Self-interacting Dark Matter Haloes Research Articles

On the late-time evolution of velocity-dependent self-interacting dark matter halos

We study the evolution of isolated self-interacting dark matter (SIDM) halos that undergo gravothermal collapse and are driven deep into the short-mean-free-path regime.We assume spherical Navarro-Frenk-White (NFW) halos as initial conditions and allow for elastic dark matter self-interactions.We discuss the structure of the halo core deep in the core-collapsed regime and how it depends on the particle physics properties of dark matter, in particular, the velocity dependence of the self-interaction cross section. We find an approximate universality deep in this regime that allows us to connect the evolution in the short- and long-mean-free-path regimes, and approximately map the velocity-dependent self-interaction cross sections to constant ones for the full gravothermal evolution. We provide a semi-analytic prescription based on our numerical results for halo evolution deep in the core-collapsed regime.Our results are essential for estimating the masses of the black holes that are likely to be left in the core of SIDM halos.

Evolution of resonant self-interacting dark matter halos

Evolution of resonant self-interacting dark matter halos

A parametric model for self-interacting dark matter halos

We propose a parametric model for studying self-interacting dark matter (SIDM) halos. The model uses an analytical density profile, calibrated using a controlled N-body SIDM simulation that covers the entire gravothermal evolution, including core-forming and -collapsing phases. By normalizing the calibrated density profile, we obtain a universal description for SIDM halos at any evolution phase. The model allows us to infer properties of SIDM halos based on their cold dark matter (CDM) counterparts. As a basic application, we only require two characteristic parameters of an isolated CDM halo at z = 0. We then extend the model to incorporate effects induced by halo mass changes, such as major mergers or tidal stripping, making it applicable to both isolated halos and subhalos. The parametric model is tested and validated using cosmological zoom-in SIDM simulations available in the literature.

Formation of Massive Black Holes with M = (103–108) M ⊙ at Pre-quasar Epochs through Hoyle–Lyttleton–Bondi Accretion of Self-interacting Dark Matter onto a Moving Seed

The presence of supermassive black holes with M ∼ 109 M ⊙ hosted by the luminous quasars at cosmological redshift z ≥ 6 is still an open problem in astrophysical cosmology. Here we study the formation of massive black holes at high redshift (z ≫ 7) through Hoyle–Lyttleton–Bondi accretion of self-interacting dark matter (SIDM) onto a 20 M ⊙ seed black hole moving with a velocity ∼100 km s−1 inside the short, mean-free path region of an SIDM halo. We consider observational constraints on a specific SIDM cross section, σ/m dm = (0.1–5) cm2 g−1. Formation timescale of massive black holes with M = (103–108) M ⊙ is calculated for the universal Navarro–Frenk–White (NFW) profile, singular isothermal sphere (SIS), other power-law profiles with a cusp index 2.19 ≤ γ ≤ 2.5 of accreted dark matter, and modified-core isothermal profiles. The ambient sound speed is taken as C s = (10–100) km s−1. It is found that an NFW profile with halo concentration C = 4.75–32.58 estimated at z = 20 and 30 for halo masses M 200 = (1012–1014) M ⊙ favors formation of massive black holes with M = (103–108) M ⊙ at high redshift, well before quasar epoch. In this profile, these black holes grow within timescales (0.1–69) Myr at z = 16–20. For the SIS profile, the black hole formation timescales are short compared to NFW. For power-law profiles, massive black holes with M = (106–108) M ⊙ grow within a few tens to 100 Myr (z = 5–30). For modified-core isothermal profiles, the timescale of massive black hole formation is in the range (0.79–464.08) Myr (z = 8–30).

The impact of baryonic potentials on the gravothermal evolution of self-interacting dark matter haloes

ABSTRACT The presence of a central baryonic potential can have a significant impact on the gravothermal evolution of self-interacting dark matter (SIDM) haloes. We extend a semi-analytical fluid model to incorporate the influence of a static baryonic potential and calibrate it using controlled N-body simulations. We construct benchmark scenarios with varying baryon concentrations and different SIDM models, including constant and velocity-dependent self-interacting cross-sections. The presence of the baryonic potential induces changes in SIDM halo properties, including central density, core size, and velocity dispersion, and it accelerates the halo’s evolution in both expansion and collapse phases. Furthermore, we observe a quasi-universality in the gravothermal evolution of SIDM haloes with the baryonic potential, resembling a previously known feature in the absence of the baryons. By appropriately rescaling the physical quantities that characterize the SIDM haloes, the evolution of all our benchmark cases exhibits remarkable similarity. Our findings offer a framework for testing SIDM predictions using observations of galactic systems where baryons play a significant dynamical role.

Testing the Collisionless Nature of Dark Matter with the Radial Acceleration Relation in Galaxy Clusters

The radial acceleration relation (RAR) represents a tight empirical relation between the inferred total and baryonic centripetal accelerations, g tot = GM tot(< r)/r 2 and g bar = GM bar(< r)/r 2, observed in galaxies and galaxy clusters. The tight correlation between these two quantities can provide insight into the nature of dark matter. Here we use BAHAMAS, a state-of-the-art suite of cosmological hydrodynamical simulations, to characterize the RAR in cluster-scale halos for both cold and collisionless dark matter (CDM) and self-interacting dark matter (SIDM) models. SIDM halos generally have reduced central dark matter densities, which reduces the total acceleration in the central region when compared with CDM. We compare the RARs in galaxy clusters simulated with different dark matter models to the RAR inferred from CLASH observations. Our comparison shows that the cluster-scale RAR in the CDM model provides an excellent match to the CLASH RAR obtained by Tian et al. including the high-acceleration regime probed by the brightest cluster galaxies (BCGs). By contrast, models with a larger SIDM cross section yield increasingly poorer matches to the CLASH RAR. Excluding the BCG regions results in a weaker but still competitive constraint on the SIDM cross section. Using the RAR data outside the central r < 100 kpc region, an SIDM model with σ/m = 0.3 cm2 g−1 is disfavored at the 3.8σ level with respect to the CDM model. This study demonstrates the power of the cluster-scale RAR for testing the collisionless nature of dark matter.

Universal gravothermal evolution of isolated self-interacting dark matter halos for velocity-dependent cross-sections

ABSTRACT We study the evolution of isolated self-interacting dark matter halos using spherically symmetric gravothermal equations allowing for the scattering cross-section to be velocity dependent. We focus our attention on the large class of models where the core is in the long mean free path regime for a substantial time. We find that the temporal evolution exhibits an approximate universality that allows velocity-dependent models to be mapped onto velocity-independent models in a well-defined way using the scattering time-scale computed when the halo achieves its minimum central density. We show how this time-scale depends on the halo parameters and an average cross-section computed at the central velocity dispersion when the central density is minimum. The predicted collapse time is fully defined by the scattering time-scale, with negligible variation due to the velocity dependence of the cross-section. We derive new self-similar solutions that provide an analytic understanding of the numerical results.

Gravothermal collapse of self-interacting dark matter halos as the origin of intermediate mass black holes in Milky Way satellites

Milky Way (MW) satellites exhibit a diverse range of internal kinematics, reflecting in turn a diverse set of subhalo density profiles. These profiles include large cores and dense cusps, which any successful dark matter model must explain simultaneously. A plausible driver of such diversity is self-interactions between dark matter particles (SIDM) if the cross section passes the threshold for the gravothermal collapse phase at the characteristic velocities of the MW satellites. In this case, some of the satellites are expected to be hosted by subhalos that are still in the classical SIDM core phase, while those in the collapse phase would have cuspy inner profiles, with a SIDM-driven intermediate mass black hole (IMBH) in the centre as a consequence of the runaway collapse. We develop an analytical framework that takes into account the cosmological assembly of halos and is calibrated to previous simulations; we then predict the timescales and mass scales ($M_{\rm BH}$) for the formation of IMBHs in velocity-dependent SIDM (vdSIDM) models as a function of the present-day halo mass, $M_0$. Finally, we estimate the region in the parameter space of the effective cross section and $M_0$ for a subclass of vdSIDM models that result in a diverse MW satellite population, as well as their corresponding fraction of SIDM-collapsed halos and those halos' inferred IMBH masses. We predict the latter to be in the range $0.1-1000~ {\rm M_\odot}$ with a $M_{\rm BH}-M_0$ relation that has a similar slope, but lower normalization, than the extrapolated empirical relation of super-massive black holes found in massive galaxies.

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

ABSTRACT We combine the isothermal Jeans model and the model of adiabatic halo contraction into a semi-analytic procedure for computing the density profile of self-interacting dark-matter (SIDM) haloes with the gravitational influence from the inhabitant galaxies. The model agrees well with cosmological SIDM simulations over the entire core-forming stage 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 feature in the context of the structural diversity of bright dwarfs. The fast speed of the method facilitates analyses that would be challenging for numerical simulations – notably, 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, Mb/Mvir, and galaxy compactness, r1/2/Rvir; we show with high statistical precision that for typical Milky-Way-like systems, the SIDM profiles are similar to their CDM counterparts; and we delineate the regime of core-collapse in the Mb/Mvir − r1/2/Rvir space, for a given cross section and 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 improvements of the fluid model. We have made our model publicly available at https://github.com/JiangFangzhou/SIDM.

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 the parameter space favored by the rotation curve measurement.

The local dark matter distribution in self-interacting dark matter halos

We study the effects of dark matter self-interactions on the local dark matter distribution in selected Milky Way-like galaxies in the EAGLE hydrodynamical simulations. The simulations were run with two different self-interacting dark matter models, a constant and velocity-dependent self-interaction cross-section. We find that the local dark matter velocity distribution of the Milky Way-like halos in the simulations with dark matter self-interactions and baryons are generally similar to those extracted from cold collisionless dark matter simulations with baryons. In both cases, the local dark matter speed distributions agree well with their best fit Maxwellian distributions. Including baryons in the simulations with or without dark matter self-interactions increases the local dark matter density and shifts the dark matter speed distributions to higher speeds. To study the implications for direct detection, we compute the dark matter halo integrals obtained directly from the simulations and compare them to those obtained from the best fit Maxwellian velocity distribution. We find that a Maxwellian distribution provides a good fit to the halo integrals of most halos, without any significant difference between the results of different dark matter self-interaction models.

Discriminating power of milli-lensing observations for dark matter models

Context. The nature of dark matter (DM) is still under intense debate. Subgalactic scales are particularly critical, as different, currently viable DM models make diverse predictions on the expected abundance and density profile of DM haloes on these scales. Aims. We investigate the ability of subgalactic DM haloes to act as strong lenses on background compact sources, producing gravitational lensing events on milli-arcsecond scales (milli-lenses), for different DM models. For each DM scenario, we explore whether a sample of ∼5000 distant sources is sufficient to detect at least one milli-lens. Methods. We developed a semi-analytical model to estimate the milli-lensing optical depth as a function of the source’s redshift for various DM models. We employed the Press-Schechter formalism, as well as results from recent N-body simulations to compute the halo mass function, taking into account the appropriate spherically averaged density profile of haloes for each DM model. We treated the lensing system as a point-mass lens and invoked the effective surface mass density threshold to calculate the fraction of a halo that acts as a gravitational lens. We studied three classes of dark matter models: cold DM, warm DM, and self-interacting DM. Results. We find that haloes consisting of warm DM turn out to be optically thin for strong gravitational milli-lensing (zero expected lensing events). Cold DM haloes may produce lensing events depending on the steepness of the concentration-mass relation. Self-interacting DM haloes can efficiently act as gravitational milli-lenses only if haloes experience gravothermal collapse, resulting in highly dense central cores.

Modelling self-interacting dark matter substructures – I. Calibration with N-body simulations of a Milky-Way-sized halo and its satellite

ABSTRACT We study evolution of single subhaloes with their masses of ∼109 M⊙ 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 subhaloes can be described with a framework developed for the case of collision-less cold dark matter (CDM), but a shorter typical time-scale for the mass loss due to tidal stripping is required to explain our SIDM simulation results. As long as the cross-section is less than $\sim \! 10\, \mathrm{cm}^2\,\mathrm{g}^{ -1}$ and initial states of subhaloes are set within a 2σ-level scatter at redshifts of ∼2 predicted by the standard ΛCDM cosmology, our simulations do not exhibit a prominent feature of gravothermal collapse in the subhalo central density for 10 Gyr. We develop a semi-analytic model of SIDM subhaloes in a time-evolving density core of the host with tidal stripping and self-scattering ram pressure effects. Our semi-analytic approach provides a simple, efficient, and physically intuitive prediction of SIDM subhaloes, but further improvements are needed to account for baryonic effects in the host and the gravothermal instability accelerated by tidal stripping effects.

Dark stars powered by self-interacting dark matter

Dark matter annihilation might power the first luminous stars in the Universe. These types of stars, known as dark stars, could form in $(10^6\mathrm{-}10^8)\,M_\odot$ protohalos at redshifts $z \sim 20$, and they could be much more luminous and larger in size than ordinary stars powered by nuclear fusion. We investigate the formation of dark stars in the self-interacting dark matter (SIDM) scenario. We present a concrete particle physics model of SIDM that can simultaneously give rise to the observed dark matter density, satisfy constraints from astrophysical and terrestrial searches, and address the various small-scale problems of collisionless dark matter via the self-interactions. In this model, the power from dark matter annihilation is deposited in the baryonic gas in environments where dark stars could form. We further study the evolution of SIDM density profiles in the protohalos at $z \sim 20$. As the baryon cloud collapses due to the various cooling processes, the deepening gravitational potential can speed up gravothermal evolution of the SIDM halo, yielding sufficiently high dark matter densities for dark stars to form. We find that SIDM-powered dark stars can have similar properties, such as their luminosity and size, as dark stars predicted in collisionless dark matter models.

Dynamical instability of collapsed dark matter halos

A self-interacting dark matter halo can experience gravothermal collapse, resulting in a central core with an ultrahigh density. It can further contract and collapse into a black hole, a mechanism proposed to explain the origin of supermassive black holes. We study dynamical instability of the core in general relativity. We use a truncated Maxwell-Boltzmann distribution to model the dark matter distribution and solve the Tolman-Oppenheimer-Volkoff equation. For given model parameters, we obtain a series of equilibrium configurations and examine their dynamical instability based on considerations of total energy, binding energy, fractional binding energy, and adiabatic index. Our numerical results indicate that the core can collapse into a black hole when the fractional binding energy reaches 0.035 with a central gravitational redshift of 0.5. We further show for the instability to occur in the classical regime, the boundary temperature of the core should be at least 10% of the mass of dark matter particles; for a 109 M⊙ seed black hole, the particle mass needs to be larger than a few keV. These results can be used to constrain different collapse models, in particular, those with dissipative dark matter interactions. https://github.com/michaelwxfeng/truncated-Maxwell-Boltzmann.

Primordial black hole merger rate in self-interacting dark matter halo models

We study the merger rate of primordial black holes (PBHs) in self-interacting dark matter (SIDM) halo models. To explore a numerical description for the density profile of SIDM halo models, we use the result of a previously performed simulation for SIDM halo models with $\sigma/m=10~{\rm cm^{2}g^{-1}}$. We also propose a concentration-mass-time relation that can explain the evolution of the halo density profile related to SIDM models. Furthermore, we investigate the encounter condition of PBHs that may have been randomly distributed in the medium of dark matter halos. Under these assumptions, we calculate the merger rate of PBHs within each halo considering SIDM halo models and compare the results with that obtained for cold dark matter (CDM) halo models. To do this, we employ the definition of the time after halo virialization as a function of halo mass. We indicate that SIDM halo models for $f_{\rm PBH}>0.32$ can generate sufficient PBH mergers in such a way that those exceed the one resulted from CDM halo models. By considering the spherical-collapse halo mass function, we obtain similar results for the cumulative merger rate of PBHs. Moreover, we calculate the redshift evolution of the PBH total merger rate. To determine a constraint on the PBH abundance, we study the merger rate of PBHs in terms of their fraction and masses and compare those with the black hole merger rate estimated by the Advanced LIGO (aLIGO)-Advanced Virgo (aVirgo) detectors during the third observing run. The results demonstrate that within the context of SIDM halo models, the merger rate of $10~M_{\odot}-10~M_{\odot}$ events can potentially fall within the aLIGO-aVirgo window. We also estimate a relation between the fraction of PBHs and their masses, which is well consistent with our findings.

Density spikes near black holes in self-interacting dark matter halos and indirect detection constraints

Self-interacting dark matter (SIDM) naturally gives rise to a cored isothermal density profile, which is favored in observations of many dwarf galaxies. The dark matter distribution in the presence of a central black hole in an isothermal halo develops a density spike with a power law of ${r}^{\ensuremath{-}7/4}$, which is shallower than ${r}^{\ensuremath{-}7/3}$ as expected for collisionless dark matter (CDM). Thus, indirect detection constraints on dark matter annihilations from the density spike could be relaxed in SIDM. Taking the most dense satellite galaxy of the Milky Way Draco as an example, we derive upper limits on the annihilation cross section and the black hole mass for both SIDM and CDM halos. For the former case, Draco could host an intermediate mass black hole even if dark matter is composed of thermal relics. We further explore the constraints from the Milky Way and M87, which host supermassive black holes, and show the upper limits on the annihilation cross section are significantly weakened in SIDM. Our results also indicate that the Event Horizon Telescope could provide a unique test of SIDM spikes.

Strong lensing signatures of self-interacting dark matter in low-mass haloes

ABSTRACT Core formation and runaway core collapse in models with self-interacting dark matter (SIDM) significantly alter the central density profiles of collapsed haloes. Using a forward modelling inference framework with simulated data-sets, we demonstrate that flux ratios in quadruple image strong gravitational lenses can detect the unique structural properties of SIDM haloes, and statistically constrain the amplitude and velocity dependence of the interaction cross-section in haloes with masses between 106 and 1010 M⊙. Measurements on these scales probe self-interactions at velocities below $30 \ \rm {km} \ \rm {s^{-1}}$, a relatively unexplored regime of parameter space, complimenting constraints at higher velocities from galaxies and clusters. We cast constraints on the amplitude and velocity dependence of the interaction cross-section in terms of σ20, the cross-section amplitude at $20 \ \rm {km} \ \rm {s^{-1}}$. With 50 lenses, a sample size available in the near future, and flux ratios measured from spatially compact mid-IR emission around the background quasar, we forecast $\sigma _{20} \lt 11\rm {\small {--}}23 \ \rm {cm^2} \rm {g^{-1}}$ at $95 {{\ \rm per\ cent}}$ CI, depending on the amplitude of the subhalo mass function, and assuming cold dark matter (CDM). Alternatively, if $\sigma _{20} = 19.2 \ \rm {cm^2}\rm {g^{-1}}$ we can rule out CDM with a likelihood ratio of 20:1, assuming an amplitude of the subhalo mass function that results from doubly efficient tidal disruption in the Milky Way relative to massive elliptical galaxies. These results demonstrate that strong lensing of compact, unresolved sources can constrain SIDM structure on sub-galactic scales across cosmological distances, and the evolution of SIDM density profiles over several Gyr of cosmic time.

The central densities of Milky Way-mass galaxies in cold and self-interacting dark matter models

ABSTRACT We present a suite of baryonic cosmological zoom-in simulations of self-interacting dark matter (SIDM) haloes within the ‘Feedback In Realistic Environment’ (FIRE) project. The three simulated haloes have virial masses of $\sim 10^{12}\, \text{M}_\odot$ at z = 0, and we study velocity-independent self-interaction cross sections of 1 and 10 ${\rm cm^2 \, g^{-1}}$. We study star formation rates and the shape of dark matter density profiles of the parent haloes in both cold dark matter (CDM) and SIDM models. Galaxies formed in the SIDM haloes have higher star formation rates at z ≤ 1, resulting in more massive galaxies compared to the CDM simulations. While both CDM and SIDM simulations show diverse shape of the dark matter density profiles, the SIDM haloes can reach higher and more steep central densities within few kpcs compared to the CDM haloes. We identify a correlation between the build-up of the stars within the half-mass radii of the galaxies and the growth in the central dark matter densities. The thermalization process in the SIDM haloes is enhanced in the presence of a dense stellar component. Hence, SIDM haloes with highly concentrated baryonic profiles are predicted to have higher central dark matter densities than the CDM haloes. Overall, the SIDM haloes are more responsive to the presence of a massive baryonic distribution than their CDM counterparts.

Seeding Supermassive Black Holes with Self-interacting Dark Matter: A Unified Scenario with Baryons

Abstract Observations show that supermassive black holes (SMBHs) with a mass of ∼109 M ⊙ exist when the universe is just 6% of its current age. We propose a scenario where a self-interacting dark matter halo experiences gravothermal instability and its central region collapses into a seed black hole. The presence of baryons in protogalaxies could significantly accelerate the gravothermal evolution of the halo and shorten collapse timescales. The central halo could dissipate its angular momentum remnant via viscosity induced by the self-interactions. The host halo must be on high tails of density fluctuations, implying that high-z SMBHs are expected to be rare in this scenario. We further derive conditions for triggering general relativistic instability of the collapsed region. Our results indicate that self-interacting dark matter can provide a unified explanation for diverse dark matter distributions in galaxies today and the origin of SMBHs at redshifts z ∼ 6–7.