The dwarf spheroidal companions to M31: Variable stars in Andromeda I and Andromeda III

We present the results of variable star searches of the M31 dwarf spheroidal (dSph) companions Andromeda I and Andromeda III using the Hubble Space Telescope. A total of 100 variable stars were found in And I, while 56 were found in And III. One variable found in And I and another in And III may be type II Cepheids. In addition to this variable in And III, another four variables are anomalous Cepheids (ACs). So far, no definite ACs have been discovered in And I. We discuss the properties of these variables with respect to those found in the other dSph galaxies and revisit the AC period-luminosity relations. We found 72 fundamental mode RR Lyrae (RRab) stars and 26 first-overtone mode RR Lyrae (RRc) stars in And I giving mean periods of 0.575 and 0.388 days, respectively. One likely RR Lyrae star in And I remains unclassified because of a lack of F555W data. For And III, 39 RR Lyrae stars are pulsating in the fundamental mode with a mean period of 0.657 days, and 12 are in the first-overtone mode with a mean period of 0.402 days. Using the mean metal abundances derived from the red giant branch colors, the mean RRab period for And I is consistent with the mean period-metallicity relation seen in the RR Lyrae populations of Galactic globular clusters, while And III is not, having too large a mean RRab period for its abundance. In And I, we found two RR Lyrae stars that are noticeably fainter than the horizontal branch. We discuss the possibility that these stars are associated with the recently discovered stellar stream in the halo of M31. Using various methods, we estimate the mean metallicity of the RR Lyrae stars to be [[Fe/H]]approximate to -1.5 for And I and approximate to - 1.8 for And III. These estimates match well with other mean metallicity estimates for the galaxies. Interestingly, a comparison of the period-amplitude diagrams for these two galaxies with other dSph galaxies shows that And III is lacking in shorter period, higher amplitude RR Lyrae stars. This may be a consequence of the very red horizontal branch morphology in this dSph. Not including the two faint RR Lyrae stars, we find [V-RR] = 25.14 +/- 0.04 mag for And I, resulting in a distance of 765 +/- 25 kpc. For And III, [V-RR] = 25.01 +/- 0.04 mag, giving a distance of 740 +/- 20 kpc. These distance estimates are consistent with those previously found for these galaxies. We discuss the relation between the specific frequency of the ACs in dSph galaxies and the mean metallicity of the galaxy, finding that the M31 dSph galaxies follow the same relations as the Galactic dSph galaxies. We also find that the period-luminosity relations of ACs and short-period Cepheids are distinct, with the short-period Cepheids having higher luminosities at a given period.