Almost every known low-luminosity Milky Way dwarf spheroidal ( dSph ) satellite galaxy contains at least one RR Lyrae star .
Assuming that a fraction of distant ( 60 < d _ { helio } < 100 kpc ) Galactic halo RR Lyrae stars are members of yet to be discovered low-luminosity dSph galaxies , we perform a guided search for these low-luminosity dSph galaxies .
In order to detect the presence of dSph galaxies , we combine stars selected from more than 123 sightlines centered on RR Lyrae stars identified by the Palomar Transient Factory .
We find that this method is sensitive enough to detect the presence of Segue 1-like galaxies ( M _ { V } = -1.5 ^ { +0.6 } _ { -0.8 } , r _ { h } = 30 pc ) even if only \sim 20 sightlines were occupied by such dSph galaxies .
Yet , when our method is applied to the SDSS DR10 imaging catalog , no signal is detected .
An application of our method to sightlines occupied by pairs of close ( < 200 pc ) horizontal branch stars , also did not yield a detection .
Thus , we place upper limits on the number of low-luminosity dSph galaxies with half-light radii from 30 pc to 120 pc , and in the probed volume of the halo .
Stronger constraints on the luminosity function may be obtained by applying our method to sightlines centered on RR Lyrae stars selected from the Pan-STARRS1 survey , and eventually , from LSST .
In the Appendix , we present spectroscopic observations of an RRab star in the Boötes 3 dSph and a light curve of an RRab star near the Boötes 2 dSph .