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(Abridged) We carried out a period analysis on ~3700 RR Lyrae stars spreadover ~50 square degrees towards the Sagittarius dwarf galaxy (Sgr). The RRLyraes are distributed almost evenly between Sgr and the Milky Way. For Sgrmembers, the average periods are 0.574 day and 0.322 day for RRab and RRc starsrespectively. This places Sgr in the long-period tail of the Oosterhoff Igroup. We report the detection of 53 double-mode RR Lyrae stars (RRd) withinour sample. The magnitude of 40 of these stars is consistent with membership inSgr whereas 13 RRds are located within our Galaxy. We also found 13 RR Lyraes(5 in Sgr and 8 in the Galaxy) exhibiting two closely spaced frequencies, mostprobably related to non-radial pulsations. The period distribution of the RRLyrae variables in Sgr is compared to those of other Milky Way satellites. Wefind a remarkable similarity between the RR Lyrae populations in Sgr and theLarge Magellanic Cloud (LMC), suggesting that these galaxies have similarhorizontal branch morphologies. This may indicate that Sgr and the LMC startedtheir formation under similar conditions. Using various photometric indicators,we estimate the metallicity of the RR Lyrae stars in Sgr and find <[Fe/H]>~-1.6dex with a dispersion of ~ +/-0.5 dex around this value and a minor butsignificant population at <-2.0 dex. We do not find evidence for a spatialmetallicity gradient in the RR Lyrae population of Sgr. From the spatialdistribution of RR Lyraes, we estimate the RRab content and total luminosity ofthis galaxy and find MV(Sgr)~-14.7 mag, a value that would be consistent withthe empirical metallicity/luminosity relation for Dsph galaxies.Comment: 13 pages, 10 figures, 4 tables. Accepted for publication in A&

RR Lyrae stars in the Sagittarius dwarf galaxy: Period analysis