An upper limit on primordial magnetic fields from ultra-faint dwarf galaxies

The presence of primordial magnetic fields increases the minimum halo mass in which star formation is possible at high redshifts. Estimates of the dynamical mass of ultra-faint dwarf galaxies (UFDs) within their half-light radius constrain their virialized halo mass before their infall into the Milky Way. The inferred halo mass and formation redshift of the UFDs place upper bounds on the primordial comoving magnetic field, $B_0$. We derive an upper limit of $0.50\pm 0.086$ ($0.31\pm 0.04$) nG on $B_0~$ assuming the average formation redshift of the UFD host halos is $z_{\rm form}=$ 10 (20), respectively.