Detectability of dark matter subhalo impacts in Milky Way stellar streams

TL;DR

This paper develops a fast analytic framework to assess the detectability of low-mass dark matter subhalos via perturbations in Milky Way stellar streams. By modeling subhalo impacts on a circular stream with impulse approximation and combining it with simulated stream dispersions, the authors derive a minimum detectable subhalo mass $M_{\mathrm{sh}}^{\min}$ as a function of stream properties and observational setup, culminating in a simple fitting formula. They quantify detection significance with a likelihood-ratio statistic $q_0$ and provide Asimov-based confidence intervals, showing that Gaia-era data and LSST-era data drastically widen sensitivity (e.g., GD-1 from $\sim 6\times10^{6} M_{\odot}$ to $\sim 8\times10^{5} M_{\odot}$). The method is applied to a catalog of Milky Way streams to rank candidates by subhalo detectability, discuss generalization to more realistic stream geometries, and compare with prior work, setting the stage for optimized target selection in forthcoming surveys.

Abstract

Stellar streams are a promising way to probe the gravitational effects of low-mass dark matter (DM) subhalos. In recent years, there has been a remarkable explosion in the number of stellar streams detected in the Milky Way, and hundreds more may be discovered with future surveys such as LSST. Studies of DM subhalo impacts on streams have so far focused on a few of the thinnest and brightest streams, and it is not known how much information can be gained from the others. In this work, we develop a method to quickly estimate the minimum detectable DM subhalo mass of a given stream, depending on its width, length, distance, and stellar density. We use an analytic model for the impacts and apply a test statistic to determine whether they are detectable. We consider several observational scenarios, based on current and future surveys including Gaia, DESI, Via, and LSST. We find that at 95% confidence level, a stream like GD-1 has a minimum detectable subhalo mass of $\sim 6\times 10^6~\mathrm{M}_\odot$ in Gaia data and $\sim 8\times 10^5~\mathrm{M}_\odot$ with LSST 10 year sensitivity. Applying our results to confirmed Milky Way streams, we rank order them by their sensitivity to DM subhalos and identify promising ones for further study.

Figures (25)

• Figure 1: Left: The geometry of a subhalo passing by a stellar stream. The stream is moving in a circular orbit in the $xy$ plane of the galaxy. At every point on the stream, the stars are moving along the tangential $\hat{t}$ direction. At the point of closest approach, the subhalo passes by the stream with distance $b$, and velocity $(w_r, w_t, w_z)$ in the Galactic frame. Right: A comparison between the observables and uncertainties from simulated perturbed streams (blue) versus using the analytic model combined with random Gaussian noises generated based on uncertainties of simulated unperturbed streams (orange). The blue dots show the simulated stars in the perturbed stream. The stream is generated with $\sigma_\theta=0.2^\circ$, $r_0=10~\mathrm{kpc}$ and $\lambda=10~\mathrm{deg}^{-1}$. The subhalo impact is parametrized by $M_{\mathrm{sh}} = 10^{7.5}~\mathrm{M}_{\odot}$, $r_s = 0.91~\mathrm{kpc}$, $b=0~\mathrm{kpc}$, $t=315~\mathrm{Myr}$, $w_r=0~\mathrm{km/s}$, $w_t=0~\mathrm{km/s}$ and $w_z=180~\mathrm{km/s}$.
• Figure 2: Dependence of some key observables, $\overline{\Delta \theta}$ and $\overline{\Delta v_r}$, on stream properties. The subhalo impact is the same as the right panel of Fig. \ref{['fig:subhalo_geometry_and_observables']}. In each column, we vary one stream property and fix the others to demonstrate how a given property affects either the size of the error bars or the shape of the signal. The default stream properties are $\sigma_\theta = 0.2$ deg, $r_0=10~\mathrm{kpc}$ and $\lambda=32~\mathrm{deg}^{-1}$. Signals here are only calculated from the analytic model and do not account for the uncertainties. Error bars here are only due to stream dispersion. When observational errors are included (Sec. \ref{['sec:observations']}), changing $r_0$ will also affect the error bars.
• Figure 3: The fraction of observable stream stars, $n_\mathrm{obs}/n$, as a function of the stream distance $r_0$ and for various magnitude cutoffs in different surveys. LSST10 is the 10-year sensitivity of LSST.
• Figure 4: Top left: Observational errors on radial velocity as a function of the apparent magnitude G for the Via survey (green) and the DESI survey (orange) and as a function of apparent magnitude V for 4MOST (purple). Top right: The cumulative apparent magnitude distribution for Via (green), DESI (orange) and 4MOST (purple) at different stream distances $r_0$. Bottom left: The survey-effective uncertainty $\sigma_{v_r}^{\star}$ as defined in Eq. \ref{['eq:error_with_obs']} and calculated according to Eq. \ref{['eq:error_kin_with_obs_star']} as a function of magnitude cutoff for Via (green), DESI(orange) and 4MOST (purple) at distance of $r_0=10$ kpc. The error for different widths of streams are shown in different levels of darkness. The survey-effective uncertainty $\sigma_{v_r}^\star$ is normalized to the total intrinsic number of stream stars and should not be interpreted as the uncertainty of an individual observed star. As the magnitude cutoff increases, a survey observes more stars and $\sigma_{v_r}^\star$ decreases. However, observing additional stars with very large individual uncertainties eventually provides diminishing returns, leading to the plateau at the end. Bottom right: The same thing as bottom left but at $r_0=30$ kpc. In this case, there is a rapid decrease in $\sigma^\star_{v_r}$ at $G \approx 18$, corresponding to the increased number of stars when the red clump is accessible (also visible in the top right figure).
• Figure 5: Top left: Observational errors on $v_z$ as a function of the apparent magnitude G for Gaia (red) and as a function of the apparent magnitude r for LSST (blue) for different stream distances $r_0$. Top right: The cumulative apparent magnitude distribution for Gaia and LSST at different stream distances $r_0$. Bottom left: The survey-effective uncertainty $\sigma_{v_z}^{\star}$ as defined in Eq. \ref{['eq:error_with_obs']} and calculated according to Eq. \ref{['eq:error_kin_with_obs_star']} as a function of magnitude cutoff for Gaia (red) and Gaia + LSST (blue), at distance of $r_0=10$ kpc. The errors for different widths of streams are shown in different levels of darkness. The survey-effective uncertainty $\sigma_{v_z}^\star$ is normalized to the total intrinsic number of stream stars and should not be interpreted as the uncertainty of an individual observed star. As the magnitude cutoff increases, a survey observes more stars and $\sigma_{v_z}^\star$ decreases. However, observing additional stars with very large individual uncertainties eventually provides diminishing returns, leading to the plateau at the end. Bottom right: Same as bottom left but at $r_0=30$ kpc. In the bottom panels, there is a rapid decrease in $\sigma^\star_{v_z}$ at $G \approx 15$ (left) and $G \approx 18$ (right), corresponding to the increased number of stars when the red clump is accessible (also visible in the top right figure).