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Marginal likelihoods of distances and extinctions to stars: computation and compact representation

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 Added by Stuart Sale
 Publication date 2014
  fields Physics
and research's language is English




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We present a method for obtaining the likelihood function of distance and extinction to a star given its photometry. The other properties of the star (its mass, age, metallicity and so on) are marginalised assuming a simple Galaxy model. We demonstrate that the resulting marginalised likelihood function can be described faithfully and compactly using a Gaussian mixture model. For dust mapping applications we strongly advocate using monochromatic over bandpass extinctions, and provide tables for converting from the former to the latter for different stellar types.



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Understanding the formation and evolution of our Galaxy requires accurate distances, ages and chemistry for large populations of field stars. Here we present several updates to our spectro-photometric distance code, that can now also be used to estimate ages, masses, and extinctions for individual stars. Given a set of measured spectro-photometric parameters, we calculate the posterior probability distribution over a given grid of stellar evolutionary models, using flexible Galactic stellar-population priors. The code (called {tt StarHorse}) can acommodate different observational datasets, prior options, partially missing data, and the inclusion of parallax information into the estimated probabilities. We validate the code using a variety of simulated stars as well as real stars with parameters determined from asteroseismology, eclipsing binaries, and isochrone fits to star clusters. Our main goal in this validation process is to test the applicability of the code to field stars with known {it Gaia}-like parallaxes. The typical internal precision (obtained from realistic simulations of an APOGEE+Gaia-like sample) are $simeq 8%$ in distance, $simeq 20%$ in age,$simeq 6 %$ in mass, and $simeq 0.04$ mag in $A_V$. The median external precision (derived from comparisons with earlier work for real stars) varies with the sample used, but lies in the range of $simeq [0,2]%$ for distances, $simeq [12,31]%$ for ages, $simeq [4,12]%$ for masses, and $simeq 0.07$ mag for $A_V$. We provide StarHorse distances and extinctions for the APOGEE DR14, RAVE DR5, GES DR3 and GALAH DR1 catalogues.
We infer distances and their asymmetric uncertainties for two million stars using the parallaxes published in the Gaia DR1 (GDR1) catalogue. We do this with two distance priors: A minimalist, isotropic prior assuming an exponentially decreasing space density with increasing distance, and an anisotropic prior derived from the observability of stars in a Milky Way model. We validate our results by comparing our distance estimates for 105 Cepheids which have more precise, independently estimated distances. For this sample we find that the Milky Way prior performs better (the RMS of the scaled residuals is 0.40) than the exponentially decreasing space density prior (RMS is 0.57), although for distances beyond 2 kpc the Milky Way prior performs worse, with a bias in the scaled residuals of -0.36 (vs. -0.07 for the exponentially decreasing space density prior). We do not attempt to include the photometric data in GDR1 due to the lack of reliable colour information. Our distance catalogue is available at http://www.mpia.de/homes/calj/tgas distances/main.html as well as at CDS. This should only be used to give individual distances. Combining data or testing models should be done with the original parallaxes, and attention paid to correlated and systematic uncertainties.
Our work presents an independent calibration of the J-region Asymptotic Giant Branch (JAGB) method using Infrared Survey Facility (IRSF) photometric data and a custom luminosity function profile to determine JAGB mean magnitudes for nine galaxies. We determine a mean absolute magnitude of carbon stars of $M_{LMC}=-6.212 pm 0.010$ (stat.) $pm 0.030$ (syst.) mag. We then use near-infrared photometry of a number of nearby galaxies, originally obtained by our group to determine their distances from Cepheids using the Leavitt law, in order to independently determine their distances with the JAGB method. We compare the JAGB distances obtained in this work with the Cepheid distances resulting from the same photometry and find very good agreement between the results from the two methods. The mean difference is 0.01 mag with an rms scatter of 0.06 mag after taking into account seven out of the eight analyzed galaxies that had their distances determined using Cepheids. The very accurate distance to the Small Magellanic Cloud (SMC) based on detached eclipsing binaries (Graczyk et al. 2020) is also in very good agreement with the distance obtained from carbon stars.
Combining the precise parallaxes and optical photometry delivered by Gaias second data release (Gaia DR2) with the photometric catalogues of PanSTARRS-1, 2MASS, and AllWISE, we derive Bayesian stellar parameters, distances, and extinctions for 265 million stars brighter than G=18. Because of the wide wavelength range used, our results substantially improve the accuracy and precision of previous extinction and effective temperature estimates. After cleaning our results for both unreliable input and output data, we retain 137 million stars, for which we achieve a median precision of 5% in distance, 0.20 mag in V-band extinction, and 245 K in effective temperature for G<14, degrading towards fainter magnitudes (12%, 0.20 mag, and 245 K at G=16; 16%, 0.23 mag, and 260 K at G=17, respectively). We find a very good agreement with the asteroseismic surface gravities and distances of 7000 stars in the Kepler, the K2-C3, and the K2-C6 fields, with stellar parameters from the APOGEE survey, as well as with distances to star clusters. Our results are available through the ADQL query interface of the Gaia mirror at the Leibniz-Institut f{u}r Astrophysik Potsdam (gaia.aip.de) and as binary tables at data.aip.de. As a first application, in this paper we provide distance- and extinction-corrected colour-magnitude diagrams, extinction maps as a function of distance, and extensive density maps, demonstrating the potential of our value-added dataset for mapping the three-dimensional structure of our Galaxy. In particular, we see a clear manifestation of the Galactic bar in the stellar density distributions, an observation that can almost be considered a direct imaging of the Galactic bar.
We combine high-resolution spectroscopic data from APOGEE-2 Survey Data Release 16 (DR16) with broad-band photometric data from several sources, as well as parallaxes from {it Gaia} Data Release 2 (DR2). Using the Bayesian isochrone-fitting code {tt StarHorse}, we derive distances, extinctions and astrophysical parameters for around 388,815 APOGEE stars, achieving typical distance uncertainties of $sim 6%$ for APOGEE giants, $sim 2%$ for APOGEE dwarfs, as well as extinction uncertainties of $sim 0.07$ mag when all photometric information is available, and $sim 0.17$ mag if optical photometry is missing. {tt StarHorse} uncertainties vary with the input spectroscopic catalogue, with the available photometry, and with the parallax uncertainties. To illustrate the impact of our results, we show that, thanks to {it Gaia} DR2 and the now larger sky coverage of APOGEE-2 (including APOGEE-South), we obtain an extended map of the Galactic plane, providing unprecedented coverage of the disk close to the Galactic mid-plane ($|Z_{Gal}|<1$ kpc) from the Galactic Centre out to $R_{rm Gal}sim 20$ kpc. The improvements in statistics as well as distance and extinction uncertainties unveil the presence of the bar in stellar density, as well as the striking chemical duality in the innermost regions of the disk, now clearly extending to the inner bulge. We complement this paper with distances and extinctions for stars in other public released spectroscopic surveys: 324,999 in GALAH DR2, 4,928,715 in LAMOST DR5, 408,894 in RAVE DR6, and 6,095 in GES DR3
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