Bibcode
Rubiño-Martín, J. A.; Betancort-Rijo, J. E.; Patiri, Santiago G.
Bibliographical reference
Monthly Notices of the Royal Astronomical Society, Volume 386, Issue 4, pp. 2181-2193.
Advertised on:
6
2008
Citations
8
Refereed citations
6
Description
The unconditional mass function (UMF) of dark matter haloes has been
determined accurately in the literature, showing excellent agreement
with high-resolution numerical simulations. However, this is not the
case for the conditional mass function (CMF). Here, we propose a simple
analytical procedure to derive the CMF by rescaling the UMF to the
constrained environment using the appropriate mean and variance of the
density field at the constrained point. This method introduces two major
modifications with respect to the standard rescaling procedure. First of
all, rather than using in the scaling procedure the properties of the
environment averaged over all the conditioning regions, we implement the
rescaling locally. We show that for high masses this modification may
lead to substantially different results. Secondly, we modify the (local)
standard rescaling procedure in such a manner as to force normalization,
in the sense that when one integrates the CMF over all possible values
of the constraint multiplied by their corresponding probability
distribution, the UMF is recovered. In practice, we do this by replacing
in the standard procedure the value δc (the linear
density contrast for collapse) by certain adjustable effective parameter
δeff. In order to test the method, we compare our
prescription with the results obtained from numerical simulations in
voids. We find that when our modified rescaling is applied locally to
any existing numerical fit of the UMF, and the appropriate value for
δeff is chosen, the resulting CMF is, in all cases, in
very good agreement with the numerical results. Based on these results,
we finally present a very accurate analytical fit to the (accumulated)
CMF obtained with our procedure, as a function of the parameters that
describe the conditioning region (size and mean linear density
contrast), the redshift and the relevant cosmological parameters
(σ8 and Γ). This analytical fit may be useful for
any theoretical treatment of the large-scale structure, and has been
already used successfully in regard with the statistic of voids.
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