We present a study of the stellar populations in two faint M31 dwarf satellites, Andromeda XI and Andromeda XIII. Using archival images from the Wide Field Planetary Camera 2 onboard the
Hubble Space Telescope, we characterize the horizontal branch (HB) morphologies and the RR Lyrae (RRL) populations of these two faint dwarf satellites. Our new template light-curve fitting routine [Robust RR Lyrae light curve FITing (RRFIT)] has been used to detect and characterize RRL populations in both galaxies. The mean periods of RRab (RR0) stars in And XI and And XIII are <
Pab>= 0.621 ± 0.026 (error1)±0.022 (error2) and 0.648±0.026 (error1)±0.022 (error2), respectively, where `error1' represents the standard error of the mean, while `error2' is based on our synthetic light-curve simulations. The RRL populations in these galaxies show a lack of RRab stars with high amplitudes [Amp (
V) > 1.0 mag] and relatively short periods (P
ab ∼ 0.5d), yet their period-
V-band amplitude [
P- Amp (
V)] relations track the relation defined by the M31 field halo RRL populations at ∼ 11 kpc from the centre of M31. The metallicities of the RRab stars are calculated via a relationship between [Fe/H], log
Pab and Amp(
V). The resultant abundances ([ Fe/H ]_ And XI_=-1.75; [ Fe/H ]_And XIII_=-1.74) are consistent with the values calculated from the red giant branch slope, indicating that our measurements are not significantly affected by RRL evolutionary away from the zero-age HB. The distance to each galaxy, based on the absolute
V magnitudes of the RRab stars, is (
m-
M)_0,
V_= 24.33 ±0.05 for And XI and (
m-
M)_0,
V_= 24.62±0.05 for And XIII. We discuss the origins of And XI and And XIII based on a comparative analysis of the luminosity-metallicity relation of Local Group dwarf galaxies.
Based on observations taken with the NASA/ESA
Hubble Space Telescope, obtained at the Space Telescope Science Institute.