MUSCLE-UPS: Improved Approximations of the Matter Field with the Extended Press-Schechter Formalism and Lagrangian Perturbation Theory. (arXiv:2012.14446v2 [astro-ph.CO] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Tosone_F/0/1/0/all/0/1">Federico Tosone</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Neyrinck_M/0/1/0/all/0/1">Mark C. Neyrinck</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Granett_B/0/1/0/all/0/1">Benjamin R. Granett</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Guzzo_L/0/1/0/all/0/1">Luigi Guzzo</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Vittorio_N/0/1/0/all/0/1">Nicola Vittorio</a>
Lagrangian algorithms to simulate the evolution of cold dark matter (CDM) are
invaluable tools to generate large suites of mock halo catalogues. However,
their precision may not be up to the challenge of upcoming surveys. In this
paper, we first show that the main limitation of current schemes is their
inability to model the evolution of overdensities in the initial density field,
a limit that can be circumvented by detecting halo particles in the initial
conditions. We thus propose a new scheme, dubbed muscleups, which reproduces
the results from Lagrangian perturbation theory on large scales, while
improving the modelling of the overdensities on small scales. muscleups uses
the extended Press and Schechter (EPS) formalism, adapted to a Lagrangian
picture. For regions exceeding a collapse threshold in the density smoothed at
a radius $R$, we consider all particles within a radius $R$ collapsed.
Exploiting a multi-scale smoothing of the initial density, we build a halo
catalogue on the fly by optimizing the selection of halo candidates. This
allows us to generate a density field with a halo mass function that matches
one measured in $N$-body simulations. We further explicitly gather particles in
each halo together in a profile, providing a numerical, Lagrangian-based
implementation of the halo model. Compared to previous semi-analytical
Lagrangian methods, we find that muscleups improves the recovery of the
statistics of the density field at the level of the probability density
function (PDF), the power spectrum, and the cross correlation with the $N$-body
result.
Lagrangian algorithms to simulate the evolution of cold dark matter (CDM) are
invaluable tools to generate large suites of mock halo catalogues. However,
their precision may not be up to the challenge of upcoming surveys. In this
paper, we first show that the main limitation of current schemes is their
inability to model the evolution of overdensities in the initial density field,
a limit that can be circumvented by detecting halo particles in the initial
conditions. We thus propose a new scheme, dubbed muscleups, which reproduces
the results from Lagrangian perturbation theory on large scales, while
improving the modelling of the overdensities on small scales. muscleups uses
the extended Press and Schechter (EPS) formalism, adapted to a Lagrangian
picture. For regions exceeding a collapse threshold in the density smoothed at
a radius $R$, we consider all particles within a radius $R$ collapsed.
Exploiting a multi-scale smoothing of the initial density, we build a halo
catalogue on the fly by optimizing the selection of halo candidates. This
allows us to generate a density field with a halo mass function that matches
one measured in $N$-body simulations. We further explicitly gather particles in
each halo together in a profile, providing a numerical, Lagrangian-based
implementation of the halo model. Compared to previous semi-analytical
Lagrangian methods, we find that muscleups improves the recovery of the
statistics of the density field at the level of the probability density
function (PDF), the power spectrum, and the cross correlation with the $N$-body
result.
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