Sizes and Stellar Masses of the Little Red Dots Imply Immense Stellar Densities

The ``Little Red Dots'' (LRDs) are red and compact galaxies detected in JWST deep fields, mainly in the redshift range $z=4-8$. Given their compactness and the inferred stellar masses in the hypothesis that LRDs are starburst galaxies, the implied stellar densities are immense. This Research Note uses an extensive catalog of LRDs from the PRIMER and the COSMOS-Web surveys to investigate these densities. We find a median (upper limit) on the effective radius of $80$ pc, which leads to median (lower limit) values of the core density of $\sim 10^4 \, \rm M_\odot \, pc^{-3}$, and individual densities as high as $\sim 10^8 \, \rm M_\odot \, pc^{-3}$, which is $\sim 10$ times higher than the density necessary for runaway collisions to take place. For $\sim 35\%$ of the LRDs investigated, the lower limits are higher than the highest stellar densities observed in any system in any redshift range.