[Paper Review] Milky Way satellite velocities reveal the Dark Matter power spectrum at small scales

Ivan Esteban, Annika H. G. Peter+1 more|arXiv (Cornell University)|Jun 7, 2023

Dark Matter and Cosmic Phenomena4 citations

TL;DR

This paper introduces a novel probe of dark matter (DM) properties at small scales using the correlation between internal velocities, sizes, and total abundances of Milky Way satellite dwarf galaxies. By modeling modified DM power spectra from inflationary DM production (Lumpy Dark Matter), the authors constrain the power spectrum in the range $4\,\mathrm{Mpc}^{-1} < k < 37\,\mathrm{Mpc}^{-1}$, finding it must deviate from scale invariance by no more than a factor of 2, robustly independent of baryonic uncertainties.

ABSTRACT

Dark Matter (DM) properties at small scales remain uncertain. Recent theoretical and observational advances have provided the tools to narrow them down. Here, we show for the first time that the correlation between internal velocities and sizes of dwarf galaxies is a sharp probe of small-scale DM properties. We study modified DM power spectra, motivated by DM production during inflation. Using semi-analytic models and scaling relations, we show that such models can change the kinematics and structure of dwarf galaxies without strongly affecting their total abundance. We analyze data from Milky Way classical satellite galaxies and those discovered with the Sloan Digital Sky Survey (SDSS), finding that the DM power spectrum at comoving scales ${4\, \mathrm{Mpc}^{-1} &lt; k &lt; 37\,\mathrm{Mpc}^{-1}}$ cannot deviate by more than a factor of $\sim 2.5$ from scale invariance. Our results are robust against baryonic uncertainties such as the stellar mass-halo mass relation, halo occupation fraction, and subhalo tidal disruption; allowing us to independently constrain them. This work thus opens a window to probe both dwarf galaxy formation models and small-scale DM properties.

Motivation & Objective

• To develop a new observational probe of dark matter (DM) properties at small scales using dwarf galaxy kinematics and structural correlations.
• To test Lumpy Dark Matter (LDM) models—where DM power is enhanced at small scales due to primordial fluctuations during inflation—against observed Milky Way satellite data.
• To disentangle constraints on DM physics from uncertainties in galaxy formation, such as the stellar mass-halo mass relation and tidal disruption.
• To provide a robust, baryon-insensitive constraint on the comoving DM power spectrum in the range $4\,\mathrm{Mpc}^{-1} < k < 37\,\mathrm{Mpc}^{-1}$.

Proposed method

• The authors use semi-analytic models and scaling relations calibrated to simulations to link DM power spectrum modifications to observable dwarf galaxy properties.
• They model the primordial curvature power spectrum as $\mathcal{P}_{\mathcal{R}}(k) \propto k^{n_s-1} \left[1 + \left(k/k_{\mathrm{cut}}\right)^{n_{\mathrm{cut}}-n_s}\right]$, with $n_s \approx 0.97$, $k_{\mathrm{cut}}$ as the scale of enhanced power, and $n_{\mathrm{cut}} > n_s$.
• A statistical likelihood analysis is performed on classical and SDSS Milky Way satellite data, incorporating velocity dispersions, sizes, and total counts.
• The analysis marginalizes over 8 galaxy-halo connection and baryonic physics parameters (e.g., stellar mass-halo mass relation, halo core threshold) to isolate DM constraints.
• The likelihood is minimized using Py-BOBYQA and integrals are computed with the vegas package, assuming Wilks’ theorem for $\chi^2$-based confidence intervals.
• The method isolates the dependence of galaxy kinematics and abundance on the DM power spectrum, showing it is largely independent of galaxy formation uncertainties.

Experimental results

Research questions

• RQ1 Can the correlation between internal velocity dispersion, size, and total abundance of Milky Way satellites serve as a sharp probe of small-scale dark matter power spectrum?
• RQ2 To what extent can Lumpy Dark Matter models—featuring enhanced small-scale power from inflationary DM production—be constrained by observed satellite kinematics?
• RQ3 How robust are constraints on the DM power spectrum to uncertainties in baryonic physics, such as the stellar mass-halo mass relation and tidal disruption?
• RQ4 What is the allowed range of deviation from scale invariance in the small-scale DM power spectrum, as inferred from satellite data?

Key findings

• The dark matter power spectrum in the comoving wavenumber range $4\,\mathrm{Mpc}^{-1} < k < 37\,\mathrm{Mpc}^{-1}$ cannot deviate from scale invariance by more than a factor of 2.
• This constraint is robust against uncertainties in the stellar mass-halo mass relation, halo occupation fraction, and subhalo tidal disruption.
• The method successfully disentangles DM physics from galaxy formation effects, with the main degeneracy being between the DM power spectrum and the halo mass threshold above which baryonic feedback cores DM profiles.
• The analysis constrains key galaxy-halo connection parameters, such as the slope of the stellar mass-halo mass relation and the scatter in this relation, with $1\sigma$ ranges derived from the likelihood.
• The preferred $1\sigma$ range for $n_{\mathrm{cut}}$ is $1.0$ to $1.7$ when marginalized over other parameters, indicating a mild enhancement in power at small scales.
• The study demonstrates that joint observables (velocity, size, abundance) provide a powerful, independent probe of small-scale DM structure, complementary to strong lensing.