Halo statistics in non-gaussian cosmologies: The collapsed fraction, conditional mass function and halo bias from the path-integral excursion set method

Anson D'Aloisio, Jun Zhang, Donghui Jeong, Paul R. Shapiro

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Characterizing the level of primordial non-Gaussianity (PNG) in the initial conditions for structure formation is one of the most promising ways to test inflation and differentiate among different scenarios. The scale-dependent imprint of PNG on the large-scale clustering of galaxies and quasars has already been used to place significant constraints on the level of PNG in our observed Universe. Such measurements depend upon an accurate and robust theory of how PNG affects the bias of galactic haloes relative to the underlying matter density field. We improve upon previous work by employing a more general analytical method - the path-integral extension of the excursion set formalism - which is able to account for the non-Markovianity caused by PNG in the random-walk model used to identify haloes in the initial density field. This non-Markovianity encodes information about environmental effects on halo formation which have so far not been taken into account in analytical bias calculations. We compute both scale-dependent and scale-independent corrections to the halo bias, along the way presenting an expression for the conditional collapsed fraction for the first time, and a new expression for the conditional halo mass function. To leading order in our perturbative calculation, we recover the halo bias results of Desjacques et al., including the new scale-dependent correction reported there. However, we show that the non-Markovian dynamics from PNG can lead to marked differences in halo bias when next-to-leading-order terms are included. We quantify these differences here. We find that the next-to-leading-order corrections suppress the amplitudes of both the scale-dependent and scale-independent bias by ~5-10 per cent for massive haloes with M ~ 1015Mh-1, and ~30-40 per cent for haloes with M ~ 1014M h-1. The corrections appear to be more significant as the halo mass is lowered, though we caution that the apparently large effects we observe in the low-mass regime likely signal a breakdown of the perturbative approach taken here.

Original languageEnglish (US)
Pages (from-to)2765-2788
Number of pages24
JournalMonthly Notices of the Royal Astronomical Society
Volume428
Issue number3
DOIs
StatePublished - Jan 1 2013

Fingerprint

halos
statistics
inflation
environmental effect
analytical method
method
galactic halos
random walk
quasars
universe
breakdown
galaxies
formalism
calculation

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

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title = "Halo statistics in non-gaussian cosmologies: The collapsed fraction, conditional mass function and halo bias from the path-integral excursion set method",
abstract = "Characterizing the level of primordial non-Gaussianity (PNG) in the initial conditions for structure formation is one of the most promising ways to test inflation and differentiate among different scenarios. The scale-dependent imprint of PNG on the large-scale clustering of galaxies and quasars has already been used to place significant constraints on the level of PNG in our observed Universe. Such measurements depend upon an accurate and robust theory of how PNG affects the bias of galactic haloes relative to the underlying matter density field. We improve upon previous work by employing a more general analytical method - the path-integral extension of the excursion set formalism - which is able to account for the non-Markovianity caused by PNG in the random-walk model used to identify haloes in the initial density field. This non-Markovianity encodes information about environmental effects on halo formation which have so far not been taken into account in analytical bias calculations. We compute both scale-dependent and scale-independent corrections to the halo bias, along the way presenting an expression for the conditional collapsed fraction for the first time, and a new expression for the conditional halo mass function. To leading order in our perturbative calculation, we recover the halo bias results of Desjacques et al., including the new scale-dependent correction reported there. However, we show that the non-Markovian dynamics from PNG can lead to marked differences in halo bias when next-to-leading-order terms are included. We quantify these differences here. We find that the next-to-leading-order corrections suppress the amplitudes of both the scale-dependent and scale-independent bias by ~5-10 per cent for massive haloes with M ~ 1015M⊙h-1, and ~30-40 per cent for haloes with M ~ 1014M⊙ h-1. The corrections appear to be more significant as the halo mass is lowered, though we caution that the apparently large effects we observe in the low-mass regime likely signal a breakdown of the perturbative approach taken here.",
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Halo statistics in non-gaussian cosmologies : The collapsed fraction, conditional mass function and halo bias from the path-integral excursion set method. / D'Aloisio, Anson; Zhang, Jun; Jeong, Donghui; Shapiro, Paul R.

In: Monthly Notices of the Royal Astronomical Society, Vol. 428, No. 3, 01.01.2013, p. 2765-2788.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Halo statistics in non-gaussian cosmologies

T2 - The collapsed fraction, conditional mass function and halo bias from the path-integral excursion set method

AU - D'Aloisio, Anson

AU - Zhang, Jun

AU - Jeong, Donghui

AU - Shapiro, Paul R.

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AB - Characterizing the level of primordial non-Gaussianity (PNG) in the initial conditions for structure formation is one of the most promising ways to test inflation and differentiate among different scenarios. The scale-dependent imprint of PNG on the large-scale clustering of galaxies and quasars has already been used to place significant constraints on the level of PNG in our observed Universe. Such measurements depend upon an accurate and robust theory of how PNG affects the bias of galactic haloes relative to the underlying matter density field. We improve upon previous work by employing a more general analytical method - the path-integral extension of the excursion set formalism - which is able to account for the non-Markovianity caused by PNG in the random-walk model used to identify haloes in the initial density field. This non-Markovianity encodes information about environmental effects on halo formation which have so far not been taken into account in analytical bias calculations. We compute both scale-dependent and scale-independent corrections to the halo bias, along the way presenting an expression for the conditional collapsed fraction for the first time, and a new expression for the conditional halo mass function. To leading order in our perturbative calculation, we recover the halo bias results of Desjacques et al., including the new scale-dependent correction reported there. However, we show that the non-Markovian dynamics from PNG can lead to marked differences in halo bias when next-to-leading-order terms are included. We quantify these differences here. We find that the next-to-leading-order corrections suppress the amplitudes of both the scale-dependent and scale-independent bias by ~5-10 per cent for massive haloes with M ~ 1015M⊙h-1, and ~30-40 per cent for haloes with M ~ 1014M⊙ h-1. The corrections appear to be more significant as the halo mass is lowered, though we caution that the apparently large effects we observe in the low-mass regime likely signal a breakdown of the perturbative approach taken here.

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