A Catalog of Distance Determinations for the LAMOST DR8 K Giants in the Galactic Halo

We present a catalog of distances for 19544 K giants drawn from LAMOST DR8. Most of them are located in the halo of the Milky Way up to ~120~kpc. There are 15% K giants without SDSS photometry, for which we supplements with Pan-STARRS1 (PS1) photometry calibrated to SDSS photometric system. The possible contamination of the red clumps/horizontal branch are removed according to metallicities and colors before the distance determination. Combining the LAMOST spectroscopic metallicities with the SDSS/PS1 photometry, we estimate the absolute magnitudes in SDSS $r-$band, the distance moduli, and the corresponding uncertainties through an Bayesian approach devised by Xue et al. (2014) for the SEGUE halo K-giants. The typical distance precision is about 11%. The stars in the catalog lie in a region of 4-126 kpc from the Galactic center, of which with 6, 320 stars beyond 20 kpc and 273 stars beyond 50 kpc, forming the largest spectroscopic sample of distant tracers in the Milky Way halo so far.


INTRODUCTION
K giants, a kind of luminous stars with typical absolute magnitudes of −3 < M r < 1, are ideal tracers to map the Milky Way halo far beyond the solar neighborhood. For instance, exploring the formation of the Milky Way by quantifying the substructures in the Galactic halo (Starkenburg et al. 2009;Xue et al. 2011;Yang et al. 2019), estimating the total mass of the Milky Way by kinematics of the tracers (Xue et al. 2008), or probing the Milky Way stellar halo profile (Xue et al. 2015;Xu et al. 2018; Thomas et al. 2018), and so on. Good distances and corresponding errors are fundamental to address such interesting and important questions of our Galaxy, Xue et al. (2014, hereafter X14) devised a Bayesian approach to estimate the distances of the Galactic halo K giant, and applied to SEGUE (the Sloan Extension for Galactic understanding and exploration, Yanny et al. 2009). In X14, three priors are considered, which are the stellar number density profile in the galactic halo, the giant-branch luminosity function, and the different metallicity distributions of the SEGUE K-giant target subclass. Among them, the prior of the luminosity function plays the biggest role in the distance estimates. Neglecting it could cause a systematic bias up to 0.25 mag in distance modulus (DM). Therefore, the Bayesian approach is optimal to get unbiased distance estimates for stars.
Thanks to the huge number of spectra observed in the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST, also called the Guo Shou Jing Telescope, Zhao et al. 2006;Cui et al. 2012) and the fact that giants occupy a larger fraction of bright stars, generating a large sample of the halo K giants has been made possible. In this work, adopting the photometry from SDSS and spectra covering a wavelength range of 3700 < λ < 9000Å of stars with r < 19 can be obtained simultaneously at one exposure (Zhao et al. 2006. We aim to derive distance moduli following the procedure of X14 for K-giant halo stars selected from the LAMOST DR8. With this method, the absolute magnitude of each star is estimated from the empirically calibrated color-magnitude fiducials with metallicities in the range of −2.38 < [Fe/H] < +0.39. The main observables adopted are [Fe/H], log g and T eff derived from LAMOST stellar spectra, the g and r band magnitudes from the Sloan Digital Sky Survey (SDSS, York et al. 2000) or the Pan-STARRS1 survey (PS1, Chambers & Pan-STARRS Team 2016). In addition, to eliminate possible red clump stars, 2MASS (Skrutskie et al. 2006) J and K s band magnitudes are also used. Details of the observables are described below.
Stellar atmospheric parameters are derived by the official LAMOST Stellar Parameter pipeline (LASP; Wu et al. 2011;Luo et al. 2015), in which the stellar parameters are determined iteratively by minimizing the χ 2 between the observed spectrum and the model spectrum from ELODIE stellar library (Prugniel et al. 2007). From all the survey spectra, the K giants used in the study were identified by the selection criteria presented in Liu et al. (2014, Figure 3), that is, 4000 < T eff < 5600 K, and log g < 3.5 for stars whose T eff < 4600 K, while log g < 4.0 for stars with 4600 ≤ T eff < photometries taken from 2MASS.
Photometries are firstly adopted from SDSS which use the 2.5 m Sloan Foundation Telescope (Gunn et al. 2006) at Apache Point Observatory (APO). The 16th public data release (DR16; Ahumada et al. 2020) was from the SDSS-IV (Blanton et al. 2017), which contains all prior SDSS ugriz imaging data. (Fukugita et al. 1996;Gunn et al. 1998;York et al. 2000;Stoughton et al. 2002;Pier et al. 2003;Eisenstein et al. 2011;Blanton et al. 2017). For K giants without SDSS photometry, we took the broadband data grizy P1 from the second data release (DR2; Flewelling 2016;Magnier et al. 2020a,b,c;Waters et al. 2020) of PS1 instead, while the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) is an innovative wide-field astronomical imaging and data processing facility developed at the University of Hawaii's Institute for Astronomy (Kaiser et al. 2002(Kaiser et al. , 2010. The DR2 of PS1 data used in the present work can be found in MAST: 10.17909/s0zg-jx37. Finally, there are 45% and 83% stars with SDSS and PS1 photometric data, respectively. Moreover, to select halo K giants with good data quality, only stars whose E(B − V ) estimated from Schlegel et al. (1998) and less than 0.25 mag. are adopted. Hence, there are 57% stars left.
Then the extinctions in different bandpass were calculated by Fitzpatrick (1999) reddening law with measurements of Schlafly & Finkbeiner (2011).

PHOTOMETRY CALIBRATION AND DISTANCE ESTIMATES
For stars without SDSS photometry, the PS1 data is taken as a complement. From common stars both observed by SDSS and PS1, trends in the difference between the PS1 and SDSS photometry ∆ m = m PS1 − m SDSS with PS1 colors (g − i) PS1 can be found (see Figure 1). Thus, we need to remove the trends by calibrating the PS1 photometry to match the SDSS one before distance estimates.
Here we perform the calibration by fitting an empirical curve to ∆ m , where m represents apparent magnitudes g and r, as a function of PS1 color (g − i), and thus adjusting the PS1 photometry.
We find the best fit slopes of lines in ∆ m vs. (g − i) PS1 space with least absolute deviation line fitting, which minimizes the absolute value of the residuals, to exclude outliers. The standard errors of the fitted slopes are estimated via bootstrapping. Figure 1 shows the best fits in ∆ m − (g − i) PS1 space, the fittings are: and The calibrated results are shown in Figure 2. The upper panels present that the calibrated g PS1 and r PS1 show very good consistency with the SDSS photometry. In the lower panels, it can be seen that the mean values of adjusted ∆ m are 0.0 with standard errors of 0.025 and 0.023 for g and r mags, respectively, which proves the validity of the calibration in this work.
With the calibrated results, we converted PS1 photometries to SDSS ones for stars without SDSS observation. Finally, we obtains 375, 585 stars with g 0 , r 0 , i 0 , and E(B − V ) < 0.25. The present distance measurement is for halo stars only. Therefore, we selected halo K giants preliminarily before the distance measurements. Considering the colors and metallicities of used giant-branch fiducials of clusters, only K giants whose [Fe/H] < +0.39 and 0.5 ≤ (g − r) 0 ≤ 1.4 are taken. We further excluded stars labeled as RC and stars below the level of the horizontal branch (BH) by using a quadratic polynomial of (g − r) HB We then implemented a Bayesian approach to derive the posterior PDF of DM for each K giant, and hence to provide both a distance estimate and its uncertainty. According to X14, the relative probability of different DM is defined as where   In the sample, 6, 320 stars are in the region of r gc > 20 kpc, including 221 stars in 52 < r gc < 80 kpc and 68 stars whose r gc are larger than 80 kpc.
The sample size is as double as SEGUE K giants in X14. The large sample can help us to trace the mass density for both of the Galactic inner and outer halos in the following works.
To check the validation of our distance estimates in this work, we also compare our results with the parallaxes adopted from Gaia EDR3. Only stars in σ / < 0.1 and σ D /D < 0.15 are taken, which results 5, 497 K giants. The comparison result is shown in Figure 9, in which our distance estimates show very good consistency with parallaxes from Gaia EDR3 catalog for stars with precise parallax measurements.

SUMMARY
We have selected the K giants from LAMSOT DR8, excluding red clumps and stars below the horizontal branch carefully. After calibrating the PS1 photometry gi PS1 to the gr SDSS of SDSS DR16, Galactic potential, it results 19, 544 halo K giants, which is three times larger than the number of X14 from SEGUE K giants. In the catalog, 6, 320 stars are in the region of r gc > 20 kpc, including 221 stars in 50 < r gc < 80 kpc and 52 stars whose r gc are larger than 80 kpc. Furthermore, we compared the distances with parallaxes from Gaia EDR3 catalog for stars with precise parallax measurements.
The result presents a very good consistency, which proves the validation of the estimates in this work.
We finally present an online catalog containing the DM, and LASP atmospheric parameters for the 19, 544 halo K giants. For each object in the catalog, we also list the basic observables such as (R.A., Dec.), extinction corrected apparent magnitudes and de-reddened colors, and heliocentric radial velocities from LAMOST. The Bayesian estimates of the DM, heliocentric distance, Galactocentric