Constraining the potential of the Milky Way using stellar streams and the Inverse Time Integration method

TL;DR

The paper introduces Inverse Time Integration (invi), a method that constrains the Milky Way potential by backwards integrating stellar streams in angle-action space to recover their stripping points relative to the progenitor. Focusing on the M68 stream Fjörm, the authors build a realistic N-body simulation, compute angle-action coordinates via AvGF, and model stripping with a forward-backward simple linear framework, then optimize a four-parameter inner Galaxy potential (disc mass M_d, disc scale a_d, halo axis ratio q_h, halo scale a_h) by maximizing clustering of stripping points. Using realistic Gaia-like data (including DR3 and projected DR5 uncertainties) and distance/radial-velocity estimates from the cluster orbit, they demonstrate that invi can recover the true potential to ~2% accuracy under Gaia-like conditions, with biases addressable via orientation corrections and robust statistics. A key finding is a strong correlation between disc mass and halo axis ratio due to the stream's geometry near the disc, highlighting the need for careful modeling of the disc-halo transition and possibly multiple streams to break degeneracies. The results hold promise for exploiting Gaia DR5 data and future surveys to tightly constrain the inner Milky Way's potential from stellar streams.

Abstract

We develop a method for constraining the potential of the Milky Way using stellar streams with a known progenitor. The method expresses the stream in angle-action coordinates and integrates the orbits of the stars backwards in time to obtain the stripping point positions of the stream stars relative to the cluster. In the potential that generated the stream, the stars return approximately to the cluster centre. In a different potential, they are redirected to different locations. The free parameters of the model are estimated by maximising the degree of clustering of the stripping point distribution. We test this method with the stellar stream of the globular cluster M68 (NGC 4590). We use an N-body code to simulate the stream and generate a realistic star sample using a model of the Gaia selection function. We also simulate the expected observational uncertainties, and estimate the heliocentric distances and radial velocities of the stream stars from the cluster orbit. Using this sample of stars, we recover the values of four free parameters characterising the potential of the disc and the dark halo to an accuracy of about 10 per cent of the correct values. We show that this accuracy is improved up to about 2 per cent using the expected end-of-mission Gaia data. In addition, we obtain a strong correlation between the mass of the disc and the dark halo axis ratio, which is explained by the fact that the stream flows close and parallel to the disc plane.

Figures (16)

• Figure 1: Hertzsprung-Russell diagram of the synthetic population of the globular cluster M68, generated by PARSEC/COLIBRI. Each coloured dot represents a star in the synthetic population, with colour proportional to its mass. The black dots are GDR3 stars selected from the cluster. We indicate the Gaia colour index ${G_{\rm BP}\!-\!G_{\rm RP}}$, the absolute magnitude $M_{\rm G}$, the apparent magnitude $G$ assuming a distance of 10.404 kpc for all the stars, and the effective temperature $T_{\rm eff}$. The dashed horizontal grey line marks the Gaia observational limit of $G=20.5$ mag.
• Figure 2: Orbit of the globular cluster M68. The large red dot marks the current position of the cluster, and the solid black line its orbit during the last 1.5 Gyr. The dashed black line marks its forward orbit during 250 Myr. The projection of the volume covered by the entire orbit is shown as a grey shaded area. The simulated stellar stream stars are shown as small red dots. Left and Middle: Galactic plane and perpendicular plane in cartesian coordinates. Right: Perpendicular plane in cylindrical coordinates.
• Figure 3: Actions (a), frequencies (b), and angles (c) of the M68 simulated stream stars in the reference frame defined by the eigenvectors that diagonalize the Hessian matrix (Eq. \ref{['Hessian']}). The black dots indicate the leading arm, and the blue dots the trailing arm. The centre of the cluster is marked by a large red dot. In the (c) panels, the area containing 68 per cent of the cluster's stars is marked with a red contour line.
• Figure 4: Positions of the stripping points of the stream stars with respect to the cluster centre in the reference frame defined by the principal axes of the stream. The stripping points corresponding to the stars of the leading arm are shown as black dots, and the stars of the trailing arm as blue dots. The medians of these distributions are shown as crosses, and the position of the cluster is shown as a large red dot. Left: Principal axis of the stream $\Delta\bar{\varOmega}_1$ and the perpendicular direction $\Delta\bar{\varOmega}_3$. Right: Plane perpendicular to the principal axis.
• Figure 5: Left: Histogram of the distances from the cluster centre to the stripping points of the stream stars in the plane perpendicular to the principal axis of the stream. The red line shows the Hoyt distribution, characterised by the standard deviations $\sigma_i$ expressed in mrad and the correlation coefficient $\rho$ given in the legend. Right: Histogram of the distances from the cluster centre to the stripping points of the stream stars. The green line shows the best-fitting Rayleigh distribution. Its parameter $\sigma$ is given in mrad in the legend. The vertical grey dashed line marks the mean of the distribution at $\mu_0 \simeq 6.83$ mrad.