Probing the shape of the brown dwarf desert around main-sequence A-F-G-type stars using post-common-envelope WD$-$BD binaries

Brown dwarfs (BDs) possessing masses within the range $40-60 M_{\rm Jup}$ are rare around solar-type main-sequence (MS) stars, which gives rise to the brown dwarf desert (BDD). One caveat associated with previous studies of BDD is the relatively limited sample size of MS$-$BD binaries with accurately determined BD masses. We aim to produce a large sample of brown dwarf companions with precisely determined mass around main-sequence A-F-G type stars using observations of post common-envelope white dwarf (WD)$-$BD binaries. We employ the rapid binary evolution code COMPAS to deduce the properties of MS$-$BD binary progenitors from post common-envelope WD$-$BD binaries. This method supplements the directly observed MS$-$BD binary sample, enriching the data available for analyzing BDD around main-sequence A-F-G type stars. Our study opens a new window for studying the shape of BDD around A-F-G type main-sequence stars in the short period regime. We find tentative evidence that the `driest' part of BDD around A-F-G type stars may extend into an orbital period of several hundred days, albeit with a small sample size. More post common-envelope WD$-$BD binaries detected in the future will advance our understanding of the BDD around A-F-G type stars.