Bayesian analysis of resolved stellar spectra: application to MMT/Hectochelle Observations of the Draco dwarf spheroidal

We introduce a Bayesian method for fitting faint, resolved stellar spectra in order to obtain simultaneous estimates of redshift and stellar-atmospheric parameters. We apply the method to thousands of spectra---covering 5160-5280 Angs. at resolution R~20,000---that we have acquired with the MMT/Hectochelle fibre spectrograph for red-giant and horizontal branch candidates along the line of sight to the Milky Way's dwarf spheroidal satellite in Draco. The observed stars subtend an area of ~4 deg^2, extending ~3 times beyond Draco's nominal `tidal' radius. For each spectrum we tabulate the first four moments---central value, variance, skewness and kurtosis---of posterior probability distribution functions representing estimates of the following physical parameters: line-of-sight velocity v_los, effective temperature (T_eff), surface gravity (logg) and metallicity ([Fe/H]). After rejecting low-quality measurements, we retain a new sample consisting of 2813 independent observations of 1565 unique stars, including 1879 observations for 631 stars with (as many as 13) repeat observations. Parameter estimates have median random errors of sigma_{v_los}=0.88 km/s, sigma_{T_eff}=162 K, sigma_logg=0.37 dex and sigma_[Fe/H]=0.20 dex. Our estimates of physical parameters distinguish ~470 likely Draco members from interlopers in the Galactic foreground.Comment: published in Monthly Notices of the Royal Astronomical Society, all data are publicly available at the following address: http://www.andrew.cmu.edu/user/mgwalker/hectochelle

Systemic Proper Motions of Milky Way Satellites from Stellar Redshifts: the Carina, Fornax, Sculptor and Sextans Dwarf Spheroidals

The transverse motions of nearby dwarf spheroidal (dSph) galaxies contribute line-of-sight components that increase with angular distance from the dSph centers, inducing detectable gradients in stellar redshift. In the absence of an intrinsic velocity gradient (e.g., due to rotation or streaming), an observed gradient in the heliocentric rest frame (HRF) relates simply to a dSph's systemic proper motion (PM). Kinematic samples for the Milky Way's brightest dSph satellites are now sufficiently large that we can use stellar redshifts to constrain systemic PMs independently of astrometric data. Data from our Michigan/MIKE Fiber System (MMFS) Survey reveal significant HRF velocity gradients in Carina, Fornax and Sculptor, and no significant gradient in Sextans. Assuming there are no intrinsic gradients, the data provide a relatively tight constraint on the PM of Fornax, (mu_{alpha}^{HRF},mu_{delta}^{HRF})=(+48 +/- 15,-25 +/- 14) mas/century, that agrees with published HST astrometric measurements. Smaller data sets yield weaker constraints in the remaining galaxies, but our Carina measurement, (mu_{alpha}^{HRF},mu_{delta}^{HRF})=(+25 +/- 36,+16 +/- 43) mas/century, agrees with the published astrometric value. The disagreement of our Sculptor measurement, (mu_{alpha}^{HRF},mu_{delta}^{HRF})= (-40 +/- 29, -69 +/- 47) mas/century, with astrometric measurements is expected if Sculptor has a rotational component as reported by Battaglia et al. (2008). For Sextans, which at present lacks an astrometric measurement, we measure (mu_{alpha}^{HRF},mu_{delta}^{HRF})=(-26 +/- 41, +10 +/- 44) mas/century.Comment: Accepted for Publication by ApJ Letter

Clean Kinematic Samples in Dwarf Spheroidals: An Algorithm for Evaluating Membership and Estimating Distribution Parameters When Contamination is Present

(abridged) We develop an algorithm for estimating parameters of a distribution sampled with contamination, employing a statistical technique known as ``expectation maximization'' (EM). Given models for both member and contaminant populations, the EM algorithm iteratively evaluates the membership probability of each discrete data point, then uses those probabilities to update parameter estimates for member and contaminant distributions. The EM approach has wide applicability to the analysis of astronomical data. Here we tailor an EM algorithm to operate on spectroscopic samples obtained with the Michigan-MIKE Fiber System (MMFS) as part of our Magellan survey of stellar radial velocities in nearby dwarf spheroidal (dSph) galaxies. These samples are presented in a companion paper and contain discrete measurements of line-of-sight velocity, projected position, and Mg index for ~1000 - 2500 stars per dSph, including some fraction of contamination by foreground Milky Way stars. The EM algorithm quantifies both dSph and contaminant distributions, returning maximum-likelihood estimates of the means and variances, as well as the probability that each star is a dSph member. Applied to our MMFS data, the EM algorithm identifies more than 5000 probable dSph members. We test the performance of the EM algorithm on simulated data sets that represent a range of sample size, level of contamination, and amount of overlap between dSph and contaminant velocity distributions. The simulations establish that for samples ranging from large (N ~3000) to small (N~30), the EM algorithm distinguishes members from contaminants and returns accurate parameter estimates much more reliably than conventional methods of contaminant removal (e.g., sigma clipping).Comment: Accepted for publication in The Astronomical Journal. Download pdf with full-resolution figures from http://www.ast.cam.ac.uk/~walker/dsph_em.pd

The Velocity Dispersion Profile of the Remote Dwarf Spheroidal Galaxy Leo I: A Tidal Hit and Run?

(abridged) We present kinematic results for a sample of 387 stars located near Leo I based on spectra obtained with the MMT's Hectochelle spectrograph near the MgI/Mgb lines. We estimate the mean velocity error of our sample to be 2.4 km/s, with a systematic error of < 1 km/s. We produce a final sample of 328 Leo I red giant members, from which we measure a mean heliocentric radial velocity of 282.9 +/- 0.5 km/s, and a mean radial velocity dispersion of 9.2 +/- 0.4 km/s for Leo I. The dispersion profile of Leo I is flat out to beyond its classical `tidal' radius. We fit the profile to a variety of equilibrium dynamical models and can strongly rule out models where mass follows light. Two-component Sersic+NFW models with tangentially anisotropic velocity distributions fit the dispersion profile well, with isotropic models ruled out at a 95% confidence level. The mass and V-band mass-to-light ratio of Leo I estimated from equilibrium models are in the ranges 5-7 x 10^7 M_sun and 9-14 (solar units), respectively, out to 1 kpc from the galaxy center. Leo I members located outside a `break radius' (about 400 arcsec = 500 pc) exhibit significant velocity anisotropy, whereas stars interior appear to have isotropic kinematics. We propose the break radius represents the location of the tidal radius of Leo I at perigalacticon of a highly elliptical orbit. Our scenario can account for the complex star formation history of Leo I, the presence of population segregation within the galaxy, and Leo I's large outward velocity from the Milky Way. The lack of extended tidal arms in Leo I suggests the galaxy has experienced only one perigalactic passage with the Milky Way, implying that Leo I may have been injected into its present orbit by a third body a few Gyr before perigalacticon.Comment: ApJ accepted, 23 figures, access paper as a pdf file at http://www.astro.lsa.umich.edu/~mmateo/research.htm

Magellan/M2FS Spectroscopy of Galaxy Clusters: Stellar Population Model and Application to Abell 267

We report the results of a pilot program to use the Magellan/M2FS spectrograph to survey the galactic populations and internal kinematics of galaxy clusters. For this initial study, we present spectroscopic measurements for $223$ quiescent galaxies observed along the line of sight to the galaxy cluster Abell 267 ($z\sim0.23$). We develop a Bayesian method for modeling the integrated light from each galaxy as a simple stellar population, with free parameters that specify redshift ($v_\mathrm{los}/c$) and characteristic age, metallicity ($\mathrm{[Fe/H]}$), alpha-abundance ($[\alpha/\mathrm{Fe}]$), and internal velocity dispersion ($\sigma_\mathrm{int}$) for individual galaxies. Parameter estimates derived from our 1.5-hour observation of A267 have median random errors of $\sigma_{v_\mathrm{los}}=20\ \mathrm{km\ s^{-1}}$, $\sigma_{\mathrm{Age}}=1.2\ \mathrm{Gyr}$, $\sigma_{\mathrm{[Fe/H]}}=0.11\ \mathrm{dex}$,$\sigma_{[\alpha/\mathrm{Fe}]}=0.07\ \mathrm{dex}$, and$\sigma_{\sigma_\mathrm{int}}=20\ \mathrm{km\ s^{-1}}$. In a companion paper, we use these results to model the structure and internal kinematics of A267.Comment: 16 pages, 11 figures, accepted for publication in The Astronomical Journa

Exploring the Chemical Composition and Double Horizontal Branch of the Bulge Globular Cluster NGC 6569

Photometric and spectroscopic analyses have shown that the Galactic bulge cluster Terzan 5 hosts several populations with different metallicities and ages that manifest as a double red horizontal branch (HB). A recent investigation of the massive bulge cluster NGC 6569 revealed a similar, though less extended, HB luminosity split, but little is known about the cluster's detailed chemical composition. Therefore, we have used high-resolution spectra from the Magellan-M2FS and VLT-FLAMES spectrographs to investigate the chemical compositions and radial velocity distributions of red giant branch and HB stars in NGC 6569. We found the cluster to have a mean heliocentric radial velocity of -48.8 km/s (sigma = 5.3 km/s; 148 stars) and a mean [Fe/H] =-0.87 dex (19 stars), but the cluster's 0.05 dex [Fe/H] dispersion precludes a significant metallicity spread. NGC 6569 exhibits light- and heavy-element distributions that are common among old bulge/inner Galaxy globular clusters, including clear (anti)correlations between [O/Fe], [Na/Fe], and [Al/Fe]. The light-element data suggest that NGC 6569 may be composed of at least two distinct populations, and the cluster's low mean [La/Eu] = -0.11 dex indicates significant pollution with r-process material. We confirm that both HBs contain cluster members, but metallicity and light-element variations are largely ruled out as sources for the luminosity difference. However, He mass fraction differences as small as delta Y ~ 0.02 cannot be ruled out and may be sufficient to reproduce the double HB.Comment: 72 pages, 14 figures, 8 tables; published in The Astronomical Journal; electronic versions of all tables are available in the published versio

On Kinematic Substructure in the Sextans Dwarf Spheroidal Galaxy

We present multifiber echelle radial velocity results for 551 stars in the Sextans dwarf spheroidal galaxy and identify 294 stars as probable Sextans members. The projected velocity dispersion profile of the binned data remains flat to a maximum angular radius of $30^{\prime}$. We introduce a nonparametric technique for estimating the projected velocity dispersion surface, and use this to search for kinematic substructure. Our data do not confirm previous reports of a kinematically distinct stellar population at the Sextans center. Instead we detect a region near the Sextans core radius that is kinematically colder than the overall Sextans sample with 95% confidence.Comment: accepted for publication in ApJ Letters; 4 figures (2 color