A robust measurement of the first higher-derivative bias of dark matter halos

We present a new simulation technique in which any chosen mode k of the density contrast field can be amplified by an amplitude Delta. These amplified-mode simulations allow us to study the response of the halo density field to a long-wavelength mode other than the DC mode. In this sense they are a generalization of the separate-universe simulations to finite-wavelength modes. In particular, we use these simulations to obtain robust measurements of the first higher-derivative bias of dark matter halos b(del 2 delta). We find a negative bias at all mass considered, roughly following the -R-L(2) (M) relation, the Lagrangian radius of halos squared, as naively expected. We compare our results with those obtained from a fit to the 1-loop halo-matter power spectrum, as well as with the recent results from Abidi and Baldauf (2018), and to the prediction from the peak theory.