Documented halo-model computation of line power spectrum, including clustering and stochastic contributions beyond Poisson limit. More...

#include "header.h"

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Functions
double	PS_line_HM (struct Cosmology *Cx, double k, double z, double M_min, long mode_mf, long line_type, int line_id)
	Compute the clustering contribution to the line power spectrum using halo-model. More...

double	PS_shot_HM (struct Cosmology Cx, double k, double z, double M_min, double input, long mode_mf, long line_type, int line_id)
	Compute the shot noise contributions, including corrections beyond poisson limit (see 1706.08738 for more details) If nfw=1, the dependance of the power spectrum on the halo profile is neglected. More...

static int	mhmc_integ (const int ndim, const cubareal x[], const int ncomp, cubareal ff[], void *p)
	The integrand function passed passed to Cuhre integration routine of CUBA library to compute the corrections to mass integration. More...

void	mhmc (struct Cosmology Cx, double z, long mode_mf, double result)
	Compute the corrections to mass integration of HM matter power spectrum. More...

static int	HM_1h2h_integ (const int ndim, const cubareal x[], const int ncomp, cubareal ff[], void *p)
	The integrand function passed passed to Cuhre integration routine to compute 1- and 2-halo integrals. More...

void	HM_1h2h (struct Cosmology Cx, double k, double z, double M_min, long mode_mf, long line_type, long mode_hm, double result)
	Compute the mass integrals needed for 1- and 1-halo line, line-matter and matter power spectrum If nfw=1, the dependance of the power spectrum on the halo profile is neglected. More...

static int	b22_ls_integrand (const int ndim, const cubareal x[], const int ncomp, cubareal ff[], void *p)
	The integrand function passed passed to Cuhre integration routine to compute large-scale limit of b22 (shot-noise contribution) More...

double	b22_ls (struct Cosmology *Cx, double z)
	Compute the large-scale limit of P_b2b2 loop. More...

Detailed Description

Documented halo-model computation of line power spectrum, including clustering and stochastic contributions beyond Poisson limit.

Azadeh Moradinezhad Dizgah, November 4th 2021

This module has two main functions:

PS_line_HM() to compute clustering (1- and 2-halo terms). The 2-halo term, includes nonlinear corrections to halo power spectrum arising from nonlinearities of matter fluctuations and halo biases.
PS_shot_HM() to compute the stochastic contrubutions beyond Poisson shot noise (see arXiv:1706.08738)

The other functions in these modules are utilities for computing the above two main functions.

In summary, the following functions can be called from other modules:

PS_line_HM() computes the 1loop-HM line power spectrum
PS_shot_HM() computes the full line power spectrum, beyond poisson limit
mhmc() computes th corrections to mass integration of halo-model matter power spectrum
HM_1h2h() performs the mass integraks for computing 1- and 2-halo terms of line-line, line-matter and matter-matter power spectra.
b22_ls() computes the large-scale limit of P_b2b2 loop which behaves like a constant and so contributes to the shot noise.

Function Documentation

◆ b22_ls()

double b22_ls	(	struct Cosmology *	Cx,
		double	z
	)

Compute the large-scale limit of P_b2b2 loop.

Parameters

Cx	Input: Cosmology structure
z	Input: redshift

Returns: b22_ls

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◆ b22_ls_integrand()

static int b22_ls_integrand	(	const int *	ndim,
		const cubareal	x[],
		const int *	ncomp,
		cubareal	ff[],
		void *	p
	)

static

The integrand function passed passed to Cuhre integration routine to compute large-scale limit of b22 (shot-noise contribution)

Parameters

ndim	Input: Dimensionality of the domain of integration
x	Input: An array of integration variables
ncomp	Input: Dimensionality of the integrand function
ff	Input: Array of values of the integrand of dimension fdim
p	Input: integration parmaeters return the error status

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◆ HM_1h2h()

void HM_1h2h	(	struct Cosmology *	Cx,
		double	k,
		double	z,
		double	M_min,
		long	mode_mf,
		long	line_type,
		long	mode_hm,
		double *	result
	)

Compute the mass integrals needed for 1- and 1-halo line, line-matter and matter power spectrum If nfw=1, the dependance of the power spectrum on the halo profile is neglected.

Otherwise, NFW halo profile is assumed

Parameters

Cx	Input: Cosmology structure
k	Input: wavenumber in unit of 1/Mpc.
z	Input: redshift
M_min	Input: minimum halo mass for mass integrals
mode_mf	Input: theoretical model of halo mass function to use. It can be set to sheth-Tormen (ST), Tinker (TR) or Press-Schecter (PSC)
line_type	Input: name of the line to compute. It can be set to CII, CO10, CO21, CO32, CO43, CO54, CO65
mode_hm	Input: a switch to decide whetehr to compute gthe mass integrations. It can be set to: LINE for line power spectrum, LINEMATTER for line-matter cross spectrum MATTER for matter power spectrum
result	Output: anarray of the integration results. Number of elements varies depending on mode_hm switch: 3 elements if mode_hm = LINE, 1 element if mode_hm = LINEMATTER 2 element if mode_hm = MATTER esults[0]: correction to 1-halo term, result[1]: correcrions to 2-halo term assuming linear halo bias

Returns: void in unit of M_sun/Mpc^3

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◆ HM_1h2h_integ()

static int HM_1h2h_integ	(	const int *	ndim,
		const cubareal	x[],
		const int *	ncomp,
		cubareal	ff[],
		void *	p
	)

static

The integrand function passed passed to Cuhre integration routine to compute 1- and 2-halo integrals.

Parameters

ndim	Input: Dimensionality of the domain of integration
x	Input: An array of integration variables
ncomp	Input: Dimensionality of the integrand function
ff	Input: Array of values of the integrand of dimension fdim
p	Input: integration parmaeters return the error status

we assume the profile of both matter and line are NFW

integrand of line 1halo term

integrand of 2halo term proportional to b1, the linear local-in-matter halo bias

integrand of 1halo term of line-matter cross-spectrum

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◆ mhmc()

void mhmc	(	struct Cosmology *	Cx,
		double	z,
		long	mode_mf,
		double *	result
	)

Compute the corrections to mass integration of HM matter power spectrum.

Parameters

Cx	Input: Cosmology structure
z	Input: redshift
mode_mf	Inpute: theoretical model of halo mass function to use. It can be set to Press-Schecter (PSC), sheth-Tormen (ST), Tinker (TR)
result	Output: a 2d array of the integration results, results[0]: correction to 1-halo term, result[1]: correcrions to 2-halo term assuming linear halo bias

Returns: void

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◆ mhmc_integ()

static int mhmc_integ	(	const int *	ndim,
		const cubareal	x[],
		const int *	ncomp,
		cubareal	ff[],
		void *	p
	)

static

The integrand function passed passed to Cuhre integration routine of CUBA library to compute the corrections to mass integration.

When computing the matter power spectrum using halo-model, the mass integrations for 1- and 2-loop terms get contributions from halos of all masses. For numerical computation, we need to impose a lower and upper integration limit. While the result of the integration are not sensitive to the upper bound (due to the fact that the mass function drops rapidly at high M_h) the choice of the lower bound affects the results. We can compute the leading order corrections to the integral that are accurate up to (k R_s)^2. (see App. A of arXiv:1511.02231 for more details.)

Parameters

ndim	Input: Dimensionality of the domain of integration
x	Input: An array of integration variables
ncomp	Input: Dimensionality of the integrand function
ff	Input: Array of values of the integrand of dimension fdim
p	Input: integration parmaeters return the error status

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◆ PS_line_HM()

double PS_line_HM	(	struct Cosmology *	Cx,
		double	k,
		double	z,
		double	M_min,
		long	mode_mf,
		long	line_type,
		int	line_id
	)

Compute the clustering contribution to the line power spectrum using halo-model.

If nfw=1, the dependance of the power spectrum on the halo profile is neglected. Otherwise, NFW halo profile is assumed

Parameters

Cx	Input: pointer to Cosmology structure
k	Input: wavenumber in unit of 1/Mpc.
z	Input: redshift
M_min	Input: minimum halo mass for mass integrals
mode_mf	Inpute: theoretical model of halo mass function to use. It can be set to sheth-Tormen (ST), Tinker (TR) or Press-Schecter (PSC)
line_type	Inpute: name of the line to compute. It can be set to CII, CO10, CO21, CO32, CO43, CO54, CO65
line_id	Inpute: id of the line to be considered.

Returns: P_clust(k)

Boltzmann constant in unit of erg K^-1

in unit of erg/s

CII

to plot the power spectrum in units of micro K^2 Mpc^3

in unit of M_sun/Mpc^3

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◆ PS_shot_HM()

double PS_shot_HM	(	struct Cosmology *	Cx,
		double	k,
		double	z,
		double	M_min,
		double *	input,
		long	mode_mf,
		long	line_type,
		int	line_id
	)

Compute the shot noise contributions, including corrections beyond poisson limit (see 1706.08738 for more details) If nfw=1, the dependance of the power spectrum on the halo profile is neglected.

Otherwise, NFW halo profile is assumed

Parameters

Cx	Input: Cosmology structure
k	Input: wavenumber in unit of 1/Mpc.
z	Input: redshift
M_min	Input: minimum halo mass for mass integrals
input	inpute: an array of input values with 4 values, Tave_line, b1_line, pb22_ls, line_shot, rhom_bar
mode_mf	Inpute: theoretical model of halo mass function to use. It can be set to sheth-Tormen (ST), Tinker (TR) or Press-Schecter (PSC)
line_type	Inpute: name of the line to compute. It can be set to CII, CO10, CO21, CO32, CO43, CO54, CO65

Returns: P_stoch(k)

Boltzmann constant in unit of erg K^-1

in unit of erg/s

CII

Since the following quantities do not depend on k, I am computing them once and pass them as input to this function

to plot the power spectrum in units of micro K^2 Mpc^3

in unit of M_sun/Mpc^3

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Functions

Detailed Description

Function Documentation

◆ b22_ls()

◆ b22_ls_integrand()

◆ HM_1h2h()

◆ HM_1h2h_integ()

◆ mhmc()

◆ mhmc_integ()

◆ PS_line_HM()

◆ PS_shot_HM()