Accurately predicting the abundance and structural evolution of dark matter subhaloes is crucial for understanding galaxy formation, modeling galaxy clustering, and constraining the nature of dark matter. Due to the nonlinear nature of subhalo evolution, cosmological $N$-body simulations remain its primary method of investigation. However, it has recently been demonstrated that such simulations are still heavily impacted by artificial disruption, diminishing the information content on small scales and reducing the reliability of all simulation-calibrated semi-analytical models. In this paper, we utilize the recently released DASH library of high-resolution, idealized simulations of the tidal evolution of subhaloes, which are unhindered by numerical overmerging due to discreteness noise or force softening, to calibrate an improved, more-accurate model of the evolution of the density profiles of subhaloes that undergo tidal heating and stripping within their host halo. By testing previous findings that the structural evolution of a tidally truncated subhalo depends solely on the fraction of mass stripped, independent of the details of the stripping, we identify an additional dependence on the initial subhalo concentration. We provide significantly improved fitting functions for the subhalo density profiles and structural parameters ($V_\mathrm{max}$ and $r_\mathrm{max}$) that are unimpeded by numerical systematics and applicable to a wide range of parameter space. This model will be an integral component of a future semi-analytical treatment of substructure evolution, which can be used to predict key quantities, such as the evolved subhalo mass function and annihilation boost factors, and validate such calculations performed with cosmological simulations.
Several recent studies have indicated that artificial subhalo disruption (the spontaneous, non-physical disintegration of a subhalo) remains prevalent in state-of-the-art dark matter-only cosmological simulations. In order to quantify the impact of disruption on the inferred subhalo demographics, we augment the semi-analytical SatGen dynamical subhalo evolution model with an improved treatment of tidal stripping that is calibrated using the DASH database of idealized high-resolution simulations of subhalo evolution, which are free from artificial disruption. We also develop a model of artifici…
Dark matter halos grow by hierarchical clustering as they merge together to produce ever larger structures. During these merger processes, the smaller halo can potentially survive as a subhalo of the larger halo, so a galaxy-scale halo today likely possesses a rich abundance of substructure. This substructure can greatly boost the rate of dark matter annihilation within the host halo, but the precise magnitude of this boost is clouded by uncertainty about the survival prospects of these subhalos. In particular, tidal forces gradually strip material from the subhalos, reducing their annihilatio…
The predicted abundance and properties of the low-mass substructures embedded inside larger dark matter haloes differ sharply among alternative dark matter models. Too small to host galaxies themselves, these subhaloes may still be detected via gravitational lensing, or via perturbations of the Milky Way's globular cluster streams and its stellar disk. Here we use the Apostle cosmological simulations to predict the abundance and the spatial and velocity distributions of subhaloes in the range 10^6.5-10^8.5 solar masses inside haloes of mass ~ 10^12 solar masses in LCDM. Although these subhaloe…
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 m…
The demographics of dark matter substructure depend sensitively on the nature of dark matter. Optimally leveraging this probe requires accurate theoretical predictions regarding the abundance of subhaloes. These predictions are hampered by artificial disruption in numerical simulations, by large halo-to-halo variance, and by the fact that the results depend on the baryonic physics of galaxy formation. In particular, numerical simulations have shown that the formation of a central disc can drastically reduce the abundance of substructure compared to a dark matter-only simulation, which has been…
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 …
We present the first comprehensive analysis of the segregation of dark matter subhaloes in their host haloes. Using numerical simulations, we examine the segregation of twelve different subhalo properties with respect to both orbital energy and halo-centric radius (in real space as well as in projection). Subhaloes are strongly segregated by accretion redshift, which is an outcome of the inside-out assembly of their host haloes. Since subhaloes that were accreted earlier have experienced more tidal stripping, subhaloes that have lost a larger fraction of their mass at infall are on more bound …
To gain understanding of the complicated, non-linear and numerical processes associated with the tidal evolution of dark matter subhaloes in numerical simulation, we perform a large suite of idealized simulations that follow individual N-body subhaloes in a fixed, analytical host halo potential. By varying both physical and numerical parameters, we investigate under what conditions the subhaloes undergo disruption. We confirm the conclusions from our more analytical assessment in van den Bosch et al. that most disruption is numerical in origin; as long as a subhalo is resolved with sufficient …
New insights on low-mass dark matter subhalo tidal tracks via numerical simulations
Durham University（杜伦大学）；Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid（马德里自治大学-西班牙国家科学研究委员会理论物理研究所）；Universidad Autónoma de Madrid（马德里自治大学）；Zhejiang University（浙江大学）
Through numerical simulations, we study the dissolution timescale of the Ursa Minor cold stellar clump, due to the combination of phase-mixing and gravitational encounters with compact dark substructures in the halo of Ursa Minor. We compare two scenarios; one where the dark halo is made up by a smooth mass distribution of light particles and one where the halo contains 10% of its mass in the form of substructures (subhalos). In a smooth halo, the stellar clump survives for a Hubble time provided that the dark matter halo has a big core. In contrast, when the point-mass dark substructures are …
The presence of an invisible substructure has previously been detected in the gravitational lens galaxy SDSSJ0946+1006 through its perturbation of the lensed images. Using flexible models for the main halo and the subhalo perturbation to fit the lensed images, we demonstrate that the subhalo has an extraordinarily high central density and steep density slope. The inferred concentration for the subhalo is well above the expected scatter in concentrations for $Λ$CDM halos of similar mass. We robustly infer the subhalo's projected mass within 1 kpc to be $\sim 2$-$3.7\times 10^9$M$_\odot$ at $>$9…
Tiny galaxies and dark substructures: exploring the "dark" subhaloes in TNG50
Durham University（杜伦大学）；University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；University of Hertfordshire（赫特福德大学）；STAR Institute（STAR研究所）；Stockholm University（斯德哥尔摩大学）
Strong gravitational lensing observations can test structure formation models by constraining the masses and concentrations of subhaloes in massive galaxy clusters. Recent work has concluded that cluster subhaloes are more abundant and/or concentrated than predicted by $Λ$CDM simulations; this finding has been interpreted as arising from unidentified issues with simulations or an incorrect understanding of the nature of dark matter. We test these hypotheses by comparing observed subhalo masses and maximum circular velocities $v_\mathrm{max}$ to predictions from the high resolution Hydrangea ga…
Accurately predicting the demographics of dark matter (DM) substructure is of paramount importance for many fields of astrophysics, including gravitational lensing, galaxy evolution, halo occupation modeling, and constraining the nature of dark matter. Because of its strongly non-linear nature, DM substructure is typically modeled using N-body simulations, which reveal that large fractions of DM subhaloes undergo complete disruption. In this paper we use both analytical estimates and idealized numerical simulations to investigate whether this disruption is mainly physical, due to tidal heating…
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 pericenter. It is also found that the often used Coulomb logarithm $\ln M/m$ has to be revised to best fit the merging time-scales fro…
A defining prediction of the cold dark matter (CDM) cosmological model is the existence of a very large population of low mass haloes, down to planet-size masses. However, their fate as they are accreted onto haloes many orders of magnitude more massive remains fundamentally uncertain. A number of numerical explorations have found subhaloes to be very resilient to tides, but resolution limits make it difficult to explore tidal evolution at arbitrarily low masses. What are the structural properties of heavily stripped subhaloes? Do tidal effects destroy low-mass CDM subhaloes? Here we focus on …
We present a study of unprecedented statistical power regarding the halo-to-halo variance of dark matter substructure. Using a combination of N-body simulations and a semi-analytical model, we investigate the variance in subhalo mass fractions and subhalo occupation numbers, with an emphasis on how these statistics scale with halo formation time. We demonstrate that the subhalo mass fraction, f_sub, is mainly a function of halo formation time, with earlier forming haloes having less substructure. At fixed formation redshift, the average f_sub is virtually independent of halo mass, and the mass…
When dark matter halos are accreted by massive host clusters, strong gravitational tidal forces begin stripping mass from the accreted subhalos. This stripping eventually removes all mass beyond a subhalo's tidal radius, but the unbound mass remains in the vicinity of the satellite for at least a dynamical time t_dyn. The N-body subhalo study of Chamberlain et al. verified this picture and pointed out a useful observational consequence: measurements of subhalo correlations beyond the tidal radius are sensitive to the infall time, t_infall, of the subhalo onto its host. We perform this cross-co…
The cold dark matter (CDM) scenario predicts that galactic halos should host a huge amount of subhalos possibly lighter than planets, depending on the nature of dark matter. Predicting their abundance and distribution has important implications for dark matter searches and searches for subhalos themselves, as they could provide a decisive test of the CDM paradigm. A major difficulty in subhalo population model building is to account for the gravitational stripping induced by baryons, which strongly impact on the overall dynamics inside galaxies. In this paper, we focus on these "baryonic" tide…
We compare the results of high-resolution simulations of individual dark matter subhalos evolving in external tidal fields with and without baryonic bulge and disk components, where the average dark matter particle mass is three orders of magnitude smaller than cosmological zoom-in simulations of galaxy formation. The Via Lactea II simulation is used to setup our initial conditions and provides a basis for our simulations of subhalos in a dark matter-only tidal field, while an observationally motivated model for the Milky Way is used for the tidal field that is comprised of a dark matter halo,…
The cold dark matter scenario of hierarchical large-scale structure formation predicts the existence of abundant subhalos around large galaxies. However, the number of observed dwarf galaxies is far from this theoretical prediction, suggesting that most of the subhalos could be dark or quite faint. Gravitational lensing is a powerful tool to probe the mass distribution directly irrespective of whether it is visible or dark. Time delay anomalies in strongly lensed quasar systems are complementary to flux ratio anomalies in probing dark matter substructure in galaxies. Here we propose that lense…
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 t…
We introduce a machine learning method for estimating the sensitivity of strong lens observations to dark matter subhaloes in the lens. Our training data include elliptical power-law lenses, Hubble Deep Field sources, external shear, and noise and PSF for the Euclid VIS instrument. We set the concentration of the subhaloes using a $v_\mathrm{max}$-$r_\mathrm{max}$ relation. We then estimate the dark matter subhalo sensitivity in $16{,}000$ simulated strong lens observations with depth and resolution resembling Euclid VIS images. We find that, with a $3σ$ detection threshold, $2.35$ per cent of…
Bloodhound Unleashed: Particle-based Substructure Tracking for Cosmological Simulations
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Rensselaer Polytechnic Institute（伦斯勒理工学院）；University of California, Irvine（加州大学尔湾分校）；University of Southern California（南加州大学）
Dynamical evolution of dark matter subhaloes in the Milky Way: role of the Galactic disc
Institute for Astronomy, School of Physics, Zhejiang University（浙江大学物理学院天体物理研究所）；Center for Cosmology and Computational Astrophysics, Zhejiang University（浙江大学宇宙学与计算天体物理中心）；Institute for Astronomy, University of Vienna（维也纳大学天体物理研究所）
Strong gravitational lenses can be used to detect low mass subhalos, 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 OSIRIS on the Keck I Telescope, using a Bayesian method that accounts for uncertainti…
Self-interacting dark matter (SIDM) cosmologies admit an enormous diversity of dark matter (DM) halo density profiles, from low-density cores to high-density core-collapsed cusps. The possibility of the growth of high central density in low-mass halos, accelerated if halos are subhalos of larger systems, has intriguing consequences for small-halo searches with substructure lensing. However, following the evolution of $\lesssim 10^8 M_\odot$ subhalos in lens-mass systems ($\sim 10^{13}M_\odot$) is computationally expensive with traditional N-body simulations. In this work, we develop a new hybr…
We present a comprehensive study on how perturbations due to a distribution of $Λ$CDM dark matter subhalos can lead to star clusters deviating from their orbits. Through a large suite of massless test particle simulations, we find that (1) subhalos with masses less than $10^8 M_{\odot}$ negligibly affect test particle orbits, (2) perturbations lead to orbital deviations only in environments with substructure fractions $f_{sub} \geq 1\%$, (3) perturbations from denser subhalos produce larger orbital deviations, and (4) subhalo perturbations that are strong relative to the background tidal field…
Detecting the dark matter annihilation signal from Galactic substructure, or subhalos, is an important challenge for high-energy gamma-ray experiments. In this paper we discuss detection prospects by combining two different aspects of the gamma-ray signal: the angular distribution and the photon counts probability distribution function (PDF). The true PDF from subhalos has been shown recently (by Lee et al.) to deviate from Poisson; we extend this analysis and derive the signal PDF from a detailed Lambda-CDM-based model for the properties of subhalos. We combine our PDF with a model for Galact…
The clumpiness of dark matter on sub-kpc scales is highly sensitive to the tidal evolution and survival of subhaloes. In agreement with previous studies, we show that N-body realisations of cold dark matter subhaloes with centrally-divergent density cusps form artificial constant-density cores on the scale of the resolution limit of the simulation. These density cores drive the artificial tidal disruption of subhaloes. We run controlled simulations of the tidal evolution of a single subhalo where we repeatedly reconstruct the density cusp, preventing artificial disruption. This allows us to fo…
Measurement of Substructure from the Kinematics of the GD-1 Stellar Stream
Princeton University（普林斯顿大学）；The Observatories of the Carnegie Institution for Science（卡内基科学研究所天文台）；Center for Computational Astrophysics, Flatiron Institute（平顿研究所计算天体物理学中心）
We use a catalogue of stellar binaries with wide separations (up to 1 pc) identified by the Gaia satellite to constrain the presence of extended substructure within the Milky Way galaxy. Heating of the binaries through repeated encounters with substructure results in a characteristic distribution of binary separations, allowing constraints to be placed independent of the formation mechanism of wide binaries. Across a wide range of subhalo density profiles, we show that subhalos with masses $\gtrsim 65 \ M_\odot$ and characteristic length scales similar to the separation of these wide binaries …
The observed population of the Milky Way satellite galaxies offer a unique testing ground for galaxy formation theory on small-scales. Our novel approach was to investigate the clustering of the known Milky Way satellite galaxies and to quantify the amount of substructure within their distribution using a two-point correlation function statistic in each of three spaces: configuration space, line-of-sight velocity space, and four-dimensional phase-space. These results were compared to those for three sets of subhaloes in the Via Lactea II Cold Dark Matter simulation defined to represent the lum…
We study tidal stripping of fuzzy dark matter (FDM) subhalo cores using simulations of the Schrödinger-Poisson equations and analyze the dynamics of tidal disruption, highlighting the differences with standard cold dark matter. Mass loss outside of the tidal radius forces the core to relax into a less compact configuration, lowering the tidal radius. As the characteristic radius of a solitonic core scales inversely with its mass, tidal stripping results in a runaway effect and rapid tidal disruption of the core once its central density drops below $4.5$ times the average density of the host wi…
We describe a simple extension to existing models for the tidal heating of dark matter subhalos 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 subhalos 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 subhalos arising from finite resolution effects. Combining these results we co…
We carry out a detailed study of the orbital dynamics and structural evolution of over 6000 subhalos in the Via Lactea II simulation, from infall to present. By analyzing subhalos with masses down to m = 4e5 Msun, we find that lower mass subhalos, which are not strongly affected by dynamical friction, exhibit behaviors qualitatively different from those found previously for more massive ones. Furthermore, there is a clear trend of subhalos that fell into the host earlier being less concentrated. We show that the concentration at infall characterizes various aspects of subhalo evolution. In par…
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 $(v_r, r)$ space, corresponding to stripes in $(E, θ_r)$ 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…
We present a model for the dynamical evolution of subhaloes based on an approach combining numerical and analytical methods. Our method is based on tracking subhaloes in an N-body simulation up to the last point that it can be resolved, and applying an analytic prescription for its merger timescale that takes dynamical friction and tidal disruption into account. When applied to cosmological N-body simulations with mass resolutions that differ by two orders of magnitude, the technique produces halo occupation distributions that agree to within 3%.
We use high-resolution Aquarius simulations of Milky Way-sized haloes in the LCDM cosmology to study the effects of dark matter substructures on gravitational lensing. Each halo is resolved with ~ 10^8 particles (at a mass resolution ~ 10^3-4 M_sun/h) within its virial radius. Subhaloes with masses larger than 10^5 M_sun/h are well resolved, an improvement of at least two orders of magnitude over previous lensing studies. We incorporate a baryonic component modelled as a Hernquist profile and account for the response of the dark matter via adiabatic contraction. We focus on the "anomalous" flu…
We study evolution of single subhaloes with their masses of $\sim10^9 M_\odot$ in a Milky-Way-sized host halo for self-interacting dark matter (SIDM) models. We perform dark-matter-only N-body simulations of dynamical evolution of individual subhaloes orbiting its host by varying self-scattering cross sections (including a velocity-dependent scenario), subhalo orbits, and internal properties of the subhalo. We calibrate a gravothermal fluid model to predict time evolution in spherical mass density profiles of isolated SIDM haloes with the simulations. We find that tidal effects of SIDM subhalo…
We study the impact of baryons on the distribution of dark matter in a Milky Way-size halo by comparing a high-resolution, moving-mesh cosmological simulation with its dark matter-only counterpart. We identify three main processes related to baryons -- adiabatic contraction, tidal disruption and reionization -- which jointly shape the dark matter distribution in both the main halo and its subhalos. The relative effect of each baryonic process depends strongly on the subhalo mass. For massive subhalos with maximum circular velocity $v_{\rm max} > 35 km/s$, adiabatic contraction increases the da…
We study the substructure population of Milky Way (MW)-mass halos in the $Λ$CDM cosmology using a novel procedure to extrapolate subhalo number statistics beyond the resolution limit of N-body simulations. The technique recovers the mean and the variance of the subhalo abundance, but not its spatial distribution. It extends the dynamic range over which precise statistical predictions can be made by the equivalent of performing a simulation with 50 times higher resolution, at no additional computational cost. We apply this technique to MW-mass halos, but it can easily be applied to halos of any…
We present initial results from the "Ponos" zoom-in numerical simulations of dark matter substructures in massive ellipticals. Two very highly resolved dark matter halos with $M_{\rm vir}=1.2\times 10^{13}$ $M_{\odot}$ and $M_{\rm vir}=6.5\times 10^{12}$ $M_{\odot}$ and different ("violent" vs. "quiescent") assembly histories have been simulated down to $z=0$ in a $Λ$CDM cosmology with a total of 921,651,914 and 408,377,544 particles, respectively. Within the virial radius, the total mass fraction in self-bound $M_{\rm sub}>10^6$ $M_{\odot}$ subhalos at the present epoch is 15% for the violent…
Cold or Warm, the Dark Matter substructure spectrum must extend to objects with masses as low as $10^7 M_\odot$, according to the most recent Lyman-$α$ measurements. Around a Milky Way-like galaxy, more than a thousand of these subhaloes will not be able to form stars but are dense enough to survive even deep down in the potential well of their host. There, within the stellar halo, these dark pellets will bombard tidal streams as they travel around the Galaxy, causing small but recognizable damage to the stream density distribution. The detection and characterization of these stream ruptures w…
We use the IllustrisTNG100 hydrodynamical simulation to study the dependence of the galaxy two-point correlation function on a broad range of secondary subhalo and galactic properties. We construct galaxy mock catalogues adopting a standard sub-halo abundance matching scheme coupled with a secondary assignment between galaxy colour or specific star formation rate and the following subhalo properties: starvation redshift z$_{\rm starve}$, concentration at infall, overdensity $δ_R^{\rm env}$, tidal anisotropy $α_R$, and tidal overdensity $δ_R$. The last two quantities allow us to fully character…
We use the Copernicus Complexio (COCO) high resolution $N$-body simulations to investigate differences in the properties of small-scale structures in the standard cold dark matter (CDM) model and in a model with a cutoff in the initial power spectrum of density fluctuations consistent with both a thermally produced warm dark matter (WDM) particle or a sterile neutrino with mass 7 keV and leptogenesis parameter $L_6=8.7$. The latter corresponds to the "coldest" model with this sterile neutrino mass compatible with the identification of the recently detected 3.5 keV X-ray line as resulting from …
A large population of extended substructures generates a stochastic gravitational field that is fully specified by the function $p({\bf F})$, which defines the probability that a tracer particle experiences a force $\bf F$ within the interval ${\bf F},{\bf F}+ d\bf F$. This paper presents a statistical technique for deriving the spectrum of random fluctuations directly from the number density of substructures with known mass and size functions. Application to the subhalo population found in cold dark matter simulations of Milky Way-sized haloes shows that, while the combined force distribution…
