A constant characteristic volume density of dark matter haloes from SPARC rotation curve fits

We study the scaling relations between dark matter (DM) haloes and galaxy discs using 175 galaxies from the SPARC database. We explore two cosmologically motivated DM halo profiles: the Einasto profile from DM-only simulations and the DC14 profile from hydrodynamic simulations. We fit the observed rotation curves using a Markov Chain Monte Carlo method and break the disc-halo degeneracy using near-infrared photometry and $\mathrm{\Lambda }$CDM-motivated priors. We find that the characteristic volume density ${\rho }_{\mathrm{s}}$ of DM haloes is nearly constant over $\sim$5 decades in galaxy luminosity. The scale radius $r_s$ and the characteristic surface density ${\rho }_s\cdot r_s$, instead, correlate with galaxy luminosity. These scaling relations provide an empirical benchmark to cosmological simulations of galaxy formation.