Modelling the M68 stellar stream with realistic mass loss and frequency distributions in angle-action coordinates

TL;DR

The paper presents a semi-analytic method to model stellar streams from globular clusters in angle-action coordinates, incorporating time-varying mass loss and stripping-frequency distributions along eccentric orbits. By calibrating a double-exponential description of the stripping rate and frequency statistics against N-body simulations, the authors generate large samples rapidly and convolve them with Gaia-like observational effects. Applied to the M68 stream, the approach infers an accretion time of about 3.0 Gyr and a mass-loss rate near 0.5 M_sun Myr^{-1} per arm, while highlighting that the observed width may require additional physics beyond a simple, constant-mass model. The method advances stream modeling for potential-distance inference and stream-based Galactic constraints, with clear pathways for refinement in mass evolution, correlated kinematics, and more realistic Milky-Way potentials.

Abstract

We develop a new method for simulating stellar streams generated by globular clusters using angle-action coordinates. This method reproduces the variable mass-loss and variable frequency of the stripped stars caused by the changing tidal forces acting on the cluster as it moves along an eccentric orbit. The model incorporates realistic distributions for the stripping angle and frequency of the stream stars both along and perpendicular to the stream. The stream is simulated by generating random samples of stripped stars and integrating them forward in time in angle-frequency space. Once the free parameters are calibrated, this method can be used to simulate the internal structure of stellar streams more quickly than N-body simulations, while achieving a similar level of accuracy. We use this model to study the surface density of the stellar stream produced by the globular cluster M68 (NGC 4590). We select $291$ stars from the Gaia-DR3 catalogue along the observable section that are likely to be members of the stream. We find that the width of the stream is too large to be explained by stars stripped from the cluster alone. We simulate the stream using the present method and include the Gaia selection function and observational errors, and the process of separating the stream stars from the foreground. By comparing these results with the observed data, we estimate the age of the stream, or equivalently the cluster accretion time, to be $3.04_{-0.29}^{+5.63}$ Gyr, and the mass-loss of the cluster to be $0.496 \pm 0.030$ M$_{\odot}$ Myr$^{-1}$ arm$^{-1}$.

Figures (22)

• Figure 1: Top left: Mass of the M68 globular cluster $M_{\rm gc}$ as a function of the simulation time $t$. The coloured dashed lines mark the time of the first (red), second (green), and third (blue) pericentre passages, while the grey dashed lines mark the start and end of the simulation. The solid grey line marks the initial mass of the cluster $M_{\rm ini}$. Bottom left: Histogram of the mass loss as a function of the simulation time in bins of 7.5 Myr. Right: Relative angle and frequency along the principal axis of the stream {$\Delta\bar{\theta}_1, \Delta\bar{\varOmega}_1$}. The large grey dot marks the position of the cluster and the grey contour line the area containing 68 per cent of the cluster stars. The coloured dashed lines mark the frequency of test particles ejected at the pericentre passages with frequencies distributed uniformly as a function of the angle.
• Figure 2: Top: Number of stream stars as a function of the angle along the principal axis of the stream $\Delta\bar{\theta}_1$ within bins of $18.5$ mrad. The stream stars (black) are divided into three internal components generated by tidal shocks during the first (red), second (green), and third (blue) pericentre passages. Bottom: Stream stars and internal components in angle space. The separation between each stream in $\Delta\bar{\theta}_2$ is arbitrary.
• Figure 3: Top: Histogram of the number of stripped stars $N_{\rm s}$ as a function of the radial angle of the globular cluster $\theta_r^{\hbox{:!GC}}$ in bins of $4\pi/139\simeq0.09$ rad. The stripping time $t_{\rm s}$ of the stream stars is indicated on the top coordinate axis. The coloured dashed lines mark the first (red), second (green), and third (blue) pericentre passages, while the grey dashed lines mark the start and end of the simulation. Bottom:$N_{\rm s}$ as a function of the radial angle of the globular cluster, corrected for the delay $\theta_r^{\hbox{:!M}}$. The angles correspond to the centre of the bins. The red solid line shows the best-fitting double exponential model (Eq. \ref{['double_exp']}). The vertical dashed grey lines indicate the limits of the radial period, and the solid grey line indicates the angle at which the two exponentials are equal $\theta_r^{\hbox{:!L}}$. The second exponential is also shown in grey at the beginning of the period.
• Figure 4: Left: Distribution of stripping points along the principal axis of the stream $\Delta\bar{\alpha}_1$ (black) and the first component of the best-fitting multivariate Gaussian distribution (red). The symbol $\kappa$ indicates that both arms are shown together. The vertical dashed blue line marks the position of the cluster centre. Right: Small black dots show the positions of the stripping points in the plane perpendicular to the stream ($\Delta\bar{\alpha}_2, \Delta\bar{\alpha}_3$). The red lines show the $1$, $2$, and $3\text{-}\sigma$ levels of the best-fitting multivariate Gaussian distribution. The large red dot indicates the median of the distribution and the large blue dot marks the cluster centre.
• Figure 5: Frequency along the principal axis of the stream of the stripped stars $\Delta\bar{\varOmega}_1$ as a function of the radial angle of the globular cluster $\theta_r^{\hbox{:!GC}}$. The symbol $\kappa$ indicates that both arms are shown together. The stripping time $t_{\rm s}$ of the stream stars is indicated on the top coordinate axis. The coloured dashed lines mark the first (red), second (green), and third (blue) pericentre passages, while the grey dashed lines mark the start and end of the simulation.