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Register a new userSubstructure at High Speed I: Inferring the Escape Velocity in the Presence of Kinematic Substructure
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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.
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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.
Tidal debris from infalling satellites can leave observable structure in the phase-space distribution of the Galactic halo. Such substructure can be manifest in the spatial and/or velocity distributions of the stars in the halo. This paper focuses on a class of substructure that is purely kinematic in nature, with no accompanying spatial features. To study its properties, we use a simulated stellar halo created by dynamically populating the Via Lactea II high-resolution N-body simulation with stars. A significant fraction of the stars in the inner halo of Via Lactea share a common speed and metallicity, despite the fact that they are spatially diffuse. We argue that this kinematic substructure is a generic feature of tidal debris from older mergers and may explain the detection of radial-velocity substructure in the inner halo made by the Sloan Extension for Galactic Understanding and Exploration. The GAIA satellite, which will provide the proper motions of an unprecedented number of stars, should further characterize the kinematic substructure in the inner halo. Our study of the Via Lactea simulation suggests that the stellar halo can be used to map the speed distribution of the local dark-matter halo, which has important consequences for dark-matter direct-detection experiments.
We present and analyze the positions, distances, and radial velocities for over 4000 blue horizontal-branch (BHB) stars in the Milky Ways halo, drawn from SDSS DR8. We search for position-velocity substructure in these data, a signature of the hierarchical assembly of the stellar halo. Using a cumulative close pair distribution (CPD) as a statistic in the 4-dimensional space of sky position, distance, and velocity, we quantify the presence of position-velocity substructure at high statistical significance among the BHB stars: pairs of BHB stars that are close in position on the sky tend to have more similar distances and radial velocities compared to a random sampling of these overall distributions. We make analogous mock-observations of 11 numerical halo formation simulations, in which the stellar halo is entirely composed of disrupted satellite debris, and find a level of substructure comparable to that seen in the actually observed BHB star sample. This result quantitatively confirms the hierarchical build-up of the stellar halo through a signature in phase (position-velocity) space. In detail, the structure present in the BHB stars is somewhat less prominent than that seen in most simulated halos, quite possibly because BHB stars represent an older sub-population. BHB stars located beyond 20 kpc from the Galactic center exhibit stronger substructure than at $rm r_{gc} < 20$ kpc.
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.
We confirm, quantify, and provide a table of the coherent velocity substructure of the Milky Way disk within 2 kpc of the Sun towards the Galactic anticenter, with 0.2 kpc resolution. We use the radial velocities of ~340,000 F-type stars obtained with the Guoshoujing Telescope (also known as the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, LAMOST), and proper motions derived from the PPMXL catalog. The PPMXL proper motions have been corrected to remove systematic errors by subtracting the average proper motions of galaxies and QSOs that have been confirmed in the LAMOST spectroscopic survey, and that are within 2.5 degrees of the stars position. We provide the resulting table of systematic offsets derived from the PPMXL proper motion measurements of extragalactic objects identified in the LAMOST spectroscopic survey. Using the corrected phase- space stellar sample, we find statistically significant deviations in the bulk disk velocity of 20 km/s or more in the three dimensional velocities of Galactic disk stars. The bulk velocity varies significantly over length scales of half a kpc or less. The rotation velocity of the disk increases by 20 km/s from the Suns position to 1.5 kpc outside the solar circle. Disk stars in the second quadrant, within 1 kpc of the Sun, are moving radially towards the Galactic center and vertically towards a point a few tenths of a kpc above the Galactic plane; looking down on the disk, the stars appear to move in a circular streaming motion with a radius of order 1 kpc.
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