Evolution Of Subhalos Research Articles

JWST lensed quasar dark matter survey – II. Strongest gravitational lensing limit on the dark matter free streaming length to date

ABSTRACT This is the second in a series of papers in which we use JWST Mid Infrared Instrument multiband imaging to measure the warm dust emission in a sample of 31 multiply imaged quasars, to be used as a probe of the particle nature of dark matter. We present measurements of the relative magnifications of the strongly lensed warm dust emission in a sample of nine systems. The warm dust region is compact and sensitive to perturbations by populations of haloes down to masses $\sim 10^6$ M$_{\odot }$. Using these warm dust flux-ratio measurements in combination with five previous narrow-line flux-ratio measurements, we constrain the halo mass function. In our model, we allow for complex deflector macromodels with flexible third- and fourth-order multipole deviations from ellipticity, and we introduce an improved model of the tidal evolution of subhaloes. We constrain a WDM model and find an upper limit on the half-mode mass of $10^{7.6}\, {\rm M}_\odot$ at posterior odds of 10:1. This corresponds to a lower limit on a thermally produced dark matter particle mass of 6.1 keV. This is the strongest gravitational lensing constraint to date, and comparable to those from independent probes such as the Ly $\alpha$ forest and Milky Way satellite galaxies.

A universal model for the evolution of tidally stripped systems

ABSTRACT 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 satellites with initial NFW profiles, and showed that the energy-truncation model accurately predicts both the mass-loss and density profiles. In this work, we apply the model to a variety of Hernquist, Einasto, and King profiles. We show that it matches the simulation results quite closely in all cases, indicating that it may serve as a universal model to describe tidally stripped collision-less systems. A key prediction of the energy-truncation model is that the central density of dark matter subhaloes is conserved as they lose mass; this has important implications for dark matter annihilation calculations, and for other observational tests of dark matter.

Core-collapse, evaporation, and tidal effects: the life story of a self-interacting dark matter subhalo

ABSTRACT 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 haloes, accelerated if haloes are subhaloes of larger systems, has intriguing consequences for small-halo searches with substructure lensing. However, following the evolution of ${\lesssim}10^8 \, \mathrm{M}_\odot$ subhaloes in lens-mass systems (${\sim}10^{13}\, \mathrm{M}_\odot$) is computationally expensive with traditional N-body simulations. In this work, we develop a new hybrid semi-analytical + N-body method to study the evolution of SIDM subhaloes with high fidelity, from core formation to core-collapse, in staged simulations. Our method works best for small subhaloes (≲1/1000 host mass), for which the error caused by dynamical friction is minimal. We are able to capture the evaporation of subhalo particles by interactions with host halo particles, an effect that has not yet been fully explored in the context of subhalo core-collapse. We find three main processes drive subhalo evolution: subhalo internal heat outflow, host-subhalo evaporation, and tidal effects. The subhalo central density grows only when the heat outflow outweighs the energy gain from evaporation and tidal heating. Thus, evaporation delays or even disrupts subhalo core-collapse. We map out the parameter space for subhaloes to core-collapse, finding that it is nearly impossible to drive core-collapse in subhaloes in SIDM models with constant cross-sections. Any discovery of ultracompact dark substructures with future substructure lensing observations favours additional degrees of freedom, such as velocity-dependence, in the cross-section.

An accurate comprehensive approach to substructure – II. Stripped subhaloes

ABSTRACT In Salvador-Solé, Manrique & Botella (Paper I), we used the ConflUent System of Peak trajectories (CUSP) formalism to derive from first principles and no single free parameter the accurate abundance and radial distribution of both diffuse dark matter (dDM) and subhaloes accreted on to haloes and their progenitors at all previous times. Here we use those results as initial conditions for the monitoring of the evolution of subhaloes and dDM within the host haloes. Specifically, neglecting dynamical friction, we accurately calculate the effects of repetitive tidal stripping and heating on subhaloes as they orbit inside the host halo and infer the amount of dDM and subsubhaloes they release into the intrahalo medium. We then calculate the expected abundance and radial distribution of stripped subhaloes and dDM. This derivation clarifies the role of halo concentration in substructure and unravels the origin of some key features found in simulations including the dependence of substructure on halo mass. In addition, it unveils the specific effects of dynamical friction on substructure. The results derived here are for purely accreting haloes. In Salvador-Solé et al. (Paper III), we complete the study by addressing the case of low-mass subhaloes, unaffected by dynamical friction, in ordinary haloes having suffered major mergers.

Machine learning the fates of dark matter subhaloes: a fuzzy crystal ball

ABSTRACT The evolution of a dark matter halo in a dark matter only simulation is governed purely by Newtonian gravity, making a clean testbed to determine what halo properties drive its fate. Using machine learning, we predict the survival, mass loss, final position, and merging time of subhaloes within a cosmological N-body simulation, focusing on what instantaneous initial features of the halo, interaction, and environment matter most. Survival is well predicted, with our model achieving 94.25 per cent out-of-bag accuracy using only three model inputs (redshift, subhalo-to-host-halo mass ratio, and the impact angle of the subhalo into its host) taken at the time immediately before the subhalo enters its host. However, the mass loss, final location, and merging times are much more stochastic processes, with significant errors between true and predicted quantities for much of our sample. Only five inputs (redshift, impact angle, relative velocity, and the masses of the host and subhalo) determine almost all of the subhalo evolution learned by our models. Generally, subhaloes that enter their hosts at a mid-range of redshifts (z = 0.67–0.43) are the most challenging to make predictions for, across all of our final outcomes. Subhalo orbits that come in more perpendicular to the host are easier to predict, except for in the case of predicting disruption, where the opposite appears to be true. We conclude that the detailed evolution of individual subhaloes within N-body simulations is difficult to predict, pointing to a stochasticity in the merging process. We discuss implications for both simulations and observations.

The tidal evolution of dark matter substructure – II. The impact of artificial disruption on subhalo mass functions and radial profiles

ABSTRACT 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 (DM)-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 Dynamical Aspects of SubHaloes database of idealized high-resolution simulations of subhalo evolution, which are free from artificial disruption. We also develop a model of artificial disruption that reproduces the statistical properties of disruption in the Bolshoi simulation. Using this framework, we predict subhalo mass functions (SHMFs), number density profiles, and substructure mass fractions and study how these quantities are impacted by artificial disruption and mass resolution limits. We find that artificial disruption affects these quantities at the $10{-}20{{\ \rm per\ cent}}$ level, ameliorating previous concerns that it may suppress the SHMF by as much as a factor of 2. We demonstrate that semi-analytical substructure modelling must include orbit integration in order to properly account for splashback haloes, which make up roughly half of the subhalo population. We show that the resolution limit of N-body simulations, rather than artificial disruption, is the primary cause of the radial bias in subhalo number density found in DM-only simulations. Hence, we conclude that the mass resolution remains the primary limitation of using such simulations to study subhaloes. Our model provides a fast, flexible, and accurate alternative to studying substructure statistics in the absence of both numerical resolution limits and artificial disruption.

Can tides disrupt cold dark matter subhaloes?

ABSTRACT 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 follow the evolution of the subhalo for arbitrarily large fractions of tidally stripped mass. Based on this numerical evidence in combination with simple dynamical arguments, we argue that cuspy dark matter subhaloes cannot be completely disrupted by smooth tidal fields. Modelling stars as collisionless tracers of the underlying potential, we furthermore study the tidal evolution of Milky Way dwarf spheroidal galaxies. Using a model of the Tucana III dwarf as an example, we show that tides can strip dwarf galaxies down to sub-solar luminosities. The remnant micro-galaxies would appear as co-moving groups of metal-poor, low-mass stars of similar age, embedded in sub-kpc dark matter subhaloes.

The tidal evolution of dark matter substructure – I. subhalo density profiles

ABSTRACT Accurately predicting the abundance and structural evolution of dark matter subhaloes is crucial for understanding galaxy formation, modelling galaxy clustering, and constraining the nature of dark matter. Due to the non-linear 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 (Vmax and rmax) 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.

DASH: a library of dynamical subhalo evolution

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 calibrate semi-analytical models and to complement cosmological simulations. The simulations focus on minor mergers, i.e., the mass of the subhalo is much smaller than that of the host halo, such that the impact of dynamical friction is negligible. This setup allows the adoption of a fixed analytical potential for modelling the host halo. The dynamical evolution of subhaloes is followed with $N$-body computations. In the library, four parameters, two of which characterize the subhalo orbit with respect to the host halo, and the two concentrations of the host- and subhalo, are varied over the ranges encountered in cosmological simulations. We show several representative examples from the library that illustrate the evolution of the subhalo mass and velocity dispersion profiles. Additionally, we make publicly available a pre-trained non-parametric model of the subhalo mass evolution based on random forest regression. This model is able to interpolate the simulation data at the 0.1\,dex level and provides efficient access to the data for further use in modelling.

Constraining the Nature of Dark Matter with the Star-formation History of the Faintest Local Group Dwarf Galaxy Satellites

Abstract Λ warm dark matter (ΛWDM), realized by collisionless particles of 1–3 keV, has been proposed as an alternative scenario to Λ-Cold-Dark Matter (ΛCDM) for the dwarf galaxy scale discrepancies. We present an approach to test the viability of such WDM models using star-formation histories (SFHs) of the dwarf spheroidal galaxies (dSphs) in the Local Group. We compare their high-time-resolution SFHs with the collapse redshift of their dark halos in CDM and WDM. Collapse redshift is inferred after determining the subhalo infall mass. This is based on the dwarf current mass inferred from stellar kinematics, combined with cosmological simulation results on subhalo evolution. WDM subhalos close to the filtering mass scale, forming significantly later than CDM, are the most difficult to reconcile with early truncation of star formation (z ≥ 3). The ultra-faint dwarfs (UFDs) provide the most stringent constraints. Using six UFDs and eight classical dSphs, we show that a 1 keV particle is strongly disfavored, consistently with other reported methods. Excluding other models is only hinted for a few UFDs. Other UFDs for which the lack of robust constraints on halo mass prevents us from carrying out our analysis rigorously, show a very early onset of star formation that will strengthen the constraints delivered by our method in the future. We discuss the various caveats, notably the low number of dwarfs with accurately determined SFHs and the uncertainties when determining the subhalo infall mass, most notably the baryonic physics. Our preliminary analysis may serve as a pathfinder for future investigations that will combine accurate SFHs for local dwarfs with direct analysis of WDM simulations with baryons.

Statistics of dark matter substructure – III. Halo-to-halo variance

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 dependence of f_sub is therefore mainly a manifestation of more massive haloes assembling later. We compare observational constraints on f_sub from gravitational lensing to our model predictions and simulation results. Although the inferred f_sub are substantially higher than the median LCDM predictions, they fall within the 95th percentile due to halo-to-halo variance. We show that while the halo occupation distribution of subhaloes, P(N|M), is super-Poissonian for large <N>, a well established result, it becomes sub-Poissonian for <N> < 2. Ignoring the non-Poissonity results in systematic errors of the clustering of galaxies of a few percent, and with a complicated scale- and luminosity-dependence. Earlier-formed haloes have P(N|M) closer to a Poisson distribution, suggesting that the dynamical evolution of subhaloes drives the statistics towards Poissonian. Contrary to a recent claim, the non-Poissonity of subhalo occupation statistics does not vanish by selecting haloes with fixed mass and fixed formation redshift. Finally, we use subhalo occupation statistics to put loose constraints on the mass and formation redshift of the Milky Way halo. Using observational constraints on the V_max of the most massive satellites, we infer that 0.25<M_vir/10^12M_sun/h<1.4 and 0.1<z_f<1.4 at 90% confidence.

Modelling galaxy merger time-scales and tidal destruction

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%.

EVOLUTION OF LOW MASS GALACTIC SUBHALOS AND DEPENDENCE ON CONCENTRATION

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 particular, tidal effects truncate the growth of less concentrated subhalos at larger distances from the host; subhalos with smaller concentrations have larger infall radii. The concentration at infall is further shown to be a determining factor for the subsequent mass loss of subhalos within the host, and also for the evolution of their internal structure in the v_max-r_max plane. Our findings raise the prospects of using the concentration to predict the tidal evolution of subhalos, which will be useful for obtaining analytic models of galaxy formation, as well as for near field cosmology.

NEUTRON STAR MERGERS AS THE ORIGIN OF r -PROCESS ELEMENTS IN THE GALACTIC HALO BASED ON THE SUB-HALO CLUSTERING SCENARIO

Binary mergers (NSMs) of double neutron star (and black hole-neutron star) systems are suggested to be major sites of r-process elements in the Galaxy by recent hydrodynamical and nucleosynthesis studies. It has been pointed out, however, that the estimated long lifetimes of neutron star binaries are in conflict with the presence of r-process-enhanced halo stars at metallicities as low as [Fe/H] ~ -3. To resolve this problem, we examine the role of NSMs in the early Galactic chemical evolution on the assumption that the Galactic halo was formed from merging sub-halos. We present simple models for the chemical evolution of sub-halos with total final stellar masses between 10^4 M_solar and 2 x 10^8 M_solar. Typical lifetimes of compact binaries are assumed to be 100 Myr (for 95% of their population) and 1 Myr (for 5%), according to recent binary population synthesis studies. The resulting metallcities of sub-halos and their ensemble are consistent with the observed mass-metallicity relation of dwarf galaxies in the Local Group, and the metallicity distribution of the Galactic halo, respectively. We find that the r-process abundance ratios [r/Fe] start increasing at [Fe/H] <= -3 if the star formation efficiencies are smaller for less massive sub-halos. In addition, the sub-solar [r/Fe] values (observed as [Ba/Fe] ~ -1.5 for [Fe/H] < -3) are explained by the contribution from the short-lived (~1 Myr) binaries. Our results indicate that NSMs may have a substantial contribution to the r-process element abundances throughout the Galactic history.

Resolving subhaloes’ lives with the Hierarchical Bound-Tracing algorithm

We develop a new code, the Hierarchical Bound-Tracing (HBT for short) code, to find and trace dark matter subhaloes in simulations based on the merger hierarchy of dark matter haloes. Application of this code to a recent benchmark test of finding subhaloes demonstrates that HBT stands as one of the best codes to trace the evolutionary history of subhaloes. The success of the code lies in its careful treatment of the complex physical processes associated with the evolution of subhaloes and in its robust unbinding algorithm with an adaptive source subhalo management. We keep a full record of the merger hierarchy of haloes and subhaloes, and allow growth of satellite subhaloes through accretion from its "satellite-of-satellites", hence allowing mergers among satellites. Local accretion of background mass is omitted, while rebinding of stripped mass is allowed. The justification of these treatments is provided by case studies of the lives of individual subhaloes and by the success in finding the complete subhalo catalogue. We compare our result to other popular subhalo finders and show that HBT is able to well resolve subhaloes in high density environment and keep strict physical track of subhaloes' merger history. This code is fully parallelized and freely available upon request to the authors.

AN ANALYTICAL MODEL FOR THE ACCRETION OF DARK MATTER SUBHALOS

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

On the orbits of infalling satellite haloes

The orbital properties of infalling satellite halos set the initial conditions which control the subsequent evolution of subhalos and the galaxies that they host, with implications for mass stripping, star formation quenching, and merging. Using a high-resolution, cosmological N-body simulation, I examine the orbital parameters of satellite halos as they merge with larger host halos, focusing primarily on orbital circularity and pericenter. I explore in detail how these orbital parameters depend on mass and redshift. Satellite orbits become more radial and plunge deeper into their host halo at higher host halo mass, but they do not significantly depend on satellite halo mass. Additionally, satellite orbits become more radial and plunge deeper into their host halos at higher redshift. I also examine satellite velocities, finding that most satellites infall with less specific angular momentum than the host halo virial value, but that satellites are `hotter' than the host virial velocity. I discuss the implications of these results to the processes of galaxy formation and evolution, and I provide fitting formulas to the mass and redshift dependence of satellite orbital circularity and pericenter.

An improved model for the dynamical evolution of dark matter subhaloes

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

Cluster galaxies die hard

We investigate how the specific star formation rates of galaxies of different masses depend on cluster-centric radius and on the central/satellite dichotomy in both field and cluster environments. Recent data from a variety of sources, including the cluster catalogue of von der Linden et al. are compared to the semi-analytic models of De Lucia & Blaizot. We find that these models predict too many passive satellite galaxies in clusters, too few passive central galaxies with low stellar masses, and too many passive central galaxies with high masses. We then outline a series of modifications to the model necessary to solve these problems: a) Instead of instantaneous stripping of the external gas reservoir after a galaxy becomes a satellite, the gas supply is assumed to decrease at the same rate that the surrounding halo loses mass due to tidal stripping, b) The AGN feedback efficiency is lowered to bring the fraction of massive passive centrals in better agreement with the data. We also allow for radio mode AGN feedback in satellite galaxies. c) We assume that satellite galaxies residing in host haloes with masses below 10^12 M_sun do not undergo any stripping. We highlight the fact that in low mass galaxies, the external reservoir is composed primarily of gas that has been expelled from the galactic disk by supernovae driven winds. This gas must remain available as a future reservoir for star formation, even in satellite galaxies. Finally, we present a simple recipe for the stripping of gas and dark matter in satellites that can be used in models where subhalo evolution is not followed in detail.

ON THE SIZE EVOLUTION OF A GALACTIC DISK IN HIERARCHICAL MERGING OF COLD DARK MATTER HALOS

We investigate the dynamical effects of dark matter subhalos on the structure and evolution of a galactic disk, using the semi-analytic method that includes approximated and empirical relations as achieved in detailed numerical simulations of the cold dark matter model. We calculate the upper limit for the size of a galactic disk at a specific redshift z, based on the orbital properties of subhalos characterized by their pericentric distances from the center of a host halo. We find that this possibly largest size of a disk as determined by the smallest pericentric distances of subhalos shows the characteristic properties, which are basically in agreement with an observed galactic disk at low and high z. Namely, it is found that a massive disk can have a larger size than a less massive one, because of its stability against the destruction effect of subhalos. Also, with fixed mass, the size of a galactic disk at low z can be larger than that at high z, reflecting the orbital evolution of subhalos with respect to a host halo. These results suggest that the presence and structure of a galactic disk may be dynamically limited by the interaction with dark matter substructures, especially at high z.