Measurement of Dark Matter Substructure from the Kinematics of the GD-1 Stellar Stream

TL;DR

This study uses the GD-1 stellar stream to constrain low-mass dark matter substructure by linking the observed intrinsic radial velocity dispersion to subhalo population parameters via perturbation theory. Through four-radial-velocity catalogs and a hierarchical Bayesian treatment of measurement error and binarity, the authors measure a central dispersion around several km s$^{-1}$, with a pronounced excess in the middle stream region. They implement two DM subhalo modeling frameworks (Model I: suppressed SHMF with fixed $r_s/r_{CDM}$ and a half-mode mass; Model II: CDM SHMF with a mass-dependent $r_s/r_{CDM}$) and perform ABC-based inference across millions of simulations to constrain $f_{sub}$, $M_{hm}$, and the subhalo concentration. The results favor a subhalo mass fraction around CDM expectations, while indicating subhalos may be more compact than CDM across the relevant mass range, a pattern that could be consistent with SIDM or ADM scenarios; joint density–kinematics analyses with more streams will sharpen these inferences.

Abstract

Stellar streams are sensitive tracers of low-mass dark matter subhalos and provide a means to test the Cold Dark Matter (CDM) paradigm on small scales. In this work, we connect the intrinsic velocity dispersion of the GD-1 stream to the number density and internal structure of dark matter subhalos in the mass range $10^5$-$10^9\ M_\odot$. We measure the radial velocity dispersion of GD-1 based on 160 identified member stars across four different spectroscopic catalogs. We use repeat observations of the same stars to constrain binarity. We find that the stream's intrinsic radial velocity dispersion ranges from approximately 2-5 km/s across its length. The region of GD-1 with the highest velocity dispersion represents a $4σ$ deviation from unperturbed stream models formed in a smooth Milky Way potential, which are substantially colder. We use perturbation theory to model the stream's velocity dispersion as a function of dark matter subhalo population parameters, including the number of low-mass subhalos in the Milky Way, the dark matter half-mode mass, and the mass-concentration relation of subhalos. We find that the observed velocity dispersion can be explained by numerous impacts with low-mass dark matter subhalos, or by a single impact with a very compact subhalo with $M \gtrsim 10^8\ M_\odot$. Our constraint on the fraction of mass in subhalos is $f_{\mathrm{sub}} = 0.05^{+0.08}_{-0.03}$ (68\% confidence). In both scenarios, our model prefers subhalos that are more compact compared to CDM mass-size expectations. These results suggest a possible deviation from CDM at low subhalo masses, which may be accounted for by dark matter self-interactions that predict higher concentrations in lower-mass subhalos.

Figures (12)

• Figure 1: Top panel: Sky-positions of the GD-1 members with radial velocities used in this work. Black vertical lines indicate the three $\phi_1$ bins. Middle panel: solar-reflex correct radial velocities of GD-1 member stars relative to the unperturbed stream's track. Color-coding indicates the survey, consisting of DESI (gray), SDSS (blue) LAMOST (orange), and MMT (red). Bottom panel: black points indicate the intrinsic dispersion measured from the stream, after accounting for the observational uncertainties and systematic sources of scatter (e.g., due to binarity). The colorful points represent the dispersion from unperturbed models in each bin. Triangles (plus symbols) are for a $2\times10^4~M_\odot$ ($10^5~M_\odot$) progenitor. Navy, pink, and green points are for dynamical ages of $3.5, 5,$ and $8~\rm{Gyr}$, respectively.
• Figure 2: Graphical representation of the statistical model for the radial velocity dispersion. We combine information across four datasets, accounting for the observational errors associated with each measurement. Free parameters include a mean for each dataset ($\mu_X$), radial velocity jitter due to binaries ($\sigma_{\rm binary}$), and the intrinsic radial velocity dispersion ($\sigma_{\Delta v_r}$).
• Figure 3: Illustration of the two modeling scenarios. Lines show example draws from the two models, color-coded by the concentration factor $r_s/r_{s,\rm cdm}$. Model I (dashed lines) allow for a suppression in the subhalo mass function at low masses. The concentration factor is independent of mass in this model. Model II allows for a mass-dependent concentration factor, and has a fixed slope corresponding to CDM expectations. Both models allow the normalization of the mass function to vary.
• Figure 4: Illustration of how we connect our model to the data. In both panels we plot the intrinsic velocity dispersion of GD-1 ($\sigma_{\Delta v_r}$, green errorbar), and the upper bound on the stream's width ($\sigma_{\Delta \phi_2}$). The blue points and contours represent many realizations of the model stream under CDM assumptions for the number and size of subhalos. Contours enclose 95% of samples, and the data is excluded. Red points and contours indicate acceptable models that overlap with the data. Model I (top panel) has subhalos with 30% the scale radius of CDM subhalos, and $M_{hm} = 10^3~M_\odot$. Model II (bottom panel) illustrates the power-law model for subhalo scale-radii, where low-mass subhalos are more concentrated than high mass subhalos. In the $(\sigma_{\Delta v_r}, \sigma_{\Delta \phi_2})$ plane the models are indistinguishable.
• Figure 5: Posterior distribution for Model I. Dark and light blue indicate regions of 68 and 95% confidence, respectively. There is a degeneracy between the number of subhalos ($f_{\rm sub}$) and the dark matter half-mode mass ($M_{hm}$), such that higher $M_{hm}$ implies fewer subhalos. Fewer subhalos imply more compact central densities (lower $r_s/r_{s,\rm{cdm}}$).