The vertical motions of mono-abundance sub-populations in the Milky Way disk

We present the vertical kinematics of stars in the Milky Way's stellar disk inferred from SDSS/SEGUE G-dwarf data, deriving the vertical velocity dispersion, \sigma_z, as a function of vertical height |z| and Galactocentric radius R for a set of 'mono-abundance' sub-populations of stars with very similar elemental abundances [\alpha/Fe] and [Fe/H]. We find that all components exhibit nearly isothermal kinematics in |z|, and a slow outward decrease of the vertical velocity dispersion: \sigma_z (z,R|[\alpha/Fe],[Fe/H]) ~ \sigma_z ([\alpha/Fe],[Fe/H]) x \exp (-(R-R_0)/7 kpc}). The characteristic velocity dispersions of these components vary from ~ 15 km/s for chemically young, metal-rich stars, to >~ 50 km/s for metal poor stars. The mean \sigma_z gradient away from the mid plane is only 0.3 +/- 0.2 km/s/kpc. We find a continuum of vertical kinetic temperatures (~\sigma^2_z) as function of ([\alpha/Fe],[Fe/H]), which contribute to the stellar surface mass density as \Sigma_{R_0}(\sigma^2_z) ~ \exp(-\sigma^2_z). The existence of isothermal mono-abundance populations with intermediate dispersions reject the notion of a thin-thick disk dichotomy. This continuum of disks argues against models where the thicker disk portions arise from massive satellite infall or heating; scenarios where either the oldest disk portion was born hot, or where internal evolution plays a major role, seem the most viable. The wide range of \sigma_z ([\alpha/Fe],[Fe/H]) combined with a constant \sigma_z(z) for each abundance bin provides an independent check on the precision of the SEGUE abundances: \delta_[\alpha/Fe] ~ 0.07 dex and \delta_[Fe/H] ~ 0.15 dex. The radial decline of the vertical dispersion presumably reflects the decrease in disk surface-mass density. This measurement constitutes a first step toward a purely dynamical estimate of the mass profile the disk in our Galaxy. [abridged

The Milky Way's circular velocity curve between 4 and 14 kpc from APOGEE data

We measure the Milky Way's rotation curve over the Galactocentric range 4 kpc <~ R <~ 14 kpc from the first year of data from the Apache Point Observatory Galactic Evolution Experiment (APOGEE). We model the line-of-sight velocities of 3,365 stars in fourteen fields with b = 0 deg between 30 deg < l < 210 deg out to distances of 10 kpc using an axisymmetric kinematical model that includes a correction for the asymmetric drift of the warm tracer population (\sigma_R ~ 35 km/s). We determine the local value of the circular velocity to be V_c(R_0) = 218 +/- 6 km/s and find that the rotation curve is approximately flat with a local derivative between -3.0 km/s/kpc and 0.4 km/s/kpc. We also measure the Sun's position and velocity in the Galactocentric rest frame, finding the distance to the Galactic center to be 8 kpc < R_0 < 9 kpc, radial velocity V_{R,sun} = -10 +/- 1 km/s, and rotational velocity V_{\phi,sun} = 242^{+10}_{-3} km/s, in good agreement with local measurements of the Sun's radial velocity and with the observed proper motion of Sgr A*. We investigate various systematic uncertainties and find that these are limited to offsets at the percent level, ~2 km/s in V_c. Marginalizing over all the systematics that we consider, we find that V_c(R_0) 99% confidence. We find an offset between the Sun's rotational velocity and the local circular velocity of 26 +/- 3 km/s, which is larger than the locally-measured solar motion of 12 km/s. This larger offset reconciles our value for V_c with recent claims that V_c >~ 240 km/s. Combining our results with other data, we find that the Milky Way's dark-halo mass within the virial radius is ~8x10^{11} M_sun.Comment: submitted to Ap

The stellar population structure of the Galactic disk

The spatial structure of stellar populations with different chemical abundances in the Milky Way contains a wealth of information on Galactic evolution over cosmic time. We use data on 14,699 red-clump stars from the APOGEE survey, covering 4 kpc <~ R <~ 15 kpc, to determine the structure of mono-abundance populations (MAPs)---stars in narrow bins in [a/Fe] and [Fe/H]---accounting for the complex effects of the APOGEE selection function and the spatially-variable dust obscuration. We determine that all MAPs with enhanced [a/Fe] are centrally concentrated and are well-described as exponentials with a scale length of 2.2+/-0.2 kpc over the whole radial range of the disk. We discover that the surface-density profiles of low-[a/Fe] MAPs are complex: they do not monotonically decrease outwards, but rather display a peak radius ranging from ~5 kpc to ~13 kpc at low [Fe/H]. The extensive radial coverage of the data allows us to measure radial trends in the thickness of each MAP. While high-[a/Fe] MAPs have constant scale heights, low-[a/Fe] MAPs flare. We confirm, now with high-precision abundances, previous results that each MAP contains only a single vertical scale height and that low-[Fe/H], low-[a/Fe] and high-[Fe/H], high-[a/Fe] MAPs have intermediate (h_Z~300 to 600 pc) scale heights that smoothly bridge the traditional thin- and thick-disk divide. That the high-[a/Fe], thick disk components do not flare is strong evidence against their thickness being caused by radial migration. The correspondence between the radial structure and chemical-enrichment age of stellar populations is clear confirmation of the inside-out growth of galactic disks. The details of these relations will constrain the variety of physical conditions under which stars form throughout the MW disk.Comment: Code available at https://github.com/jobovy/apogee-map

The Stellar Metallicity Distribution Function of the Galactic Halo from SDSS Photometry

We explore the stellar metallicity distribution function of the Galactic halo based on SDSS ugriz photometry. A set of stellar isochrones is calibrated using observations of several star clusters and validated by comparisons with medium-resolution spectroscopic values over a wide range of metal abundance. We estimate distances and metallicities for individual main-sequence stars in the multiply scanned SDSS Stripe 82, at heliocentric distances in the range 5 - 8 kpc and |b| > 35 deg, and find that the in situ photometric metallicity distribution has a shape that matches that of the kinematically-selected local halo stars from Ryan & Norris. We also examine independent kinematic information from proper-motion measurements for high Galactic latitude stars in our sample. We find that stars with retrograde rotation in the rest frame of the Galaxy are generally more metal poor than those exhibiting prograde rotation, which is consistent with earlier arguments by Carollo et al. that the halo system comprises at least two spatially overlapping components with differing metallicity, kinematics, and spatial distributions. The observed photometric metallicity distribution and that of Ryan & Norris can be described by a simple chemical evolution model by Hartwick (or by a single Gaussian distribution); however, the suggestive metallicity-kinematic correlation contradicts the basic assumption in this model that the Milky Way halo consists primarily of a single stellar population. When the observed metallicity distribution is deconvolved using two Gaussian components with peaks at [Fe/H] ~ -1.7 and -2.3, the metal-poor component accounts for ~20% - 35% of the entire halo population in this distance range.Comment: Accepted for publication in Ap

N=1,2 supersymmetric vacua of IIA supergravity and SU(2) structures

We consider backgrounds of (massive) IIA supergravity of the form of a warped product $M_{1,3}\times_{\omega} X_6$, where $X_6$ is a six-dimensional compact manifold and $M_{1,3}$ is $AdS_4$ or a four-dimensional Minkowski space. We analyse conditions for $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry on manifolds of SU(2) structure. We prove the absence of solutions in certain cases.Comment: 24 pages; v2: reference adde

THE IMPRINT of RADIAL MIGRATION on the VERTICAL STRUCTURE of GALAXY DISKS

We use numerical simulations to examine the effects of radial migration on the vertical structure of galaxy disks. The simulations follow three exponential disks of different mass but similar circular velocity, radial scalelength, and (constant) scale height. The disks develop different non-axisymmetric patterns, ranging from feeble, long-lived multiple arms to strong, rapidly evolving few-armed spirals. These fluctuations induce radial migration through secular changes in the angular momentum of disk particles, mixing the disk radially and blurring pre-existing gradients. Migration primarily affects stars with small vertical excursions, regardless of spiral pattern. This "provenance bias" largely determines the vertical structure of migrating stars: inward migrators thin down as they move in, whereas outward migrators do not thicken up but rather preserve the disk scale height at their destination. Migrators of equal birth radius thus develop a strong scale-height gradient, not by flaring out as commonly assumed, but by thinning down as they spread inward. Similar gradients have been observed for low-[α/Fe] mono-abundance populations (MAPs) in the Galaxy, but our results argue against interpreting them as a consequence of radial migration. This is because outward migration does not lead to thickening, implying that the maximum scale height of any population should reflect its value at birth. In contrast, Galactic MAPs have scale heights that increase monotonically outward, reaching values that greatly exceed those at their presumed birth radii. Given the strong vertical bias affecting migration, a proper assessment of the importance of radial migration in the Galaxy should take carefully into account the strong radial dependence of the scale heights of the various stellar populations. © 2016. The American Astronomical Society. All rights reserved