Distance to M31 With the HST and Hipparcos Red Clump Stars

Following an approach by Paczy\'nski & Stanek we compare red clump stars with parallaxes known to better than 10% in the Hipparcos catalog with the red clump stars observed in three fields in M31 using the HST. There are $\sim 600$ and $\sim 6,300$ such stars in the two data sets, respectively. The local red clump luminosity function is well represented by a Gaussian with the peak at $M_{I,m}=-0.23$, and the dispersion $\sigma_{RC}\approx0.2 $mag. This allows a single step determination of the distance modulus to M31 $\mu_{0,M31} = 24.471\pm 0.035 \pm 0.045 $mag (statistical plus systematic error) and the corresponding distance $R_{M31}= 784\pm 13\pm 17 kpc$. The number of red clump stars is large enough that the formal statistical error in the distance is only $\lesssim 2$%. We also correct the treatment of the local interstellar extinction by Paczy\'nski & Stanek and we obtain the Galactocentric distance modulus $\mu_{0,GC}=14.57 \pm0.04 \pm 0.04 $mag (statistical plus systematic error), and the corresponding Galactocentric distance $R_0=8.2 \pm0.15 \pm 0.15 kpc$.