Subhalo Mass Function Research Articles

Cosmological simulations of scale-dependent primordial non-Gaussianity

We present the results of a set of cosmological N-body simulations with standard ΛCDM cosmology but characterized by a scale-dependent primordial non-Gaussianity of the local type featuring a power-law dependence of the f NL loc(k) at large scales followed by a saturation to a constant value at smaller scales where non-linear growth leads to the formation of collapsed cosmic structures. Such models are built to ensure consistency with current Cosmic Microwave Background bounds on primordial non-Gaussianity yet allowing for large effects of the non-Gaussian statistics on the properties of non-linear structure formation. We show the impact of such scale-dependent non-Gaussian scenarios on a wide range of properties of the resulting cosmic structures, such as the non-linear matter power spectrum, the halo and sub-halo mass functions, the concentration-mass relation, the halo and void density profiles, and we highlight for the first time that some of these models might mimic the effects of Warm Dark Matter for several of such observables.

Forecasting the Population of Globular Cluster Streams in Milky Way–type Galaxies

Thin stellar streams originating from globular clusters (GCs) are among the most sensitive tracers of low-mass dark matter subhalos. Joint analysis of the entire population of stellar streams will place the most robust constraints on the dark matter subhalo mass function, and therefore the nature of dark matter. Here we use a hierarchical model of GC formation to forecast the total number, masses, and radial distribution of dissolved GC in Milky Way–like galaxies. Furthermore, we generate mock stellar streams from these progenitors’ orbital histories taking into account the clusters’ formation and accretion times, mass, and metallicity. Out of ∼10,000 clusters more massive than 104 M ⊙, ∼9000 dissolved in the central bulge and are fully phase mixed at the present, while the remaining ∼1000 survive as coherent stellar streams. This suggests that the current census of ∼80 GC streams in the Milky Way is severely incomplete. Beyond 15 kpc from the Galactic center we are missing ∼100 streams, of which the vast majority are from accreted GCs. Deep Rubin photometry (g ≲ 27.5) would be able to detect these streams, even the most distant ones beyond >75 kpc. We also find that M31 will have an abundance of streams at galactocentric radii of 30–100 kpc. We conclude that future surveys will find a multitude of stellar streams from GCs, which can be used for dark matter subhalo searches.

Measuring the Conditional Luminosity and Stellar Mass Functions of Galaxies by Combining the Dark Energy Spectroscopic Instrument Legacy Imaging Surveys Data Release 9, Survey Validation 3, and Year 1 Data

In this investigation, we leverage the combination of the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys Data Release 9, Survey Validation 3, and Year 1 data sets to estimate the conditional luminosity functions and conditional stellar mass functions (CLFs and CSMFs) of galaxies across various halo mass bins and redshift ranges. To support our analysis, we utilize a realistic DESI mock galaxy redshift survey (MGRS) generated from a high-resolution Jiutian simulation. An extended halo-based group finder is applied to both MGRS catalogs and DESI observation. By comparing the r- and z-band luminosity functions (LFs) and stellar mass functions (SMFs) derived using both photometric and spectroscopic data, we quantified the impact of photometric redshift (photo-z) errors on the galaxy LFs and SMFs, especially in the low-redshift bin at the low-luminosity/mass end. By conducting prior evaluations of the group finder using MGRS, we successfully obtain a set of CLF and CSMF measurements from observational data. We find that at low redshift, the faint-end slopes of CLFs and CSMFs below ∼109 h −2 L ⊙ (or h −2 M ⊙) evince a compelling concordance with the subhalo mass functions. After correcting the cosmic variance effect of our local Universe following Chen et al., the faint-end slopes of the LFs/SMFs turn out to also be in good agreement with the slope of the halo mass function.

Forecasts for Galaxy Formation and Dark Matter Constraints from Dwarf Galaxy Surveys

The abundance of faint dwarf galaxies is determined by the underlying population of low-mass dark matter (DM) halos and the efficiency of galaxy formation in these systems. Here, we quantify potential galaxy formation and DM constraints from future dwarf satellite galaxy surveys. We generate satellite populations using a suite of Milky Way (MW)–mass cosmological zoom-in simulations and an empirical galaxy–halo connection model, and assess sensitivity to galaxy formation and DM signals when marginalizing over galaxy–halo connection uncertainties. We find that a survey of all satellites around one MW-mass host can constrain a galaxy formation cutoff at peak virial masses of M50=108M⊙ at the 1σ level; however, a tail toward low M50 prevents a 2σ measurement. In this scenario, combining hosts with differing bright satellite abundances significantly reduces uncertainties on M50 at the 1σ level, but the 2σ tail toward low M50 persists. We project that observations of one (two) complete satellite populations can constrain warm DM models with m WDM ≈ 10 keV (20 keV). Subhalo mass function (SHMF) suppression can be constrained to ≈70%, 60%, and 50% that in cold dark matter (CDM) at peak virial masses of 108, 109, and 1010 M ⊙, respectively; SHMF enhancement constraints are weaker (≈20, 4, and 2 times that in CDM, respectively) due to galaxy–halo connection degeneracies. These results motivate searches for faint dwarf galaxies beyond the MW and indicate that ongoing missions like Euclid and upcoming facilities including the Vera C. Rubin Observatory and Nancy Grace Roman Space Telescope will probe new galaxy formation and DM physics.

A too-many-dwarf-galaxy-satellites problem in the M 83 group

Dwarf galaxies in groups of galaxies provide excellent test cases for models of structure formation. This led to a so-called small-scale crisis, including the famous missing-satellites and too-big-to-fail problems. It was suggested that these two problems can be resolved by introducing baryonic physics to cosmological simulations. We tested the nearby grand spiral M 83 – a Milky Way sibling – to determine whether its number of dwarf galaxy companions is compatible with today’s Λ cold dark matter model using two methods: with cosmological simulations that include baryons and with theoretical predictions from the subhalo mass function. By employing distance measurements, we recovered a list of confirmed dwarf galaxies within 330 kpc of M 83 down to a magnitude of MV = −10. We find that both the state-of-the-art hydrodynamical cosmological simulation Illustris-TNG50 and theoretical predictions agree with the number of confirmed satellites around M 83 at the bright end of the luminosity function (> 108 solar masses) but underestimate it at the faint end (down to 106 solar masses) at more than 3σ and 5σ levels, respectively. This indicates a too-many-satellites problem for M 83 in the Λ cold dark matter model. The actual degree of tension with cosmological models is underestimated because the number of observed satellites is incomplete due to the high contamination of spurious stars and Galactic cirrus.

Prospects for Detecting Gaps in Globular Cluster Stellar Streams in External Galaxies with the Nancy Grace Roman Space Telescope

Stellar streams form through the tidal disruption of satellite galaxies or globular clusters orbiting a host galaxy. Globular cluster streams are exciting since they are thin (dynamically cold) and therefore sensitive to perturbations from low-mass subhalos. Since the subhalo mass function differs depending on the dark matter composition, these gaps can provide unique constraints on dark matter models. However, current samples are limited to the Milky Way. With its large field of view, deep imaging sensitivity, and high angular resolution, the upcoming Nancy Grace Roman Space Telescope (Roman) presents a unique opportunity to increase the number of observed streams and gaps significantly. This paper presents a first exploration of the prospects for detecting gaps in streams in M31 and other nearby galaxies with resolved stars. We simulate the formation of gaps in a Palomar 5–like stream and generate mock observations of these gaps with background stars in M31 and foreground Milky Way stellar fields. We assess Roman's ability to detect gaps out to 10 Mpc through visual inspection and with the gap-finding tool FindTheGap. We conclude that gaps of ≈1.5 kpc in streams that are created from subhalos of masses ≥5 × 106 M ⊙ are detectable within a 2–3 Mpc volume in exposure times of 1000 s to 1 hr. This volume contains ≈150 galaxies, including ≈eight galaxies with luminosities >109 L ⊙. Large samples of stream gaps in external galaxies will open up a new era of statistical analyses of gap characteristics in stellar streams and help constrain dark matter models.

The Three Hundred: Msub–Vcirc relation

ABSTRACT In this study, we investigate a recent finding based on strong lensing observations, which suggests that the sub-haloes observed in clusters exhibit greater compactness compared to those predicted by ΛCDM simulations. To address this discrepancy, we compare the cumulative sub-halo mass function and the Msub–Vcirc relation between observed clusters and 324 simulated clusters from $\rm \small {The\,Three\,\,Hundred}$ project, focusing on the hydrodynamic resimulations using $\rm \small {Gadget-X}$ and $\rm \small {Gizmo-Simba}$ baryonic models. The cumulative sub-halo mass function of $\rm \small {Gizmo-Simba}$ simulated clusters aligns with observations, while $\rm \small {Gadget-X}$ simulations exhibit discrepancies in the lower sub-halo mass range, possibly due to its strong supernova feedback. Both $\rm \small {Gadget-X}$ and $\rm \small {Gizmo-Simba}$ simulations demonstrate a redshift evolution of the sub-halo mass function and the Vcirc function, with slightly fewer sub-haloes observed at lower redshifts. Neither the $\rm \small {Gadget-X}$ nor $\rm \small {Gizmo-Simba}$ (albeit a little closer) simulated clusters’ predictions for the Msub–Vcirc relation align with the observational result. Further investigations on the correlation between sub-halo/halo properties and the discrepancy in the Msub–Vcirc relation reveal that the sub-halo’s half mass radius and galaxy stellar age, the baryon fraction, and sub-halo distance from the cluster’s centre, as well as the halo relaxation state, play important roles on reproducing this relation. Nonetheless, challenges persist in accurately reproducing the observed Msub–Vcirc relationship within our current hydrodynamic cluster simulation that adheres to the standard ΛCDM cosmology. These challenges may stem from shortcomings in our baryon modelling, numerical intricacies within the simulation, or even potential limitations of the ΛCDM framework.

Extending the unified subhalo model to warm dark matter

ABSTRACT Using a set of high-resolution N-body simulations, we extend the unified distribution model of cold dark matter (CDM) subhaloes to the warm dark matter (WDM) case. The same model framework combining the unevolved mass function, unevolved radial distribution, and tidal stripping can predict the mass function and spatial distribution of subhaloes in both CDM and WDM simulations. The dependence of the model on the DM particle property is universally parametrized through the half-mode mass of the initial power spectrum. Compared with the CDM model, the WDM model differs most notably in two aspects. (1) In contrast to the power-law form in CDM, the unevolved subhalo mass function for WDM is scale-dependent at the low mass end due to the cut-off in the initial power spectrum. (2) WDM subhaloes are more vulnerable to tidal stripping and disruption due to their lower concentrations at accretion time. Their survival rate is also found to depend on the infall mass. Accounting for these differences, the model predicts a final WDM subhalo mass function that is also proportional to the unevolved subhalo mass function. The radial distribution of WDM subhaloes is predicted to be mass-dependent. For low mass subhaloes, the radial distribution is flatter in the inner halo and steeper in the outer halo compared to the CDM counterpart, due to the scale-dependent unevolved mass function and the enhanced tidal stripping. The code for sampling subhaloes according to our generalized model is available at https://github.com/fhtouma/subgen2.

Detecting low-mass perturbers in cluster lenses using curved arc bases

ABSTRACT Strong gravitationally lensed arcs produced by galaxy clusters have been observationally detected for several decades now. These strong lensing constraints provided high-fidelity mass models for cluster lenses that include substructure down to $10^{9{-}10}\, \mathrm{M}_\odot$. Optimizing lens models, where the cluster mass distribution is modelled by a smooth component and subhaloes associated with the locations of individual cluster galaxies, has enabled deriving the subhalo mass function, providing important constraints on the nature and granularity of dark matter. In this work, we explore and present a novel method to detect and measure individual perturbers (subhaloes, line-of-sight haloes, and wandering supermassive black holes) by exploiting their proximity to highly distorted lensed arcs in galaxy clusters, and by modelling the local lensing distortions with curved arc bases. This method offers the possibility of detecting individual low-mass perturber subhaloes in clusters and haloes along the line of sight down to a mass resolution of $10^8\, \mathrm{M}_\odot$. We quantify our sensitivity to low-mass perturbers ($M\sim 10^{7{-}9}\, \mathrm{M}_\odot$) in clusters (M ∼ 1014–15 M⊙), by creating realistic mock data. Using three lensed images of a background galaxy in the cluster SMACS J0723, taken by JWST, we study the retrieval of the properties of potential perturbers with masses $M=10^{7{-}9}\, \mathrm{M}_\odot$. From the derived posterior probability distributions for the perturber, we constrain its concentration, redshift, and ellipticity. By allowing us to probe lower mass substructures, the use of curved arc bases can lead to powerful constraints on the nature of dark matter as discrimination between dark matter models appears on smaller scales.

Strong lensing constraints on primordial black holes as a dark matter candidate

ABSTRACT Dark matter could comprise, at least in part, primordial black holes (PBHs). To test this hypothesis, we present an approach to constrain the PBH mass (MPBH) and mass fraction (fPBH) from the flux ratios of quadruply imaged quasars. Our approach uses an approximate Bayesian computation forward modelling technique to directly sample the posterior distribution of MPBH and fPBH, while marginalizing over the subhalo mass function amplitude, spatial distribution, and the size of the lensed source. We apply our method to 11 quadruply imaged quasars and derive a new constraint on the intermediate-mass area of PBH parameter space 104 M⊙ < MPBH < 106 M⊙. We obtain an upper limit fPBH < 0.17 (95 per cent confidence limit). This constraint is independent of all other previously published limits.

Symphony: Cosmological Zoom-in Simulation Suites over Four Decades of Host Halo Mass

We present Symphony, a compilation of 262 cosmological, cold-dark-matter-only zoom-in simulations spanning four decades of host halo mass, from 1011–1015 M ⊙. This compilation includes three existing simulation suites at the cluster and Milky Way–mass scales, and two new suites: 39 Large Magellanic Cloud-mass (1011 M ⊙) and 49 strong-lens-analog (1013 M ⊙) group-mass hosts. Across the entire host halo mass range, the highest-resolution regions in these simulations are resolved with a dark matter particle mass of ≈3 × 10−7 times the host virial mass and a Plummer-equivalent gravitational softening length of ≈9 × 10−4 times the host virial radius, on average. We measure correlations between subhalo abundance and host concentration, formation time, and maximum subhalo mass, all of which peak at the Milky Way host halo mass scale. Subhalo abundances are ≈50% higher in clusters than in lower-mass hosts at fixed sub-to-host halo mass ratios. Subhalo radial distributions are approximately self-similar as a function of host mass and are less concentrated than hosts’ underlying dark matter distributions. We compare our results to the semianalytic model Galacticus, which predicts subhalo mass functions with a higher normalization at the low-mass end and radial distributions that are slightly more concentrated than Symphony. We use UniverseMachine to model halo and subhalo star formation histories in Symphony, and we demonstrate that these predictions resolve the formation histories of the halos that host nearly all currently observable satellite galaxies in the universe. To promote open use of Symphony, data products are publicly available at http://web.stanford.edu/group/gfc/symphony.

From Images to Dark Matter: End-to-end Inference of Substructure from Hundreds of Strong Gravitational Lenses

Constraining the distribution of small-scale structure in our universe allows us to probe alternatives to the cold dark matter paradigm. Strong gravitational lensing offers a unique window into small dark matter halos (<1010 M ⊙) because these halos impart a gravitational lensing signal even if they do not host luminous galaxies. We create large data sets of strong lensing images with realistic low-mass halos, Hubble Space Telescope (HST) observational effects, and galaxy light from HST’s COSMOS field. Using a simulation-based inference pipeline, we train a neural posterior estimator of the subhalo mass function (SHMF) and place constraints on populations of lenses generated using a separate set of galaxy sources. We find that by combining our network with a hierarchical inference framework, we can both reliably infer the SHMF across a variety of configurations and scale efficiently to populations with hundreds of lenses. By conducting precise inference on large and complex simulated data sets, our method lays a foundation for extracting dark matter constraints from the next generation of wide-field optical imaging surveys.

Ironing the folds: the phase space chevrons of a GSE-like merger as a dark matter subhalo detector

ABSTRACT Recent work uncovered features in the phase space of the Milky Way’s stellar halo which may be attributed to the last major merger. When stellar material from a satellite is accreted onto its host, it phase mixes and appears finely substructured in phase space. For a high-eccentricity merger, this substructure most clearly manifests as numerous wrapping chevrons in (vr, r) space, corresponding to stripes in (E, θr) space. We introduce the idea of using this substructure as an alternative subhalo detector to cold stellar streams. We simulate an N-body merger akin to the GSE and assess the impact of subhaloes on these chevrons. We examine how their deformation depends on the mass, pericentre, and number of subhaloes. To quantify the impact of perturbers in our simulations, we utilize the appearance of chevrons in (E, θr) space to introduce a new quantity – the ironing parameter. We show that: (1) a single flyby of a massive (∼1010 M⊙) subhalo with pericentre comparable to, or within, the shell’s apocentre smooths out the substructure, (2) a single flyby of a low mass (≲ 108 M⊙) has negligible effect, (3) multiple flybys of subhalos derived from a subhalo mass function between 107 and 1010 M⊙ cause significant damage if deep within the potential, (4) the effects of known perturbers (e.g. Sagittarius) should be detectable and offer constraints on their initial mass. The sensitivity to the populations of subhaloes suggests that we should be able to place an upper limit on the Milky Way’s subhalo mass function.

ΛCDM halo substructure properties revealed with high-resolution and large-volume cosmological simulations

ABSTRACT In this work, we investigate the structural properties, distribution and abundance of ΛCDM dark matter subhaloes using the Phi-4096 and Uchuu suite of N-body cosmological simulations. Thanks to the combination of their large volume, high mass resolution and superb statistics, we are able to quantify – for the first time consistently over more than seven decades in ratio of subhalo-to-host-halo mass – dependencies of subhalo properties on mass, maximum circular velocity, Vmax, host halo mass, and distance to host halo centre. We also dissect the evolution of these dependencies over cosmic time. We provide accurate fits for the subhalo mass and velocity functions, both exhibiting decreasing power-law slopes and with no significant dependence on redshift. We also find subhalo abundance to depend weakly on host halo mass. Subhalo structural properties are codified via a concentration parameter, cV, that does not depend on any pre-defined density profile and relies only on Vmax. We derive the cV−Vmax relation and find an important dependence on distance of the subhalo to the host halo centre. Interestingly, we also find subhaloes of the same mass to be significantly more concentrated when they reside inside more massive hosts. Finally, we investigate the redshift evolution of cV, and provide accurate fits. Our results offer an unprecedented detailed characterization of the subhalo population, consistent over a wide range of subhalo and host halo masses, as well as cosmic times. Thus, we expect our work to be particularly useful for any future research involving dark matter halo substructure.

Can ultralight dark matter explain the age–velocity dispersion relation of the Milky Way disc: A revised and improved treatment

ABSTRACT Ultralight axion-like particles ma ∼ 10−22 eV, or Fuzzy Dark Matter (FDM), behave comparably to cold dark matter (CDM) on cosmological scales and exhibit a kpc-size de Broglie wavelength capable of alleviating established (sub-)galactic-scale problems of CDM. Substructures inside an FDM halo incur gravitational potential perturbations, resulting in stellar heating sufficient to account for the Galactic disc thickening over a Hubble time, as first demonstrated by Church et al. We present a more sophisticated treatment that incorporates the full baryon and dark matter distributions of the Milky Way and adopts stellar disc kinematics inferred from recent Gaia, APOGEE, and LAMOST surveys. Ubiquitous density granulation and subhalo passages, respectively, drive inner disc thickening and flaring of the outer disc, resulting in an observationally consistent ‘U-shaped’ disc vertical velocity dispersion profile with the global minimum located near the solar radius. The observed age–velocity dispersion relation in the solar vicinity can be explained by the FDM-substructure-induced heating and places an exclusion bound ma ≳ 0.4 × 10−22 eV. We assess non-trivial uncertainties in the empirical core–halo relation, FDM subhalo mass function and tidal stripping, and stellar heating estimate. The mass range ma ≃ 0.5–0.7 × 10−22 eV favoured by the observed thick disc kinematics is in tension with several exclusion bounds inferred from dwarf density profiles, stellar streams, and Milky Way satellite populations, which could be significantly relaxed due to the aforesaid uncertainties. Additionally, strongly anisotropic heating could help explain the formation of ultra-thin disc galaxies.

Inferring subhalo effective density slopes from strong lensing observations with neural likelihood-ratio estimation

ABSTRACT Strong gravitational lensing has emerged as a promising approach for probing dark matter (DM) models on sub-galactic scales. Recent work has proposed the subhalo effective density slope as a more reliable observable than the commonly used subhalo mass function. The subhalo effective density slope is a measurement independent of assumptions about the underlying density profile and can be inferred for individual subhaloes through traditional sampling methods. To go beyond individual subhalo measurements, we leverage recent advances in machine learning and introduce a neural likelihood-ratio estimator to infer an effective density slope for populations of subhaloes. We demonstrate that our method is capable of harnessing the statistical power of multiple subhaloes (within and across multiple images) to distinguish between characteristics of different subhalo populations. The computational efficiency warranted by the neural likelihood-ratio estimator over traditional sampling enables statistical studies of DM perturbers and is particularly useful as we expect an influx of strong lensing systems from upcoming surveys.

Extracting dark-matter velocities from halo masses: A reconstruction conjecture

Increasing attention has recently focused on nontraditional dark-matter production mechanisms which result in primordial dark-matter velocity distributions with highly nonthermal shapes. In this paper, we undertake an assessment of how the detailed shape of a general dark-matter velocity distribution impacts structure formation in the nonlinear regime. In particular, we investigate the impact on the halo-mass and subhalo-mass functions, as well as on astrophysical observables such as satellite and cluster-number counts. We find that many of the standard expectations no longer hold in situations in which this velocity distribution takes a highly nontrivial, even multimodal shape. For example, we find that the nominal free-streaming scale alone becomes insufficient to characterize the effect of free-streaming on structure formation. In addition, we propose a simple one-line conjecture which can be used to ``reconstruct'' the primordial dark-matter velocity distribution directly from the shape of the halo-mass function. Although our conjecture is completely heuristic, we show that it successfully reproduces the salient features of the underlying dark-matter velocity distribution even for nontrivial distributions which are highly nonthermal and/or multimodal, such as might occur for nonminimal dark sectors. Moreover, since our approach relies only on the halo-mass function, our conjecture provides a method of probing dark-matter properties even for scenarios in which the dark and visible sectors interact only gravitationally.

Semi-analytical frameworks for subhaloes from the smallest to the largest scale

ABSTRACT Substructures of dark matter halo, called subhaloes, provide important clues to understand the nature of dark matter. We construct a useful model to describe the properties of subhalo mass functions based on the well-known analytical prescriptions, the extended Press–Schechter theory. The unevolved subhalo mass functions at arbitrary mass scales become describable without introducing free parameters. The different host halo evolution histories are directly recast to their subhalo mass functions. As applications, we quantify the effects from (i) the Poisson fluctuation, (ii) the host-mass scatter, and the (iii) different tidal evolution models on observables in the current Universe with this scheme. The Poisson fluctuation dominates in the number count of the mass ratio to the host of $\sim {\cal O}(10^{-2})$, where the intrinsic scatter is smaller by a factor of a few. The host-mass scatter around its mean does not affect the subhalo mass function. Different models of the tidal evolution predict a factor of ∼2 difference in numbers of subhaloes with $\lesssim {\cal O}(10^{-5})$, while the dependence of the Poisson fluctuation on the tidal evolution models is subtle. The scheme provides a new tool for investigating the smallest scale structures of our Universe which are to be observed in near future experiments.

Sensitivity estimation for dark matter subhalos in synthetic Gaia DR2 using deep learning

The abundance of dark matter subhalos orbiting a host galaxy is a generic prediction of the cosmological framework, and is a promising way to constrain the nature of dark matter. In this paper, we investigate the use of machine learning-based tools to quantify the magnitude of phase-space perturbations caused by the passage of dark matter subhalos. A simple binary classifier and an anomaly detection model are proposed to estimate if stars or star particles close to dark matter subhalos are statistically detectable in simulations. The simulated datasets are three Milky Way-like galaxies and nine synthetic Gaia DR2 surveys derived from these. Firstly, we find that the anomaly detection algorithm, trained on a simulated galaxy with full 6D kinematic observables and applied on another galaxy, is nontrivially sensitive to the dark matter subhalo population. On the other hand, the classification-based approach is not sufficiently sensitive due to the extremely low statistics of signal stars for supervised training. Finally, the sensitivity of both algorithms in the Gaia-like surveys is negligible. The enormous size of the Gaia dataset motivates the further development of scalable and accurate data analysis methods that could be used to select potential regions of interest for dark matter searches to ultimately constrain the Milky Way’s subhalo mass function, as well as simulations where to study the sensitivity of such methods under different signal hypotheses.

Tidal tracks and artificial disruption of cold dark matter haloes

ABSTRACT We describe a simple extension to existing models for the tidal heating of dark matter subhaloes which takes into account second-order terms in the impulse approximation for tidal heating. We show that this revised model can accurately match the tidal tracks along which subhaloes evolve as measured in high-resolution N-body simulations. We further demonstrate that, when a constant density core is introduced into a subhalo, this model is able to quantitatively reproduce the evolution and artificial disruption of N-body subhaloes arising from finite resolution effects. Combining these results we confirm prior work indicating that artificial disruption in N-body simulations can result in a factor two underestimate of the subhalo mass function in the inner regions of host haloes, and a 10–20 per cent reduction over the entire virial volume.