Are the Newly-Discovered $z \sim 13$ Drop-out Sources Starburst Galaxies or Quasars?

The detection of two $z\sim 13$ galaxy candidates has opened a new window on galaxy formation at an era only $330$ Myr after the Big Bang. Here, we investigate the physical nature of these sources: are we witnessing star forming galaxies or quasars at such early epochs? If powered by star formation, the observed ultraviolet (UV) luminosities and number densities can be jointly explained if: (i) these galaxies are extreme star-formers with star formation rates $5-24\times$ higher than those expected from extrapolations of average lower-redshift relations; (ii) the star formation efficiency increases with halo mass and is countered by increasing dust attenuation from $z \sim 10-5$; (iii) they form stars with an extremely top-heavy initial mass function. The quasar hypothesis is also plausible, with the UV luminosity produced by black holes of $\sim 10^8 \, \mathrm{M_{\odot}}$ accreting at or slightly above the Eddington rate ($f_{\rm Edd}\sim 1.0$). This black hole mass at $z\sim13$ would require very challenging, but not implausible, growth parameters. If spectroscopically confirmed, these two sources will represent a remarkable laboratory to study the Universe at previously inaccessible redshifts.