We use a new method , the cross-power spectrum between the linear density field and the halo number density field , to measure the Lagrangian bias for dark matter halos .
The method has several important advantages over the conventional correlation function analysis .
By applying this method to a set of high-resolution simulations of 256 ^ { 3 } particles , we have accurately determined the Lagrangian bias , over 4 magnitudes in halo mass , for four scale-free models with the index n = -0.5 , -1.0 , -1.5 and -2.0 and three typical CDM models .
Our result for massive halos with M \geq M _ { \ast } ( M _ { \ast } is a characteristic non-linear mass ) is in very good agreement with the analytical formula of Mo & White for the Lagrangian bias , but the analytical formula significantly underestimates the Lagrangian clustering for the less massive halos M < M _ { \ast } .
Our simulation result however can be satisfactorily described , with an accuracy better than 15 % , by the fitting formula of Jing for Eulerian bias under the assumption that the Lagrangian clustering and the Eulerian clustering are related with a linear mapping .
It implies that it is the failure of the Press-Schechter theories for describing the formation of small halos that leads to the inaccuracy of the Mo & White formula for the Eulerian bias .
The non-linear effect in the mapping between the Lagrangian clustering and the Eulerian clustering , which was speculated as another possible cause for the inaccuracy of the Mo & White formula , must be negligible compared to the linear mapping .
Our result indicates that the halo formation model adopted by the Press-Schechter theories must be improved .