Large-Scale Structure in Mixed Dark Matter Models with a Non-thermal Volatile Component

We investigate the properties of large--scale structure predicted in a class of mixed dark matter models in which the volatile component (made of particles with high rms velocity) derives from the decay of a heavier particle. Such models based on cold+volatile dark matter (CVDM) differ from the standard mixture of CDM and massive neutrinos, usually known as CHDM, in that they involve a component which has a non--thermal phase space distribution function. As a consequence, and differently from CHDM models, the value of the redshift at which volatile particles become non relativistic, $z_{nr}$, can be varied almost independently of the volatile fraction, $\Omega_X$. We compute transfer functions for a selection of such models, having $0.1\le \Omega_X\le 0.5$ and different values of $z_{nr}$. Using linear theory and assuming a scale--free primordial spectrum, we compare such models with observational constraints on large--scale galaxy clustering and bulk flows, as well as on the abundance of galaxy clusters and high--redshift damped Ly$\alpha$ systems. We find that these constraints enable us to discriminate between different $\Omega_X$ and $z_{nr}$; within the range of the models inspected, those which can be most easily accommodated by the data correspond to the parameter choice $\Omega_X\simeq 0.2$ and $z_{nr} \simeq 2\times 10^4\Omega_X$.