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We report on the discovery of 29 Cepheid variables in the galaxy M101 after using the original Wide Field Camera (WFC) and the new Wide Field and Planetary Camera (WFPC2) on the Hubble Space Telescope\/ ($HST$), to observe a field in M101 at 14 independent epochs in $V$ (F555W), five epochs in $I$ (F785LP/F814W), and one epoch in $B$ (F439W). We have found Cepheids with periods ranging from 10 to 60 days. The data have been calibrated using the Medium-Deep Survey (MDS) WFC photometric zero-points, the preliminary WFPC2 Status Report photometric calibration, and ground-based secondary standards in $V$ and $I$. We have constructed $V$, $I$, and $B$ period-luminosity (PL) relations and have derived apparent distance moduli adopting a value of 18.50 mag for the distance modulus of the Large Magellanic Cloud (LMC) and $E(B-V)=0.10$ mag for the reddening to the LMC Cepheids. Using a Galactic extinction law to fit the apparent $V$ and $I$ distance moduli, we have found a mean reddening for the M101 sample of $E(B-V)=0.02$ mag and a true distance modulus to M101 of $29.39\pm0.18$ mag, corresponding to a distance of $7.5\pm0.7$ Mpc.
The distance to M101 is one of three distance determinations to date from the $HST$ Key Project on the Extragalactic Distance Scale. These data, taken in a field 7\Min 9 from the center of M101 will be used in conjunction with Cepheid search results in a field 1\Min 7 from the center, with nearly a factor of seven increase in metal abundance, in order to empirically calibrate the abundance effects on the Cepheid PL relationship. The goal of the Key Project is to provide a value of the Hubble Constant accurate to 10\%.
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