The erasure of Galactic bar resonances by dark matter subhaloes

Abstract

In the context of increasing appreciation for the coupling between the Galactic bar and the halo, we introduce a new framework using stars trapped in resonance with the bar to probe the Galactic dark matter subhalo population. Since resonant stars occupy a finite width in action space, perturbations from subhaloes can shift a star's actions beyond this width, causing them to circulate out of resonance. Physically, the dark substructure in the Milky Way may dissolve, puff-up, or re-order the resonance features in the stellar halo. To explore the utility of this framework, we treat individual encounters in the impulse approximation and model their cumulative effect as diffusion in the relevant action. The resulting diffusion coefficient allows us to link the survival of resonant populations to the subhalo mass function, whose properties depend on the particle nature of dark matter. Test particle integration validates the impulse treatment for low-mass subhaloes and quantifies its regime of applicability. For a Milky Way-like bar, we find individual subhaloes with $M<10^7$ M$_{\odot}$ have negligible impact on stars in co-rotation resonance, where as the full cold dark matter (CDM) population could erase the resonance over the bar's lifetime. The persistence of resonances therefore implies a suppression of the local subhalo density to less than 1/3 of CDM expectations, consistent with tidal disruptions and previous literature. The narrow widths of higher-order resonances will increase the constraining power of this framework, and therefore motivates searches for bar-resonant halo features in observational data.

Figures (15)

• Figure 1: Sketch of the contours of the bar resonance Hamiltonian (Eq. \ref{['eq:resonance_hamiltonian']}) shown in the slow angle $\upphi$ and slow action $I$ space. The central point is the location of the parent orbit, exactly in resonance. The inner solid black contour is an example libration orbit around the resonance. The black dashed line is the separatrix between resonant and circulating orbits. The outer dotted black contour is an example circulating orbit. The red arrow indicates the change in slow action $I$ required to kick the parent orbit beyond the separatrix.
• Figure 2: Schematic diagram of subhalo flyby of a star in resonance with the galactic bar in the impulse approximation, where the subhalo travels on a straight line orbit in the Galactic rest frame. The top panel shows the co-rotating frame of the bar (with pattern speed $\Omega_{\rm p}$), whereas the bottom panel shows the instaneous rest frame of the star. The grey ellipse in the top panel represents the bar. The subhalo's orbit is represented by a dashed black line and circle, and the star's co-rotation resonant orbit is represented by a dashed orange line and star. In the star's rest frame, the subhalo passes with instantaneous velocity $\bm{u} = \bm{w} - \bm{v}$, where $\bm{w}$ and $\bm{v}$ are the instantaneous velocities of the subhalo and star respectively. The vector $\bm{r}(t)$ defines the local linearized trajectory, with impact parameter vector $\bm{b}$.
• Figure 3: An example orbit (black line) in co-rotation resonance with the bar. The bar's major axis is aligned with the $x$-axis, and the equipotential lines are shown in magenta.
• Figure 4: Geometry of a subhalo encounter in the star's instantaneous rest frame at time $t$. The star is located at $\bm{x}_\star(t_{\rm enc})$ and is described by the local cylindrical basis $\hat{\bm e}_R$ and $\hat{\bm e}_\varphi$. The subhalo moves on a linear trajectory with relative velocity $\bm{u} = \bm{w} - \bm{v}$. The trial impact parameter $\bm{b}_0 = b\,\hat{\bm e}_\varphi$ is decomposed into components parallel and perpendicular to the trajectory, $\bm{b}_{\parallel}$ and $\bm{b}$, respectively. This geometry defines the impulse applied to the star in the simulations.
• Figure 5: The difference between the change in azimuthal action $L_z$ predicted from the toy model and the simulation. This comparison is only for an impact by one subhalo. We show normalised $\Delta L_z$ in $v_{\rm rel}-b$ space for various subhalo masses. Blue colour indicates an under estimate by the toy analytic model relative to the simulation, whereas red colour indicates an over estimate.