Constraints on dark matter models from the stellar cores observed in ultra-faint dwarf galaxies: Self-interacting dark matter

TL;DR

The paper investigates whether the stellar cores in ultra-faint dwarfs necessitate non-CDM physics and tests self-interacting dark matter (SIDM) as the core-forming mechanism. It combines a universal SIDM halo-evolution framework with a toy model linking stellar mass to DM core radius, deriving a velocity-dependent cross-section range from core sizes and propagating uncertainties via Monte Carlo methods. The analysis finds a constrained low-velocity cross-section interval $\sigma/m \in [0.35, 199]$ cm$^2$ g$^{-1}$, consistent with broader SIDM literature, and predicts that the observable stellar core radius grows with stellar mass while the product $\rho_{DM}(0)\, r_c$ remains roughly constant around $44\,M_\odot\,\mathrm{pc}^{-2}$. If core-collapse dominates, halos thermalize on kiloparsec scales, with potential implications for substructure in more massive galaxies, motivating targeted SIDM simulations at those scales to quantify the effects on the matter-power spectrum and small-scale structure.

Abstract

It has been proposed that the stellar cores observed in ultra-faint dwarf (UFD) galaxies reflect underlying dark matter (DM) cores that cannot be formed by stellar feedback acting on collisionless cold dark matter (CDM) halos. Assuming this claim is correct, we investigate the constraints that arise if such cores are produced by self-interacting dark matter (SIDM). We derive the range of SIDM cross-sections (sigma/m) required to reproduce the observed core sizes. These can result from halos in either the core-formation phase (low sigma/m) or the core-collapse phase (high sigma/m), yielding a wide allowed range (sim 0.3 -- 200 cm2/g) consistent with values reported in the literature for more massive galaxies. We also construct a simple model relating stellar mass to core radius - two observables likely connected in SIDM. This model reproduces the stellar core sizes and masses in UFDs with sigma/m consistent with those derived above. It also predicts a trend of increasing core radius with stellar mass, in agreement with observations of more massive dwarf galaxies. The model central DM densities match observations when assuming the SIDM profile to originate from an initial CDM halo that follows the mass-concentration relation. Since stellar feedback is insufficient to form cores in these galaxies, UFDs unbiasedly anchor sigma/m at low velocities. If the core-collapse scenario holds (i.e., high sigma/m), UFD halos are thermalized on kpc scales, approximately two orders of magnitude larger than the stellar cores. These large thermalization scales could potentially influence substructure formation in more massive systems.

Figures (10)

• Figure 1: Time evolution of SIDM halos according to 2024JCAP...02..032Y. The time scale is parameterized in terms of the core-collapse timescale, $t_{cc}$ -- Eqs. (\ref{['eq:master_outm']}) and (\ref{['eq:cctime']}). The halos start off as NFW profiles of characteristic density and radius $\rho_{s0}$ and $r_{s0}$, respectively. (a) Radial density at different timesteps going from almost the initial conditions ($t_{age}/t_{cc}= 0$) to core-collapse ($t_{age}/t_{cc}= 1$), including the formation of a maximum core ($t_{age}/t_{cc}= t_c/t_{cc}\simeq 0.12$). Profiles before the maximum core formation ($t_{age} \leq t_c$) are represented as dashed lines whereas profiles after this core-formation are shown as solid lines. (b) Same profiles as (a) but normalized to the central density and to the core radius defined in Eq. (\ref{['foot:1']}). The black bullet symbol indicates the location of the core radius. (c) Time variation of the true core (the blue solid line; $r_c$ in Eq. [\ref{['eq:rcore2']}]) and of the model core (the orange dashed line; $r'_c$ in Eq. [\ref{['eq:rho_sim']}]). (d) Time variation of the central density (the blue solid line; $\rho_{\rm SIDM}(0)$) and of the characteristic density (the orange dashed line; $\rho_s'$ in Eq. [\ref{['eq:rho_sim']}]). The green arrow in (c) and (d) marks the time scale for maximum core formation.
• Figure 2: Monte-Carlo simulation used to estimate the SIDM cross-sections required to account for the DM cores of UFDs. The cross-sections depend on a number of poorly constrained parameters (the parameters in Eq. [\ref{['eq:sigmaH']}]). The Monte-Carlo simulations allows us to propagate their uncertainties on $\sigma_H/m/\beta_{age}$ (the gray histogram) and, via Eq. (\ref{['eq:sigma_range']}), on the cross-section $\sigma/m$. The blue histogram represents the distribution assuming the UFDs are in the process of forming the core whereas the green histogram assumes that DM es evolving to core-collapse. The vertical dashed lines mark the 2.3% and 97.7% percentiles used to constraint the range of viable cross-sections given in Eq. (\ref{['eq:ufdlimit']}). See the main text for further details.
• Figure 3: Summary of the SIDM cross-sections found in the literature. They are plotted versus a representative relative velocity of the DM particles in the observed object. The references are labeled in the inset with the equivalence with actual papers given in Appendix \ref{['sec:appa']}. This appendix also points out how $\sigma/m$ and $Velocity$ mean something different in the different works, which may explains part of the scatter. The value provided by the UFD s analyzed in this work is the red circle with error bars at the lowest velocities, with the two times symbols representing the median of the core formation and the core-collapse distributions shown in Fig. \ref{['fig:dmcoresize14']}. The solid lines corresponds to the analytical form in Eq. (\ref{['eq:resonance']}) where $\sigma_0/m, w_0, w_1= 30$${\rm cm^2\,g^{-1}}$ , 0, 80 ${\rm km\,s^{-1}}$ (the red line), 3 ${\rm cm^2\,g^{-1}}$ , 0, 200 ${\rm km\,s^{-1}}$ (the blue line), and 11 ${\rm cm^2\,g^{-1}}$ , 60 ${\rm km\,s^{-1}}$ , 45 ${\rm km\,s^{-1}}$ (the black line).
• Figure 4: Stellar core radius versus stellar mass as predicted by the simple model presented in Sect. \ref{['sec:toy_model_new']}. Each line corresponds to the variation of $r_{\star c}$ with $M_\star$ when the DM halo mass goes from $10^7$ to $10^{14}\,M_\odot$. The type of line depends on whether the corresponding profile is in the core-formation phase ($t_{age} < t_c$; dashed line) or in the core-collapse phase ($t_{age} > t_c$; solid line). The parameters that define the cross-sections are given in the inset, with the actual velocity dependence represented in Fig. \ref{['fig:dmcoresize13_3']} with the same color code employed here. Observations of $r_{\star c}$ versus $M_\star$ are represented as symbols, each one corresponding to an individual object. The measurements are labelled in the inset, with the UFD s analyzed in this work appearing under the label SA+24. The link between labels and references is specified in Appendix \ref{['sec:appc']}. The figure also includes the theoretical expectations from stellar feedback on C DM halos from 2020MNRAS.497.2393L.
• Figure 5: Cross sections used to compute $r_{\star c}(M_\star)$ in Fig. \ref{['fig:dmcoresize13']}. The color code is the same in both figures. The range of velocities highlighted with thicker lines corresponds to the range of effective velocities (Eq. [\ref{['eq:veff']}]) when the halo masses go from $10^7$ to $10^{14}\,M_\odot$, as used in Fig. \ref{['fig:dmcoresize13']}.