Abstract
Aims: We used 12,530 photometrically-selected blue horizontal branch (BHB) stars from the Sloan Digital Sky Survey (SDSS) to estimate the total extinction of the Milky Way at the high Galactic latitudes, $R_V$ and $A_V$ in each line of sight. Methods: A Bayesian method was developed to estimate the reddening values in the given lines of sight. Based on the most likely values of reddening in multiple colors, we were able to derive the values of $R_V$ and $A_V$. Results: We selected 94 zero-reddened BHB stars from seven globular clusters as the template. The reddening in the four SDSS colors for the northern Galactic cap were estimated by comparing the field BHB stars with the template stars. The accuracy of this estimation is around 0.01\,mag for most lines of sight. We also obtained $<R_V>$ to be around 2.40$\pm1.05$ and $A_V$ map within an uncertainty of 0.1\,mag. The results, including reddening values in the four SDSS colors, $A_V$, and $R_V$ in each line of sight, are released on line. In this work, we employ an up-to-date parallel technique on GPU card to overcome time-consuming computations. We plan to release online the C++ CUDA code used for this analysis. Conclusions: The extinction map derived from BHB stars is highly consistent with that from Schlegel, Finkbeiner & Davis(1998). The derived $R_V$ is around 2.40$\pm1.05$. The contamination probably makes the $R_V$ be larger.
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