The class HaloProfile. More...

#include "Headers/HaloProfile.h"

Public Member Functions
Constructors/destructors
	HaloProfile ()=default
	default constructor

	HaloProfile (const cbl::cosmology::Cosmology cosmology, const double redshift, const double conc, const double Mass, const double Delta, const std::string profile_author, const std::string halo_def, const double trunc_fact=3., const bool miscentering=false, const bool single_profile=false, const double sigma_off=0.1, const double f_off=1.)
	constructor that sets the halo profile parameters. If the miscentering is considered, $\Sigma(R)$ and $\Delta\Sigma(R)$ are expressed as (see e.g. Bellagamba et al. 2019): More...

	HaloProfile (const cbl::cosmology::Cosmology cosmology, const double redshift, const std::string cM_author, const double Mass, const double Delta, const std::string profile_author, const std::string halo_def, const double trunc_fact=3., const bool miscentering=false, const bool single_profile=false, const double sigma_off=0.1, const double f_off=1.)
	constructor that sets the halo profile parameters, assuming a concentration-mass relation. If the miscentering is considered, $\Sigma(R)$ and $\Delta\Sigma(R)$ are expressed as (see e.g. Bellagamba et al. 2019): More...

	~HaloProfile ()=default
	default destructor

Member functions used to get the private members or
to compute the cluster halo profiles
double	concentration ()
	get the concentration More...

double	concentration2 (const double Vmax, const double Rmax) const
	compute the halo concentration More...

double	Delta ()
	get the overdensity More...

std::vector< double >	density_profile_3D (const std::vector< double > rad)
	the 3D halo density profile. More...

double	rho_s ()
	the characteristic density of the 3D halo density profile. More...

std::vector< double >	Sigma (const std::vector< double > rad)
	the total surface density profile of the halo. More...

std::vector< double >	Sigma_mis (const std::vector< double > rad)
	the miscentering contribution to the total surface density profile of the halo. More...

std::vector< double >	Sigma_cen (const std::vector< double > rad)
	the centered contribution to the total surface density profile of the halo. More...

std::vector< double >	Sigma_2h (const std::vector< double > rad, const std::string bias_author, const std::string method_Pk="EisensteinHu", const std::string interp_type="Linear", const bool NL=false)
	the 2-halo contribution to the total surface density profile of the halo, computed by assuming a halo bias model. More...

std::vector< double >	Sigma_2h (const std::vector< double > rad, const double bias, const std::string method_Pk="EisensteinHu", const std::string interp_type="Linear", const bool NL=false)
	the 2-halo contribution to the total surface density profile of the halo. More...

std::vector< double >	DeltaSigma (const std::vector< double > rad)
	the total excess surface density profile of the halo. More...

std::vector< double >	DeltaSigma_mis (const std::vector< double > rad)
	the miscentering contribution to the excess surface density profile of the halo. More...

std::vector< double >	DeltaSigma_cen (const std::vector< double > rad)
	the centered contribution to the excess surface density profile of the halo. More...

std::vector< double >	DeltaSigma_2h (const std::vector< double > rad, const std::string bias_author, const std::string method_Pk="EisensteinHu", const std::string interp_type="Linear", const bool NL=false)
	the 2-halo contribution to the excess surface density profile of the halo, computed by assuming a halo bias model. More...

std::vector< double >	DeltaSigma_2h (const std::vector< double > rad, const double bias, const std::string method_Pk="EisensteinHu", const std::string interp_type="Linear", const bool NL=false)
	the 2-halo contribution to the excess surface density profile of the halo. More...

double	density_profile_FourierSpace (const double kk)
	the Fourier transform of the normalised halo density More...

double	Mass_Delta (const double Mass, const double Delta_in, const double Delta_out, const double conc, const bool is_input_conc, const double rRmin_guess=1.e-3, const double rRmax_guess=10.) const
	The halo mass converted to a different value of $\Delta$, assuming the Navarro-Frenk-White density profile. More...

Member functions used to set the private members
void	set_cosmology (const cbl::cosmology::Cosmology cosmology)
	set the cosmological model More...

void	set_mass (const double mass=par::defaultDouble)
	set the private member m_mass More...

void	set_concentration (const double conc=par::defaultDouble)
	set the private member m_concentration More...

void	set_f_off (const double f_off=par::defaultDouble)
	set the private member m_f_off More...

void	set_sigma_off (const double sigma_off=par::defaultDouble)
	set the private member m_sigma_off More...

void	set_trunc_fact (const double trunc_fact=par::defaultDouble)
	set the private member m_trunc_fact More...

Private Member Functions
Protected member functions
void	m_set_profile (const cbl::cosmology::Cosmology cosmology, const double redshift, const double conc, const double Mass, const double Delta, const std::string profile_author, const std::string halo_def, const double trunc_fact=3., const bool miscentering=false, const bool single_profile=false, const double sigma_off=0.1, const double f_off=1.)
	private function that sets the halo profile parameters. If the miscentering is considered, $\Sigma(R)$ and $\Delta\Sigma(R)$ are expressed as (see e.g. Bellagamba et al. 2019): More...

double	m_return_set_concentration ()
	Return the concentration set by the user. More...

double	m_concentration_Duffy ()
	The concentration-mass relation by Duffy et al. (2008): More...

double	m_rho_s_NFW ()
	Characteristic density of the NFW profile. More...

double	m_rho_s_NFW_trunc ()
	Characteristic density of the truncated NFW profile. More...

std::vector< double >	m_rho_NFW (const std::vector< double > rad)
	The NFW 3D density profile. More...

std::vector< double >	m_rho_NFW_trunc (const std::vector< double > rad)
	The truncated NFW 3D density profile. More...

std::vector< double >	m_Sigma_NFW (const std::vector< double > rad)
	Surface density of the NFW profile. More...

std::vector< double >	m_Sigma_mean_NFW (const std::vector< double > rad)
	Mean surface density of the NFW profile. More...

std::vector< double >	m_Sigma_NFW_trunc (const std::vector< double > rad)
	Surface density of the truncated NFW profile. More...

std::vector< double >	m_Sigma_mean_NFW_trunc (const std::vector< double > rad)
	Mean surface density of the truncated NFW profile. More...

std::vector< double >	m_Sigma_mis (const std::vector< double > rad)
	the mis-centered surface density profile of the halo (see e.g. Bellagamba et al. 2019). More...

std::vector< double >	m_Sigma_including_miscentering (const std::vector< double > rad)
	Surface density including the miscentering contribution. More...

std::vector< double >	m_DeltaSigma_cen (const std::vector< double > rad)
	Excess surface density without the miscentering contribution. More...

std::vector< double >	m_DeltaSigma_mis (const std::vector< double > rad)
	the mis-centered excess surface density profile of the halo (see e.g. Bellagamba et al. 2019). More...

std::vector< double >	m_DeltaSigma_including_miscentering (const std::vector< double > rad)
	Excess surface density including the miscentering contribution. More...

void	m_set_cM_relation (const std::string cM_author="Duffy")
	set the concentration-mass relation. A function is set, computing the concentration of a dark matter halo of a given a mass, at a given redshift; the models implemented are the following: More...

Private Attributes
std::shared_ptr< cosmology::Cosmology >	m_cosmology = NULL
	pointer to the input cosmology

std::string	m_profile_author = par::defaultString
	cluster density profile author

std::string	m_halo_def
	halo (overdensity) definition

double	m_Delta
	overdensity factor

std::function< double(const double, cbl::cosmology::Cosmology, const double)>	m_Delta_func
	function returning the overdensity factor

double	m_trunc_fact
	truncation factor $F_t$ defining the truncation radius, that is $r_t = F_t*r_{\Delta}$

bool	m_miscentering
	if true, account for the miscentering

double	m_sigma_off
	rms of the off-centered cluster distribution

double	m_f_off
	fraction of off-centered clusters

double	m_sigma_off_threshold
	lower threshold for sigma_off

double	m_f_off_threshold
	lower threshold for f_off

double	m_min_Smis
	minimum value where the off-centered Sigma(R) is computed

double	m_max_Smis
	maxmimum value where the off-centered Sigma(R) is computed

bool	m_single_profile
	if true, the miscetering is related to a single cluster. Otherwise, a population of clusters is considered

std::vector< double >(HaloProfile::*	m_rho_ptr )(const std::vector< double >)
	cluster 3D density profile function

double(HaloProfile::*	m_rho_s_ptr )()
	function returning the characteristic density of the cluster profile

std::vector< double >(HaloProfile::*	m_Sigma_mis_ptr )(const std::vector< double >)
	function returning the miscentering contribution to the total cluster surface density for a given radius

std::vector< double >(HaloProfile::*	m_Sigma_cen_ptr )(const std::vector< double >)
	function returning the centered cluster surface density for a given radius

std::vector< double >(HaloProfile::*	m_Sigma_mean_cen_ptr )(const std::vector< double >)
	function returning the centered mean cluster surface density for a given radius

std::vector< double >(HaloProfile::*	m_Sigma_ptr )(const std::vector< double >)
	function returning the cluster surface density for a given radius

std::vector< double >(HaloProfile::*	m_DeltaSigma_mis_ptr )(const std::vector< double >)
	function returning the miscentering contribution to the total cluster excess surface density for a given radius

std::vector< double >(HaloProfile::*	m_DeltaSigma_cen_ptr )(const std::vector< double >)
	function returning the centered cluster excess surface density for a given radius

std::vector< double >(HaloProfile::*	m_DeltaSigma_ptr )(const std::vector< double >)
	function returning the excess cluster surface density for a given radius

bool	m_isSet_cM_relation = false
	if true, the concentration-mass relation is set

double(HaloProfile::*	m_return_concentration )()
	pointer returning the concentration, the one set by the user or from a concentration-mass relation function

double	m_A = par::defaultDouble
	parameter A in the c-M relation

double	m_B = par::defaultDouble
	parameter B in the c-M relation

double	m_C = par::defaultDouble
	parameter C in the c-M relation

double	m_mass = par::defaultDouble
	halo mass

double	m_concentration = par::defaultDouble
	halo concentration

double	m_redshift = par::defaultDouble
	halo redshift

Detailed Description

The class HaloProfile.

Definition at line 52 of file HaloProfile.h.

Constructor & Destructor Documentation

◆ HaloProfile() [1/2]

cbl::cosmology::HaloProfile::HaloProfile	(	const cbl::cosmology::Cosmology	cosmology,
		const double	redshift,
		const double	conc,
		const double	Mass,
		const double	Delta,
		const std::string	profile_author,
		const std::string	halo_def,
		const double	trunc_fact = `3.`,
		const bool	miscentering = `false`,
		const bool	single_profile = `false`,
		const double	sigma_off = `0.1`,
		const double	f_off = `1.`
	)

constructor that sets the halo profile parameters. If the miscentering is considered, $\Sigma(R)$ and $\Delta\Sigma(R)$ are expressed as (see e.g. Bellagamba et al. 2019):

$\Sigma_{\rm 1h}(R)=(1-f_{\rm off})\Sigma_{\rm cen}(R)+ f_{\rm off}\Sigma_{\rm off}(R),\,\,\,\,(1)$

$\Delta\Sigma_{\rm 1h}(R)=(1-f_{\rm off})\Delta\Sigma_{\rm cen}(R)+ f_{\rm off}\Delta\Sigma_{\rm off}(R).\,\,\,\,(2)$

Parameters

cosmology	the cosmology
redshift	the redshift
conc	halo concentration
Mass	halo mass
Delta	overdensity factor which needs to be multiplied to the critical density in order to define an overdensity
profile_author	the density profile author(s); available options are: "NFW" $\rightarrow$ Navarro-Frenk-White profile; "NFW_trunc" $\rightarrow$ truncated Navarro-Frenk-White profile
halo_def	the halo definition; available options are: "vir" $\rightarrow$ all matter within the radius $r_{vir}$ for which the mean internal density is cbl::cosmology::Cosmology::Delta_c times the critical density $\rho_{crit}=3H^2/8\pi G$; "critical" $\rightarrow$ all matter within the radius $r_{200}$ for which the mean internal density is 200 times the critical density; "mean" $\rightarrow$ all matter within the radius $r_{\Delta}$ for which the mean internal density is $\Delta\Omega_m$ times the critical mean background density
trunc_fact	factor $F_t$ defining the truncation radius, that is $r_t = F_tr_{\Delta}$
miscentering	if true, account for the miscentering
single_profile	if true, the miscetering is related to a single cluster. Otherwise, a population of clusters is considered (the latter is the case of stacked weak lensing analyses)
sigma_off	if single_profile=false, this is the standard deviation of the miscentered cluster population, $\sigma_{\rm off}$, in Mpc $/h$. Otherwise, it is the miscentering of a single cluster profile
f_off	fraction of miscentered clusters, $f_{\rm off}$. Used only if single_profile=false

Warning: If the miscentering is considered, the methods HaloProfile::Sigma() and HaloProfile::DeltaSigma() include the miscentering contribution (i.e. Eq. 1 and Eq. 2).; If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities (e.g. $\Sigma$, $\Delta\Sigma$) are in units of $h$

Definition at line 45 of file HaloProfile.cpp.

◆ HaloProfile() [2/2]

cbl::cosmology::HaloProfile::HaloProfile	(	const cbl::cosmology::Cosmology	cosmology,
		const double	redshift,
		const std::string	cM_author,
		const double	Mass,
		const double	Delta,
		const std::string	profile_author,
		const std::string	halo_def,
		const double	trunc_fact = `3.`,
		const bool	miscentering = `false`,
		const bool	single_profile = `false`,
		const double	sigma_off = `0.1`,
		const double	f_off = `1.`
	)

constructor that sets the halo profile parameters, assuming a concentration-mass relation. If the miscentering is considered, $\Sigma(R)$ and $\Delta\Sigma(R)$ are expressed as (see e.g. Bellagamba et al. 2019):

$\Sigma_{\rm 1h}(R)=(1-f_{\rm off})\Sigma_{\rm cen}(R)+ f_{\rm off}\Sigma_{\rm off}(R),\,\,\,\,(1)$

$\Delta\Sigma_{\rm 1h}(R)=(1-f_{\rm off})\Delta\Sigma_{\rm cen}(R)+ f_{\rm off}\Delta\Sigma_{\rm off}(R).\,\,\,\,(2)$

Parameters

cosmology	the cosmology
redshift	the redshift
cM_author	author(s) who proposed the concentration-mass relation. Possibilities are: "Duffy" (Duffy et al. 2008)
Mass	halo mass
Delta	overdensity factor which needs to be multiplied to the critical density in order to define an overdensity
profile_author	the density profile author(s); available options are: "NFW" $\rightarrow$ Navarro-Frenk-White profile; "NFW_trunc" $\rightarrow$ truncated Navarro-Frenk-White profile
halo_def	the halo definition; available options are: "vir" $\rightarrow$ all matter within the radius $r_{vir}$ for which the mean internal density is cbl::cosmology::Cosmology::Delta_c times the critical density $\rho_{crit}=3H^2/8\pi G$; "critical" $\rightarrow$ all matter within the radius $r_{200}$ for which the mean internal density is 200 times the critical density; "mean" $\rightarrow$ all matter within the radius $r_{\Delta}$ for which the mean internal density is $\Delta\Omega_m$ times the critical mean background density
trunc_fact	factor $F_t$ defining the truncation radius, that is $r_t = F_tr_{\Delta}$
miscentering	if true, account for the miscentering
single_profile	if true, the miscetering is related to a single cluster. Otherwise, a population of clusters is considered (the latter is the case of stacked weak lensing analyses)
sigma_off	if single_profile=false, this is the standard deviation of the miscentered cluster population, $\sigma_{\rm off}$, in Mpc $/h$. Otherwise, it is the miscentering of a single cluster profile
f_off	fraction of miscentered clusters, $f_{\rm off}$. Used only if single_profile=false

Warning: the Duffy et al. concentrantion-mass relation refers to the 0<z<2 redshift range, obtained from their full samples (see Table 1 of Duffy et al. 2008).; If the miscentering is considered, the methods HaloProfile::Sigma() and HaloProfile::DeltaSigma() include the miscentering contribution (i.e. Eq. 1 and Eq. 2).; If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities (e.g. $\Sigma$, $\Delta\Sigma$) are in units of $h$

Definition at line 54 of file HaloProfile.cpp.

Member Function Documentation

◆ concentration()

double cbl::cosmology::HaloProfile::concentration ( )

inline

get the concentration

Returns: the concentration of the halo

Warning: if a concentration-mass relation is set, the output concentration is derived from such relation

Definition at line 567 of file HaloProfile.h.

◆ concentration2()

double cbl::cosmology::HaloProfile::concentration2	(	const double	Vmax,
		const double	Rmax
	)		const

compute the halo concentration

Author: Carlo Giocoli; cgioc.nosp@m.oli@.nosp@m.gmail.nosp@m..com

Parameters

Vmax	V_max
Rmax	R_max

Returns: the halo concentration

Definition at line 861 of file HaloProfile.cpp.

◆ Delta()

double cbl::cosmology::HaloProfile::Delta ( )

inline

get the overdensity

Returns: the overdensity which needs to be multiplied to the critical density in order to define an overdensity. Given an overdensity factor $\Delta$, this function returns $\Delta$ for a critical overdensity, $\Delta\Omega_{\rm m}(z)$ for a mean overdensity, and cbl::cosmology::Cosmology::Delta_c for a overdensity defined with respect to the critical density.

Definition at line 592 of file HaloProfile.h.

◆ DeltaSigma()

std::vector< double > cbl::cosmology::HaloProfile::DeltaSigma ( const std::vector< double > rad )

the total excess surface density profile of the halo.

Parameters

rad radius

Returns: the halo excess surface density profile in $M_{\odot} / $pc^2

Warning: If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities are in units of $h$

Definition at line 757 of file HaloProfile.cpp.

◆ DeltaSigma_2h() [1/2]

std::vector< double > cbl::cosmology::HaloProfile::DeltaSigma_2h	(	const std::vector< double >	rad,
		const double	bias,
		const std::string	method_Pk = `"EisensteinHu"`,
		const std::string	interp_type = `"Linear"`,
		const bool	NL = `false`
	)

the 2-halo contribution to the excess surface density profile of the halo.

Parameters

rad	radius
bias	the halo bias value
method_Pk	method used for the computation of the power spectrum. Valid choices for method_Pk are: CAMB [http://camb.info/], CLASS [http://class-code.net/], MPTbreeze-v1 [http://arxiv.org/abs/1207.1465], EisensteinHu [http://background.uchicago.edu/~whu/transfer/transferpage.html]
interp_type	method to interpolate the power spectrum. Possibilities are: "Linear", "Poly", "Spline", "Spline_periodic", "Akima", "Akima_periodic", "Steffen"
NL	false $\rightarrow$ linear power spectrum; true $\rightarrow$ non-linear power spectrum

Returns: the halo excess surface density profile in $M_{\odot} / $pc^2

Warning: If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities are in units of $h$

Definition at line 790 of file HaloProfile.cpp.

◆ DeltaSigma_2h() [2/2]

std::vector< double > cbl::cosmology::HaloProfile::DeltaSigma_2h	(	const std::vector< double >	rad,
		const std::string	bias_author,
		const std::string	method_Pk = `"EisensteinHu"`,
		const std::string	interp_type = `"Linear"`,
		const bool	NL = `false`
	)

the 2-halo contribution to the excess surface density profile of the halo, computed by assuming a halo bias model.

Parameters

rad	radius
bias_author	author(s) who proposed the bias; valid authors are: ST99 (Sheth & Tormen 1999), SMT01 (Sheth, Mo & Tormen 2001), SMT01_WL04 (Sheth, Mo & Tormen 2001 with the correction of Warren 2004), Tinker (Tinker et al. 2010)
method_Pk	method used for the computation of the power spectrum. Valid choices for method_Pk are: CAMB [http://camb.info/], CLASS [http://class-code.net/], MPTbreeze-v1 [http://arxiv.org/abs/1207.1465], EisensteinHu [http://background.uchicago.edu/~whu/transfer/transferpage.html]
interp_type	method to interpolate the power spectrum. Possibilities are: "Linear", "Poly", "Spline", "Spline_periodic", "Akima", "Akima_periodic", "Steffen"
NL	false $\rightarrow$ linear power spectrum; true $\rightarrow$ non-linear power spectrum

Returns: the halo excess surface density profile in $M_{\odot} / $pc^2

Warning: If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities are in units of $h$

Definition at line 835 of file HaloProfile.cpp.

◆ DeltaSigma_cen()

std::vector< double > cbl::cosmology::HaloProfile::DeltaSigma_cen ( const std::vector< double > rad )

the centered contribution to the excess surface density profile of the halo.

Parameters

rad radius

Returns: the halo excess surface density profile in $M_{\odot} / $pc^2

Warning: If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities are in units of $h$

Definition at line 778 of file HaloProfile.cpp.

◆ DeltaSigma_mis()

std::vector< double > cbl::cosmology::HaloProfile::DeltaSigma_mis ( const std::vector< double > rad )

the miscentering contribution to the excess surface density profile of the halo.

Parameters

rad radius

Returns: the halo excess surface density profile in $M_{\odot} / $pc^2

Warning: If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities are in units of $h$

Definition at line 766 of file HaloProfile.cpp.

◆ density_profile_3D()

std::vector< double > cbl::cosmology::HaloProfile::density_profile_3D ( const std::vector< double > rad )

the 3D halo density profile.

Parameters

rad radius

Returns: the halo density profile

Warning: If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities are in units of $h$

Definition at line 655 of file HaloProfile.cpp.

◆ density_profile_FourierSpace()

double cbl::cosmology::HaloProfile::density_profile_FourierSpace ( const double kk )

the Fourier transform of the normalised halo density

this function computes the Fourier transform of the normalised density distribution of dark matter haloes; the Navarro-Frenk-White profile is the only one currently implemented (see e.g. eq. 81 of Cooray & Sheth 2002 and 70 of van den Bosch et al. 2012)

\[\tilde{u}_h(k, M_h, z) = \frac{4\pi\rho_sr_s^3}{M_h} \left[\cos\mu\left[{\rm Ci}(\mu+\mu c) - {\rm Ci}(\mu)\right] + \sin\mu\left[{\rm Si}(\mu+\mu c) - {\rm Si}(\mu)\right] - \frac{\sin\mu c}{\mu+\mu c}\right]\]

where

\[\mu\equiv kr_s\,,\]

\[\rho_s = \frac{\rho_{crit}\Delta_c}{3} \frac{c^3}{\ln(1+c)-c/(1+c)}\,,\]

\[{\rm Ci}(x)=-\int_x^\infty\frac{\cos t}{t}\,{\rm d}t\,,\]

\[{\rm Si}(x)=-\int_x^\infty\frac{\sin t}{t}\,{\rm d}t\]

the relation between the halo concentration, $c=c_{vir}=r_{vir}/r_s$, and halo mass, $M_h$, is computed by cbl::modelling::twopt::concentration; $\Delta_c(z)$ is computed by cbl::cosmology::Cosmology::Delta_c and $\rho_{crit}(z)$ is computed by cbl::cosmology::Cosmology::rho_crit; $r_{vir}(M_h, z)$ is computed by cbl::cosmology::Cosmology::r_vir

Parameters

kk	the wave vector module at which the model is computed

Returns: the halo density profile

Definition at line 847 of file HaloProfile.cpp.

◆ m_concentration_Duffy()

double cbl::cosmology::HaloProfile::m_concentration_Duffy ( )

private

The concentration-mass relation by Duffy et al. (2008):

\[c(M_h, z) = A(M_h/M_{pivot})^B\,(1+z)^C\]

Returns: the concentration

Definition at line 64 of file HaloProfile.cpp.

◆ m_DeltaSigma_cen()

std::vector< double > cbl::cosmology::HaloProfile::m_DeltaSigma_cen ( const std::vector< double > rad )

private

Excess surface density without the miscentering contribution.

Parameters

rad radius

Returns: the excess surface density

Definition at line 412 of file HaloProfile.cpp.

◆ m_DeltaSigma_including_miscentering()

std::vector< double > cbl::cosmology::HaloProfile::m_DeltaSigma_including_miscentering ( const std::vector< double > rad )

private

Excess surface density including the miscentering contribution.

Parameters

rad radius

Returns: the excess surface density

Definition at line 464 of file HaloProfile.cpp.

◆ m_DeltaSigma_mis()

std::vector< double > cbl::cosmology::HaloProfile::m_DeltaSigma_mis ( const std::vector< double > rad )

private

the mis-centered excess surface density profile of the halo (see e.g. Bellagamba et al. 2019).

Parameters

rad radius

Returns: the halo excess surface density profile in $M_{\odot} / $pc^2

Definition at line 429 of file HaloProfile.cpp.

◆ m_return_set_concentration()

double cbl::cosmology::HaloProfile::m_return_set_concentration ( )

inlineprivate

Return the concentration set by the user.

Returns: the concentration

Definition at line 226 of file HaloProfile.h.

◆ m_rho_NFW()

std::vector< double > cbl::cosmology::HaloProfile::m_rho_NFW ( const std::vector< double > rad )

private

The NFW 3D density profile.

Parameters

rad radius

Returns: the NFW density profile

Definition at line 108 of file HaloProfile.cpp.

◆ m_rho_NFW_trunc()

std::vector< double > cbl::cosmology::HaloProfile::m_rho_NFW_trunc ( const std::vector< double > rad )

private

The truncated NFW 3D density profile.

Parameters

rad radius

Returns: the truncated NFW density profile

Definition at line 128 of file HaloProfile.cpp.

◆ m_rho_s_NFW()

double cbl::cosmology::HaloProfile::m_rho_s_NFW ( )

private

Characteristic density of the NFW profile.

Returns: the NFW characteristic density

Definition at line 76 of file HaloProfile.cpp.

◆ m_rho_s_NFW_trunc()

double cbl::cosmology::HaloProfile::m_rho_s_NFW_trunc ( )

private

Characteristic density of the truncated NFW profile.

Returns: the truncated NFW characteristic density

Definition at line 89 of file HaloProfile.cpp.

◆ m_set_cM_relation()

void cbl::cosmology::HaloProfile::m_set_cM_relation ( const std::string cM_author = "Duffy" )

private

set the concentration-mass relation. A function is set, computing the concentration of a dark matter halo of a given a mass, at a given redshift; the models implemented are the following:

Duffy et al. 2008:
\[c(M_h, z) = A(M_h/M_{pivot})^B\,(1+z)^C\]

Parameters

cM_author author(s) who proposed the concentration-mass relation. Possibilities are: "Duffy" (Duffy et al. 2008)

Warning: the Duffy et al. concentrantion-mass relation refers to the 0<z<2 redshift range, obtained from their full samples (see Table 1 of Duffy et al. 2008).

Definition at line 484 of file HaloProfile.cpp.

◆ m_set_profile()

void cbl::cosmology::HaloProfile::m_set_profile	(	const cbl::cosmology::Cosmology	cosmology,
		const double	redshift,
		const double	conc,
		const double	Mass,
		const double	Delta,
		const std::string	profile_author,
		const std::string	halo_def,
		const double	trunc_fact = `3.`,
		const bool	miscentering = `false`,
		const bool	single_profile = `false`,
		const double	sigma_off = `0.1`,
		const double	f_off = `1.`
	)

private

private function that sets the halo profile parameters. If the miscentering is considered, $\Sigma(R)$ and $\Delta\Sigma(R)$ are expressed as (see e.g. Bellagamba et al. 2019):

$\Sigma_{\rm 1h}(R)=(1-f_{\rm off})\Sigma_{\rm cen}(R)+ f_{\rm off}\Sigma_{\rm off}(R),\,\,\,\,(1)$

$\Delta\Sigma_{\rm 1h}(R)=(1-f_{\rm off})\Delta\Sigma_{\rm cen}(R)+ f_{\rm off}\Delta\Sigma_{\rm off}(R).\,\,\,\,(2)$

Parameters

cosmology	the cosmology
redshift	the redshift
conc	halo concentration
Mass	halo mass
Delta	overdensity factor which needs to be multiplied to the critical density in order to define an overdensity
profile_author	the density profile author(s); available options are: "NFW" $\rightarrow$ Navarro-Frenk-White profile; "NFW_trunc" $\rightarrow$ truncated Navarro-Frenk-White profile
halo_def	the halo definition; available options are: "vir" $\rightarrow$ all matter within the radius $r_{vir}$ for which the mean internal density is cbl::cosmology::Cosmology::Delta_c times the critical density $\rho_{crit}=3H^2/8\pi G$; "critical" $\rightarrow$ all matter within the radius $r_{200}$ for which the mean internal density is 200 times the critical density; "mean" $\rightarrow$ all matter within the radius $r_{\Delta}$ for which the mean internal density is $\Delta\Omega_m$ times the critical mean background density
trunc_fact	factor $F_t$ defining the truncation radius, that is $r_t = F_tr_{\Delta}$
miscentering	if true, account for the miscentering
single_profile	if true, the miscetering is related to a single cluster. Otherwise, a population of clusters is considered (the latter is the case of stacked weak lensing analyses)
sigma_off	if single_profile=false, this is the standard deviation of the miscentered cluster population, $\sigma_{\rm off}$, in Mpc $/h$. Otherwise, it is the miscentering of a single cluster profile
f_off	fraction of miscentered clusters, $f_{\rm off}$. Used only if single_profile=false

Warning: If the miscentering is considered, the methods HaloProfile::Sigma() and HaloProfile::DeltaSigma() include the miscentering contribution (i.e. Eq. 1 and Eq. 2).; If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities (e.g. $\Sigma$, $\Delta\Sigma$) are in units of $h$

Definition at line 541 of file HaloProfile.cpp.

◆ m_Sigma_including_miscentering()

std::vector< double > cbl::cosmology::HaloProfile::m_Sigma_including_miscentering ( const std::vector< double > rad )

private

Surface density including the miscentering contribution.

Parameters

rad radius

Returns: the surface density

Definition at line 392 of file HaloProfile.cpp.

◆ m_Sigma_mean_NFW()

std::vector< double > cbl::cosmology::HaloProfile::m_Sigma_mean_NFW ( const std::vector< double > rad )

private

Mean surface density of the NFW profile.

Parameters

rad radius

Returns: the NFW surface density

Definition at line 178 of file HaloProfile.cpp.

◆ m_Sigma_mean_NFW_trunc()

std::vector< double > cbl::cosmology::HaloProfile::m_Sigma_mean_NFW_trunc ( const std::vector< double > rad )

private

Mean surface density of the truncated NFW profile.

Parameters

rad radius

Returns: the truncated NFW surface density

Definition at line 270 of file HaloProfile.cpp.

◆ m_Sigma_mis()

std::vector< double > cbl::cosmology::HaloProfile::m_Sigma_mis ( const std::vector< double > rad )

private

the mis-centered surface density profile of the halo (see e.g. Bellagamba et al. 2019).

Parameters

rad radius

Returns: the halo surface density profile in $M_{\odot} / $pc^2

Definition at line 322 of file HaloProfile.cpp.

◆ m_Sigma_NFW()

std::vector< double > cbl::cosmology::HaloProfile::m_Sigma_NFW ( const std::vector< double > rad )

private

Surface density of the NFW profile.

Parameters

rad radius

Returns: the NFW surface density

Definition at line 149 of file HaloProfile.cpp.

◆ m_Sigma_NFW_trunc()

std::vector< double > cbl::cosmology::HaloProfile::m_Sigma_NFW_trunc ( const std::vector< double > rad )

private

Surface density of the truncated NFW profile.

Parameters

rad radius

Returns: the truncated NFW surface density

Definition at line 209 of file HaloProfile.cpp.

◆ Mass_Delta()

double cbl::cosmology::HaloProfile::Mass_Delta	(	const double	Mass,
		const double	Delta_in,
		const double	Delta_out,
		const double	conc,
		const bool	is_input_conc,
		const double	rRmin_guess = `1.e-3`,
		const double	rRmax_guess = `10.`
	)		const

The halo mass converted to a different value of $\Delta$, assuming the Navarro-Frenk-White density profile.

This function converts a given input mass $M_\Delta$ to $M_{\Delta^{new}}$ (e.g. $M_{500} \rightarrow M_{200}$).

Specifically, the algorithm currently implemented can be derived as follows. Given the Navarro-Frenk-White profile:

\[ \rho(r) = \frac{\rho_0}{\frac{r}{R_s} \left(1+\frac{r}{R_s} \right)^2} \]

the total halo mass contained within a radius $R_\Delta$ is:

\[ M_\Delta = \int_0^{R_\Delta} 4\pi r^2\rho(r)dr = 4\pi \rho_0 R_s^3 \left[ \ln(1+c_\Delta)-\frac{c_\Delta}{1+c_\Delta} \right] \]

where the concentration is defined as $c_\Delta\equiv R_\Delta/R_s$. Thus, we can write:

\[ \frac{\ln(1+c_\Delta) - \frac{c_\Delta}{1+c_\Delta}} {M_\Delta} = \frac{\ln(1+c_{\Delta^{new}}) - \frac{c_{\Delta^{new}}}{1+c_{\Delta^{new}}}} {M_{\Delta^{new}}} \]

$ M_\Delta $ can be written as follows:

\[ M_\Delta = \frac{4}{3}\pi\Delta\rho_{crit}R_\Delta^3 = \frac{\Delta}{\Delta^{new}} \left(\frac{R_\Delta}{R_{\Delta^{new}}} \right)^3 M_{\Delta^{new}} = \frac{\Delta}{\Delta^{new}} x^3 M_{\Delta^{new}} \]

where $ x\equiv R_\Delta/R_{\Delta^{new}} $. Thus we have:

\[ \frac{M_\Delta}{M_{\Delta^{new}}} \left[ \ln(1+c_{\Delta^{new}}) - \frac{c_{\Delta^{new}}}{1+c_{\Delta^{new}}} \right] - \left[ \ln(1+c_\Delta) - \frac{c_\Delta}{1+c_\Delta} \right] = 0 \]

where $ c_{\Delta^{new}} \equiv R_{\Delta^{new}}/R_s = c_\Delta R_{\Delta^{new}}/R_\Delta = c_\Delta/x $. The algorithm solves the above equation as a function of $ x $, providing in output:

\[ M_{\Delta^{new}} = \frac{1}{x^3}\frac{\Delta^{new}}{\Delta} M_\Delta \]

Parameters

Mass	the input mass $M_\Delta$ (e.g. $M_{500}$)
Delta_in	the input $\Delta$ (e.g. $\Delta=500$)
Delta_out	the output $\Delta^{new}$ (e.g. $\Delta^{new}=200$)
conc	the concentration related to either the input $\Delta$, or the output $\Delta^{new}$ (this is specified by is_input_conc)
is_input_conc	true $\rightarrow$ the given concentration is related to the input $\Delta$; false $\rightarrow$ the given concentration is related to the output $\Delta^{new}$
rRmin_guess	the minimum guess value of $r_\Delta/r_{\Delta^{new}}$ used by the gsl minimisation function
rRmax_guess	the maximum guess value of $r_\Delta/r_{\Delta^{new}}$ used by the gsl minimisation function

Returns: $M_{\Delta^{new}}$

Warning: the current implementation assumes the Navarro-Frenk-White profile

Definition at line 878 of file HaloProfile.cpp.

◆ rho_s()

double cbl::cosmology::HaloProfile::rho_s ( )

the characteristic density of the 3D halo density profile.

Returns: the halo density profile

Definition at line 647 of file HaloProfile.cpp.

◆ set_concentration()

void cbl::cosmology::HaloProfile::set_concentration ( const double conc = par::defaultDouble )

inline

set the private member m_concentration

Parameters

conc	concentration

Definition at line 984 of file HaloProfile.h.

◆ set_cosmology()

void cbl::cosmology::HaloProfile::set_cosmology ( const cbl::cosmology::Cosmology cosmology )

set the cosmological model

Parameters

cosmology the cosmology

Definition at line 638 of file HaloProfile.cpp.

◆ set_f_off()

void cbl::cosmology::HaloProfile::set_f_off ( const double f_off = par::defaultDouble )

inline

set the private member m_f_off

Parameters

f_off f_off

Definition at line 991 of file HaloProfile.h.

◆ set_mass()

void cbl::cosmology::HaloProfile::set_mass ( const double mass = par::defaultDouble )

inline

set the private member m_mass

Parameters

mass	the mass of the cluster

Definition at line 977 of file HaloProfile.h.

◆ set_sigma_off()

void cbl::cosmology::HaloProfile::set_sigma_off ( const double sigma_off = par::defaultDouble )

inline

set the private member m_sigma_off

Parameters

sigma_off sigma_off

Definition at line 998 of file HaloProfile.h.

◆ set_trunc_fact()

void cbl::cosmology::HaloProfile::set_trunc_fact ( const double trunc_fact = par::defaultDouble )

inline

set the private member m_trunc_fact

Parameters

trunc_fact trunc_fact

Definition at line 1005 of file HaloProfile.h.

◆ Sigma()

std::vector< double > cbl::cosmology::HaloProfile::Sigma ( const std::vector< double > rad )

the total surface density profile of the halo.

Parameters

rad radius

Returns: the halo surface density profile in $M_{\odot} / $pc^2

Warning: If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities are in units of $h$

Definition at line 664 of file HaloProfile.cpp.

◆ Sigma_2h() [1/2]

std::vector< double > cbl::cosmology::HaloProfile::Sigma_2h	(	const std::vector< double >	rad,
		const double	bias,
		const std::string	method_Pk = `"EisensteinHu"`,
		const std::string	interp_type = `"Linear"`,
		const bool	NL = `false`
	)

the 2-halo contribution to the total surface density profile of the halo.

Parameters

rad	radius
bias	the halo bias value
method_Pk	method used for the computation of the power spectrum. Valid choices for method_Pk are: CAMB [http://camb.info/], CLASS [http://class-code.net/], MPTbreeze-v1 [http://arxiv.org/abs/1207.1465], EisensteinHu [http://background.uchicago.edu/~whu/transfer/transferpage.html]
interp_type	method to interpolate the power spectrum. Possibilities are: "Linear", "Poly", "Spline", "Spline_periodic", "Akima", "Akima_periodic", "Steffen"
NL	false $\rightarrow$ linear power spectrum; true $\rightarrow$ non-linear power spectrum

Returns: the halo surface density profile in $M_{\odot} / $pc^2

Warning: If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities are in units of $h$

Definition at line 700 of file HaloProfile.cpp.

◆ Sigma_2h() [2/2]

std::vector< double > cbl::cosmology::HaloProfile::Sigma_2h	(	const std::vector< double >	rad,
		const std::string	bias_author,
		const std::string	method_Pk = `"EisensteinHu"`,
		const std::string	interp_type = `"Linear"`,
		const bool	NL = `false`
	)

the 2-halo contribution to the total surface density profile of the halo, computed by assuming a halo bias model.

Parameters

rad	radius
bias_author	author(s) who proposed the bias; valid authors are: ST99 (Sheth & Tormen 1999), SMT01 (Sheth, Mo & Tormen 2001), SMT01_WL04 (Sheth, Mo & Tormen 2001 with the correction of Warren 2004), Tinker (Tinker et al. 2010)
method_Pk	method used for the computation of the power spectrum. Valid choices for method_Pk are: CAMB [http://camb.info/], CLASS [http://class-code.net/], MPTbreeze-v1 [http://arxiv.org/abs/1207.1465], EisensteinHu [http://background.uchicago.edu/~whu/transfer/transferpage.html]
interp_type	method to interpolate the power spectrum. Possibilities are: "Linear", "Poly", "Spline", "Spline_periodic", "Akima", "Akima_periodic", "Steffen"
NL	false $\rightarrow$ linear power spectrum; true $\rightarrow$ non-linear power spectrum

Returns: the halo surface density profile in $M_{\odot} / $pc^2

Warning: If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities are in units of $h$

Definition at line 745 of file HaloProfile.cpp.

◆ Sigma_cen()

std::vector< double > cbl::cosmology::HaloProfile::Sigma_cen ( const std::vector< double > rad )

the centered contribution to the total surface density profile of the halo.

Parameters

rad radius

Returns: the halo surface density profile in $M_{\odot} / $pc^2

Warning: If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities are in units of $h$

Definition at line 688 of file HaloProfile.cpp.

◆ Sigma_mis()

std::vector< double > cbl::cosmology::HaloProfile::Sigma_mis ( const std::vector< double > rad )

the miscentering contribution to the total surface density profile of the halo.

Parameters

rad radius

Returns: the halo surface density profile in $M_{\odot} / $pc^2

Warning: If in the cbl::cosmology::Cosmology object the $h$ units are set, both the input quantities (e.g. mass, radius) and the output quantities are in units of $h$

Definition at line 673 of file HaloProfile.cpp.

The documentation for this class was generated from the following files:

Headers/HaloProfile.h
Cosmology/Lib/HaloProfile.cpp

Mass	the input mass \(M_\Delta\) (e.g. \(M_{500}\))
Delta_in	the input \(\Delta\) (e.g. \(\Delta=500\))
Delta_out	the output \(\Delta^{new}\) (e.g. \(\Delta^{new}=200\))
conc	the concentration related to either the input \(\Delta\), or the output \(\Delta^{new}\) (this is specified by is_input_conc)
is_input_conc	true \(\rightarrow\) the given concentration is related to the input \(\Delta\); false \(\rightarrow\) the given concentration is related to the output \(\Delta^{new}\)
rRmin_guess	the minimum guess value of \(r_\Delta/r_{\Delta^{new}}\) used by the gsl minimisation function
rRmax_guess	the maximum guess value of \(r_\Delta/r_{\Delta^{new}}\) used by the gsl minimisation function

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ HaloProfile() [1/2]

◆ HaloProfile() [2/2]

Member Function Documentation

◆ concentration()

◆ concentration2()

◆ Delta()

◆ DeltaSigma()

◆ DeltaSigma_2h() [1/2]

◆ DeltaSigma_2h() [2/2]

◆ DeltaSigma_cen()

◆ DeltaSigma_mis()

◆ density_profile_3D()

◆ density_profile_FourierSpace()

◆ m_concentration_Duffy()

◆ m_DeltaSigma_cen()

◆ m_DeltaSigma_including_miscentering()

◆ m_DeltaSigma_mis()

◆ m_return_set_concentration()

◆ m_rho_NFW()

◆ m_rho_NFW_trunc()

◆ m_rho_s_NFW()

◆ m_rho_s_NFW_trunc()

◆ m_set_cM_relation()

◆ m_set_profile()

◆ m_Sigma_including_miscentering()

◆ m_Sigma_mean_NFW()

◆ m_Sigma_mean_NFW_trunc()

◆ m_Sigma_mis()

◆ m_Sigma_NFW()

◆ m_Sigma_NFW_trunc()

◆ Mass_Delta()

◆ rho_s()

◆ set_concentration()

◆ set_cosmology()

◆ set_f_off()

◆ set_mass()

◆ set_sigma_off()

◆ set_trunc_fact()

◆ Sigma()

◆ Sigma_2h() [1/2]

◆ Sigma_2h() [2/2]

◆ Sigma_cen()

◆ Sigma_mis()