Final Results of Search for New Milky Way Satellites in the Hyper Suprime-Cam Subaru Strategic Program Survey: Discovery of Two More Candidates

We present the final results of our search for new Milky Way (MW) satellites using the data from the Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP) survey over $\sim 1,140$ deg$^2$. In addition to three candidates that we already reported, we have identified two new MW satellite candidates in the constellation of Sextans at a heliocentric distance of $D_{\odot} \simeq 126$kpc, and Virgo at $D_{\odot} \simeq 151$kpc, named Sextans II and Virgo III, respectively. Their luminosities (Sext II:$M_V\simeq-3.9$mag; Vir III:$M_V\simeq-2.7$mag) and half-light radii (Sext II:$r_h\simeq154$ pc; Vir III:$r_h\simeq 44$ pc) place them in the region of size-luminosity space of ultra-faint dwarf galaxies (UFDs). Including four previously known satellites, there are a total of nine satellites in the HSC-SSP footprint. This discovery rate of UFDs is much higher than that predicted from the recent models for the expected population of MW satellites in the framework of cold dark matter models, thereby suggesting that we encounter a too many satellites problem. Possible solutions to settle this tension are also discussed.