Using $N$-body simulations with massive neutrino density perturbations, we detect the scale-dependent linear halo bias with high significance. This is the first time that this effect is detected in simulations containing neutrino density perturbations on all scales, confirming the same finding from separate universe simulations. The scale dependence is the result of the additional scale in the system, i.e., the massive neutrino free-streaming length, and it persists even if the bias is defined with respect to the cold dark matter plus baryon (instead of total matter) power spectrum. The separate universe approach provides a good model for the scale-dependent linear bias, and the effect is approximately $0.25f_{\nu }$ and $0.43f_{\nu }$ for halos with bias of 1.7 and 3.5, respectively. While the size of the effect is small, it is not insignificant in terms of $f_{\nu }$ and should therefore be included to accurately constrain neutrino mass from clustering statistics of biased tracers. More importantly, this feature is a distinct signature of free-streaming particles and cannot be mimicked by other components of the standard cosmological model.

• Received 7 December 2018
• Revised 15 January 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.041302