We use N-body simulations to study the evolution of cuspy cold dark matter (CDM) halos in the gravitational potential of a massive host. Tidal mass losses reshape CDM halos, leaving behind bound remnants whose characteristic densities are set by the mean density of the host at the pericentre of their respective orbit. The evolution to the final bound remnant state is essentially complete after ~5 orbits for nearly circular orbits, while reaching the same remnant requires ~25 and ~40 orbits for eccentric orbits with 1:5 and 1:20 pericentre-to-apocentre ratios, respectively. The density profile of tidal remnants is fully specified by the fraction of mass lost, and approaches an exponentially-truncated Navarro-Frenk-White profile in the case of heavy mass loss. Resolving tidal remnants requires excellent numerical resolution; poorly resolved subhalos have systematically lower characteristic densities and are more easily disrupted. Even simulations with excellent spatial and time resolution fail when the final remnant is resolved with fewer than 3000 particles. We derive a simple empirical model that describes the evolution of the mass and the density profile of the tidal remnant applicable to a wide range of orbital eccentricities and pericentric distances. Applied to the Milky Way, our results suggest that $10^8$ - $10^{10}$ solar mass halos accreted ~10 Gyrs ago on 1:10 orbits with pericentric distance ~10 kpc should have been stripped to 0.1 - 1 per cent of their original mass. This implies that estimates of the survival and structure of such halos (the possible hosts of ultra-faint Milky Way satellites) based on direct cosmological simulations may be subject to substantial revision.
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 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…
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…
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…
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…
We simulate the tidal disruption of a collisionless N-body globular star cluster in a total of 300 different orbits selected to have galactocentric radii between 10 and 30 kpc in four dark matter halos: (a) a spherical halo with no subhalos, (b) a spherical halo with subhalos, (c) a realistic halo with no subhalos, and (d) a realistic halo with subhalos. This allows us to isolate and study how the halo's (lack of) dynamical symmetry and substructures affect the dispersal of tidal debris. The realistic halos are constructed from the snapshot of the Via Lactea II simulation at redshift zero. We …
We use N-body simulations to model the tidal evolution of dark matter-dominated dwarf spheroidal galaxies embedded in cuspy Navarro-Frenk-White subhalos. Tides gradually peel off stars and dark matter from a subhalo, trimming it down according to their initial binding energy. This process strips preferentially particles with long orbital times, and comes to an end when the remaining bound particles have crossing times shorter than a fraction of the orbital time at pericentre. The properties of the final stellar remnant thus depend on the energy distribution of stars in the progenitor subhalo, …
Investigating the spin parameter distribution of subhaloes in two high resolution isolated halo simulations, re- cent work by Onions et al. suggested that typical subhalo spins are consistently lower than the spin distribution found for field haloes. To further examine this puzzle, we have analyzed simulations of a cosmological volume with sufficient resolution to resolve a significant subhalo population. We confirm the result of Onions et al. and show that the typical spin of a subhalo decreases with decreasing mass and increasing proximity to the host halo center. We interpret this as the gr…
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, …
Accurate models of the structural evolution of dark matter subhaloes, as they orbit within larger systems, are fundamental to understanding the detailed distribution of dark matter at the present day. Numerical simulations of subhalo evolution support the idea that the mass loss associated with tidal stripping is most naturally understood in energy space, with the particles that are the least bound being removed first. Starting from this premise, we recently proposed a zero-parameter "energy-truncation model" for subhalo evolution. We tested this model with simulations of tidal stripping of sa…
We model the time evolution of gaps in tidal streams caused by the impact of a dark matter subhalo, while both orbit a spherical gravitational potential. To this end, we make use of the simple behaviour of orbits in action-angle space. A gap effectively results from the divergence of two nearby orbits whose initial phase-space separation is, for very cold thin streams, largely given by the impulse induced by the subhalo. We find that in a spherical potential the size of a gap increases linearly with time for sufficiently long timescales. We have derived an analytic expression that shows how th…
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）
Dark matter subhalos, predicted in large numbers in the cold dark matter scenario, should have an impact on particle dark matter searches. Recent results show that tidal disruption of these objects in computer simulations is over-efficient due to numerical artifacts and resolution effects. Accounting for these results, we re-estimate the subhalo abundance in the Milky Way using semi-analytical techniques. In particular, we show that the boost factor for gamma rays and cosmic-ray antiprotons is increased by roughly a factor of two.
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 …
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…
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…
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 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…
A few dark matter substructures have recently been detected in strong gravitational lenses though their perturbations of highly magnified images. We derive a characteristic scale for lensing perturbations and show that this is significantly larger than the perturber's Einstein radius. We show that the perturber's projected mass enclosed within this radius, scaled by the log-slope of the host galaxy's density profile, can be robustly inferred even if the inferred density profile and tidal radius of the perturber are biased. We demonstrate the validity of our analytic derivation by using several…
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…
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）
The shape-velocity alignment of satellites forged by tidal locking and dynamical friction
Tsung-Dao Lee Institute & School of Physics and Astronomy, Shanghai Jiao Tong University（上海交大李政道研究所与物理与天文学院）；Key Laboratory for Particle Astrophysics and Cosmology (MOE)/Shanghai Key Laboratory for Particle Physics and Cosmology（粒子天体物理与宇宙学重点实验室（教育部）/上海粒子物理与宇宙学重点实验室）；University of Toronto（多伦多大学）；Institute for Astronomy, University of Edinburgh（爱丁堡大学天体物理研究所）；Institute of Astronomy, University of Cambridge（剑桥大学天体物理研究所）；Shanghai Jiao Tong University（上海交通大学）
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…
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 investigate dynamical self-friction, the process by which material that is stripped from a subhalo torques its remaining bound remnant, which causes it to lose orbital angular momentum. By running idealized simulations of a subhalo orbiting within an analytical host halo potential, we isolate the effect of self-friction from traditional dynamical friction due to the host halo. While at some points in a subhalo's orbit the torque of the stripped material can boost the orbital angular momentum of the remnant, the net effect over the long term is orbital decay regardless of the initial orbital…
The Sinking Statistics of Dark Matter Subhalos Across Hierarchical Levels
Shanghai Jiao Tong University（上海交通大学）；University of Pennsylvania（宾夕法尼亚大学）；Leiden University（莱顿大学）；Peking University（北京大学）；Nanjing University（南京大学）；Chinese Academy of Sciences（中国科学院）
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 simulate tidal streams in the presence and absence of substructures inside the zero redshift snapshot of the Via Lactea II (VL-2) simulation. A halo finder is used to remove and isolate the subhalos found inside the high resolution dark matter halo of VL-2, and the potentials for both the main halo and all the subhalos are constructed individually using the self-consistent field (SCF) method. This allows us to make direct comparison of tidal streams between a smooth halo and a lumpy halo without assuming idealized profiles or triaxial fits. We simulate the kinematics of a star cluster start…
Which Milky Way Streams Make the Best Dark Matter Detectors?
MIT Kavli Institute for Astrophysics and Space Research（麻省理工学院卡弗里天体物理学与空间研究研究所）；Kavli Institute for Particle Astrophysics and Cosmology, Stanford University（斯坦福大学卡弗里粒子天体物理学与宇宙学研究所）；Department of Physics, Stanford University（斯坦福大学物理系）；SLAC National Accelerator Laboratory（斯坦福直线加速器国家实验室）；The Observatories of the Carnegie Institution for Science（卡内基科学机构天文台）；Department of Astrophysical Sciences, Princeton University（普林斯顿大学天体物理科学系）
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…
The distribution of dark matter (DM) subhalos in our Galaxy remains disputed, leading to varying $γ$-ray and $ν$ flux predictions from their annihilation or decay. In this work, we study how, in the inner Galaxy, subhalo tidal disruption from the Galactic baryonic potential impacts these signals. Based on state-of-the art modeling of this effect from numerical simulations and semi-analytical results, updated subhalo spatial distributions are derived and included in the CLUMPY code. The latter is used to produce a thousand realizations of the $γ$-ray and $ν$ sky. Compared to predictions based o…
Simulations of tidal streams show that close encounters with dark matter subhalos induce density gaps and distortions in on-sky path along the streams. Accordingly, observing disrupted streams in the Galactic halo would substantiate the hypothesis that dark matter substructure exists there, while in contrast, observing collimated streams with smoothly varying density profiles would place strong upper limits on the number density and mass spectrum of subhalos. Here, we examine several measures of stream "disruption" and their power to distinguish between halo potentials with and without substru…
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 …
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…
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…
We present a model for the remnants of haloes that have gone through an adiabatic tidal stripping process. We show that this model exactly reproduces the remnant of an NFW halo that is exposed to a slowly increasing isotropic tidal field and approximately for an anisotropic tidal field. The model can be used to predict the asymptotic mass loss limit for orbiting subhaloes, solely as a function of the initial structure of the subhalo and the value of the tidal field at pericentre. Predictions can easily be made for differently concentrated host-haloes with and without baryonic components, which…
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 …
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…
The abundance and demographics of dark matter substructure is important for many areas in astrophysics and cosmological $N$-body simulations have been the primary tool used to investigate them. However, it has recently become clear that the simulations are subject to numerical artefacts, which hampers a proper treatment of the tidal evolution of subhaloes. Unfortunately, no analytical models that accurately describe subhalo evolution exist either. We therefore present a library of idealized, high resolution $N$-body simulations of the tidal evolution of individual subhaloes that can be used to…
Cosmological simulations of the same spiral galaxy: satellite properties, the role of baryonic physics and star formation history in shaping dark matter cores/cusps
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…
Ample observational capabilities exist today to detect the small density perturbations that low-mass dark matter subhaloes impart on stellar streams from disrupting Galactic satellites. In anticipation of these observations, we investigate the expected number and size of gaps by combining an analytic prescription for gap evolution on circular orbits with the flux of subhaloes near the stream. We explore the distribution of gap sizes and depths for a typical cold stream around the Milky Way and find that for a given stream age and gap depth, each subhalo mass produces a characteristic gap size.…
We study evolution of self-interacting dark matter (SIDM) subhalos in the Milky Way (MW) tidal field. The interaction between the subhalos and the MW's tides lead to more diverse dark matter distribution in the inner region, compared to their cold dark matter counterparts. We test this scenario with two MW satellite galaxies, Draco and Fornax, opposite extremes in the inner dark matter content, and find that they can be accommodated within the SIDM model proposed to explain the diverse rotation curves of spiral galaxies in the field.
We perform the first self-consistent measurement of the rate of interactions between stellar tidal streams created by disrupting satellites and dark subhalos in a cosmological simulation of a Milky-Way-mass galaxy. Using a retagged version of the Aquarius A dark-matter-only simulation, we selected 18 streams of tagged star particles that appear thin at the present day and followed them from the point their progenitors accrete onto the main halo, recording in each snapshot the characteristics of all dark-matter subhalos passing within several distance thresholds of any tagged star particle in e…
