Distance Estimations of Blue Horizontal-branch Stars from the LAMOST and Sloan Digital Sky Survey Spectroscopic Surveys

Blue horizontal-branch (BHB) stars are standard candles for tracing the structure and assembly history of the Galactic halo. We present color–absolute-magnitude relations for BHB stars in multiple optical and near-infrared bands. Using a calibration sample of 164 BHB stars with precise Gaia Early Data Release 3 (EDR3) parallaxes, we derive linear relations in the observed Gaia ( BP , G , RP ) and Two Micron All Sky Survey ( J , H , K s ) systems. We also provide supplementary calibrations from Gaia DR3 synthetic photometry for commonly used optical bands, including UBVI , griz , y , and Hubble Space Telescope F606W and F814W. The M G –( G − RP ) 0 relation, with an intrinsic scatter of 0.143 mag, is applied to 8767 BHB stars from LAMOST and Sloan Digital Sky Survey (SDSS). The distances are up to ∼101 kpc, with a median uncertainty of 6.7%. We validate our distance scale through comparison with Gaia EDR3 geometric distances for 1143 high-quality stars, finding a median difference of 6.4%. Additional tests using globular clusters and two high-precision reference catalogs get median offsets of −1.1% and −5.8%, respectively. These results show that our calibrations provide reliable BHB distances and offer a useful complement to Gaia parallaxes in the distant Galactic halo.