A lower bound on the Milky Way mass from general phase-space distribution function models

Abstract

We model the phase-space distribution of the kinematic tracers using general, smooth distribution functions to derive a conservative lower bound on the total mass within ≈150−200 kpc. By approximating the potential as Keplerian, the phase-space distribution can be simplified to that of a smooth distribution of energies and eccentricities. Our approach naturally allows for calculating moments of the distribution function, such as the radial profile of the orbital anisotropy. We systematically construct a family of phase-space functions with the resulting radial velocity dispersion overlapping with the one obtained using data on radial motions of distant kinematic tracers, while making no assumptions about the density of the tracers and the velocity anisotropy parameter β regarded as a function of the radial variable. While there is no apparent upper bound for the Milky Way mass, at least as long as only the radial motions are concerned, we find a sharp lower bound for the mass that is small. In particular, a mass value of 2.4 × 10 11 M , obtained in the past for lower and intermediate radii, is still consistent with the dispersion profile at larger radii. Compared with much greater mass values in the literature, this result shows that determining the Milky Way mass is strongly model-dependent. We expect a similar reduction of mass estimates in models assuming more realistic mass profiles.

Disentangling the Potential Dark Matter Origin of LIGO’s Black Holes

“…Many of these parameters remain poorly constrained and have changed since the initial microlensing results; for example, the rotational speed of the Milky Way at 50kpc was formerly assumed to be ∼ 200km/s, whereas current observations suggest a speed of 136 ± 56km/s (Sofue 2013) and 178 ± 17km/2 (Bhattacharjee et al 2014) at 53 ± 15kpc and ∼ 50kpc respectively. Similarly, stellar velocity dispersion observations now appear to show a rotation curve that falls off with distance (Deason et al 2012) rather than remaining flat as was previously assumed, and Bratek et al (2014) showed that determining the mass of the Milky Way is strongly dependent on the assumed galaxy model. These studies show that the accepted values of important astrophysical parameters have changed and that these variations can affect predictions of other halo parameters.…”

Motion of halo tracer objects in the gravitational potential of a low-mass model of the Galaxy

“…A motivation behind this mapping and its explicit construction is given in Bratek et al (2014). the local standard of rest frame (LSR) to the Galacto-centric frame.…”

“…To eliminate a possible decrease in the RVD at lower radii due to circular orbits in the disk, we excluded tracers in the neighbourhood (R/20) 2 + (Z/4) 2 < 1 (in units of kpc) of the mid-plane. We also did not take into account: a) a distant Leo T, located at r > 400 kpc; b) Leo I, rejected for reasons largely discussed in Bratek et al (2014); c) a single star for which rv 2 r /(2G) > 5.6 × 10 11 M ; and d) four additional objects for which r v 2 r /(2G) 3.5 × 10 11 M (these are: 88-TARG37, Hercules, J234809.03-010737.6 and J124721.34+384157.9). As shown with the help of a simple asymptotic estimator ), had we not excluded d) the total expected mass would have been increased by only a factor of ≈1.16.…”

“…The initial conditions for the simulation in the perturbed field should be chosen close to a known stationary solution of a Jeans problem in the non-perturbed field. For this purpose we make use of a PDF to be found similar to that found in Bratek et al (2014), but it is not obvious if this initial PDF and the resulting RVD profile would be stable against such a perturbation. Running a simulation with an initial PDF consistent with the observed high RVD could lead to an RVD profile with a value that is quickly and steadily decreasing.…”

Modelling vertical structure in circular velocity of spiral galaxy NGC 4244

“…In modeling the mass distribution and the vertical gradient, we limit ourselves to using the thin disk model, instead of applying a finite-width disk, because, as it was illustrated by Ja locha et al ( 2014), when the gradient is calculated above the mid-plane, outside the main concentration of masses characterized by some vertical width-scale, then the vertical structure becomes insignificant for the gradient determination in this region and one can use a simpler model. We determine a surface density in thin disk model based on a given circular velocity, by using a formula turning the velocity squared to the surface density as derived by Bratek et al (2014):…”