Weighing the Milky Way's Satellite Galaxies Using Pulsar Accelerations

TL;DR

This study introduces a novel method to constrain the Milky Way's satellite masses using direct, instantaneous pulsar accelerations rather than stellar kinematics, addressing systematic disequilibria in the Galaxy. By running self-consistent $N$-body simulations of a MW-like host with the LMC and Sgr over 3 Gyr and comparing simulated vertical acceleration asymmetries to pulsar-derived data, the authors infer $M_{LMC,tot}\approx(2.0\pm0.5)\times10^{11} m M_igodot$ and $M_{Sgr,tot}\approx(4.4\pm3.1)\times10^{9} m M_igodot$ at the start of the simulation, with present-day tidal masses of $M_{LMC,tidal}\approx4.1\times10^{10} m M_igodot$ (16.6 kpc) and $M_{Sgr,tidal}\approx3.5\times10^{8} m M_igodot$ (5 kpc). The results are broadly consistent with previous estimates but are independent of stellar kinematic data, showcasing the diagnostic power of pulsar accelerations for probing both satellite properties and the Galactic potential. The analysis also finds that halo triaxiality plays a subdominant role and that the Sagittarius mass is more uncertain due to nonlinear dynamical effects and orbital timing. Looking ahead, incorporating more accelerations and adopting a fully Bayesian, 3D fit could substantially improve the precision and extend the method to additional satellites.

Abstract

The properties of dwarf galaxies orbiting the Milky Way (MW) are useful for testing models of the formation of our Galaxy, and by extension various theories of cosmology. Recent efforts to measure the masses of the MW's satellite dwarf galaxies have relied on the motions and positions of stars in the MW's disk and halo, which are perturbed by the passage of satellite galaxies. As there are many known processes in our Galaxy that lead to observed disequilibrium in stars, these kinematic methods have been limited by the inherent difficulty in identifying only the perturbations due to particular satellite galaxies. We present a novel method for determining the masses of two MW satellite galaxies -- the Large Magellanic Cloud (LMC) and the Sagittarius Dwarf Spheroidal Galaxy (Sgr dSph) -- using only direct, instantaneous acceleration data derived from extremely precise timing of millisecond pulsars near the Sun. As the LMC and Sgr dSph orbit the MW, they cause wave-like distortions in the structure of the disk plus a large-scale offset in the centers of mass of the dark matter halo and the baryonic disk. These two effects lead to asymmetric accelerations above and below the disk midplane near the Sun, which is observed in the pulsar acceleration data. Notably, the amplitude of this asymmetry is shown to depend on the masses of the orbiting satellites. We analyze a grid of simulations with varying masses of each satellite. We find the total (dark + baryon) mass enclosed within the tidal radius at the present day for the LMC to be 4.1 $\pm$ 1.0 $\times$ 10$^{10}$ M$_\odot$ within a radius of 16.6 kpc, and for Sgr to be 3.5 $\pm$ 2.4 $\times$ 10$^8$ M$_\odot$ within a radius of 5 kpc. These results are generally consistent and competitive with previous determinations of the masses of these objects, but entirely independent of any stellar kinematic data for the first time.

Figures (8)

• Figure 1: Panel (a): Simulation of the Milky Way, the LMC and the Sgr dwarf galaxy/tidal stream. The density of the dwarf galaxies and their stripped material have been enhanced compared to the host galaxy to make them more visible. The locations and velocities of the orbiting satellites match their observed present-day locations. Panel (b): The locations of the pulsar data compared to the Sun, plotted on top of the simulated vertical accelerations (shown as colored contours). The accelerations above the disk are stronger than the accelerations below the disk; near the midplane, this is shown by the "lopsided" contours on either side of the white horizontal line.
• Figure 2: The simulated and observed acceleration asymmetry. Panel (a) shows the vertical component of the line-of-sight acceleration ($a_{\mathrm{los},z}$) for the best-fit simulation above and below the Solar position. The acceleration below the midplane has been mirrored to positive $z$ for easier comparison (dashed lines). This acceleration is shown at the beginning of the simulation (red), where the profile is identical above and below the midplane. At the end of the simulation, after the effects of the satellites have perturbed the galaxy, the acceleration profile is asymmetric, with larger magnitude (more negative) at positive $z$ than at the same distance from the midplane, but negative $z$. This asymmetry can be visualized as the difference between the solid and dashed blue lines, and is plotted in panel (b). The acceleration asymmetry determined from the observed MW pulsar data is also plotted as a black dashed line in panel (b), and the 1$\sigma$ and 2$\sigma$ errors are shown as gray regions around the central value. The simulation agrees with the observed pulsar data within this error region.
• Figure 3: The vertical acceleration asymmetry at the location of the Sun for simulations with different masses of the LMC and Sgr dwarfs. Each column corresponds to a different mass of the LMC, and each row corresponds to a different mass of the Sgr dSph (see Table \ref{['tab:sat_masses']}). Each panel shows the simulated acceleration asymmetry (acceleration above the disk minus acceleration below the disk) vs. distance from the midplane in blue, and the observed asymmetry as a dashed black line with 1$\sigma$ error bars. The thin horizontal gray line corresponds to no asymmetry. The simulation that best recovered the observed asymmetry has a heavy LMC and a medium-sized Sgr.
• Figure 4: Mass profiles as a function of radius for the best-fit satellite models. Also shown are various literature values for the masses; bound and/or total masses are shown as horizontal lines, and masses enclosed within some radius are shown as points with error bars. Our determination of the LMC mass broadly agrees with previous measurements of the enclosed mass at various radii. Although our best-fit total mass is somewhat large compared to the literature values, note that the definition of "total mass" is generally not the same across studies, which can lead to systematic differences. Our best-fit Sgr mass is on the lower end of the literature values when comparing the bound mass of the satellite (mass enclosed within the vertical dashed line). Estimates for the total mass of Sgr (both present-day and original) are not shown here because they are far off the vertical scale of the plot (see Table \ref{['tab:sat_masses']}).
• Figure 5: The vertical acceleration asymmetry across a face-on projection of the disk for simulations with different masses of the LMC and Sgr dwarfs. Columns and rows are the same as in Figure \ref{['fig:supp_asym_grid']}. Each panel shows the simulated acceleration asymmetry (acceleration above the disk minus acceleration below the disk) as color, where positive asymmetry is shown in red, and negative asymmetry (like that observed at the Sun) is blue. The location of the Sun is shown as a gold star. The structure induced by the two satellites is complicated and nonlinear, although there are potentially patterns in the asymmetries along the same rows or columns.