Subhalo Mass Function Research Articles

Cosmic degeneracies – II. Structure formation in joint simulations of warm dark matter and f(R) gravity

We present for the first time the outcomes of a cosmological N-body simulation that simultaneously implements a warm dark matter (WDM) particle candidate and a modified gravitational interaction in the form of f(R) gravity, and compare its results with the individual effects of these two independent extensions of the standard ΛCDM scenario, and with the reference cosmology itself. We consider a rather extreme value of the WDM particle mass (mWDM = 0.4 keV) and a single realization of f(R) gravity with |$|\bar{f}_{R0}|=10^{-5}$|⁠, and we investigate the impact of these models and of their combination on a wide range of cosmological observables with the aim to identify possible observational degeneracies. Differently from the case of combining f(R) gravity with massive neutrinos, we find that most of the considered observables do not show any significant degeneracy due to the fact that WDM and f(R) gravity are characterized by individual observational signatures with a very different functional dependence on cosmic scales and halo masses. In particular, this is the case for the non-linear matter power spectrum in real space, for the halo and subhalo mass functions, for the halo density profiles and for the concentration–mass relation. However, other observables – like e.g. the halo bias – do show some level of degeneracy between the two models, while a very strong degeneracy is observed for the non-linear matter power spectrum in redshift space, for the density profiles of small cosmic voids, and for the voids abundance as a function of the void core density.

Subhalo demographics in the Illustris simulation: effects of baryons and halo-to-halo variation

We study the abundance of subhaloes in the hydrodynamical cosmological simulation Illustris, which includes both baryons and dark matter in a $\Lambda$CDM volume 106.5 Mpc a side. We compare Illustris to its dark matter-only (DMO) analogue, Illustris-Dark, and quantify the effects of baryonic processes on the demographics of subhaloes in the host mass range $10^{11}$ to $3 \times 10^{14} \msun$. We focus on both the evolved ($z=0$) subhalo cumulative mass functions (SHMF) and the statistics of subhaloes ever accreted, i.e. infall subhalo mass function. We quantify the variance in subhalo abundance at fixed host mass and investigate the physical reasons responsible for such scatter. We find that in Illustris, baryonic physics impacts both the infall and $z=0$ subhalo abundance by tilting the DMO function and suppressing the abundance of low-mass subhaloes. The breaking of self-similarity in the subhalo abundance at $z=0$ is enhanced by the inclusion of baryonic physics. The non-monotonic alteration of the evolved subhalo abundances can be explained by the modification of the concentration--mass relation of Illustris hosts compared to Illustris-Dark.Interestingly, the baryonic implementation in Illustris does not lead to an increase in the halo-to-halo variation compared to Illustris-Dark. In both cases, the normalized intrinsic scatter today is larger for Milky Way-like haloes than for cluster-sized objects. For Milky Way-like haloes, it increases from about eight per cent at infall to about 25 per cent at the current epoch. In both runs, haloes of fixed mass formed later host more subhaloes than early formers.

Unbiased constraints on ultralight axion mass from dwarf spheroidal galaxies

It has been suggested that the internal dynamics of dwarf spheroidal galaxies (dSphs) can be used to test whether or not ultralight axions with $m_a\sim 10^{-22}\text{eV}$ are a preferred dark matter candidate. However, comparisons to theoretical predictions tend to be inconclusive for the simple reason that while most cosmological models consider only dark matter, one observes only baryons. Here we use realistic kinematic mock data catalogs of Milky Way dSph's to show that the "mass-anisotropy degeneracy" in the Jeans equations leads to biased bounds on the axion mass in galaxies with unknown dark matter halo profiles. In galaxies with multiple chemodynamical components this bias can be partly removed by modelling the mass enclosed within each subpopulation. However, analysis of the mock data reveals that the least-biased constraints on the axion mass result from fitting the luminosity-averaged velocity dispersion of the individual chemodynamical components directly. Applying our analysis to two dSph's with reported stellar subcomponents, Fornax and Sculptor, and assuming that the halo profile has not been acted on by baryons, yields core radii $r_{c}>1.5$ kpc and $r_c> 1.2$ kpc respectively, and $m_a<0.4\times 10^{-22}\text{eV}$ at 97.5\% confidence. These bounds are in tension with the number of observed satellites derived from simple (but conservative) estimates of the subhalo mass function in Milky Way-like galaxies. We discuss how baryonic feedback might affect our results, and the impact of such a small axion mass on the growth of structures in the Universe.

Accurate mass and velocity functions of dark matter haloes

$N$-body cosmological simulations are an essential tool to understand the observed distribution of galaxies. We use the MultiDark simulation suite, run with the Planck cosmological parameters, to revisit the mass and velocity functions. At redshift $z=0$, the simulations cover four orders of magnitude in halo mass from $\sim10^{11}M_\odot$ with 8,783,874 distinct halos and 532,533 subhalos. The total volume used is $\sim$515 Gpc$^3$, more than 8 times larger than in previous studies. We measure and model the halo mass function, its covariance matrix w.r.t halo mass and the large scale halo bias. With the formalism of the excursion-set mass function, we explicit the tight interconnection between the covariance matrix, bias and halo mass function. We obtain a very accurate ($<2\%$ level) model of the distinct halo mass function. We also model the subhalo mass function and its relation to the distinct halo mass function. The set of models obtained provides a complete and precise framework for the description of halos in the concordance Planck cosmology. Finally, we provide precise analytical fits of the $V_{max}$ maximum velocity function up to redshift $z<2.3$ to push for the development of halo occupation distribution using $V_{max}$. The data and the analysis code are made publicly available in the \textit{Skies and Universes} database.

The impact of baryonic physics on the subhalo mass function and implications for gravitational lensing

We investigate the impact of baryonic physics on the subhalo population by analyzing the results of two recent hydrodynamical simulations (EAGLE and Illustris), which have very similar configuration, but a different model of baryonic physics. We concentrate on haloes with a mass between $10^{12.5}$ and $10^{14}M_{\odot}h^{-1}$ and redshift between 0.2 and 0.5, comparing with observational results and subhalo detections in early-type galaxy lenses. We compare the number and the spatial distribution of subhaloes in the fully hydro runs and in their dark matter only counterparts, focusing on the differences between the two simulations. We find that the presence of baryons reduces the number of subhaloes, especially at the low mass end ($\leq 10^{10}M_{\odot}h^{-1}$), by different amounts depending on the model. The variations in the subhalo mass function are strongly dependent on those in the halo mass function, which is shifted by the effect of stellar and AGN feedback. Finally, we search for analogues of the observed lenses (SLACS) in the simulations, selecting them in velocity dispersion and dynamical properties. We use the selected galaxies to quantify detection expectations based on the subhalo populations in the different simulations, calculating the detection probability and the predicted values for the projected dark matter fraction in subhaloes $f_{DM}$ and the slope of the mass function $\alpha$. We compare these values with those derived from subhalo detections in observations and conclude that the dark-matter-only and hydro EAGLE runs are both compatible with observational results, while results from the hydro Illustris run do not lie within the errors.

Modeling dark matter subhalos in a constrained galaxy: Global mass and boosted annihilation profiles

The interaction properties of cold dark matter (CDM) particle candidates, such as those of weakly interacting massive particles (WIMPs), generically lead to the structuring of dark matter on scales much smaller than typical galaxies, potentially down to $\sim 10^{-10}M_\odot$. This clustering translates into a very large population of subhalos in galaxies and affects the predictions for direct and indirect dark matter searches (gamma rays and antimatter cosmic rays). In this paper, we elaborate on previous analytic works to model the Galactic subhalo population, while consistently with current observational dynamical constraints on the Milky Way. In particular, we propose a self-consistent method to account for tidal effects induced by both dark matter and baryons. Our model does not strongly rely on cosmological simulations as they can hardly be fully matched to the real Milky Way, but for setting the initial subhalo mass fraction. Still, it allows to recover the main qualitative features of simulated systems. It can further be easily adapted to any change in the dynamical constraints, and be used to make predictions or derive constraints on dark matter candidates from indirect or direct searches. We compute the annihilation boost factor, including the subhalo-halo cross-product. We confirm that tidal effects induced by the baryonic components of the Galaxy play a very important role, resulting in a local average subhalo mass density $\lesssim 1\%$ of the total local dark matter mass density, while selecting in the most concentrated objects and leading to interesting features in the overall annihilation profile in the case of a sharp subhalo mass function. Values of global annihilation boost factors range from $\sim 2$ to $\sim 20$, while the local annihilation rate is about half as much boosted.

Mapping substructure in the HST Frontier Fields cluster lenses and in cosmological simulations

We map the lensing-inferred substructure in the first three clusters observed by the Hubble Space Telescope Frontier Fields Initiative (HSTFF): Abell 2744 (z = 0.308), MACSJ0416, (z = 0.396) and MACSJ1149 (z = 0.543). Statistically resolving dark-matter subhaloes down to ~10^{9.5} solar masses, we compare the derived subhalo mass functions (SHMFs) to theoretical predictions from analytical models and with numerical simulations in a Lambda Cold Dark Matter (LCDM) cosmology. Mimicking our observational cluster member selection criteria in the HSTFF, we report excellent agreement in both amplitude and shape of the SHMF over four decades in subhalo mass (10^{9-13} solar masses). Projection effects do not appear to introduce significant errors in the determination of SHMFs from simulations. We do not find evidence for a substructure crisis, analogous to the missing satellite problem in the Local Group, on cluster scales, but rather excellent agreement of the count-matched HSTFF SHMF down to M_{sub halo}/M_{halo} ~ 10^{-5}. However, we do find discrepancies in the radial distribution of sub haloes inferred from HSTFF cluster lenses compared to determinations from simulated clusters. This suggests that although the selected simulated clusters match the HSTFF sample in mass, they do not adequately capture the dynamical properties and complex merging morphologies of these observed cluster lenses. Therefore, HSTFF clusters are likely observed in a transient evolutionary stage that is presently insufficiently sampled in cosmological simulations. The abundance and mass function of dark matter substructure in cluster lenses continues to offer an important test of the LCDM paradigm, and at present we find no tension between model predictions and observations.

Linear perturbation theory for tidal streams and the small-scale CDM power spectrum

Tidal streams in the Milky Way are sensitive probes of the population of dark-matter subhalos predicted in cold-dark-matter (CDM) simulations. We present a new calculus for computing the effect of subhalo fly-bys on cold tidal streams based on the action-angle representation of streams. The heart of this calculus is a line-of-parallel-angle approach that calculates the perturbed distribution function of a given stream segment by undoing the effect of all impacts. This approach allows one to compute the perturbed stream density and track in any coordinate system in minutes for realizations of the subhalo distribution down to 10^5 Msun, accounting for the stream's internal dispersion and overlapping impacts. We study the properties of density and track fluctuations with suites of simulations. The one-dimensional density and track power spectra along the stream trace the subhalo mass function, with higher-mass subhalos producing power only on large scales, while lower mass subhalos cause structure on smaller scales. The time-dependence of impacts and of the evolution of the stream after an impact gives rise to bispectra. We further find that tidal streams are essentially corrugated sheets in the presence of subhalo perturbations: different projections of the track all reflect the same pattern of perturbations, facilitating their observational measurement. We apply this formalism to density data for the Pal 5 stream and make a first rigorous determination of 10^{+11}_{-6} dark-matter subhalos with masses between 3x10^6 and 10^9 Msun within 20 kpc from the Galactic center (corresponding to 1.4^{+1.6}_{-0.9} times the number predicted by CDM-only simulations or to f_{sub}(r<20 kpc) ~ 0.2%). Improved data will allow measurements of the subhalo mass function down to 10^5 Msun, thus definitively testing whether dark matter clumps on the smallest scales relevant for galaxy formation.

Dark census: Statistically detecting the satellite populations of distant galaxies

In the standard structure formation scenario based on the cold dark matter paradigm, galactic halos are predicted to contain a large population of dark matter subhalos. While the most massive members of the subhalo population can appear as luminous satellites and be detected in optical surveys, establishing the existence of the low mass and mostly dark subhalos has proven to be a daunting task. Galaxy-scale strong gravitational lenses have been successfully used to study mass substructures lying close to lensed images of bright background sources. However, in typical galaxy-scale lenses, the strong lensing region only covers a small projected area of the lens's dark matter halo, implying that the vast majority of subhalos cannot be directly detected in lensing observations. In this paper, we point out that this large population of dark satellites can collectively affect gravitational lensing observables, hence possibly allowing their statistical detection. Focusing on the region of the galactic halo outside the strong lensing area, we compute from first principles the statistical properties of perturbations to the gravitational time delay and position of lensed images in the presence of a mass substructure population. We find that in the standard cosmological scenario, the statistics of these lensing observables are well approximated by Gaussian distributions. The formalism developed as part of this calculation is very general and can be applied to any halo geometry and choice of subhalo mass function. Our results significantly reduce the computational cost of including a large substructure population in lens models and enable the use of Bayesian inference techniques to detect and characterize the distributed satellite population of distant lens galaxies.

ARE SOME MILKY WAY GLOBULAR CLUSTERS HOSTED BY UNDISCOVERED GALAXIES?

ABSTRACT The confirmation of a globular cluster (GC) in the recently discovered ultrafaint galaxy Eridanus II (Eri II) motivated us to examine the question posed in the title. After estimating the halo mass of Eri II using a published stellar mass—halo mass relation, the one GC in this galaxy supports extending the relationship between the number of GCs hosted by a galaxy and the galaxy’s total mass about two orders of magnitude in stellar mass below the previous limit. For this empirically determined specific frequency of between 0.06 and 0.39 GCs per 109 M ⊙ of total mass, the surviving Milky Way (MW) subhalos with masses smaller than 1010 M ⊙ could host as many as 5–31 GCs, broadly consistent with the actual population of outer halo MW GCs, although matching the radial distribution in detail remains a challenge. Using a subhalo mass function from published high-resolution numerical simulations and a Poissonian model for populating those halos with the aforementioned empirically constrained frequency, we find that about 90% of these GCs lie in lower-mass subhalos than that of Eri II. From what we know about the stellar mass–halo mass function, the subhalo mass function, and the mass-normalized GC specific frequency, we conclude that some of the MW’s outer halo GCs are likely to be hosted by undetected subhalos with extremely modest stellar populations.

Constraints on the identity of the dark matter from strong gravitational lenses

The cold dark matter (CDM) cosmological model unambigously predicts that a large number of haloes should survive as subhaloes when they are accreted into a larger halo. The CDM model would be ruled out if such substructures were shown not to exist. By contrast, if the dark matter consists of warm particles (WDM), then below a threshold mass that depends on the particle mass far fewer substructures would be present. Finding subhaloes below a certain mass would then rule out warm particle masses below some value. Strong gravitational lensing provides a clean method to measure the subhalo mass function through distortions in the structure of Einstein rings and giant arcs.Using mock lensing observations constructed from high-resolution N-body simulations, we show that measurements of approximately 100 strong lens systems with a detection limit of $10^7 h^{-1} M_{\odot}$ would clearly distinguish CDM from WDM in the case where this consists of 7 keV sterile neutrinos such as those that might be responsible for the 3.5 keV X-ray emission line recently detected in galaxies and clusters.

Dark matter cores all the way down

We use high resolution simulations of isolated dwarf galaxies to study the physics of dark matter cusp-core transformations at the edge of galaxy formation: M200 = 10^7 - 10^9 Msun. We work at a resolution (~4 pc minimum cell size; ~250 Msun per particle) at which the impact from individual supernovae explosions can be resolved, becoming insensitive to even large changes in our numerical 'sub-grid' parameters. We find that our dwarf galaxies give a remarkable match to the stellar light profile; star formation history; metallicity distribution function; and star/gas kinematics of isolated dwarf irregular galaxies. Our key result is that dark matter cores of size comparable to the stellar half mass radius (r_1/2) always form if star formation proceeds for long enough. Cores fully form in less than 4 Gyrs for the M200 = 10^8 Msun and 14 Gyrs for the 10^9 Msun dwarf. We provide a convenient two parameter 'coreNFW' fitting function that captures this dark matter core growth as a function of star formation time and the projected stellar half mass radius. Our results have several implications: (i) we make a strong prediction that if LCDM is correct, then 'pristine' dark matter cusps will be found either in systems that have truncated star formation and/or at radii r > r_1/2; (ii) complete core formation lowers the projected velocity dispersion at r_1/2 by a factor ~2, which is sufficient to fully explain the 'too big to fail problem'; and (iii) cored dwarfs will be much more susceptible to tides, leading to a dramatic scouring of the subhalo mass function inside galaxies and groups.

Statistics of dark matter substructure – II. Comparison of model with simulation results

We compare subhalo mass and velocity functions obtained from different simulations with different subhalo finders among each other, and with predictions from the new semi-analytical model of Jiang & van den Bosch (2014). We find that subhalo mass functions (SHMFs) obtained using different subhalo finders agree with each other at the level of � 20 percent, but only at the low mass end. At the massive end, subhalo finders that identify subhaloes based purely on density in configuration space dramatically underpredict the subhalo abundances by more than an order of magnitude. These problems are much less severe for subhalo velocity functions (SHVFs), indicating that they arise from issues related to assigning masses to the subhaloes, rather than from detecting them. Overall the predictions from the semi-analytical model are in excellent agreement with simulation results obtained using the more advanced subhalo finders that use information in six dimensional phase-space. In particular, the model accurately reproduces the slope and host-mass-dependent normalization of both the subhalo mass and velocity functions. We find that the SHMFs and SHVFs have power-law slopes of 0.82 and 2.6, respectively, significantly shallower than what has been claimed in several studies in the literature.

Statistics of dark matter substructure – I. Model and universal fitting functions

We present a new, semi-analytical model describing the evolution of dark matter subhaloes. The model uses merger trees constructed using the method of Parkinson et al. (2008) to describe the masses and redshifts of subhaloes at accretion, which are subsequently evolved using a simple model for the orbit-averaged mass loss rates. The model is extremely fast, treats subhaloes of all orders, accounts for scatter in orbital properties and halo concentrations, and uses a simple recipe to convert subhalo mass to maximum circular velocity. The model accurately reproduces the average subhalo mass and velocity functions in numerical simulations. The inferred subhalo mass loss rates imply that an average dark matter subhalo loses in excess of 80 percent of its infall mass during its first radial orbit within the host halo. We demonstrate that the total mass fraction in subhaloes is tightly correlated with the `dynamical age' of the host halo, defined as the number of halo dynamical times that have elapsed since its formation. Using this relation, we present universal fitting functions for the evolved and unevolved subhalo mass and velocity functions that are valid for any host halo mass, at any redshift, and for any {\Lambda}CDM cosmology.

The Copernicus Complexio: a high-resolution view of the small-scale Universe

We introduce Copernicus Complexio (COCO), a high-resolution cosmological N-body simulation of structure formation in the $\Lambda{\rm CDM}{}$ model. COCO follows an approximately spherical region of radius $\sim 17.4h^{-1}\,{\rm Mpc}$ embedded in a much larger periodic cube that is followed at lower resolution. The high resolution volume has a particle mass of $1.135\times10^5h^{-1}{\rm M}_{\odot}$ (60 times higher than the Millennium-II simulation). COCO gives the dark matter halo mass function over eight orders of magnitude in halo mass; it forms $\sim 60$ haloes of galactic size, each resolved with about 10 million particles. We confirm the power-law character of the subhalo mass function, $\bar{N}(>\mu)\propto\mu^{-s}$, down to a reduced subhalo mass $M_{sub}/M_{200}\equiv\mu=10^{-6}$, with a best-fit power-law index, $s=0.94$, for hosts of mass $\langle M_{200}\rangle=10^{12}h^{-1}{\rm M}_{\odot}$. The concentration-mass relation of COCO haloes deviates from a single power law for masses $M_{200}<\textrm{a few}\times 10^{8}h^{-1}{\rm M}_{\odot}$, where it flattens, in agreement with results by Sanchez-Conde et al. The host mass invariance of the reduced maximum circular velocity function of subhaloes, $\nu\equiv V_{max}/V_{200}$, hinted at in previous simulations, is clearly demonstrated over five orders of magnitude in host mass. Similarly, we find that the average, normalised radial distribution of subhaloes is approximately universal (i.e. independent of subhalo mass), as previously suggested by the Aquarius simulations of individual haloes. Finally, we find that at fixed physical subhalo size, subhaloes in lower mass hosts typically have lower central densities than those in higher mass hosts.

A unified model for the spatial and mass distribution of subhaloes

N-body simulations suggest that the substructures that survive inside dark matter haloes follow universal distributions in mass and radial number density. We demonstrate that a simple analytical model can explain these subhalo distributions as resulting from tidal stripping which increasingly reduces the mass of subhaloes with decreasing halo-centric distance. As a starting point, the spatial distribution of subhaloes of any given infall mass is shown to be largely indistinguishable from the overall mass distribution of the host halo. Using a physically motivated statistical description of the amount of mass stripped from individual subhaloes, the model fully describes the joint distribution of subhaloes in final mass, infall mass and radius. As a result, it can be used to predict several derived distributions involving combinations of these quantities including, but not limited to, the universal subhalo mass function, the subhalo spatial distribution, the gravitational lensing profile, the dark matter annihilation radiation profile and boost factor. This model clarifies a common confusion when comparing the spatial distributions of galaxies and subhaloes, the so called "anti-bias", as a simple selection effect. We provide a Python code SubGen for populating haloes with subhaloes at http://icc.dur.ac.uk/data/

Boosting the annihilation boost: Tidal effects on dark matter subhalos and consistent luminosity modeling

In the cold dark matter paradigm, structures form hierarchically, implying that large structures contain smaller substructures. These subhalos will enhance signatures of dark matter annihilation such as gamma rays. In the literature, typical estimates of this boost factor assume a concentration-mass relation for field halos, to calculate the luminosity of subhalos. However, since subhalos accreted in the gravitational potential of their host loose mass through tidal stripping and dynamical friction, they have a quite characteristic density profile, different from that of the field halos of the same mass. In this work, we quantify the effect of tidal stripping on the boost factor, by developing a semi-analytic model that combines mass-accretion history of both the host and subhalos as well as subhalo accretion rates. We find that when subhalo luminosities are treated consistently, the boost factor increases by a factor 2-5, compared to the typical calculation assuming a field-halo concentration. This holds for host halos ranging from sub-galaxy to cluster masses and is independent of the subhalo mass function or specific concentration-mass relation. The results are particularly relevant for indirect dark matter searches in the extragalactic gamma-ray sky.

Comprehensive assessment of the too big to fail problem

We use a semi-analytical model for the substructure of dark matter haloes to assess the too-big-to-fail (TBTF) problem. The model accurately reproduces the average subhalo mass and velocity functions, as well as their halo-to-halo variance, in N-body simulations. We construct thousands of realizations of Milky Way (MW) size host haloes, allowing us to investigate the TBTF problem with unprecedented statistical power. We examine the dependence on host halo mass and cosmology, and explicitly demonstrate that a reliable assessment of TBTF requires large samples of hundreds of host haloes. We argue that previous statistics used to address TBTF suffer from the look-elsewhere effect and/or disregard certain aspects of the data on the MW satellite population. We devise a new statistic that is not hampered by these shortcomings, and, using only data on the 9 known MW satellite galaxies with $V_{\rm max}>15{\rm kms}^{-1}$, demonstrate that $1.4^{+3.3}_{-1.1}\%$ of MW-size host haloes have a subhalo population in statistical agreement with that of the MW. However, when using data on the MW satellite galaxies down to $V_{\rm max}=8{\rm kms}^{-1}$, this MW consistent fraction plummets to $<5\times10^{-4}$ (at 68% CL). Hence, if it turns out that the inventory of MW satellite galaxies is complete down to 8km/s, then the maximum circular velocities of MW satellites are utterly inconsistent with $\Lambda$CDM predictions, unless baryonic effects can drastically increase the spread in $V_{\rm max}$ values of satellite galaxies compared to that of their subhaloes.

Hierarchical Formation of Dark Matter Halos near the Cutoff Scale and Their Impact on Indirect Detections

AbstractThe smallest dark matter halos are formed first in the early universe (e.g., Hofmann et al. 2001; Berezinsky et al. 2003; Ishiyama et al. 2010). We present results of very large cosmological N-body simulations of the hierarchical formation and evolution of halos over a wide mass range, beginning from the formation of the smallest halos. In the largest simulation, the motions of 40963 particles in comoving boxes of side lengths 400 pc and 200 pc were followed. The particle masses were 3.4 × 10−11M⊙ and 4.3 × 10−12M⊙, ensuring that halos at the cutoff scale were represented by 30,000 and 230,000 particles, respectively. We found that the central density cusp is much steeper in these halos than in larger halos (dwarf-galaxy-sized to cluster-sized halos), and scales as ρ ∝ r-(1.5–1.3). The cusp slope gradually becomes shallower as the halo mass increases.The slope of halos 50 times more massive than the smallest halo is approximately −1.3. No strong correlation exists between inner slope and the collapse epoch. The cusp slope of halos above the cutoff scale seems to be reduced primarily due to major merger processes. The concentration, estimated at the present universe, is predicted to be 60–70, consistent with theoretical models and earlier simulations, and ruling out simple power law mass-concentration relations. Such halos could still exist in the present universe with the same steep density profiles. Strongly depending on the subhalo mass function and the adopted concentration model, the steeper inner cusps of halos near the cutoff scale enhance the annihilation luminosity of a Milky Way sized halo between 12 to 67 (Ishiyama 2014).

DARK MATTER HALO MODELS OF STELLAR MASS-DEPENDENT GALAXY CLUSTERING IN PRIMUS+DEEP2 AT 0.2 &lt;z&lt; 1.2

We utilize $\Lambda$CDM halo occupation models of galaxy clustering to investigate the evolving stellar mass dependent clustering of galaxies in the PRIsm MUlti-object Survey (PRIMUS) and DEEP2 Redshift Survey over the past eight billion years of cosmic time, between $0.2<z<1.2$. These clustering measurements provide new constraints on the connections between dark matter halo properties and galaxy properties in the context of the evolving large-scale structure of the universe. Using both an analytic model and a set of mock galaxy catalogs, we find a strong correlation between central galaxy stellar mass and dark matter halo mass over the range $M_\mathrm{halo}\sim10^{11}$-$10^{13}~h^{-1}M_\odot$, approximately consistent with previous observations and theoretical predictions. However, the stellar-to-halo mass relation (SHMR) and the mass scale where star formation efficiency reaches a maximum appear to evolve more strongly than predicted by other models, including models based primarily on abundance-matching constraints. We find that the fraction of satellite galaxies in haloes of a given mass decreases significantly from $z\sim0.5$ to $z\sim0.9$, partly due to the fact that haloes at fixed mass are rarer at higher redshift and have lower abundances. We also find that the $M_1/M_\mathrm{min}$ ratio, a model parameter that quantifies the critical mass above which haloes host at least one satellite, decreases from $\approx20$ at $z\sim0$ to $\approx13$ at $z\sim0.9$. Considering the evolution of the subhalo mass function vis-\`{a}-vis satellite abundances, this trend has implications for relations between satellite galaxies and halo substructures and for intracluster mass, which we argue has grown due to stripped and disrupted satellites between $z\sim0.9$ and $z\sim0.5$.