Parallaxes of W UMa stars in the Hipparcos catalogue have been analyzed .
31 W UMa stars , which have the most accurate parallaxes ( \sigma _ { \pi } / \pi < 0.15 ) which are neither associated with a photometric tertiary nor with evidence of a visual companion , were selected for re-calibrating the Period–Luminosity–Color ( PLC ) relation of W UMa stars .
Using the Lutz–Kelker ( LK ) bias corrected ( most probable ) parallaxes , periods ( 0.26 < P ( day ) < 0.87 ) , and colors ( 0.04 < ( B - V ) _ { 0 } < 1.28 ) of the 31 selected W UMa , the PLC relation have been revised and re-calibrated .
The difference between the old ( revised but not bias corrected ) and the new ( LK bias corrected ) relations are almost negligible in predicting the distances of W UMa stars up to about 100 parsecs .
But , it increases and may become intolerable as distances of stars increase .
Additionally , using ( J– - H ) _ { 0 } and ( H– - K _ { s } ) _ { 0 } colors from 2MASS ( Two Micron All Sky Survey ) data , a PLC relation working with infrared data was derived .
It can be used with infrared colors in the range -0.01 < ( J - H ) _ { 0 } < 0.58 , and -0.10 < ( H - K _ { s } ) _ { 0 } < 0.18 .
Despite 2MASS data are single epoch observations , which are not guaranteed at maximum brightness of the W UMa stars , the established relation has been found surprisingly consistent and reliable in predicting LK corrected distances of W UMa stars .