Inferring the density and membership of stellar streams with flexible models: The GD-1 stream in Gaia Data Release 3

Abstract

Stellar streams provide one of the most promising avenues for constraining the global mass distribution of the Milky Way and the nature of dark matter (DM). The stream stars' kinematic "track" enables inference of large-scale properties of the DM distribution, while density variations and anomalies provide information about local DM clumps (e.g., from DM subhalos). Using precise astrometric data from the Gaia Mission, which enables clean selections of Milky Way stream stars, we now know of a few streams with perturbations and density anomalies. A full accounting of the density tracks and substructures within all $>100$ Milky Way stellar streams will therefore enable powerful new constraints on DM. However, methods for discovering and characterizing membership of streams are heterogeneous and often highly customized to individual streams. Here, we present a new, flexible framework for modeling stellar stream density and membership. With it, one can empirically model a given stream in a variety of coordinate spaces (\eg on-sky position and velocity) using probability distributions, thereby generating membership probabilities. The most significant improvement over previous methods is the inclusion of off-track or non-Gaussian components to the stream density, meaning we can capture anomalous features (such as the GD-1 steam's spur). We test our model on GD-1, where we characterize previously-known features and provide the largest catalog of probable member stars to date (1689 stars). We then use the derived model to provide measurements of GD-1's density and kinematic tracks, velocity dispersion, as well as its initial and current mass. Our framework (built on JAX and numpyro) provides a path toward uniform analysis of all Milky Way streams, enabling tight constraints on the Galactic mass distribution and its dark matter.

Figures (12)

• Figure 1: The distribution of all stars in our Gaia--PS1 cross-matched sample in the sky region near GD-1 (grayscale) and a visualization of our initial selections (blue and red polygons). The color scale of the grayscale images is logarithmic. Left: The distribution of proper motions in stream-aligned coordinates ($\phi_1, \phi_2$). The blue rectangle shows the initial selection we make in this space to create the input data for our model. Right: The distribution of stars in PS1 $g-r$ color and absolute $g$-band magnitude $M_g$, using a previously inferred distance track Valluri:25. The red polygons show the selections we make to create the input data for our model.
• Figure 2: Three different projections of the sample of stars used as input to the density model, all as a function of stream longitude $\phi_1$. These stars pass the proper motion and CMD selections described in Section \ref{['sec:data']} (and shown in Figure \ref{['fig:gaia_cuts']}). The grayscale images show the number of stars in each bin, and the red shaded regions show the mean track and dispersion of the stream from galstreamsMateu:2023 that are used for initialization of the density model (described in Appendix \ref{['app:initialization']}). Top: Sky positions of stars in stream longitude $\phi_1$ and latitude $\phi_2$Koposov:10. Middle: Proper motion in $\phi_1$ for stars in the above sky region. The extent of the y-axis in this panel shows the selection in $\mu_1$ used to create the model input dataset. Bottom: Proper motion in $\phi_2$ for stars in the above sky region. The extent of the y-axis in this panel shows the selection in $\mu_2$ used to create the model input dataset.
• Figure 3: The complete model for GD-1. The left column shows the data, while the right column shows the model. The bottom panel shows the residual between the data and the model in position space. Each row displays a different space in which the model is created ($\phi_2 - \phi_1$, $\mu_1 - \phi_1$, $\mu_2 - \phi_1$, and $v_r - \phi_1$ from the first to the fourth row).
• Figure 4: Top: The off-track model for GD-1 on a logarithmic color scale, as described in Section \ref{['sec:offtrack_choices']}. The blue points represent the centers of our 2D normals used to create the off-track density.
• Figure 5: Properties of the GD-1 stream as a function of $\phi_1$. Top panel: Linear density of GD-1. The blue shaded region represents the linear density on the main stream track and the red shaded region shows the linear density of the off-track components. The black line traces the combined linear density from both components. The green dashed lines show the locations of the density peaks expected from the best-fit epicycles (2.35 kpc apart). We indicate the knot separations for our stream and off-track $\phi_1$ Gaussian mixture model in the upper right corner of the panel. Second panel: Mean $\phi_2$ track (traced by the black line) and $1\sigma$ width (shown as the blue shaded region) of our GD-1 model's stream component. We indicate the knot separations for our stream and off-track velocity splines ($\mu_1, \mu_2$, and $v_r$) in the upper right corner of the panel. Third panel: Mean $\mu_1$ track (traced by the black line) and $1\sigma$ width (shown as the blue shaded region) of our GD-1 model's stream component. The red shaded region shows the $1\sigma$ width of the off-track $\mu_1$ track. Fourth panel: Same as the third panel but for $\mu_2$. Fifth panel: Same as the third panel but for $v_r$. Bottom row: The width of the main stream track (also represented by the red shaded region in the second panel). The solid curve traces the width of the main stream track when including the off-track component and the dashed line shows the width when only using background and stream components. This shows the importance of using an off-track component to characterize GD-1 properly. In the third and fourth panel, we show the median proper motion errors of high probability GD-1 members ($\approx 0.35 \mathrm{\,mas}\xspace~\mathrm{\,yr}\xspace^{-1}\xspace$)