We have performed the largest ever particle simulation of a Milky Way-sized dark matter halo, and present the most comprehensive convergence study for an individual dark matter halo carried out thus far. We have also simulated a sample of 6 ultra-highly resolved Milky-way sized halos, allowing us to estimate the halo-to-halo scatter in substructure statistics. In our largest simulation, we resolve nearly 300,000 gravitationally bound subhalos within the virialized region of the halo. Simulations of the same object differing in mass resolution by factors up to 1800 accurately reproduce the largest subhalos with the same mass, maximum circular velocity and position, and yield good convergence for the abundance and internal properties of dark matter substructures. We detect up to four generations of subhalos within subhalos, but contrary to recent claims, we find less substructure in subhalos than in the main halo when regions of equal mean overdensity are compared. The overall substructure mass fraction is much lower in subhalos than in the main halo. Extrapolating the main halo's subhalo mass spectrum down to an Earth mass, we predict the mass fraction in substructure to be well below 3% within 100 kpc, and to be below 0.1% within the Solar Circle. The inner density profiles of subhalos show no sign of converging to a fixed asymptotic slope and are well fit by gently curving profiles of Einasto form. The mean concentrations of isolated halos are accurately described by the fitting formula of Neto et al. down to maximum circular velocities of 1.5 km/s, an extrapolation over some 5 orders of magnitude in mass. However, at equal maximum circular velocity, subhalos are more concentrated than field halos, with a characteristic density that is typically ~2.6 times larger and increases towards the halo centre.
We use a large cosmological simulation and a variety of high resolution resimulations of individual cluster and galaxy haloes to study the systematics of subhalo populations over ranges of 1000 in halo mass and 1000 in the ratio of subhalo to parent halo mass. The subhalo populations of different haloes are not scaled copies of each other, but vary systematically with halo properties. On average, the amount of substructure increases with halo mass. At fixed mass, it decreases with halo concentration and with halo formation redshift. These trends are comparable in size to the scatter in subhalo…
We analyzed the statistics of subhalo abundance of galaxy-sized and giant-galaxy-sized halos formed in a high-resolution cosmological simulation of a 46.5Mpc cube with the uniform mass resolution of $10^6 M_{\odot}$. We analyzed all halos with mass more than $1.5 \times 10^{12}M_{\odot}$ formed in this simulation box. The total number of halos was 125. We found that the subhalo abundance, measured by the number of subhalos with maximum rotation velocity larger than 10% of that of the parent halo, shows large halo-to-halo variations. The results of recent ultra-high-resolution runs fall within …
Using a high-resolution cosmological $N$-body simulation, we identify the ejected population of subhalos, which are halos at redshift $z=0$ but were once contained in more massive `host' halos at high redshifts. The fraction of the ejected subhalos in the total halo population of the same mass ranges from 9% to 4% for halo masses from $\sim 10^{11}$ to $\sim 10^{12}\msun$. Most of the ejected subhalos are distributed within 4 times the virial radius of their hosts. These ejected subhalos have distinct velocity distribution around their hosts in comparison to normal halos. The number of subhalo…
Recent high-resolution simulations of the formation of dark-matter halos have shown that the distribution of subhalos is scale-free, in the sense that if scaled by the velocity dispersion of the parent halo, the velocity distribution function of galaxy-sized and cluster-sized halos are identical. For cluster-sized halos, simulation results agreed well with observations. Simulations, however, predicted far too many subhalos for galaxy-sized halos. Our galaxy has several tens of known dwarf galaxies. On the other hands, simulated dark-matter halos contain thousands of subhalos. We have performed…
We present a study of the shapes, orientations, and alignments of Galactic dark matter subhalos in the ``Via Lactea'' simulation of a Milky Way-size LCDM host halo. Whereas isolated dark matter halos tend to be prolate, subhalos are predominantly triaxial. Overall subhalos are more spherical than the host halo, with minor to major and intermediate to major axis ratios of 0.68 and 0.83, respectively. Like isolated halos, subhalos tend to be less spherical in their central regions. The principal axis ratios are independent of subhalo mass, when the shapes are measured within a physical scale lik…
(Abridged) We present a semi-analytic model for Cold Dark Matter halo substructure that can be used as a framework for studying galaxy formation and an ingredient in halo models of galaxy clustering. We perform a comprehensive comparison of the model to the results of a suite of high-resolution cosmological simulations. The comparisons reveal that subhalo statistics, such as velocity and mass functions, radial distributions, and the halo occupation distributions, agree well over three orders of magnitude in host halo mass at various redshifts. Both in the simulations and in our model, the radi…
High-resolution simulations of cosmological structure formation indicate that dark matter substructure in dense environments, like groups and clusters, may survive for a long time. These dark matter subhalos are the likely hosts of galaxies. We examine the small-scale spatial clustering of subhalo major mergers at high redshift using high-resolution N-body simulations of cosmological volumes. Recently merged, massive subhalos exhibit enhanced clustering on scales ~100-300 kpc/h, relative to all subhalos of the same infall mass, for a short time after a major merger (< 500 Myr). The small-scale…
We use the Millennium Simulation, a large, high resolution N-body simulation of the evolution of structure in a LambdaCDM cosmology, to study the properties and fate of substructures within a large sample of dark matter haloes. We find that the subhalo mass function departs significantly from a power law at the high mass end. We also find that the radial and angular distributions of substructures depend on subhalo mass. In particular, high mass subhaloes tend to be less radially concentrated and to have angular distributions closer to the direction perpendicular to the spin of the host halo th…
We present a halo model prediction of the image separation distribution of strong lenses. Our model takes account of the subhalo population, which has been ignored in previous studies, as well as the conventional halo population. Halos and subhalos are linked to central and satellite galaxies by adopting an universal scaling relation between masses of (sub-)halos and luminosities of galaxies. Our model predicts that 10%-20% of lenses should be caused by the subhalo population. The fraction of lensing by satellite galaxies (subhalos) peaks at ~1'' and decreases rapidly with increasing image sep…
[Abridged] The interaction rates of dark-matter halos and subhalos, are computed using high-resolution cosmological N-body simulations of the Lambda-CDM model. Although the number fraction of subhalos of mass $>2x10^{11}\hsolmass$ is only ~10%, we find that the interaction rate of such subhalos is relatively high because they reside in high density environments. At low redshift, the subhalo collisions dominate the total collision rate, and even at z=3 they are involved in more than 30% of all collisions. About 40% of the "major" mergers are between subhalos. Therefore subhalo interactions must…
If the concordance $Λ$CDM model is a true description of the universe, it should also properly predict the properties and structure of dark matter haloes, where galaxies are born. Using N-body simulations with a broad scale of mass and spatial resolution, we study the structure of dark matter haloes, the distribution of masses and the spatial distribution of subhaloes within the main haloes. We carry out three $Λ$CDM simulations with different resolutions using the AMIGA code. Dark matter haloes are identified using an algorithm that is based on the adaptive grid structure of the simulation co…
We present a new definition of subhalos in dissipationless dark matter N-body simulations, based on the coherent identification of their dynamically bound constituents. Whereas previous methods of determining the energetically bound components of a subhalo ignored the contribution of all the remaining particles in the halo (those not geometrically or dynamically associated with the subhalo), our method allows for all the forces, both internal and external, exerted on the subhalo. We demonstrate, using the output of a simulation at different timesteps, that our new method is more accurate at id…
We present a simple, semi-analytical model to compute the mass functions of dark matter subhaloes. The masses of subhaloes at their time of accretion are obtained from a standard merger tree. During the subsequent evolution, the subhaloes experience mass loss due to the combined effect of dynamical friction, tidal stripping, and tidal heating. Rather than integrating these effects along individual subhalo orbits, we consider the average mass loss rate, where the average is taken over all possible orbital configurations. This allows us to write the average mass loss rate as a simple function th…
The hierarchical growth of dark matter haloes, in which galaxies are hosted, has been studied and modeled using various approaches. In this paper we use a modified version the Sheth & Lemson algorithm for a $\mathrmΛ$ cold dark matter power spectrum, and model the growth of a Milky-Way sized halo with microsolar mass resolution, corresponding to the typical Jeans mass for a dark matter Weakly Interacting Massive Particle with mass of 100 GeV. We then compute the \emph{unevolved} subhalo mass function and build-up a Milky-Way halo placing and evolving its satellites. This subhalo population is …
Galaxies are believed to be in one-to-one correspondence with simulated dark matter subhalos. We use high-resolution N-body simulations of cosmological volumes to calculate the statistical properties of subhalo (galaxy) major mergers at high redshift (z=0.6-5). We measure the evolution of the galaxy merger rate, finding that it is much shallower than the merger rate of dark matter host halos at z>2.5, but roughly parallels that of halos at z<1.6. We also track the detailed merger histories of individual galaxies and measure the likelihood of multiple mergers per halo or subhalo. We examine sat…
In the standard model of cosmic structure formation, dark matter haloes form by gravitational instability. The process is hierarchical: smaller systems collapse earlier, and later merge to form larger haloes. The galaxy clusters, hosted by the largest dark matter haloes, are at the top of this hierarchy representing the largest as well as the last structures formed in the universe, while the smaller and first haloes are those Earth-sized dark subhaloes which have been both predicted by theoretical considerations and found in numerical simulations, though it does not exist any observational hin…
(Abridged) We use cosmological N-body simulations to study the properties of substructure halos in galaxy-sized dark matter halos. We extend prior work on the subject by considering the whole population of subhalos physically associated with the main system. These are defined as subhalos that have at some time in the past been within the virial radius of the halo's main progenitor and that have survived as self-bound entities to $z=0$. We find that this population extends beyond {\it three times} the virial radius, and contains objects on extreme orbits. We trace the origin of these unorthodox…
I review recent results on the spatial distribution of substructure in CDM halos. I show that the spatial distribution of subhalos is anisotropic and generally prolate with a long axis that is closely aligned with the long axis of the total mass distribution of the host halo. I show that the correlation between the subhalo distribution and the long axis of the host halo is strong both in dissipationless and dissipational gasdynamical simulations. More massive subhalos tend to be more strongly clustered along the major axis of the host halo reflecting filamentary accretion. The anisotropy of su…
We present a theoretical formalism by which the global and the local mass functions of dark matter substructures (dark subhalos) can be analytically estimated. The global subhalo mass function is defined to give the total number density of dark subhalos in the universe as a function of mass, while the local subhalo mass function counts only those subhalos included in one individual host halo. We develop our formalism by modifying the Press-Schechter theory to incorporate the followings: (i) the internal structure of dark halos; (ii) the correlations between the halos and the subhalos; (iii) th…
We use cosmological LCDM numerical simulations to model the evolution of the substructure population in sixteen dark matter haloes with resolutions of up to seven million particles within the virial radius. The combined substructure circular velocity distribution function (VDF) for hosts of 10^11 to 10^14 Msun at redshifts from zero to two or higher has a self-similar shape, is independent of host halo mass and redshift, and follows the relation: dn/dv=(1/8)(v_cmax/v_cmax,host)^-4. Halo to halo variance in the VDF is a factor of roughly two to four. At high redshifts, we find preliminary evide…
We use high-resolution numerical simulations to study the physical properties of subhalos when they merge into their host halos. An improved algorithm is used to identify the subhalos. We then examine their spatial and velocity distributions in spherical and triaxial halo models. We find that the accretion of satellites preferentially occurs along the major axis and perpendicular to the spin axis of the host halo. Furthermore, the massive subhalos show a stronger preference to be accreted along the major axis of the host halo than the low-mass ones. Approximate fitting formulae are provided fo…
Using a cosmological N-Body simulation and a sample of re-simulated cluster-like haloes, we study the mass loss rates of dark matter subhaloes, and interpret the mass function of subhaloes at redshift zero in terms of the evolution of the mass function of systems accreted by the main halo progenitor. When expressed in terms of the ratio between the mass of the subhalo at the time of accretion and the present day host mass the unevolved subhalo mass function is found to be universal. However, the subhalo mass function at redshift zero clearly depends on $M_0$, in that more massive host haloes h…
(abridged) We present a detailed analysis of the properties of tidally stripped material from disrupting substructure haloes or subhaloes in a sample of high resolution cosmological N-body host haloes ranging from galaxy- to cluster-mass scales. We focus on devising methods to recover the infall mass and infall eccentricity of subhaloes from the properties of their tidally stripped material (i.e. tidal streams). Our analysis reveals that there is a relation between the scatter of stream particles about the best-fit debris plane and the infall mass of the progenitor subhalo. This allows us to r…
We discuss structural and kinematical properties of the stellar halo and the old globular cluster system (GCS) in the Large Magellanic Cloud (LMC) based on numerical simulations of the LMC formation. We particularly discuss the observed possible GCS's rotational kinematics (V/sigma > 2) that appears to be significantly different from the stellar halo's one with a large velocity dispersion (~50 km/s). We consider that both halo field stars and old GCs can originate from low-mass subhalos virialized at high redshifts (z >6). We investigate the final dynamical properties of the two old components…
We present a non-parametric, empirically based, model for associating galaxy luminosities with halo/subhalo masses, based on a self-consistent treatment of subhalo mass loss and the subhalo mass function. We find that, at high mass, the mass-luminosity relation is almost independent of the actual luminosity function considered, when luminosity is scaled by the characteristic luminosity L*. Additionally, the shape of the total halo luminosity depends on the slope of the subhalo mass function. For these high mass, cluster sized haloes, we find that total luminosity scales as L_tot ~ M^0.88, whil…
We explore the dependence of the radial alignment of subhalos on the mass of the host halo they orbit in. As the effect is seen on a broad range of scales including massive clusters as well as galactic systems it only appears natural to explore this phenomenon by means of cosmological simulations covering the same range in masses. We have 25 well resolved host dark matter halos at our disposal ranging from 10^15 Msun/h down to 10^12 Msun/h each consisting of order of a couple of million particles within the virial radius. We observe that subhalos tend to be more spherical than isolated objects…
We present a detailed analysis of the velocity distribution and orientation of orbits of subhaloes in high resolution cosmological simulations of dark matter haloes. We find a trend for substructure to preferentially revolve in the same direction as the sense of rotation of the host halo: there is an excess of prograde satellite haloes. Throughout our suite of nine host haloes (eight cluster sized objects and one galactic halo) there are on average 59% of the satellites corotating with the host. Even when including satellites out to five virial radii of the host, the signal still remains point…
Multiresolution analysis is applied to the problem of halo identification in cosmological N-body simulations. The procedure makes use of a discrete wavelet transform known as the algorithme a trous and segmentation analysis. It has the ability to find subhalos in the dense regions of a parent halo and can discern the multiple levels of substructure expected in the hierarchical clustering scenario. As an illustration, a 500,000 particle dark matter halo is analyzed and over 600 subhalos are found. Statistical properties of the subhalo population are discussed.
The hierarchical mergers that form the haloes of dark matter surrounding galaxies, groups and clusters are not entirely efficient, leaving substantial amounts of dense substructure, in the form of stripped halo cores or `subhaloes', orbiting within these systems. Using a semi-analytic model of satellite dynamics, we study the evolution of haloes as they merge hierarchically, to determine how much substructure survives merging and how the properties of individual subhaloes change over time. We find that subhaloes evolve, due to mass loss, orbital decay, and tidal disruption, on a characteristic…
We present a study of the spatial distribution of subhalos in galactic dark matter halos using dissipationless cosmological simulations of the concordance LCDM model. We find that subhalos are distributed anisotropically and are preferentially located along the major axes of the triaxial mass distributions of their hosts. The Kolmogorov-Smirnov probability for drawing our simulated subhalo sample from an isotropic distribution is P_KS \simeq 1.5 \times 10^{-4}. An isotropic distribution of subhalos is thus not the correct null hypothesis for testing the CDM paradigm. The nearly planar distribu…
We use large cosmological N-body simulations to study the subhalo population in galaxy group sized halos. In particular, we look for fossil group candidates with typical masses ~10-25% of Virgo cluster but with an order of magnitude less substructure. We examine recent claims that the earliest systems to form are deficient enough in substructure to explain the luminosity function found in fossil groups. Although our simulations show a correlation between the halo formation time and the number of subhalos, the maximum suppression of subhalos is a factor of 2-2.5, whereas a factor of 6 is requir…
By comparing a collisionless cosmological N-body simulation (DM) to an SPH simulation with the same initial conditions, we investigate the correspondence between the dark matter subhalos produced by collisionless dynamics and the galaxies produced by dissipative gas dynamics in a dark matter background. When galaxies in the SPH simulation become satellites in larger groups, they retain local dark matter concentrations (SPH subhalos) whose mass is typically five times their baryonic mass. The more massive subhalos of the SPH simulation have corresponding subhalos of similar mass and position in…
We investigated the formation and evolution of CDM subhalos in galaxy-sized and cluster-sized halos by means of N-body simulations. Our aim is to make clear what the ``dwarf galaxy problem'' is. It has been argued that the number of subhalos in simulated galaxy-sized halos is too large compared to the observed number of dwarfs in the local group, while that in cluster-sized halos is consistent with observed number of galaxies in clusters such as the Virgo cluster. We simulated nine halos with several different mass resolutions and physical scales. We found that the dependence of the cumulative…
We revisit the longstanding question of whether first brightest cluster galaxies are statistically drawn from the same distribution as other cluster galaxies or are "special", using the new non-parametric, empirically based model presented in Vale&Ostriker (2006) for associating galaxy luminosity with halo/subhalo masses. We introduce scatter in galaxy luminosity at fixed halo mass into this model, building a conditional luminosity function (CLF) by considering two possible models: a simple lognormal and a model based on the distribution of concentration in haloes of a given mass. We show that…
We study the structure of Milky Way (MW)- and cluster-sized halos in a Lambda Cold Dark Matter (CDM) cosmology with self-interacting (SI) dark particles. The cross section per unit of particle mass has the form sigma = sig_0(1/v_100)^alpha, where sig_0 is a constant in units of cm^2/gr and v_100 is the relative velocity in units of 100 km/s. Different values for sigma with alpha= 0 or 1 were used. For small values of sigma = const. (sig_0<0.5), the core density of the halos at z=0 is typically higher at a given mass for lower values of sig_0 or, at a given sig_0, for lower masses. For values o…
Much recent discussion about dark matter has been centered on two seemingly independent problems: the abundance of substructure in dark matter halos, and the cuspiness of the halos' inner density profile. We explore possible connections between the two problems by studying the gravitational scattering effects due to subhalos on the phase-space distribution of dark matter particles in the main halos. Our series of controlled numerical experiments indicates that the number and mass density of subhalos can be high enough to cause the collisionless dark matter particles in the inner part of a main…
