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Register a new userSubstructure at High Speed II: The Local Escape Velocity and Milky Way Mass with Gaia DR2
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Measuring the escape velocity of the Milky Way is critical in obtaining the mass of the Milky Way, understanding the dark matter velocity distribution, and building the dark matter density profile. In Necib $&$ Lin (2021), we introduced a strategy to robustly measure the escape velocity. Our approach takes into account the presence of kinematic substructures by modeling the tail of the stellar distribution with multiple components, including the stellar halo and the debris flow called the Gaia Sausage (Enceladus). In doing so, we can test the robustness of the escape velocity measurement for different definitions of the tail of the velocity distribution, and the consistency of the data with different underlying models. In this paper, we apply this method to the second data release of Gaia and find that a model with at least two components is preferred. Based on a fit with three bound components to account for the disk, relaxed halo, and the Gaia Sausage, we find the escape velocity of the Milky Way at the solar position to be $v_{rm{esc}}= 484.6^{+17.8}_{-7.4}$ km/s. Assuming a Navarro-Frenck-White dark matter profile, and taken in conjunction with a recent measurement of the circular velocity at the solar position of $v_c = 230 pm 10$ km/s, we find a Milky Way concentration of $c_{200} = 13.8^{+6.0}_{-4.3}$ and a mass of $M_{200} = 7.0^{+1.9}_{-1.2} times 10^{11} M_{odot}$, which is considerably lighter than previous measurements.
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The local escape velocity provides valuable inputs to the mass profile of the Galaxy, and requires understanding the tail of the stellar speed distribution. Following Leonard $&$ Tremaine (1990), various works have since modeled the tail of the stellar speed distribution as $propto (v_{rm{esc}} -v)^k$, where $v_{rm{esc}}$ is the escape velocity, and $k$ is the slope of the distribution. In such studies, however, these two parameters were found to be largely degenerate and often a narrow prior is imposed on $k$ in order to constrain $v_{rm{esc}}$. Furthermore, the validity of the power law form is likely to break down in the presence of multiple kinematic substructures. In this paper, we introduce a strategy that for the first time takes into account the presence of kinematic substructure. We model the tail of the velocity distribution as a sum of multiple power laws without imposing strong priors. Using mock data, we show the robustness of this method in the presence of kinematic structure that is similar to the recently-discovered Gaia Sausage. In a companion paper, we present the new measurement of the escape velocity and subsequently the mass of the Milky Way using Gaia DR2 data.
We measure the escape speed curve of the Milky Way based on the analysis of the velocity distribution of $sim 2850$ counter-rotating halo stars from the Gaia DR2. The distances were estimated through the StarHorse code, and only stars with distance errors smaller than 10 per cent were used in the study. The escape speed curve is measured at Galactocentric radii ranging from $sim 5$ kpc to $sim 10.5$ kpc. The local Galactic escape at the Suns position is estimated to be $v_mathrm{e}(r_odot)=580 pm 63~mathrm{km~s^{-1}}$, and it rises towards the Galactic center. Defined as the minimum speed required to reach three virial radii, our estimate of the escape speed as a function of radius implies, for a Navarro-Frenk-White profile and local circular velocity of $240~mathrm{km~s^{-1}}$, a dark matter mass $M_{200}=1.28^{+0.68}_{-0.50} times 10^{12}~M_odot$ and a high concentration $c_{200}=11.09^{+2.94}_{-1.79}$. Assuming the mass-concentration relation of $Lambda$CDM, we get $M_{200}=1.55_{-0.51}^{+0.64}times 10^{12}~M_odot$, $c_{200}=7.93_{-0.27}^{+0.33}$, for a local circular velocity of $228~mathrm{km~s^{-1}}$.
The velocity distribution of stars is a sensitive probe of the gravitational potential of the Galaxy, and hence of its dark matter distribution. In particular, the shape of the dark halo (e.g. spherical, oblate, or prolate) determines velocity correlations, and different halo geometries are expected to result in measurable differences. Here we explore and interpret the correlations in the $(v_R, v_z)$-velocity distribution as a function of position in the Milky Way. We selected a high-quality sample of stars from the Gaia DR2 catalogue and characterised the orientation of the velocity distribution or tilt angle over a radial distance range of $[4-13]~$kpc and up to $3.5~$kpc away from the Galactic plane while taking into account the effects of the measurement errors. We find that the tilt angles change from spherical alignment in the inner Galaxy ($Rsim4~$kpc) towards more cylindrical alignments in the outer Galaxy ($Rsim11~$kpc) when using distances that take a global zero-point offset in the parallax of $-29~mu$as. However, if the amplitude of this offset is underestimated, then the inferred tilt angles in the outer Galaxy only appear shallower and are intrinsically more consistent with spherical alignment for an offset as large as $-54~mu$as. We further find that the tilt angles do not seem to strongly vary with Galactic azimuth and that different stellar populations depict similar tilt angles. Therefore we introduce a simple analytic function that describes the trends found over the full radial range. Since the systematic parallax errors in Gaia DR2 depend on celestial position, magnitude, and colour in complex ways, it is not possible to fully correct for them. Therefore it will be particularly important for dynamical modelling of the Milky Way to thoroughly characterise the systematics in astrometry in future Gaia data releases.
We model the fastest moving (v_tot > 300 km/s) local (D < 3 kpc) halo stars using cosmological simulations and 6-dimensional Gaia data. Our approach is to use our knowledge of the assembly history and phase-space distribution of halo stars to constrain the form of the high velocity tail of the stellar halo. Using simple analytical models and cosmological simulations, we find that the shape of the high velocity tail is strongly dependent on the velocity anisotropy and number density profile of the halo stars --- highly eccentric orbits and/or shallow density profiles have more extended high velocity tails. The halo stars in the solar vicinity are known to have a strongly radial velocity anisotropy, and it has recently been shown the origin of these highly eccentric orbits is the early accretion of a massive (M_star ~ 10^9 M_Sun) dwarf satellite. We use this knowledge to construct a prior on the shape of the high velocity tail. Moreover, we use the simulations to define an appropriate outer boundary of 2r_200, beyond which stars can escape. After applying our methodology to the Gaia data, we find a local (r_0=8.3 kpc) escape speed of v_esc(r_0) = 528(+24,-25) km/s. We use our measurement of the escape velocity to estimate the total Milky Way mass, and dark halo concentration: M_200,tot = 1.00(+0.31,-0.24) x 10^12 M_Sun, c_200 = 10.9(+4.4,-3.3). Our estimated mass agrees with recent results in the literature that seem to be converging on a Milky Way mass of M_200,tot ~ 10^12 M_Sun.
Until the recent advent of $Gaia$ Data Release 2 (DR2) and deep multi-object spectroscopy, it has been difficult to obtain 6-D phase space information for large numbers of stars beyond 4 kpc, in particular towards the Galactic centre, where dust and crowding effects are significant. In this study we combine line-of-sight velocities from the Abundances and Radial velocity Galactic Origins Survey (ARGOS) spectroscopic survey with proper motions from $Gaia$ DR2, to obtain a sample of $sim$ 7,000 red clump stars with 3-D velocities. We perform a large scale stellar kinematics study of the Milky Way (MW) bulge to characterize the bulge velocity ellipsoids. We measure the tilt $l_{v}$ of the major-axis of the velocity ellipsoid in the radial-longitudinal velocity plane in 20 fields across the bulge. The tilt or vertex deviation, is characteristic of non-axisymmetric systems and a significant tilt is a robust indicator of non-axisymmetry or bar presence. We compare the observations to the predicted kinematics of an N-body boxy-bulge model formed from dynamical instabilities. In the model, the $l_{v}$ values are strongly correlated with the angle ($alpha$) between the bulge major-axis and the Sun-Galactic centre line-of-sight. We use a maximum likelihood method to obtain an independent measurement of $alpha$, from bulge stellar kinematics alone. The most likely value of $alpha$ given our model is $alpha = (29 pm 3)^{circ}$. In the Baades window, the metal-rich stars display a larger vertex deviation ($l_{v} = -40^{circ}$) than the metal-poor stars ($l_{v} = 10^{circ}$) but we do not detect significant $l_{v}-$metallicity trends in the other fields.
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