Subhalo Mass Function Research Articles

NONLINEAR EVOLUTION OF DARK MATTER SUBHALOS AND APPLICATIONS TO WARM DARK MATTER

We describe the methodology to include nonlinear evolution, including tidal effects, in the computation of subhalo distribution properties in both cold (CDM) and warm (WDM) dark matter universes. Using semi-analytic modeling, we include effects from dynamical friction, tidal stripping, and tidal heating, allowing us to dynamically evolve the subhalo distribution. We calibrate our nonlinear evolution scheme to the CDM subhalo mass function in the Aquarius N-body simulation, producing a subhalo mass function within the range of simulations. We find tidal effects to be the dominant mechanism of nonlinear evolution in the subhalo population. Finally, we compute the subhalo mass function for $m_\chi=1.5$ keV WDM including the effects of nonlinear evolution, and compare radial number densities and mass density profiles of subhalos in CDM and WDM models. We show that all three signatures differ between the two dark matter models, suggesting that probes of substructure may be able to differentiate between them.

Detection of substructure with adaptive optics integral field spectroscopy of the gravitational lens B1422+231

Strong gravitational lenses can be used to detect low-mass subhaloes, based on deviations in image fluxes and positions from what can be achieved with a smooth mass distribution. So far, this method has been limited by the small number of (radio-loud, microlensing-free) systems which can be analysed for the presence of substructure. Using the gravitational lens B1422+231, we demonstrate that adaptive optics integral field spectroscopy can also be used to detect dark substructures. We analyse data obtained with OH Suppressing Infra-Red Imaging Spectrograph on the Keck i Telescope, using a Bayesian method that accounts for uncertainties relating to the point spread function and image positions in the separate exposures. The narrow-line [O iii] fluxes measured for the lensed images are consistent with those measured in the radio, and show a significant deviation from what would be expected in a smooth mass distribution, consistent with the presence of a perturbing low-mass halo. Detailed lens modelling shows that image fluxes and positions are fitted significantly better when the lens is modelled as a system containing a single perturbing subhalo in addition to the main halo, rather than by the main halo on its own, indicating the significant detection of substructure. The inferred mass of the subhalo depends on the subhalo mass density profile: the 68 per cent confidence intervals for the perturber mass within 600 pc are 8.2|$^{+0.6}_{-0.8}$|⁠, 8.2|$^{+0.6}_{-1}$| and 7.6 ± 0.3 log10[Msub/M⊙], respectively, for a singular isothermal sphere, a pseudo-Jaffe and a Navarro–Frenk–White mass profile. This method can extend the study of flux ratio anomalies to virtually all quadruply imaged quasars, and therefore offers great potential to improve the determination of the subhalo mass function in the near future.

THE EFFECTS OF VARYING COSMOLOGICAL PARAMETERS ON HALO SUBSTRUCTURE

We investigate how different cosmological parameters, such as those delivered by the WMAP and Planck missions, affect the nature and evolution of dark matter halo substructure. We use a series of flat $\Lambda$ cold dark matter ($\Lambda$CDM) cosmological $N$-body simulations of structure formation, each with a different power spectrum but the same initial white noise field. Our fiducial simulation is based on parameters from the WMAP 7th year cosmology. We then systematically vary the spectral index, $n_s$, matter density, $\Omega_M$, and normalization of the power spectrum, $\sigma_8$, for 7 unique simulations. Across these, we study variations in the subhalo mass function, mass fraction, maximum circular velocity function, spatial distribution, concentration, formation times, accretion times, and peak mass. We eliminate dependence of subhalo properties on host halo mass and average over many hosts to reduce variance. While the "same" subhalos from identical initial overdensity peaks in higher $\sigma_8, n_s$, and $\Omega_m$ simulations accrete earlier and end up less massive and closer to the halo center at $z=0$, the process of continuous subhalo accretion and destruction leads to a steady state distribution of these properties across all subhalos in a given host. This steady state mechanism eliminates cosmological dependence on all properties listed above except subhalo concentration and $V_{max}$, which remain greater for higher $\sigma_8, n_s$ and $\Omega_m$ simulations, and subhalo formation time, which remains earlier. We also find that the numerical technique for computing scale radius and the halo finder used can significantly affect the concentration-mass relationship computed for a simulation.

Generating merger trees for dark matter haloes: a comparison of methods

Halo merger trees describe the hierarchical mass assembly of dark matter haloes, and are the backbone for modeling galaxy formation and evolution. Merger trees constructed using Monte Carlo algorithms based on the extended Press-Schechter (EPS) formalism are complementary to those extracted from N-body simulations, and have the advantage that they are not trammeled by limited numerical resolution and uncertainties in identifying (sub)haloes and linking them between snapshots. This paper compares multiple EPS-based merger tree algorithms to simulation results using four diagnostics: progenitor mass function (PMF), mass assembly history (MAH), merger rate per descendant halo, and the unevolved subhalo mass function (USMF). In general, algorithms based on spherical collapse yield major-merger rates that are too high by a factor of two, resulting in MAHs that are systematically offset. Assuming ellipsoidal collapse solves most of these issues, but the particular algorithm investigated here that incorporates ellipsoidal collapse dramatically overpredicts the minor-merger rate for massive haloes. The only algorithm in our comparison that yields MAHs, merger rates, and USMFs in good agreement with simulations, is that by Parkinson et al. (2008). However, this is not a true EPS-based algorithm as it draws its progenitor masses from a PMF calibrated against simulations, rather than `predicted' by EPS. Finally we emphasize that the benchmarks used to test the EPS algorithms are obtained from simulations and are hampered by significant uncertainties themselves. In particular, MAHs and halo merger rates obtained from simulations by different authors reveal discrepancies that easily exceed 50 percent, even when based on the same simulation. Given this status quo, merger trees constructed using the Parkinson et al. algorithm are as accurate as those extracted from N-body simulations.

SUBARU WEAK-LENSING SURVEY OF DARK MATTER SUBHALOS IN THE COMA CLUSTER: SUBHALO MASS FUNCTION AND STATISTICAL PROPERTIES

We present a 4 deg^2 weak gravitational lensing survey of subhalos in the very nearby Coma cluster using the Subaru/Suprime-Cam. The large apparent size of cluster subhalos allows us to measure the mass of 32 subhalos detected in a model-independent manner, down to the order of 10^-3 of the virial mass of the cluster. Weak-lensing mass measurements of these shear-selected subhalos enable us to investigate subhalo properties and the correlation between subhalo masses and galaxy luminosities for the first time. The mean distortion profiles stacked over subhalos show a sharply truncated feature which is well-fitted by a Navarro-Frenk-White (NFW) mass model with the truncation radius, as expected due to tidal destruction by the main cluster. We also found that subhalo masses, truncation radii, and mass-to-light ratios decrease toward the cluster center. The subhalo mass function, dn/dln M_sub, in the range of 2 orders of magnitude in mass, is well described by a single power law or a Schechter function. Best-fit power indices of 1.09_-0.32^+0.42 for the former model and 0.99_-0.23^+0.34 for the latter, are in remarkable agreement with slopes of ~0.9-1.0 predicted by the cold dark matter paradigm. The tangential distortion signals in the radial range of 0.02-2Mpc/h from the cluster center show a complex structure which is well described by a composition of three mass components of subhalos, the NFW mass distribution as a smooth component of the main cluster, and a lensing model from a large scale structure behind the cluster. Although the lensing signals are 1 order of magnitude lower than those for clusters at z~0.2, the total signal-to-noise ratio, S/N=13.3, is comparable to, or higher, because the enormous number of background source galaxies compensates for the low lensing efficiency of the low lensing efficiency of the nearby cluster.

The properties of warm dark matter haloes

Well-motivated elementary particle candidates for the dark matter, such as the sterile neutrino, behave as warm dark matter (WDM).For particle masses of order a keV, free streaming produces a cutoff in the linear fluctuation power spectrum at a scale corresponding to dwarf galaxies. We investigate the abundance and structure of WDM haloes and subhaloes on these scales using high resolution cosmological N-body simulations of galactic haloes of mass similar to the Milky Way's. On scales larger than the free-streaming cutoff, the initial conditions have the same power spectrum and phases as one of the cold dark matter (CDM) haloes previously simulated by Springel et al as part of the Virgo consortium Aquarius project. We have simulated four haloes with WDM particle masses in the range 1.4-2.3keV and, for one case, we have carried out further simulations at varying resolution. N-body simulations in which the power spectrum cutoff is resolved are known to undergo artificial fragmentation in filaments producing spurious clumps which, for small masses (<10^7Msun in our case) outnumber genuine haloes. We have developed a robust algorithm to identify these spurious objects and remove them from our halo catalogues. We find that the WDM subhalo mass function is suppressed by well over an order magnitude relative to the CDM case for masses <10^9Msun. Requiring that there should be at least as many subhaloes as there are observed satellites in the Milky Way leads to a conservative lower limit to the (thermal equivalent) WDM particle mass of ~1.5\rmn{keV}. WDM haloes and subhaloes have cuspy density distributions that are well described by NFW or Einasto profiles. Their central densities are lower for lower WDM particle masses and none of the models we have considered suffer from the "too big to fail" problem recently highlighted by Boylan-Kolchin et al.

The bifurcated age–metallicity relation of Milky Way globular clusters and its implications for the accretion history of the galaxy

We use recently derived ages for 61 Milky Way (MW) globular clusters (GCs) to show that their age-metallicity relation (AMR) can be divided into two distinct, parallel sequences at [Fe/H] $\ga -1.8$. Approximately one-third of the clusters form an offset sequence that spans the full range in age ($\sim 10.5$--13 Gyr), but is more metal rich at a given age by $\sim 0.6$ dex in [Fe/H]. All but one of the clusters in the offset sequence show orbital properties that are consistent with membership in the MW disk. They are not simply the most metal-rich GCs, which have long been known to have disk-like kinematics, but they are the most metal-rich clusters at all ages. The slope of the mass-metallicity relation (MMR) for galaxies implies that the offset in metallicity of the two branches of the AMR corresponds to a mass decrement of 2 dex, suggesting host galaxy masses of $M_{*} \sim 10^{7-8} \msol$ for GCs that belong to the more metal-poor AMR. We suggest that the metal-rich branch of the AMR consists of clusters that formed in-situ in the disk, while the metal-poor GCs were formed in relatively low-mass (dwarf) galaxies and later accreted by the MW. The observed AMR of MW disk stars, and of the LMC, SMC and WLM dwarf galaxies are shown to be consistent with this interpretation, and the relative distribution of implied progenitor masses for the halo GC clusters is in excellent agreement with the MW subhalo mass function predicted by simulations. A notable implication of the bifurcated AMR, is that the identical mean ages and spread in ages, for the metal rich and metal poor GCs are difficult to reconcile with an in-situ formation for the latter population.

Density profiles of CDM microhalos and their implications for annihilation boost factors

In a standard cold dark matter (CDM) cosmology, microhalos at the CDM cutoff scale are the first and smallest objects expected to form in the universe. Here we present results of high resolution simulations of three representative roughly Earth-mass microhalos in order to determine their inner density profile. We find that CDM microhalos in simulations without a cutoff in the power spectrum roughly follow the NFW density profile, just like the much larger CDM halos on galaxy and galaxy cluster scales. But having a cutoff in the initial power spectrum at a typical neutralino free streaming scale of 10−7M⊙ makes their inner density profiles considerably steeper, i.e. ρ∝r−(1.3−1.4), in good agreement with the results from Ishiyama et al. (2010). An extrapolation of the halo and subhalo mass functions down to the cutoff scale indicates that microhalos are extremely abundant throughout the present day dark matter distribution and might contribute significantly to indirect dark matter detection signals. Assuming a transition from a NFW to a steeper inner profile (ρ∝r−1.4) two orders of magnitude above the cutoff scale, the total boost factor for a Milky Way sized dark matter halo increases from about 3.5 to 4. We further find that CDM microhalo concentrations are consistent with the Bullock et al. (2001) model and clearly rule out simplistic power law models for the mass dependence of concentrations and subhalo annihilation, which would erroneously lead to very large boost factors (a few hundred for galaxy halos and over 1000 for clusters).

Subhaloes in self-interacting galactic dark matter haloes

We present N-body simulations of a new class of self-interacting dark matter models, which do not violate any astrophysical constraints due to a non-power-law velocity dependence of the transfer cross section which is motivated by a Yukawa-like new gauge boson interaction. Specifically, we focus on the formation of a Milky Way-like dark matter halo taken from the Aquarius project and re-simulate it for a couple of representative cases in the allowed parameter space of this new model. We find that for these cases, the main halo only develops a small core (~1 kpc) followed by a density profile identical to that of the standard cold dark matter scenario outside of that radius. Neither the subhalo mass function nor the radial number density of subhaloes are altered in these models but there is a significant change in the inner density structure of subhaloes resulting in the formation of a large density core. As a consequence, the inner circular velocity profiles of the most massive subhaloes differ significantly from the cold dark matter predictions and we demonstrate that they are compatible with the observational data of the brightest Milky Way dSphs in such a velocity-dependent self-interacting dark matter scenario. Specifically, and contrary to the cold dark matter case, there are no subhaloes that are more concentrated than what is inferred from the kinematics of the Milky Way dSphs. We conclude that these models offer an interesting alternative to the cold dark matter model that can reduce the recently reported tension between the brightest Milky Way satellites and the dense subhaloes found in cold dark matter simulations.

The codecs project: a publicly available suite of cosmological N-body simulations for interacting dark energy models★

We present the largest set of N-body and hydrodynamical simulations to date for cosmological models featuring a direct interaction between the dark energy (DE) scalar field, responsible for the observed cosmic acceleration, and the cold dark matter (CDM) fluid. With respect to previous works, our simulations considerably extend the statistical significance of the simulated volume and cover a wider range of different realizations of the interacting DE scenario, including the recently proposed bouncing coupled DE model. Furthermore, all the simulations are normalized in order to be consistent with the present bounds on the amplitude of density perturbations at last scattering, thereby providing the first realistic determination of the effects of a DE coupling for cosmological growth histories fully compatible with the latest cosmic microwave background data. As a first basic analysis, we have studied the impact of the coupling on the non-linear matter power spectrum and on the bias between the CDM and baryon distributions, as a function of redshift and scale. For the former, we have addressed the issue of the degeneracy between the effects of the coupling and other standard cosmological parameters, e.g. σ8, showing how the redshift evolution of the linear amplitude or the scale dependence of the non-linear power spectrum might provide a way to break the degeneracy. For the latter, instead, we have computed the redshift and scale dependence of the bias in all our different models showing how a growing coupling or a bouncing coupled DE scenario provides much stronger effects with respect to constant coupling models. Furthermore, we discuss the main features imprinted by the DE interactions on the halo and subhalo mass functions. We refer to this vast numerical initiative as the COupled Dark Energy Cosmological Simulations (codecs) project, and release all the codecs outputs for public use through a dedicated web data base, providing information on how to access and interpret the data.

AN ANALYTICAL MODEL FOR THE ACCRETION OF DARK MATTER SUBHALOS

An analytical model is developed for the mass function of cold dark matter subhalos at the time of accretion and for the distribution of their accretion times. Our model is based on the model of Zhao et al. (2009) for the median assembly histories of dark matter halos, combined with a simple log-normal distribution to describe the scatter in the main-branch mass at a given time for halos of the same final mass. Our model is simple, and can be used to predict the un-evolved subhalo mass function, the mass function of subhalos accreted at a given time, the accretion-time distribution of subhalos of a given initial mass, and the frequency of major mergers as a function of time. We test our model using high-resolution cosmological $N$-body simulations, and find that our model predictions match the simulation results remarkably well. Finally, we discuss the implications of our model for the evolution of subhalos in their hosts and for the construction of a self-consistent model to link galaxies and dark matter halos at different cosmic times.

ASTROMETRIC MICROLENSING BY LOCAL DARK MATTER SUBHALOS

High-resolution N-body simulations of dark matter halos indicate that the Milky Way contains numerous subhalos. When a dark matter subhalo passes in front of a star, the light from that star will be deflected by gravitational lensing, leading to a small change in the star's apparent position. This astrometric microlensing signal depends on the inner density profile of the subhalo and can be greater than a few microarcseconds for an intermediate-mass subhalo (Mvir > 10000 solar masses) passing within arcseconds of a star. Current and near-future instruments could detect this signal, and we evaluate SIM's, Gaia's, and ground-based telescopes' potential as subhalo detectors. We develop a general formalism to calculate a subhalo's astrometric lensing cross section over a wide range of masses and density profiles, and we calculate the lensing event rate by extrapolating the subhalo mass function predicted by simulations down to the subhalo masses potentially detectable with this technique. We find that, although the detectable event rates are predicted to be low on the basis of current simulations, lensing events may be observed if the central regions of dark matter subhalos are more dense than current models predict (>1 solar mass within 0.1 pc of the subhalo center). Furthermore, targeted astrometric observations can be used to confirm the presence of a nearby subhalo detected by gamma-ray emission. We show that, for sufficiently steep density profiles, ground-based adaptive optics astrometric techniques could be capable of detecting intermediate-mass subhalos at distances of hundreds of parsecs, while SIM could detect smaller and more distant subhalos.

An improved model for the dynamical evolution of dark matter subhaloes

Using an analytical model, we study the evolution of subhalo, including its mass, angular momentum and merging time-scale. This model considers the dominant processes governing subhalo evolution, such as dynamical friction, tidal stripping and tidal heating. We find that in order to best match the evolution of angular momentum measured from N-body simulation, mass stripping by tidal force should become inefficient after subhalo has experienced a few passages of pericentre. It is also found that the often used Coulomb logarithm ln M/m has to be revised to best fit the merging time-scales from simulation. Combining the analytical model with the extended Press–Schechter (EPS) based merger trees, we study the subhalo mass function, and their spatial distribution in a Milky Way (MW) type halo. By tuning the tidal stripping efficiency, we can gain a better match to the subhalo mass function from simulation. The predicted distribution of subhaloes is found to agree with the distribution of MW satellites, but is more concentrated than the simulation results. The radial distribution of subhaloes depends weakly on subhaloes mass at both present day and the time of accretion, but strongly on the accretion time. Using the improved model, we measure the second moment of the subhalo occupation distribution, and it agrees well with the results of Kravtsov et al. and Zheng et al.

DISSECTING GALAXY FORMATION. II. COMPARING SUBSTRUCTURE IN PURE DARK MATTER AND BARYONIC MODELS

We compare the substructure evolution in pure dark matter (DM) halos with those in the presence of baryons, hereafter PDM and BDM models, respectively. The prime halos have been analyzed in the previous work. Models have been evolved from identical initial conditions which have been constructed by means of the constrained realization method. The BDM model includes star formation and feedback from stellar evolution onto the gas. A comprehensive catalog of subhalo populations has been compiled and individual and statistical properties of subhalos analyzed, including their orbital differences. We find that subhalo population mass functions in PDM and BDM are consistent with a single power law, Mαsbh, for each of the models in the mass range of ∼2 × 108 M☉–2 × 1011 M☉. However, we detect a nonnegligible shift between these functions, the time-averaged α ∼ −0.86 for the PDM and −0.98 for the BDM models. Overall, α appears to be a nearly constant in time, with variations of ±15%. Second, we find that the radial mass distribution of subhalo populations can be approximated by a power law, with a steepening that occurs at the radius of a maximal circular velocity, Rvmax, in the prime halos. Here we find that γsbh ∼ −1.5 for the PDM and −1 for the BDM models, when averaged over time inside Rvmax. The slope is steeper outside this region and approaches −3. We detect little spatial bias (less than 10%) between the subhalo populations and the DM distribution of the main halos. Also, the subhalo population exhibits much less triaxiality in the presence of baryons, in tandem with the shape of the prime halo. Finally, we find that, counter-intuitively, the BDM population is depleted at a faster rate than the PDM one within the central 30 kpc of the prime halo. The reason for this is that although the baryons provide a substantial glue to the subhalos, the main halo exhibits the same trend. This assures a more efficient tidal disruption of the BDM subhalo population. However, this effect can be reversed for a more efficient feedback from stellar evolution and the central supermassive black holes, which will expel baryons from the center and decrease the central concentration of the prime halo. We compare our results with via Lactea and Aquarius simulations and other published results.

There's no place like home? Statistics of Milky Way-mass dark matter haloes

We present an analysis of the distribution of structural properties for Milky Way-mass haloes in the Millennium-II Simulation (MS-II). This simulation of structure formation within the standard ΛCDM cosmology contains thousands of Milky Way-mass haloes and has sufficient resolution to properly resolve many subhaloes per host. It thus provides a major improvement in the statistical power available to explore the distribution of internal structure for haloes of this mass. In addition, the MS-II contains lower-resolution versions of the Aquarius Project haloes, allowing us to compare our results to simulations of six haloes at a much higher resolution. We study the distributions of mass assembly histories, of subhalo mass functions and accretion times and of merger and stripping histories for subhaloes capable of impacting discs at the centres of haloes. We show that subhalo abundances are not well described by Poisson statistics at low mass, but rather are dominated by intrinsic scatter. Using the masses of subhaloes at infall and the abundance-matching assumption, there is less than a 10 per cent chance that a Milky Way halo with Mvir= 1012 M⊙ will host two galaxies as bright as the Magellanic Clouds. This probability rises to ∼25 per cent for a halo with Mvir= 2.5 × 1012 M⊙. The statistics relevant for disc heating are very sensitive to the mass range that is considered relevant. Mergers with infall mass : redshift zero virial mass greater than 1:30 could well impact a central galactic disc and are a near inevitability since z= 2, whereas only half of all haloes have had a merger with infall mass : redshift zero virial mass greater than 1:10 over this same period.

The substructure hierarchy in dark matter haloes

We present a new algorithm for identifying the substructure within simulated dark matter haloes. The method is an extension of that proposed by Tormen et al. (2004) and Giocoli et al. (2008a), which identifies a subhalo as a group of self-bound particles that prior to being accreted by the main progenitor of the host halo belonged to one and the same progenitor halo (hereafter satellite). However, this definition does not account for the fact that these satellite haloes themselves may also have substructure, which thus gives rise to sub-subhaloes, etc. Our new algorithm identifies substructures at all levels of this hierarchy, and we use it to determine the mass function of all substructure (counting sub-haloes, sub-subhaloes, etc.). On average, haloes which formed more recently tend to have a larger mass fraction in substructure and to be less concentrated than average haloes of the same mass. We provide quantitative fits to these correlations. Even though our algorithm is very different from that of Gao et al. (2004), we too find that the subhalo mass function per unit mass at redshift z = 0 is universal. This universality extends to any redshift only if one accounts for the fact that host haloes of a given mass are less concentrated at higher redshifts, and concentration and substructure abundance are anti-correlated. This universality allows a simple parametrization of the subhalo mass function integrated over all host halo masses, at any given time. We provide analytic fits to this function which should be useful in halo model analyses which equate galaxies with halo substructure when interpreting clustering in large sky surveys. Finally, we discuss systematic differences in the subhalo mass function that arise from different definitions of (host) halo mass.

Perspective of Galactic dark matter subhalo detection on Fermi from the EGRET observation

The perspective of the detectability of Galactic dark matter subhaloes on the Fermi satellite is investigated in this work. Under the assumptions that dark matter annihilation accounts for the “GeV excess" of the Galactic diffuse γ-rays discovered by EGRET and the γ-ray flux is dominated by the contribution from subhaloes of dark matter, we calculate the expected number of dark matter subhaloes that Fermi may detect. We show that Fermi may detect a few tens to several hundred subhaloes in a 1-year all-sky survey. Since EGRET observation is taken as a normalization, this prediction is independent of the particle physics property of dark matter. The uncertainties of the prediction are discussed in detail. We find that the major uncertainty comes from the mass function of subhaloes, i.e., whether the subhaloes are “point like" (high-mass rich) or “diffuse like" (low-mass rich). Other uncertainties like the background estimation and the observational errors will contribute a factor of 2–3.

Substructures in hydrodynamical cluster simulations

The abundance and structure of dark matter subhalos has been analyzed extensively in recent studies of dark matter-only simulations, but comparatively little is known about the impact of baryonic physics on halo substructures. We here extend the SUBFIND algorithm for substructure identification such that it can be reliably applied to dissipative hydrodynamical simulations that include star formation. This allows, in particular, the identification of galaxies as substructures in simulations of clusters of galaxies, and a determination of their content of gravitationally bound stars, dark matter, and hot and cold gas. Using a large set of cosmological cluster simulations, we present a detailed analysis of halo substructures in hydrodynamical simulations of galaxy clusters, focusing in particular on the influence both of radiative and non-radiative gas physics, and of non-standard physics such as thermal conduction and feedback by galactic outflows. We also examine the impact of numerical nuisance parameters such as artificial viscosity parameterizations. We find that diffuse hot gas is efficiently stripped from subhalos when they enter the highly pressurized cluster atmosphere. This has the effect of decreasing the subhalo mass function relative to a corresponding dark matter-only simulation. These effects are mitigated in radiative runs, where baryons condense in the central subhalo regions and form compact stellar cores. However, in all cases, only a very small fraction, of the order of one percent, of subhalos within the cluster virial radii preserve a gravitationally bound hot gaseous atmosphere. (abridged)

The fate of substructures in cold dark matter haloes

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 than their less massive counterparts. We find that mergers between subhaloes occur. These tend to be between substructures that were already dynamically associated before accretion into the main halo. For subhaloes larger than 0.001 times the mass of the host halo, it is more likely that the subhalo will merge with the central or main subhalo than with another subhalo larger than itself. For lower masses, subhalo-subhalo mergers become equally likely to mergers with the main subhalo. Our results have implications for the variation of galaxy properties with environment and for the treatment of mergers in galaxy formation models.

A NEW CHANNEL FOR DETECTING DARK MATTER SUBSTRUCTURE IN GALAXIES: GRAVITATIONAL LENS TIME DELAYS

We show that dark matter substructure in galaxy-scale halos perturbs the time delays between images in strong gravitational lens systems. The variance of the effect depends on the subhalo mass function, scaling as the product of the substructure mass fraction and a characteristic mass of subhalos (namely <m^2>/<m>). Time delay perturbations therefore complement gravitational lens flux ratio anomalies and astrometric perturbations by measuring a different moment of the subhalo mass function. Unlike flux ratio anomalies, "time delay millilensing" is unaffected by dust extinction or stellar microlensing in the lens galaxy. Furthermore, we show that time delay ratios are immune to the radial profile degeneracy that usually plagues lens modeling. We lay out a mathematical theory of time delay perturbations and find it to be tractable and attractive. We predict that in "cusp" lenses with close triplets of images, substructure may change the arrival-time order of the images (compared with smooth models). We discuss the possibility that this effect has already been observed in RX J1131-1231.