Aemulus $\nu$: Precise Predictions for Matter and Biased Tracer Power Spectra in the Presence of Neutrinos

We present the Aemulus $\nu$ simulations: a suite of 150 $(1.05 h^{-1}\rm Gpc)^3$ $N$-body simulations with a mass resolution of $3.51\times 10^{10} \frac{\Omega_{cb}}{0.3} ~ h^{-1} M_{\odot}$ in a $w\nu$CDM cosmological parameter space. The simulations have been explicitly designed to span a broad range in $\sigma_8$ to facilitate investigations of tension between large scale structure and cosmic microwave background cosmological probes. Neutrinos are treated as a second particle species to ensure accuracy to $0.5\, \rm eV$, the maximum neutrino mass that we have simulated. By employing Zel'dovich control variates, we increase the effective volume of our simulations by factors of $10-10^5$ depending on the statistic in question. As a first application of these simulations, we build new hybrid effective field theory and matter power spectrum surrogate models, demonstrating that they achieve $\le 1\%$ accuracy for $k\le 1\, h\,\rm Mpc^{-1}$ and $0\le z \le 3$, and $\le 2\%$ accuracy for $k\le 4\, h\,\rm Mpc^{-1}$ for the matter power spectrum. We publicly release the trained surrogate models, and estimates of the surrogate model errors in the hope that they will be broadly applicable to a range of cosmological analyses for many years to come.