cosmic structure formation demands equally sophisticated tools for their analysis. During the past decade, the art of object finding in these simulations has hence developed into an important discipline itself. A multitude of codes based upon a huge variety of methods and techniques have been spawned yet the question remained as to whether or not they will provide the same (physical) information about the structures of interest. Here we summarize and extent previous work of the "halo finder comparison project": we investigate in detail the (possible) origin of any deviations across finders. To this extent we decipher and discuss differences in halo finding methods, clearly separating them from the disparity in definitions of halo properties. We observe that different codes not only find different numbers of objects leading to a scatter of up to 20 per cent in the halo mass and Vmax function, but also that the particulars of those objects that are identified by all finders differ. The strength of the variation, however, depends on the property studied, e.g. the scatter in position, bulk velocity, mass, and the peak value of the rotation curve is practically below a few per cent, whereas derived quantities such as spin and shape show larger deviations. Our study indicates that the prime contribution to differences in halo properties across codes stems from the distinct particle collection methods and -- to a minor extent -- the particular aspects of how the procedure for removing unbound particles is implemented. We close with a discussion of the relevance and implications of the scatter across different codes for other fields such as semi-analytical galaxy formation models, gravitational lensing, and observables in general.

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arXiv2013

Toward an accurate mass function for precision cosmology

Cosmological surveys aim to use the evolution of the abundance of galaxy clusters to accurately constrain the cosmological model. In the context of LCDM, we show that it is possible to achieve the required percent level accuracy in the halo mass function with gravity-only cosmological simulations, and we provide simulation start and run parameter guidelines for doing so. Some previous works have had sufficient statistical precision, but lacked robust verification of absolute accuracy. Convergence tests of the mass function with, for example, simulation start redshift can exhibit false convergence of the mass function due to counteracting errors, potentially misleading one to infer overly optimistic estimations of simulation accuracy. Percent level accuracy is possible if initial condition particle mapping uses second order Lagrangian Perturbation Theory, and if the start epoch is between 10 and 50 expansion factors before the epoch of halo formation of interest. The mass function for halos with fewer than ~1000 particles is highly sensitive to simulation parameters and start redshift, implying a practical minimum mass resolution limit due to mass discreteness. The narrow range in converged start redshift suggests that it is not presently possible for a single simulation to capture accurately the cluster mass function while also starting early enough to model accurately the numbers of reionisation era galaxies, whose baryon feedback processes may affect later cluster properties. Ultimately, to fully exploit current and future cosmological surveys will require accurate modeling of baryon physics and observable properties, a formidable challenge for which accurate gravity-only simulations are just an initial step.

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arXiv2011

How common are Earth-Moon planetary systems?

The Earth's comparatively massive moon, formed via a giant impact on the proto-Earth, has played an important role in the development of life on our planet, both in the history and strength of the ocean tides and in stabilizing the chaotic spin of our planet. Here we show that massive moons orbiting terrestrial planets are not rare. A large set of simulations by Morishima et al., 2010, where Earth-like planets in the habitable zone form, provides the raw simulation data for our study. We use limits on the collision parameters that may guarantee the formation of a circumplanetary disk after a protoplanet collision that could form a satellite and study the collision history and the long term evolution of the satellites qualitatively. In addition, we estimate and quantify the uncertainties in each step of our study. We find that giant impacts with the required energy and orbital parameters for producing a binary planetary system do occur with more than 1 in 12 terrestrial planets hosting a massive moon, with a low-end estimate of 1 in 45 and a high-end estimate of 1 in 4.

astro-ph.EP↗

arXiv2011

Haloes gone MAD: The Halo-Finder Comparison Project

[abridged] We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends-of-friends (FOF), spherical-overdensity (SO) and phase-space based algorithms. We further introduce a robust (and publicly available) suite of test scenarios that allows halo finder developers to compare the performance of their codes against those presented here. This set includes mock haloes containing various levels and distributions of substructure at a range of resolutions as well as a cosmological simulation of the large-scale structure of the universe. All the halo finding codes tested could successfully recover the spatial location of our mock haloes. They further returned lists of particles (potentially) belonging to the object that led to coinciding values for the maximum of the circular velocity profile and the radius where it is reached. All the finders based in configuration space struggled to recover substructure that was located close to the centre of the host halo and the radial dependence of the mass recovered varies from finder to finder. Those finders based in phase space could resolve central substructure although they found difficulties in accurately recovering its properties. Via a resolution study we found that most of the finders could not reliably recover substructure containing fewer than 30-40 particles. However, also here the phase space finders excelled by resolving substructure down to 10-20 particles. By comparing the halo finders using a high resolution cosmological volume we found that they agree remarkably well on fundamental properties of astrophysical significance (e.g. mass, position, velocity, and peak of the rotation curve).

astro-ph.CO↗

arXiv2010

Core creation in galaxies and haloes via sinking massive objects

We perform a detailed investigation into the disruption of central cusps via the transfer of energy from sinking massive objects. Constant density inner regions form at the radius where the enclosed mass approximately matches the mass of the infalling body. We explore parameter space using numerical simulations and give an empirical relation for the size of the resulting core within structures that have different initial cusp slopes. We find that infalling bodies always stall at the edge of these newly formed cores, experiencing no dynamical friction over many dynamical times. As applications, we consider the resulting decrease in the dark matter annihilation flux due to centrally destroyed cusps, and we present a new theory for the formation of close binary nuclei -- the `stalled binary' model. We focus on one particularly interesting binary nucleus system, the dwarf spheroidal galaxy VCC 128 which is dark matter dominated at all radii. We show that its nuclei would rapidly coalesce within a few million years if it has a central dark matter cusp slope steeper than r^{-1}. However, if its initial dark matter cusp is slightly shallower than a log slope of -0.75 at ~0.1% of the virial radius, then the sinking nuclei naturally create a core equal to their observed separation and stall. This is close to the log slope measured a recent billion particle CDM halo simulation.

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arXiv2010

From planetesimals to terrestrial planets: N-body simulations including the effects of nebular gas and giant planets

We present results from a suite of N-body simulations that follow the accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially place 2000 equal size planetesimals between 0.5--4.0 AU and the collisional growth is followed until the completion of planetary accretion (> 100 Myr). All the important effect of gas in laminar disks are taken into account: the aerodynamic gas drag, the disk-planet interaction including Type I migration, and the global disk potential which causes inward migration of secular resonances as the gas dissipates. We vary the initial total mass and spatial distribution of the planetesimals, the time scale of dissipation of nebular gas, and orbits of Jupiter and Saturn. We end up with one to five planets in the terrestrial region. In order to maintain sufficient mass in this region in the presence of Type I migration, the time scale of gas dissipation needs to be 1-2 Myr. The final configurations and collisional histories strongly depend on the orbital eccentricity of Jupiter. If today's eccentricity of Jupiter is used, then most of bodies in the asteroidal region are swept up within the terrestrial region owing to the inward migration of the secular resonance, and giant impacts between protoplanets occur most commonly around 10 Myr. If the orbital eccentricity of Jupiter is close to zero, as suggested in the Nice model, the effect of the secular resonance is negligible and a large amount of mass stays for a long period of time in the asteroidal region. With a circular orbit for Jupiter, giant impacts usually occur around 100 Myr, consistent with the accretion time scale indicated from isotope records. However, we inevitably have an Earth size planet at around 2 AU in this case. It is very difficult to obtain spatially concentrated terrestrial planets together with very late giant impacts.

astro-ph.EP↗

arXiv2008

Massive Black Hole Recoil in High Resolution Hosts

The final inspiral and coalescence of a black hole binary can produce highly beamed gravitational wave radiation. To conserve linear momentum, the black hole remnant can recoil with "kick" velocity as high as 4000 km/s. We present two sets of full N-body simulations of recoiling massive black holes (MBH) in high-resolution, non-axisymmetric potentials. The host to the first set of simulations is the main halo of the Via Lactea I simulation (Diemand et al. 2007). The nature of the resulting orbits is investigated through a numerical model where orbits are integrated assuming an evolving, triaxial NFW potential, and dynamical friction is calculated directly from the velocity dispersion along the major axes of the main halo of Via Lactea I. By comparing the triaxial case to a spherical model, we find that the wandering time spent by the MBH is significantly increased due to the asphericity of the halo. For kicks larger than 200 km/s, the remnant MBH does not return to the inner 200 pc within 1 Gyr, a timescale an order of magnitude larger than the upper limit of the estimated QSO lifetime. The second set of simulations is run using the outcome of a high-resolution gas-rich merger (Mayer et al. 2007) as host potential. In this case, a recoil velocity of 500 km/s cannot remove the MBH from the nuclear region.

astro-ph↗

arXiv2008

The Graininess of Dark Matter Haloes

We use the recently completed one billion particle Via Lactea II LambdaCDM simulation to investigate local properties like density, mean velocity, velocity dispersion, anisotropy, orientation and shape of the velocity dispersion ellipsoid, as well as structure in velocity space of dark matter haloes. We show that at the same radial distance from the halo centre, these properties can deviate by orders of magnitude from the canonical, spherically averaged values, a variation that can only be partly explained by triaxiality and the presence of subhaloes. The mass density appears smooth in the central relaxed regions but spans four orders of magnitude in the outskirts, both because of the presence of subhaloes as well as of underdense regions and holes in the matter distribution. In the inner regions the local velocity dispersion ellipsoid is aligned with the shape ellipsoid of the halo. This is not true in the outer parts where the orientation becomes more isotropic. The clumpy structure in local velocity space of the outer halo can not be well described by a smooth multivariate normal distribution. Via Lactea II also shows the presence of cold streams made visible by their high 6D phase space density. Generally, the structure of dark matter haloes shows a high degree of graininess in phase space that cannot be described by a smooth distribution function.

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arXiv2008

Quantifying the heart of darkness with GHALO - a multi-billion particle simulation of our galactic halo

We perform a series of simulations of a Galactic mass dark matter halo at different resolutions, our largest uses over three billion particles and has a mass resolution of 1000 M_sun. We quantify the structural properties of the inner dark matter distribution and study how they depend on numerical resolution. We can measure the density profile to a distance of 120 pc (0.05% of R_vir) where the logarithmic slope is -0.8 and -1.4 at (0.5% of R_vir). We propose a new two parameter fitting function that has a linearly varying logarithmic density gradient which fits the GHALO and VL2 density profiles extremely well. Convergence in the density profile and the halo shape scales as N^(-1/3), but the shape converges at a radius three times larger at which point the halo becomes more spherical due to numerical resolution. The six dimensional phase-space profile is dominated by the presence of the substructures and does not follow a power law, except in the smooth under-resolved inner few kpc.

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arXiv2008

Discreteness Effects in Lambda Cold Dark Matter Simulations: A Wavelet-Statistical View

The effects of particle discreteness in N-body simulations of Lambda Cold Dark Matter (LambdaCDM) are still an intensively debated issue. In this paper we explore such effects, taking into account the scatter caused by the randomness of the initial conditions, and focusing on the statistical properties of the cosmological density field. For this purpose, we run large sets of LambdaCDM simulations and analyse them using a large variety of diagnostics, including new and powerful wavelet statistics. Among other facts, we point out (1) that dynamical evolution does not propagate discreteness noise up from the small scales at which it is introduced, and (2) that one should aim to satisfy the condition epsilon ~ 2d, where "epsilon" is the force resolution and "d" is the interparticle distance. We clarify what such a condition means, and how to implement it in modern cosmological codes.

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arXiv2008

The Causes of Halo Shape Changes Induced by Cooling Baryons: Disks Versus Substructures

Cold dark matter cosmogony predicts triaxial dark matter halos, whereas observations find quite round halos. This is most likely due to the condensation of baryons leading to rounder halos. We examine the halo phase space distribution basis for such shape changes. Triaxial halos are supported by box orbits, which pass arbitrarily close to the density center. The decrease in triaxiality caused by baryons is thought to be due to the scattering of these orbits. We test this hypothesis with simulations of disks grown inside triaxial halos. After the disks are grown we check whether the phase space structure has changed by evaporating the disks and comparing the initial and final states. While the halos are substantially rounder when the disk is at full mass, their final shape after the disk is evaporated is not much different from the initial. Likewise, the halo becomes (more) radially anisotropic when the disk is grown, but the final anisotropy is consistent with the initial. Only if the baryons are unreasonably compact or massive does the halo change irreversibly. We show that the character of individual orbits is not generally changed by the growing mass. Thus the central condensation of baryons does not destroy enough box orbits to cause the shape change. Rather, box orbits merely become rounder along with the global potential. However, if angular momentum is transferred to the halo, either via satellites or via bars, a large irreversible change in the halo distribution occurs. The ability of satellites to alter the phase space distribution of the halo is of particular concern to galaxy formation simulations since halo triaxiality can profoundly influence the evolution of disks.

astro-ph↗

arXiv2008

Formation and accretion history of terrestrial planets from runaway growth through to late time: implications for orbital eccentricity

Remnant planetesimals might have played an important role in reducing the orbital eccentricities of the terrestrial planets after their formation via giant impacts. However, the population and the size distribution of remnant planetesimals during and after the giant impact stage are unknown, because simulations of planetary accretion in the runaway growth and giant impact stages have been conducted independently. Here we report results of direct N-body simulations of the formation of terrestrial planets beginning with a compact planetesimal disk. The initial planetesimal disk has a total mass and angular momentum as observed for the terrestrial planets, and we vary the width (0.3 and 0.5AU) and the number of planetesimals (1000-5000). This initial configuration generally gives rise to three final planets of similar size, and sometimes a fourth small planet forms near the location of Mars. Since a sufficient number of planetesimals remains, even after the giant impact phase, the final orbital eccentricities are as small as those of the Earth and Venus.

astro-ph↗

arXiv2008

An optimum time-stepping scheme for N-body simulations

We present a new time-stepping criterion for N-body simulations that is based on the true dynamical time of a particle. This allows us to follow the orbits of particles correctly in all environments since it has better adaptivity than previous time-stepping criteria used in N-body simulations. Furthermore, it requires far fewer force evaluations in low density regions of the simulation and has no dependence on artificial parameters such as, for example, the softening length. This can be orders of magnitude faster than conventional ad-hoc methods that employ combinations of acceleration and softening and is ideally suited for hard problems, such as obtaining the correct dynamics in the very central regions of dark matter haloes. We also derive an eccentricity correction for a general leapfrog integration scheme that can follow gravitational scattering events for orbits with eccentricity e -> 1 with high precision. These new approaches allow us to study a range of problems in collisionless and collisional dynamics from few body problems to cosmological structure formation. We present tests of the time-stepping scheme in N-body simulations of 2-body orbits with eccentricity e -> 1 (elliptic and hyperbolic), equilibrium haloes and a hierarchical cosmological structure formation run.

astro-ph↗

arXiv2008

Multimass spherical structure models for N-body simulations

We present a simple and efficient method to set up spherical structure models for N-body simulations with a multimass technique. This technique reduces by a substantial factor the computer run time needed in order to resolve a given scale as compared to single-mass models. It therefore allows to resolve smaller scales in N-body simulations for a given computer run time. Here, we present several models with an effective resolution of up to 1.68 x 10^9 particles within their virial radius which are stable over cosmologically relevant time-scales. As an application, we confirm the theoretical prediction by Dehnen (2005) that in mergers of collisonless structures like dark matter haloes always the cusp of the steepest progenitor is preserved. We model each merger progenitor with an effective number of particles of approximately 10^8 particles. We also find that in a core-core merger the central density approximately doubles whereas in the cusp-cusp case the central density only increases by approximately 50%. This may suggest that the central region of flat structures are better protected and get less energy input through the merger process.

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arXiv2008

Reply to Melott's Comment on ``Discreteness Effects in Lambda Cold Dark Matter Simulations: A Wavelet-Statistical View'' by Romeo et al

Melott has made pioneering studies of the effects of particle discreteness in N-body simulations, a fundamental point that needs careful thought and analysis since all such simulations suffer from numerical noise arising from the use of finite-mass particles. Melott (arXiv:0804.0589) claims that the conclusions of our paper (arXiv:0804.0294) are essentially equivalent to those of his earlier work. Melott is wrong: he has jumped onto one of our conclusions and interpreted that in his own way. Here we point out the whys and the wherefores.

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