We present the first detailed study of the RR Lyrae variable population in the Local Group dSph/dIrr transition galaxy , Phoenix , using previously obtained HST/WFPC2 observations of the galaxy .
We utilize template light curve fitting routines to obtain best fit light curves for RR Lyrae variables in Phoenix .
Our technique has identified 78 highly probable RR Lyrae stars ( 54 ab-type ; 24 c-type ) with about 40 additional candidates .
We find mean periods for the two populations of \langle P _ { ab } \rangle = 0.60 \pm 0.03 days and \langle P _ { c } \rangle = 0.353 \pm 0.002 days .
We use the properties of these light curves to extract , among other things , a metallicity distribution function for ab-type RR Lyrae .
Our analysis yields a mean metallicity of \langle [ Fe / H ] \rangle = -1.68 \pm 0.06 dex for the RRab stars .
From the mean period and metallicity calculated from the ab-type RR Lyrae , we conclude that Phoenix is more likely of intermediate Oosterhoff type ; however the morphology of the Bailey diagram for Phoenix RR Lyraes appears similar to that of an Oosterhoff type I system .
Using the RRab stars , we also study the chemical enrichment law for Phoenix .
We find that our metallicity distribution is reasonably well fitted by a closed-box model .
The parameters of this model are compatible with the findings of Hidalgo et al .
( 14 ) further supporting the idea that Phoenix appears to have been chemically enriched as a closed-box-like system during the early stage of its formation and evolution .