Abstract
The small scale structure opens a window to constrain the dynamical
properties of Dark Matter. Here we study the clustering of warm dark matter
(WDM) in a semi-analytical approach and compared the linear power spectrum of
WDM with cold dark matter (CDM) employing a new transfer function $T_v(a,k)$ in
terms of the viral wave number $k_v=2\pi/łambda_v$ corresponding to a
structure with a viral radius $r_v=łambda_v/2$, half the size of the free
streaming scale radius $r_v=r_fs/2=łambda_fs/4$. The virial mass $M_v$
contained in this structure corresponds to the lightest structure formed for a
WDM particle becoming non-relativistic at the scale factor $a_nr$ with the
corresponding $łambda_fs$. The viral transfer function $T_v(a,k)=1+
łeft(k/k_v \right)^\beta_v ^\gamma_v$ is given in terms of the viral mode
$k_v$ and two constant parameters $\beta_v$ and $\gamma_v$. We compare
$T_v(a,k)$ with the Boltzmann code CLASS for WDM in the mass range 1-10 keV and
we obtain the constraint $\beta_v\gamma_v=-18$ with $\nu=1.020 0.025$. In
the standard approach the transfer function is given by
$T(a,k)=1+łeft(\alpha\, k \right)^\beta^\gamma$ Viel:2005qj where
$\alpha$ encodes the dynamical properties of WDM and must be numerically
adjusted by means of a Boltzmann code. In contrast, in our viral approach the
physical quantity $k_v$ is simply given in terms of the free streaming scale
$łambda_fs$ and can be analytically determined. Our viral proposal has a
good agreement with CLASS and improves slightly the results from the standard
transfer function. To conclude, we have proposed a new physically motivated
transfer function $T_v(a,k)$ where the properties of WDM are encoded in the
viral wave number $k_v$, is straightforward to determine and improves the
prediction of WDM clustering properties.
Users
Please
log in to take part in the discussion (add own reviews or comments).