arXiv subjects

Fangzhou Jiang

Publications and source records attributed to Fangzhou Jiang.

At least 55 records · Page 3Linked to original sources

arXiv2024

Tidal evolution of cored and cuspy dark matter halos

The internal structure and abundance of dark matter halos and subhalos are powerful probes of the nature of dark matter. In order to compare observations with dark matter models, accurate theoretical predictions of these quantities are needed. We present a fast and accurate method to describe the tidal evolution of subhalos within their parent halo, based on a semi-analytic approach. We first consider idealized N-body simulations of subhalos within their host halo, using a generalized mass density profile that describes their properties in a variety of dark matter models at infall, including popular warm, cold, and self-interacting ones. Using these simulations we construct tidal "tracks" for the evolution of subhalos based on their conditions at infall. Second, we use the results of these simulations to build semi-analytic models for tidal effects, including stripping and heating and implement them within the code GALACTICUS. Our semi-analytic models can accurately predict the tidal evolution of both cored and cuspy subhalos, including the bound mass and density profiles, providing a powerful and efficient tool for studying the post-infall properties of subhalos in different dark matter models.

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arXiv2024

Constrain the Dark Matter Distribution of Ultra-diffuse Galaxies with Globular-Cluster Mass Segregation: A Case Study with NGC5846-UDG1

The properties of globular clusters (GCs) contain valuable information of their host galaxies and dark-matter halos. In the remarkable example of ultra-diffuse galaxy, NGC5846-UDG1, the GC population exhibits strong radial mass segregation, indicative of dynamical-friction-driven orbital decay, which opens the possibility of using imaging data alone to constrain the dark-matter content of the galaxy. To explore this possibility, we develop a semi-analytical model of GC evolution, which starts from the initial mass function, the initial structure-mass relation, and the initial spatial distribution of the GC progenitors, and follows the effects of dynamical friction, tidal evolution, and two-body relaxation. Using Markov Chain Monte Carlo, we forward-model the GCs in a NGC5846-UDG1-like potential to match the observed GC mass, size, and spatial distributions, and to constrain the profile of the host halo and the origin of the GCs. We find that, with the assumptions of zero mass segregation when the star clusters were born, NGC5846-UDG1 is relatively dark-matter poor compared to what is expected from stellar-to-halo-mass relations, and its halo concentration is lower than the cosmological average, irrespective of having a cuspy or a cored profile. Its GC population has an initial spatial distribution more extended than the smooth stellar distribution. We discuss the results in the context of scaling laws of galaxy-halo connections, and warn against naively using the GC-abundance-halo-mass relation to infer the halo mass of UDGs. Our model is generally applicable to GC-rich dwarf galaxies, and is publicly available at https://github.com/JiangFangzhou/GCevo.

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arXiv2023

Wet Compaction to a Blue Nugget: a Critical Phase in Galaxy Evolution

We utilize high-resolution cosmological simulations to reveal that high-redshift galaxies tend to undergo a robust `wet compaction' event when near a `golden' stellar mass of $\sim 10^{10} M_{\odot}$. This is a gaseous shrinkage to a compact star-forming phase, a `blue nugget' (BN), followed by central quenching of star formation to a compact passive stellar bulge, a `red nugget' (RN), and a buildup of an extended gaseous disc and ring. Such nuggets are observed at cosmic noon and seed today's early-type galaxies. The compaction is triggered by a drastic loss of angular momentum due to, e.g., wet mergers, counter-rotating cold streams, or violent disc instability. The BN phase marks drastic transitions in the galaxy structural, compositional and kinematic properties. The transitions are from star-forming to quenched inside-out, from diffuse to compact with an extended disc-ring and a stellar envelope, from dark matter to baryon central dominance, from prolate to oblate stellar shape, from pressure to rotation support, from low to high metallicity, and from supernova to AGN feedback. The central black hole growth, first suppressed by supernova feedback when below the golden mass, is boosted by the compaction, and the black hole keeps growing once the halo is massive enough to lock in the supernova ejecta.

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arXiv2023

What Causes The Formation of Disks and End of Bursty Star Formation?

As they grow, galaxies can transition from irregular/spheroidal with 'bursty' star formation histories (SFHs), to disky with smooth SFHs. But even in simulations, the direct physical cause of such transitions remains unclear. We therefore explore this in a large suite of numerical experiments re-running portions of cosmological simulations with widely varied physics, further validated with existing FIRE simulations. We show that gas supply, cooling/thermodynamics, star formation model, Toomre scale, galaxy dynamical times, and feedback properties do not have a direct causal effect on these transitions. Rather, both the formation of disks and cessation of bursty star formation are driven by the gravitational potential, but in different ways. Disk formation is promoted when the mass profile becomes sufficiently centrally-concentrated in shape (relative to circularization radii): we show that this provides a well-defined dynamical center, ceases to support the global 'breathing modes' which can persist indefinitely in less-concentrated profiles and efficiently destroy disks, promotes orbit mixing to form a coherent angular momentum, and stabilizes the disk. Smooth SF is promoted by the potential or escape velocity (not circular velocity) becoming sufficiently large at the radii of star formation that cool, mass-loaded (momentum-conserving) outflows are trapped/confined near the galaxy, as opposed to escaping after bursts. We discuss the detailed physics, how these conditions arise in cosmological contexts, their relation to other correlated phenomena (e.g. inner halo virialization, vertical disk 'settling'), and observations.

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arXiv2023

Novel Conservative Methods for Adaptive Force Softening in Collisionless and Multi-Species N-Body Simulations

Modeling self-gravity of collisionless fluids (e.g. ensembles of dark matter, stars, black holes, dust, planetary bodies) in simulations is challenging and requires some force softening. It is often desirable to allow softenings to evolve adaptively, in any high-dynamic range simulation, but this poses unique challenges of consistency, conservation, and accuracy, especially in multi-physics simulations where species with different softening laws may interact. We therefore derive a generalized form of the energy-and-momentum conserving gravitational equations of motion, applicable to arbitrary rules used to determine the force softening, together with consistent associated timestep criteria, interaction terms between species with different softening laws, and arbitrary maximum/minimum softenings. We also derive new methods to maintain better accuracy and conservation when symmetrizing forces between particles. We review and extend previously-discussed adaptive softening schemes based on the local neighbor particle density, and present several new schemes for scaling the softening with properties of the gravitational field, i.e. the potential or acceleration or tidal tensor. We show that the tidal softening scheme not only represents a physically-motivated, translation and Galilean invariant and equivalence-principle respecting (and therefore conservative) method, but imposes negligible timestep or other computational penalties, ensures that pairwise two-body scattering is small compared to smooth background forces, and can resolve outstanding challenges in properly capturing tidal disruption of substructures (minimizing artificial destruction) while also avoiding excessive N-body heating. We make all of this public in the GIZMO code.

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arXiv2023

ELVES IV: The Satellite Stellar-to-Halo Mass Relation Beyond the Milky-Way

Quantifying the connection between galaxies and their host dark matter halos has been key for testing cosmological models on various scales. Below $M_\star \sim 10^9\,M_\odot$, such studies have primarily relied on the satellite galaxy population orbiting the Milky Way. Here we present new constraints on the connection between satellite galaxies and their host dark matter subhalos using the largest sample of satellite galaxies in the Local Volume ($D \lesssim 12\,\mathrm{Mpc}$) to date. We use $250$ confirmed and $71$ candidate dwarf satellites around 27 Milky Way (MW)-like hosts from the Exploration of Local VolumE Satellites (ELVES) Survey and use the semi-analytical SatGen model for predicting the population of dark matter subhalos expected in the same volume. Through a Bayesian model comparison of the observed and the forward-modeled satellite stellar mass functions (SSMF), we infer the satellite stellar-to-halo mass relation. We find that the observed SSMF is best reproduced when subhalos at the low mass end are populated by a relation of the form $M_\star \propto M^α_\mathrm{peak}$, with a moderate slope of $α_\mathrm{const}=2.10 \pm 0.01$ and a low scatter, constant as a function of the peak halo mass, of $σ_\mathrm{const}=0.06^{+0.07}_{-0.05}$. A model with a steeper slope ($α_\mathrm{grow}=2.39 \pm 0.06$) and a scatter that grows with decreasing $M_\mathrm{peak}$ is also consistent with the observed SSMF but is not required. Our new model for the satellite-subhalo connection, based on hundreds of Local Volume satellite galaxies, is in line with what was previously derived using only the Milky Way satellites.

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arXiv2023

ELVES III: Environmental Quenching by Milky Way-Mass Hosts

Isolated dwarf galaxies usually exhibit robust star formation but satellite dwarf galaxies are often devoid of young stars, even in Milky Way-mass groups. Dwarf galaxies thus offer an important laboratory of the environmental processes that cease star formation. We explore the balance of quiescent and star-forming galaxies (quenched fractions) for a sample of ~400 satellite galaxies around 30 Local Volume hosts from the Exploration of Local VolumE Satellites (ELVES) Survey. We present quenched fractions as a function of satellite stellar mass, projected radius, and host halo mass, to conclude that overall, the quenched fractions are similar to the Milky Way, dropping below 50% at satellite M* ~ 10^8 M_sun. We may see hints that quenching is less efficient at larger radius. Through comparison with the semi-analytic modeling code satgen, we are also able to infer average quenching times as a function of satellite mass in host halo-mass bins. There is a gradual increase in quenching time with satellite stellar mass rather than the abrupt change from rapid to slow quenching that has been inferred for the Milky Way. We also generally infer longer average quenching times than recent hydrodynamical simulations. Our results are consistent with models that suggest a wide range of quenching times are possible via ram-pressure stripping, depending on the clumpiness of the circumgalactic medium, the orbits of the satellites, and the degree of earlier preprocessing.

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arXiv2023

Gravothermal solutions of SIDM halos: mapping from constant to velocity-dependent cross section

The scale-free gravothermal fluid formalism has long proved effective in describing the evolution of self-interacting dark matter halos with a constant dark matter particle cross section. However, whether the gravothermal fluid solutions match numerical simulations for velocity-dependent cross-section scenarios remains untested. In this work, we provide a fast mapping method that relates the constant-cross-section gravothermal solution to models with arbitrary velocity dependence in the cross section. We show that the gravothermal solutions after mapping are in good agreement with Arepo N-Body simulation results. We illustrate the power of this approach by applying this fast mapping method to a halo hosting a low surface brightness galaxy UGC 128. We show that this fast mapping method can be used to constrain free parameters in a physically motivated cross-section model and illustrate parameter space favored by the rotation curve measurement.

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arXiv2023

Orbital Evolution of Satellite Galaxies in Self-Interacting Dark Matter Models

Dark matter self interactions can leave distinctive signatures on the properties of satellite galaxies around Milky Way--like hosts through their impact on tidal stripping, ram pressure, and gravothermal collapse. We delineate the regions of self-interacting dark matter parameter space -- specified by interaction cross section and a velocity scale -- where each of these effects dominates, and show how the relative mass loss depends on the satellite's initial mass, density profile and orbit. We obtain novel, conservative constraints in this parameter space using Milky Way satellite galaxies with notably high central densities and small pericenter distances. Our results for self-interacting dark matter models, in combination with constraints from clusters of galaxies, favor either velocity-dependent cross sections that lead to gravothermal core collapse in the densest satellites, or small cross sections which more closely resemble cold and collisionless dark matter.

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arXiv2022

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

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 hybrid semi-analytical + N-body method to study the evolution of SIDM subhalos with high fidelity, from core formation to core-collapse, in staged simulations. Our method works best for small subhalos ($\lesssim 1/1000$ 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 subhalos to core-collapse, finding that it is nearly impossible to drive core-collapse in subhalos in SIDM models with constant cross sections. Any discovery of ultra-compact dark substructures with future substructure lensing observations favors additional degrees of freedom, such as velocity-dependence, in the cross section.

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arXiv2022

Testing the key role of the stellar mass-halo mass relation in galaxy merger rates and morphologies via DECODE, a novel Discrete statistical sEmi-empiriCal mODEl

The relative roles of mergers and star formation in regulating galaxy growth are still a matter of intense debate. We here present our DECODE, a new Discrete statistical sEmi-empiriCal mODEl specifically designed to predict rapidly and efficiently, in a full cosmological context, galaxy assembly and merger histories for any given input stellar mass-halo mass (SMHM) relation. DECODE generates object-by-object dark matter merger trees (hence discrete) from accurate subhalo mass and infall redshift probability functions (hence statistical) for all subhaloes, including those residing within other subhaloes, with virtually no resolution limits on mass or volume. Merger trees are then converted into galaxy assembly histories via an input, redshift dependent SMHM relation, which is highly sensitive to the significant systematics in the galaxy stellar mass function and on its evolution with cosmic time. DECODE can accurately reproduce the predicted mean galaxy merger rates and assembly histories of hydrodynamic simulations and semi-analytic models, when adopting in input their SMHM relations. In the present work we use DECODE to prove that only SMHM relations implied by stellar mass functions characterized by large abundances of massive galaxies and significant redshift evolution, at least at $M_\star \gtrsim 10^{11} \, M_\odot$, can simultaneously reproduce the local abundances of satellite galaxies, the galaxy (major merger) pairs since $z \sim 3$, and the growth of Brightest Cluster Galaxies. The same models can also reproduce the local fraction of elliptical galaxies, on the assumption that these are strictly formed by major mergers, but not the full bulge-to-disc ratio distributions, which require additional processes.

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arXiv2022

A semi-analytic study of self-interacting dark-matter haloes with baryons

We combine the isothermal Jeans model and the model of adiabatic halo contraction into a simple semi-analytic procedure for computing the density profile of self-interacting dark-matter (SIDM) haloes with the gravitational influence from the inhabitant galaxies. We show that the model agrees well with cosmological SIDM simulations over the entire core-forming stage and up to the onset of gravothermal core-collapse. Using this model, we show that the halo response to baryons is more diverse in SIDM than in CDM and depends sensitively on galaxy size, a desirable link in the context of the structural diversity of bright dwarf galaxies. The fast speed of the method facilitates analyses that would be challenging for numerical simulations -- notably, 1) we quantify the SIDM halo response as functions of the baryonic properties, on a fine mesh grid spanned by the baryon-to-total-mass ratio, $M_{\rm b}/M_{\rm vir}$, and galaxy compactness, $r_{1/2}/R_{\rm vir}$; 2) we show with high statistical precision that for typical Milky-Way-like systems, the SIDM profiles are similar to their CDM counterparts; and 3) we delineate the regime of gravothermal core-collapse in the $M_{\rm b}/M_{\rm vir}$-$r_{1/2}/R_{\rm vir}$ space, for a given cross section and a given halo concentration. Finally, we compare the isothermal Jeans model with the more sophisticated gravothermal fluid model, and show that the former yields faster core formation and agrees better with cosmological simulations. We attribute the difference to whether the target CDM halo is used as a boundary condition or as the initial condition for the gravothermal evolution, and thus comment on possible future improvements of the fluid model. We have made our programs for the model publicly available at https://github.com/JiangFangzhou/SIDM.

astro-ph.CO↗

arXiv2022

Dissipative Dark Matter on FIRE: II. Observational signatures and constraints from local dwarf galaxies

We analyze the first set of cosmological baryonic zoom-in simulations of galaxies in dissipative self-interacting dark matter (dSIDM). The simulations utilize the FIRE-2 galaxy formation physics with the inclusion of dissipative dark matter self-interactions modelled as a constant fractional energy dissipation ($f_{\rm diss}=0.5$). In this paper, we examine the properties of dwarf galaxies with $M_{\ast} \sim 10^{5}\operatorname{-}10^{9}\,{\rm M}_{\odot}$ in both isolation and within Milky Way-mass hosts. For isolated dwarfs, we find more compact galaxy sizes and promotion of stellar/neutral gas disk formation in dSIDM with $(σ/m)\leq 1\,{\rm cm^2\,g^{-1}}$ but they are still consistent with observed galaxy sizes and masses. In addition, as a result of the steeper central density profiles developed in dSIDM, the sub-kpc circular velocities of isolated dwarfs in models with $(σ/m)\geq 0.1\,{\rm cm^2\,g^{-1}}$ are enhanced by about a factor of two, which are still consistent with the measured stellar velocity dispersions of Local Group dwarfs but in tension with the HI rotation curves of more massive field dwarfs. Meanwhile, for satellites of the simulated Milky Way-mass hosts, the median circular velocity profiles are marginally affected by dSIDM physics, but dSIDM may help address the missing compact dwarf satellites in CDM. The number of satellites is slightly enhanced in dSIDM, but the differences are small compared with the large host-to-host variations. In conclusion, the dSIDM models with constant cross-section $(σ/m) \gtrsim 0.1\,{\rm cm^2\,g^{-1}}$ (assuming $f_{\rm diss}=0.5$) are effectively ruled out in bright dwarfs ($M_{\rm halo}\sim 10^{11}\,{\rm M}_{\odot}$) by circular velocity constraints. However, models with lower effective cross-sections (at this halo mass/velocity scale) are still viable and can give rise to non-trivial observable signatures.

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arXiv2022

Galaxies lacking dark matter produced by close encounters in a cosmological simulation

The standard cold dark matter plus cosmological constant model predicts that galaxies form within dark-matter haloes, and that low-mass galaxies are more dark-matter dominated than massive ones. The unexpected discovery of two low-mass galaxies lacking dark matter immediately provoked concerns about the standard cosmology and ignited explorations of alternatives, including self-interacting dark matter and modified gravity. Apprehension grew after several cosmological simulations using the conventional model failed to form adequate numerical analogues with comparable internal characteristics (stellar masses, sizes, velocity dispersions and morphologies). Here we show that the standard paradigm naturally produces galaxies lacking dark matter with internal characteristics in agreement with observations. Using a state-of-the-art cosmological simulation and a meticulous galaxy-identification technique, we find that extreme close encounters with massive neighbours can be responsible for this. We predict that approximately 30 percent of massive central galaxies (with at least 1e11 solar masses in stars) harbour at least one dark-matter-deficient satellite (with 1e8 - 1e9 solar masses in stars). This distinctive class of galaxies provides an additional layer in our understanding of the role of interactions in shaping galactic properties. Future observations surveying galaxies in the aforementioned regime will provide a crucial test of this scenario.

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arXiv2021

SatGen -- II. Assessing the impact of a disc potential on subhalo populations

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 attributed to enhanced destruction of substructure due to disc shocking. We examine the impact of discs on substructure using the semi-analytical subhalo model SatGen, which accurately models the tidal evolution of substructure free of the numerical disruption that still hampers $N$-body simulations. Using a sample of 10,000 merger trees of Milky Way-like haloes, we study the demographics of subhaloes that are evolved under a range of composite halo-disc potentials with unprecedented statistical power. We find that the overall subhalo abundance is relatively insensitive to properties of the disc aside from its total mass. For a disc that contains $5\%$ of $M_\mathrm{vir}$, the mean subhalo abundance within $r_\mathrm{vir}$ is suppressed by ${\lesssim}10\%$ relative to the no-disc case, a difference that is dwarfed by halo-to-halo variance. For the same disc mass, the abundance of subhaloes within 50 kpc is reduced by ${\sim}30\%$. We argue that the disc mainly drives excess mass loss for subhaloes with small pericentric radii and that the impact of disc shocking is negligible.

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arXiv2021

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

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 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 $10-20\%$ level, ameliorating previous concerns that it may suppress the SHMF by as much as a factor of two. We demonstrate that semi-analytical substructure modeling 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 dark matter-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.

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arXiv2021

Dissipative Dark Matter on FIRE: I. Structural and kinematic properties of dwarf galaxies

We present the first set of cosmological baryonic zoom-in simulations of galaxies including dissipative self-interacting dark matter (dSIDM). These simulations utilize the Feedback In Realistic Environments (FIRE-2) galaxy formation physics, but allow the dark matter to have dissipative self-interactions analogous to Standard Model forces, parameterized by the self-interaction cross-section per unit mass, $(σ/m)$, and the dimensionless degree of dissipation, $0<f_{\rm diss}<1$. We survey this parameter space, including constant and velocity-dependent cross-sections, and focus on structural and kinematic properties of dwarf galaxies with $M_{\rm halo} \simeq 10^{10-11} {\rm M}_{\odot}$. Central density profiles of simulated dwarfs become cuspy when $(σ/m)_{\rm eff} \gtrsim 0.1\,{\rm cm^{2}\,g^{-1}}$ (and $f_{\rm diss}=0.5$ as fiducial). The power-law slopes asymptote to $α\approx -1.5$ in low-mass dwarfs independent of cross-section, which arises from a dark matter "cooling flow". Through comparisons with dark matter only simulations, we find the profile in this regime is insensitive to the inclusion of baryons. However, when $(σ/m)_{\rm eff} \ll 0.1\,{\rm cm^{2}\,g^{-1}}$, baryonic effects can produce cored density profiles comparable to non-dissipative cold dark matter (CDM) runs but at smaller radii. Simulated galaxies with $(σ/m) \gtrsim 10\,{\rm cm^{2}\,g^{-1}}$ develop significant coherent rotation of dark matter, accompanied by halo deformation, but this is unlike the well-defined thin "dark disks" often attributed to baryon-like dSIDM. The density profiles in this high cross-section model exhibit lower normalizations given the onset of halo deformation. For our surveyed dSIDM parameters, halo masses and galaxy stellar masses do not show appreciable difference from CDM, but dark matter kinematics and halo concentrations/shapes can differ.

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arXiv2021

Core Formation in High-z Massive Haloes: Heating by Post Compaction Satellites and Response to AGN Outflows

Observed rotation curves in star-forming galaxies indicate a puzzling dearth of dark matter in extended flat cores within haloes of mass $\geq\! 10^{12}M_\odot$ at $z\!\sim\! 2$. This is not reproduced by current cosmological simulations, and supernova-driven outflows are not effective in such massive haloes. We address a hybrid scenario where post-compaction merging satellites heat up the dark-matter cusps by dynamical friction, allowing AGN-driven outflows to generate cores. Using analytic and semi-analytic models (SatGen), we estimate the dynamical-friction heating as a function of satellite compactness for a cosmological sequence of mergers. Cosmological simulations (VELA) demonstrate that satellites of initial virial masses $>\!10^{11.3}M_\odot$, that undergo wet compactions, become sufficiently compact for significant heating. Constituting a major fraction of the accretion onto haloes $\geq\!10^{12}M_\odot$, these satellites heat-up the cusps in half a virial time at $z\!\sim\! 2$. Using a model for outflow-driven core formation (CuspCore), we demonstrate that the heated dark-matter cusps develop extended cores in response to removal of half the gas mass, while the more compact stellar systems remain intact. The mergers keep the dark matter hot, while the gas supply, fresh and recycled, is sufficient for the AGN outflows. AGN indeed become effective in haloes $\geq\!10^{12}M_\odot$, where the black-hole growth is no longer suppressed by supernovae and its compaction-driven rapid growth is maintained by a hot CGM. For simulations to reproduce the dynamical-friction effects, they should resolve the compaction of the massive satellites and avoid artificial tidal disruption. AGN feedback could be boosted by clumpy black-hole accretion and clumpy response to AGN.

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