Using a large-scale hydrodynamic simulation with heuristic criteria for galaxy formation , we investigate how the galaxy field is related to physical parameters , such as the mass density and the gas temperature .
In our flat Cold Dark Matter model with \Omega _ { 0 } = 0.37 , we find that the relation between the galaxy and mass density fields is a function of scale .
The bias b ( R ) \equiv \sigma _ { g } ( R ) / \sigma ( R ) , where \sigma _ { g } ( R ) is the variance of galaxy counts in spheres of radius R and \sigma ( R ) is the same for mass , varies from 2.6 at 1 h ^ { -1 } Mpc to 1.2 at 30 h ^ { -1 } Mpc .
Including the dependence of the galaxy density on local gas temperature as well as on local mass density can fully account for this scale dependence .
Galaxy density depends on temperature because gas which is too hot can not cool to form galaxies ; this causes scale dependence of b ( R ) because local gas temperature is related to the gravitational potential , and thus contains information about the large scale density field .
We show that temperature dependence generally causes b ( R ) to vary on quasilinear and nonlinear scales , indicating that scale dependence of bias may be a generic effect in realistic galaxy formation scenarios .
We find that the relationship between the galaxy and mass density fields is also a function of galaxy age .
On large scales , the older galaxies are highly biased ( b \approx 1.7 ) and highly correlated ( r \equiv { \langle { \delta \delta _ { g } } \rangle } / \sigma \sigma _ { g } \approx 1.0 ) with the mass density field ; younger galaxies are not biased ( b \approx 0.8 ) and are poorly correlated ( r \approx 0.5 ) with the mass .
We argue that linear bias is inadequate to describe the relationship between galaxies and mass .
We present a more physically based prescription which better fits our results and reproduces the scale dependence of the bias : \rho _ { g } / { \langle { \rho _ { g } } \rangle } = L ( \rho / { \langle { \rho } \rangle } ) ^ { M } ( 1 + T / 40 ,% 000 { ~ { } K } ) ^ { N } , where L = 1.23 , M = 1.9 , and N = -0.66 .