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

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

Different Policy Objectives of the Road Pricing Problem -a Game Theory Approach

Abstract Using game theory we investigate a new approach to formulate and solve optimal tolls with a focus on different policy objectives of the road authority. The aim is to gain more insight into determining optimal tolls as well as into the behavior of users after tolls have been imposed on the network. The problem of determining optimal tolls is stated and defined using utility maximization theory, including elastic demand on the travelers&apos; side and different objectives for the road authority. Game theory notions are adopted regarding different games and players, rules and outcomes of the games played between travelers on the one hand and the road authority on the other. Different game concepts (Cournot, Stackelberg and social planner game) are mathematically formulated and the relationship between players, their payoff functions, and rules of the games are defined. The games are solved for different scenarios and different objectives for the road authority, using the Nash equilibrium concept. Using the Stackelberg game concept as being most realistic for road pricing, a few experiments are presented illustrating the optimal toll design problem subject to different pricing policies considering different objectives of the road authority. Results show different outcomes both in terms of optimal tolls as well as in payoffs for travelers. There exist multiple optimal solutions and the objective functions may have a non-continuous shape. The main contribution is the two-level separation between the network users and the road authority in terms of their objectives and influences

A Hot Uranus Orbiting the Super Metal-rich Star HD77338 and the Metallicity - Mass Connection

We announce the discovery of a low-mass planet orbiting the super metal-rich K0V star HD77338 as part of our on-going Calan-Hertfordshire Extrasolar Planet Search. The best fit planet solution has an orbital period of 5.7361\pm0.0015 days and with a radial velocity semi-amplitude of only 5.96\pm1.74 m/s, we find a minimum mass of 15.9+4.7-5.3 Me. The best fit eccentricity from this solution is 0.09+0.25-0.09, and we find agreement for this data set using a Bayesian analysis and a periodogram analysis. We measure a metallicity for the star of +0.35\pm0.06 dex, whereas another recent work (Trevisan et al. 2011) finds +0.47\pm0.05 dex. Thus HD77338b is one of the most metal-rich planet host stars known and the most metal-rich star hosting a sub-Neptune mass planet. We searched for a transit signature of HD77338b but none was detected. We also highlight an emerging trend where metallicity and mass seem to correlate at very low masses, a discovery that would be in agreement with the core accretion model of planet formation. The trend appears to show that for Neptune-mass planets and below, higher masses are preferred when the host star is more metal-rich. Also a lower boundary is apparent in the super metal-rich regime where there are no very low-mass planets yet discovered in comparison to the sub-solar metallicity regime. A Monte Carlo analysis shows that this, low-mass planet desert, is statistically significant with the current sample of 36 planets at around the 4.5\sigma\ level. In addition, results from Kepler strengthen the claim for this paucity of the lowest-mass planets in super metal-rich systems. Finally, this discovery adds to the growing population of low-mass planets around low-mass and metal-rich stars and shows that very low-mass planets can now be discovered with a relatively small number of data points using stable instrumentation.Comment: 25 pages, 15 figures, 5 tables, accepted for publication in Ap

ON the CONSERVATION of the VERTICAL ACTION in GALACTIC DISKS

We employ high-resolution N-body simulations of isolated spiral galaxy models, from low-amplitude, multi-armed galaxies to Milky Way-like disks, to estimate the vertical action of ensembles of stars in an axisymmetrical potential. In the multi-armed galaxy the low-amplitude arms represent tiny perturbations of the potential, hence the vertical action for a set of stars is conserved, although after several orbital periods of revolution the conservation degrades significantly. For a Milky Way-like galaxy with vigorous spiral activity and the formation of a bar, our results show that the potential is far from steady, implying that the action is not a constant of motion. Furthermore, because of the presence of high-amplitude arms and the bar, considerable in-plane and vertical heating occurs that forces stars to deviate from near-circular orbits, reducing the degree at which the actions are conserved for individual stars, in agreement with previous results, but also for ensembles of stars. If confirmed, this result has several implications, including the assertion that the thick disk of our Galaxy forms by radial migration of stars, under the assumption of the conservation of the action describing the vertical motion of stars. © 2016. The American Astronomical Society. All rights reserved

Tracing chemical evolution over the extent of the Milky Way's Disk with APOGEE Red Clump Stars

We employ the first two years of data from the near-infrared, high-resolution SDSS-III/APOGEE spectroscopic survey to investigate the distribution of metallicity and alpha-element abundances of stars over a large part of the Milky Way disk. Using a sample of ~10,000 kinematically-unbiased red-clump stars with ~5% distance accuracy as tracers, the [alpha/Fe] vs. [Fe/H] distribution of this sample exhibits a bimodality in [alpha/Fe] at intermediate metallicities, -0.9<[Fe/H]<-0.2, but at higher metallicities ([Fe/H]=+0.2) the two sequences smoothly merge. We investigate the effects of the APOGEE selection function and volume filling fraction and find that these have little qualitative impact on the alpha-element abundance patterns. The described abundance pattern is found throughout the range 5<R<11 kpc and 0<|Z|<2 kpc across the Galaxy. The [alpha/Fe] trend of the high-alpha sequence is surprisingly constant throughout the Galaxy, with little variation from region to region (~10%). Using simple galactic chemical evolution models we derive an average star formation efficiency (SFE) in the high-alpha sequence of ~4.5E-10 1/yr, which is quite close to the nearly-constant value found in molecular-gas-dominated regions of nearby spirals. This result suggests that the early evolution of the Milky Way disk was characterized by stars that shared a similar star formation history and were formed in a well-mixed, turbulent, and molecular-dominated ISM with a gas consumption timescale (1/SFE) of ~2 Gyr. Finally, while the two alpha-element sequences in the inner Galaxy can be explained by a single chemical evolutionary track this cannot hold in the outer Galaxy, requiring instead a mix of two or more populations with distinct enrichment histories.Comment: 18 pages, 17 figures. Accepted for publication in Ap

The SDSS-III Baryon Oscillation Spectroscopic Survey: Quasar Target Selection for Data Release Nine

The SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), a five-year spectroscopic survey of 10,000 deg^2, achieved first light in late 2009. One of the key goals of BOSS is to measure the signature of baryon acoustic oscillations in the distribution of Ly-alpha absorption from the spectra of a sample of ~150,000 z>2.2 quasars. Along with measuring the angular diameter distance at z\approx2.5, BOSS will provide the first direct measurement of the expansion rate of the Universe at z > 2. One of the biggest challenges in achieving this goal is an efficient target selection algorithm for quasars over 2.2 < z < 3.5, where their colors overlap those of stars. During the first year of the BOSS survey, quasar target selection methods were developed and tested to meet the requirement of delivering at least 15 quasars deg^-2 in this redshift range, out of 40 targets deg^-2. To achieve these surface densities, the magnitude limit of the quasar targets was set at g <= 22.0 or r<=21.85. While detection of the BAO signature in the Ly-alpha absorption in quasar spectra does not require a uniform target selection, many other astrophysical studies do. We therefore defined a uniformly-selected subsample of 20 targets deg^-2, for which the selection efficiency is just over 50%. This "CORE" subsample will be fixed for Years Two through Five of the survey. In this paper we describe the evolution and implementation of the BOSS quasar target selection algorithms during the first two years of BOSS operations. We analyze the spectra obtained during the first year. 11,263 new z>2.2 quasars were spectroscopically confirmed by BOSS. Our current algorithms select an average of 15 z > 2.2 quasars deg^-2 from 40 targets deg^-2 using single-epoch SDSS imaging. Multi-epoch optical data and data at other wavelengths can further improve the efficiency and completeness of BOSS quasar target selection. [Abridged]Comment: 33 pages, 26 figures, 12 tables and a whole bunch of quasars. Submitted to Ap

Deterministic approach to microscopic three-phase traffic theory

Two different deterministic microscopic traffic flow models, which are in the context of the Kerner's there-phase traffic theory, are introduced. In an acceleration time delay model (ATD-model), different time delays in driver acceleration associated with driver behaviour in various local driving situations are explicitly incorporated into the model. Vehicle acceleration depends on local traffic situation, i.e., whether a driver is within the free flow, or synchronized flow, or else wide moving jam traffic phase. In a speed adaptation model (SA-model), vehicle speed adaptation occurs in synchronized flow depending on driving conditions. It is found that the ATD- and SA-models show spatiotemporal congested traffic patterns that are adequate with empirical results. In the ATD- and SA-models, the onset of congestion in free flow at a freeway bottleneck is associated with a first-order phase transition from free flow to synchronized flow; moving jams emerge spontaneously in synchronized flow only. Differences between the ATD- and SA-models are studied. A comparison of the ATD- and SA-models with stochastic models in the context of three phase traffic theory is made. A critical discussion of earlier traffic flow theories and models based on the fundamental diagram approach is presented.Comment: 40 pages, 14 figure

Type II compactifications on manifolds with SU(2) x SU(2) structure

We study compactifications of type II theories on SU(2) x SU(2) structure manifolds to six, five and four spacetime dimensions. We use the framework of generalized geometry to describe the NS-NS sector of such compactifications and derive the structure of their moduli spaces. We show that in contrast to SU(3) x SU(3) structure compactifications, there is no dynamical SU(2) x SU(2) structure interpolating between an SU(2) structure and an identity structure. Furthermore, we formulate type II compactifications on SU(2) x SU(2) structures in the context of exceptional generalized geometry which makes the U-duality group manifest and naturally incorporates the scalar degrees of freedom arising in the Ramond-Ramond sector. Via this formalism we derive the structure of the moduli spaces as it is expected from N=4 supergravity.Comment: 69 pages, v2 published versio

CHEMICAL CARTOGRAPHY with APOGEE: METALLICITY DISTRIBUTION FUNCTIONS and the CHEMICAL STRUCTURE of the MILKY WAY DISK

Using a sample of 69,919 red giants from the SDSS-III/APOGEE Data Release 12, we measure the distribution of stars in the [/Fe] versus [Fe/H] plane and the metallicity distribution functions (MDFs) across an unprecedented volume of the Milky Way disk, with radius 3 < R < 15 kpc and height kpc. Stars in the inner disk (R < 5 kpc) lie along a single track in [/Fe] versus [Fe/H], starting with -enhanced, metal-poor stars and ending at [/Fe] ∼ 0 and [Fe/H] ∼ +0.4. At larger radii we find two distinct sequences in [/Fe] versus [Fe/H] space, with a roughly solar- sequence that spans a decade in metallicity and a high- sequence that merges with the low- sequence at super-solar [Fe/H]. The location of the high- sequence is nearly constant across the disk