`ler.gw_source_population`

Submodules

Package Contents

Classes

`CBCSourceRedshiftDistribution`	Class to generate a population of source galaxies.
`CBCSourceRedshiftDistribution`	Class to generate a population of source galaxies.
`CBCSourceParameterDistribution`	Class to generate a population of compact binaries. It helps sample all the intrinsic and extrinsic parameters of compact binaries. This daughter class inherits from `CBCSourceRedshiftDistribution` class.

Functions

`interpolator_from_pickle`(param_dict_given, directory, ...)	Function to decide which interpolator to use.
`cubic_spline_interpolator`(xnew, coefficients, x)	Function to interpolate using cubic spline.
`inverse_transform_sampler`(size, cdf, x)	Function to sample from the inverse transform method.
`merger_rate_density_bbh_popI_II_oguri2018`(zs[, R0, ...])	Function to compute the merger rate density (PopI/PopII). Reference: Oguri et al. (2018). The output is in detector frame and is unnormalized.
`star_formation_rate_madau_dickinson2014`(zs[, af, bf, cf])	Function to compute star formation rate as given in Eqn. 15 Madau & Dickinson (2014). The output is in detector frame and is unnormalized.
`merger_rate_density_bbh_popIII_ken2022`(zs[, n0, aIII, ...])	Function to compute the unnormalized merger rate density (PopIII). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.
`merger_rate_density_bbh_primordial_ken2022`(zs[, ...])	Function to compute the merger rate density (Primordial). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.
`interpolator_from_pickle`(param_dict_given, directory, ...)	Function to decide which interpolator to use.
`cubic_spline_interpolator`(xnew, coefficients, x)	Function to interpolate using cubic spline.
`lognormal_distribution_2D`(size[, m_min, m_max, Mc, ...])	Function to sample from a lognormal distribution in 2D space. Reference: Ng et al. 2022. This a helper function for popIII BBH and primordial BBH merger rate density distribution functions.
`inverse_transform_sampler_m1m2`(size, inv_cdf, x)	Function to sample from a distribution using inverse transform sampling. This is a helper function BNS Alsing mass distribution function.
`inverse_transform_sampler`(size, cdf, x)	Function to sample from the inverse transform method.
`merger_rate_density_bbh_popI_II_oguri2018`(zs[, R0, ...])	Function to compute the merger rate density (PopI/PopII). Reference: Oguri et al. (2018). The output is in detector frame and is unnormalized.
`merger_rate_density_bbh_popIII_ken2022`(zs[, n0, aIII, ...])	Function to compute the unnormalized merger rate density (PopIII). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.
`star_formation_rate_madau_dickinson2014`(zs[, af, bf, cf])	Function to compute star formation rate as given in Eqn. 15 Madau & Dickinson (2014). The output is in detector frame and is unnormalized.
`merger_rate_density_bbh_primordial_ken2022`(zs[, ...])	Function to compute the merger rate density (Primordial). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.
`lognormal_distribution_2D`(size[, m_min, m_max, Mc, ...])	Function to sample from a lognormal distribution in 2D space. Reference: Ng et al. 2022. This a helper function for popIII BBH and primordial BBH merger rate density distribution functions.
`inverse_transform_sampler_m1m2`(size, inv_cdf, x)	Function to sample from a distribution using inverse transform sampling. This is a helper function BNS Alsing mass distribution function.

ler.gw_source_population.interpolator_from_pickle(param_dict_given, directory, sub_directory, name, x, pdf_func=None, y=None, conditioned_y=None, dimension=1, category='pdf', create_new=False)[source]

Function to decide which interpolator to use.

Parameters:

param_dict_givendict: dictionary of parameters.
directorystr: directory to store the interpolator.
sub_directorystr: sub-directory to store the interpolator.
namestr: name of the interpolator.
xnumpy.ndarray: x values.
pdf_funcfunction: function to calculate the pdf of x given y.
ynumpy.ndarray: y values.
conditioned_ynumpy.ndarray: conditioned y values.
dimensionint: dimension of the interpolator. Default is 1.
categorystr: category of the function. Default is “pdf”.
create_newbool: if True, create a new interpolator. Default is False.

Returns:

interpolatorfunction: interpolator function.

ler.gw_source_population.cubic_spline_interpolator(xnew, coefficients, x)[source]

Function to interpolate using cubic spline.

Parameters:

xnewnumpy.ndarray: new x values.
coefficientsnumpy.ndarray: coefficients of the cubic spline.
xnumpy.ndarray: x values.

Returns:

resultnumpy.ndarray: interpolated values.

ler.gw_source_population.inverse_transform_sampler(size, cdf, x)[source]

Function to sample from the inverse transform method.

Parameters:

sizeint: number of samples.
cdfnumpy.ndarray: cdf values.
xnumpy.ndarray: x values.

Returns:

samplesnumpy.ndarray: samples from the cdf.

ler.gw_source_population.merger_rate_density_bbh_popI_II_oguri2018(zs, R0=23.9 * 1e-09, b2=1.6, b3=2.0, b4=30)[source]

Function to compute the merger rate density (PopI/PopII). Reference: Oguri et al. (2018). The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
R0float: local merger rate density at low redshift default: 23.9*1e-9 Mpc^-3 yr^-1
b2float: Fitting paramters default: 1.6
b3float: Fitting paramters default: 2.0
b4float: Fitting paramters default: 30

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import merger_rate_density_bbh_popI_II_oguri2018
>>> rate_density = merger_rate_density_bbh_popI_II_oguri2018(zs=0.1)

ler.gw_source_population.star_formation_rate_madau_dickinson2014(zs, af=2.7, bf=5.6, cf=2.9)[source]

Function to compute star formation rate as given in Eqn. 15 Madau & Dickinson (2014). The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
affloat: Fitting paramters default: 2.7
bffloat: Fitting paramters default: 5.6
cffloat: Fitting paramters default: 2.9

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import star_formation_rate_madau_dickinson2014
>>> rate_density = star_formation_rate_madau_dickinson2014(zs=0.1)

ler.gw_source_population.merger_rate_density_bbh_popIII_ken2022(zs, n0=19.2 * 1e-09, aIII=0.66, bIII=0.3, zIII=11.6)[source]

Function to compute the unnormalized merger rate density (PopIII). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
n0float: normalization constant default: 19.2*1e-9
aIIIfloat: Fitting paramters default: 0.66
bIIIfloat: Fitting paramters default: 0.3
zIIIfloat: Fitting paramters default: 11.6

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import merger_rate_density_bbh_popIII_ken2022
>>> rate_density = merger_rate_density_bbh_popIII_ken2022(zs=0.1)

ler.gw_source_population.merger_rate_density_bbh_primordial_ken2022(zs, cosmology=cosmo, n0=0.044 * 1e-09, t0=13.786885302009708)[source]

Function to compute the merger rate density (Primordial). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.

Parameters:

zsfloat: Source redshifts
n0float: normalization constant default: 0.044*1e-9
t0float: Present age of the Universe in Gyr default: 13.786885302009708
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(t0=13.786885302009708)

Returns:

rate_densityfloat: merger rate density

class ler.gw_source_population.CBCSourceRedshiftDistribution(z_min=0.001, z_max=10.0, event_type='BBH', merger_rate_density='merger_rate_density_bbh_popI_II_oguri2018', merger_rate_density_param=None, cosmology=None, directory='./interpolator_pickle', create_new_interpolator=False)[source]

Bases: object

Class to generate a population of source galaxies. This class is inherited by CompactBinaryPopulation and LensGalaxyParameterDistribution class.

Parameters:

z_minfloat: Minimum redshift of the source population default: 0.
z_maxfloat: Maximum redshift of the source population default: 10.
event_typestr: Type of event to generate. e.g. ‘BBH’, ‘BNS’, ‘NSBH’
cosmologyastropy.cosmology: Cosmology to use default: None/astropy.cosmology.FlatLambdaCDM(H0=70, Om0=0.3)
merger_rate_densitystr or function: Type of merger rate density function to use default: ‘merger_rate_density_popI_II_oguri2018’ for others see instance method in merger_rate_density_model_list
merger_rate_density_paramdict: Dictionary of merger rate density function parameters default: None/dict(R0=25 * 1e-9, b2=1.6, b3=2.0, b4=30)
directorystr: Directory to store the interpolator pickle files default: ‘./interpolator_pickle’
create_new_interpolatordict: Dictionary of interpolator creation parameters default: None/dict(redshift_distribution=dict(create_new=False, resolution=500), z_to_luminosity_distance=dict(create_new=False, resolution=500), differential_comoving_volume=dict(create_new=False, resolution=500))

Examples

>>> from ler.gw_source_population import CBCSourceRedshiftDistribution
>>> cbc = CBCSourceRedshiftDistribution(z_min=0.001, z_max=10, merger_rate_density="merger_rate_density_bbh_popI_II_oguri2018")
>>> cbc.merger_rate_density(zs=0.0001) # local merger rate density at low redshift

Instance Attributes

SourceGalaxyPopulationModel has the following instance attributes:

Atrributes	Type
`z_min`	float
`z_max`	float
`event_type`	str
`cosmo`	astropy.cosmology
`merger_rate_density_param`	dict
`normalization_pdf_z`	float
`merger_rate_density_model_list`
	List of available merger rate density functions and its parameters
`sample_source_redshift`	Function to sample source redshifts (source frame)

Instance Methods

SourceGalaxyPopulationModel has the following instance methods:

Methods	Type
`merger_rate_density`	function
`z_to_luminosity_distance`	function
`differential_comoving_volume`	function
`pdf_z()`	Function to compute the pdf p(z)
`merger_rate_density_src_frame()`
	Function to compute the merger rate density (source frame)
`create_lookup_table()`	Function to create a lookup table for the differential comoving volume and luminosity distance wrt redshift
`merger_rate_density_bbh_popI_II_oguri2018()`
	Function to compute the merger rate density (PopI/PopII) from Oguri et al. (2018)
`star_formation_rate_madau_dickinson2014()`
	Function to compute star formation rate as given in Eqn. 15 Madau & Dickinson (2014)
`merger_rate_density_bbh_popIII_ken2022()`
	Function to compute the merger rate density (PopIII)
`merger_rate_density_bbh_primordial_ken2022()`
	Function to compute the merger rate density (Primordial)

property sample_source_redshift

Function to sample source redshifts (source frame) between z_min and z_max from the source galaxy population

Parameters:

sizeint: Number of samples to generate

Returns:

zs: Source redshifts

property merger_rate_density

Function to get the merger rate density function wrt redshift. The output is in detector frame and is unnormalized.

Parameters:

zsfloat: 1D array of floats Source redshifts

Returns:

merger_rate_densityfloat: merger rate density in detector frame (Mpc^-3 yr^-1)

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> cbc = SourceGalaxyPopulationModel()
>>> merger_rate_density = cbc.merger_rate_density(zs=0.1)

property merger_rate_density_model_list: Dictionary of available merger rate density functions and its parameters.

z_min

float

Minimum redshift of the source population

z_max

float

Maximum redshift of the source population

event_type

str

Type of event to generate.

e.g. ‘BBH’, ‘BNS’, ‘NSBH’

cosmo

astropy.cosmology

Cosmology to use for the redshift distribution.

e.g. Planck18, WMAP9, FlatLambdaCDM(H0=70, Om0=0.3) etc.

merger_rate_density_param

dict

Dictionary of merger rate density function input parameters

c_n_i

dict

c_n_i stands for ‘create new interpolator’. Dictionary of interpolator creation parameters.

e.g. dict(redshift_distribution=dict(create_new=False, resolution=500), z_to_luminosity_distance=dict(create_new=False, resolution=500), differential_comoving_volume=dict(create_new=False, resolution=500))

normalization_pdf_z

float

Normalization constant of the pdf p(z)

z_to_luminosity_distance

scipy.interpolate.interpolate

Function to convert redshift to luminosity distance

differential_comoving_volume

scipy.interpolate.interpolate

Function to calculate the differential comoving volume

pdf_z(zs, param=None)[source]

Function to compute the pdf p(z). The output is in source frame and is normalized.

Parameters:

zsfloat or numpy.ndarray (1D array of floats): Source redshifts
paramdict: Allows to pass in above parameters as dict. e.g. if the merger_rate_density is merger_rate_density_bbh_popI_II_oguri2018 param = dict(R0=23.9*1e-9, b2=1.6, b3=2.0, b4=30)

Returns:

pdfnumpy.ndarray: 1D array of floats pdf p(z)

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> cbc = SourceGalaxyPopulationModel()
>>> pdf = cbc.pdf_z(zs=0.1)

merger_rate_density_src_frame(zs, param=None)[source]

Function to compute the merger rate density (source frame). The output is in source frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (1D array of floats): Source redshifts
paramdict: Allows to pass in above parameters as dict. e.g. if the merger_rate_density is merger_rate_density_bbh_popI_II_oguri2018 param = dict(R0=23.9*1e-9, b2=1.6, b3=2.0, b4=30)

Returns:

rate_densitynumpy.ndarray: 1D array of floats merger rate density (source frame) (Mpc^-3 yr^-1)

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> cbc = SourceGalaxyPopulationModel()
>>> rate_density = cbc.merger_rate_density_src_frame(zs=0.1)

merger_rate_density_bbh_popI_II_oguri2018(zs, R0=23.9 * 1e-09, b2=1.6, b3=2.0, b4=30, param=None)[source]

Function to compute the merger rate density (PopI/PopII). Reference: Oguri et al. (2018). The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
R0float: local merger rate density at low redshift default: 23.9*1e-9 Mpc^-3 yr^-1
b2float: Fitting paramters default: 1.6
b3float: Fitting paramters default: 2.0
b4float: Fitting paramters default: 30
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(R0=23.9*1e-9, b2=1.6, b3=2.0, b4=30) default: None

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> pop = SourceGalaxyPopulationModel(z_min=0.0, z_max=10, event_type = "BBH", merger_rate_density="merger_rate_density_bbh_popI_II_oguri2018")
>>> rate_density = pop.merger_rate_density(zs=0.1)

star_formation_rate_madau_dickinson2014(zs, af=2.7, bf=5.6, cf=2.9, param=None)[source]

Function to compute star formation rate as given in Eqn. 15 Madau & Dickinson (2014). The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
affloat: Fitting paramters default: 2.7
bffloat: Fitting paramters default: 5.6
cffloat: Fitting paramters default: 2.9
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(af=2.7, bf=5.6, cf=2.9) default: None

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> pop = SourceGalaxyPopulationModel(z_min=5., z_max=40., event_type = "BBH", merger_rate_density="star_formation_rate_madau_dickinson2014")
>>> rate_density = pop.merger_rate_density(zs=10)

merger_rate_density_bbh_popIII_ken2022(zs, n0=19.2 * 1e-09, aIII=0.66, bIII=0.3, zIII=11.6, param=None)[source]

Function to compute the unnormalized merger rate density (PopIII). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
n0float: normalization constant default: 19.2*1e-9
aIIIfloat: Fitting paramters default: 0.66
bIIIfloat: Fitting paramters default: 0.3
zIIIfloat: Fitting paramters default: 11.6
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(aIII=0.66, bIII=0.3, zIII=11.6) default: None

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> pop = SourceGalaxyPopulationModel(z_min=5, z_max=40, event_type = "BBH", merger_rate_density="merger_rate_density_popIII_ken2022")
>>> rate_density = pop.merger_rate_density(zs=10)
>>> rate_density  # Mpc^-3 yr^-1
1.5107979464621443e-08

merger_rate_density_bbh_primordial_ken2022(zs, n0=0.044 * 1e-09, t0=13.786885302009708, param=None)[source]

Function to compute the merger rate density (Primordial). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.

Parameters:

zsfloat: Source redshifts
n0float: normalization constant default: 0.044*1e-9
t0float: Present age of the Universe in Gyr default: 13.786885302009708
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(t0=13.786885302009708)

Returns:

rate_densityfloat: merger rate density

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> pop = SourceGalaxyPopulationModel(z_min=5, z_max=40, event_type = "BBH", merger_rate_density="merger_rate_density_bbh_primordial_ken2022")
>>> rate_density = pop.merger_rate_density(zs=10)
>>> rate_density  # Mpc^-3 yr^-1
9.78691173794454e-10

create_lookup_table(z_min, z_max, directory)[source]

Function to create a lookup table for the differential comoving volume and luminosity distance wrt redshift.

Parameters:

z_minfloat: Minimum redshift of the source population
z_maxfloat: Maximum redshift of the source population

Attributes:

z_to_luminosity_distancescipy.interpolate.interpolate: Function to convert redshift to luminosity distance
differential_comoving_volumescipy.interpolate.interpolate: Function to calculate the differential comoving volume

ler.gw_source_population.interpolator_from_pickle(param_dict_given, directory, sub_directory, name, x, pdf_func=None, y=None, conditioned_y=None, dimension=1, category='pdf', create_new=False)[source]

Function to decide which interpolator to use.

Parameters:

param_dict_givendict: dictionary of parameters.
directorystr: directory to store the interpolator.
sub_directorystr: sub-directory to store the interpolator.
namestr: name of the interpolator.
xnumpy.ndarray: x values.
pdf_funcfunction: function to calculate the pdf of x given y.
ynumpy.ndarray: y values.
conditioned_ynumpy.ndarray: conditioned y values.
dimensionint: dimension of the interpolator. Default is 1.
categorystr: category of the function. Default is “pdf”.
create_newbool: if True, create a new interpolator. Default is False.

Returns:

interpolatorfunction: interpolator function.

ler.gw_source_population.cubic_spline_interpolator(xnew, coefficients, x)[source]

Function to interpolate using cubic spline.

Parameters:

xnewnumpy.ndarray: new x values.
coefficientsnumpy.ndarray: coefficients of the cubic spline.
xnumpy.ndarray: x values.

Returns:

resultnumpy.ndarray: interpolated values.

class ler.gw_source_population.CBCSourceRedshiftDistribution(z_min=0.001, z_max=10.0, event_type='BBH', merger_rate_density='merger_rate_density_bbh_popI_II_oguri2018', merger_rate_density_param=None, cosmology=None, directory='./interpolator_pickle', create_new_interpolator=False)[source]

Bases: object

Class to generate a population of source galaxies. This class is inherited by CompactBinaryPopulation and LensGalaxyParameterDistribution class.

Parameters:

z_minfloat: Minimum redshift of the source population default: 0.
z_maxfloat: Maximum redshift of the source population default: 10.
event_typestr: Type of event to generate. e.g. ‘BBH’, ‘BNS’, ‘NSBH’
cosmologyastropy.cosmology: Cosmology to use default: None/astropy.cosmology.FlatLambdaCDM(H0=70, Om0=0.3)
merger_rate_densitystr or function: Type of merger rate density function to use default: ‘merger_rate_density_popI_II_oguri2018’ for others see instance method in merger_rate_density_model_list
merger_rate_density_paramdict: Dictionary of merger rate density function parameters default: None/dict(R0=25 * 1e-9, b2=1.6, b3=2.0, b4=30)
directorystr: Directory to store the interpolator pickle files default: ‘./interpolator_pickle’
create_new_interpolatordict: Dictionary of interpolator creation parameters default: None/dict(redshift_distribution=dict(create_new=False, resolution=500), z_to_luminosity_distance=dict(create_new=False, resolution=500), differential_comoving_volume=dict(create_new=False, resolution=500))

Examples

>>> from ler.gw_source_population import CBCSourceRedshiftDistribution
>>> cbc = CBCSourceRedshiftDistribution(z_min=0.001, z_max=10, merger_rate_density="merger_rate_density_bbh_popI_II_oguri2018")
>>> cbc.merger_rate_density(zs=0.0001) # local merger rate density at low redshift

Instance Attributes

SourceGalaxyPopulationModel has the following instance attributes:

Atrributes	Type
`z_min`	float
`z_max`	float
`event_type`	str
`cosmo`	astropy.cosmology
`merger_rate_density_param`	dict
`normalization_pdf_z`	float
`merger_rate_density_model_list`
	List of available merger rate density functions and its parameters
`sample_source_redshift`	Function to sample source redshifts (source frame)

Instance Methods

SourceGalaxyPopulationModel has the following instance methods:

Methods	Type
`merger_rate_density`	function
`z_to_luminosity_distance`	function
`differential_comoving_volume`	function
`pdf_z()`	Function to compute the pdf p(z)
`merger_rate_density_src_frame()`
	Function to compute the merger rate density (source frame)
`create_lookup_table()`	Function to create a lookup table for the differential comoving volume and luminosity distance wrt redshift
`merger_rate_density_bbh_popI_II_oguri2018()`
	Function to compute the merger rate density (PopI/PopII) from Oguri et al. (2018)
`star_formation_rate_madau_dickinson2014()`
	Function to compute star formation rate as given in Eqn. 15 Madau & Dickinson (2014)
`merger_rate_density_bbh_popIII_ken2022()`
	Function to compute the merger rate density (PopIII)
`merger_rate_density_bbh_primordial_ken2022()`
	Function to compute the merger rate density (Primordial)

property sample_source_redshift

Function to sample source redshifts (source frame) between z_min and z_max from the source galaxy population

Parameters:

sizeint: Number of samples to generate

Returns:

zs: Source redshifts

property merger_rate_density

Function to get the merger rate density function wrt redshift. The output is in detector frame and is unnormalized.

Parameters:

zsfloat: 1D array of floats Source redshifts

Returns:

merger_rate_densityfloat: merger rate density in detector frame (Mpc^-3 yr^-1)

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> cbc = SourceGalaxyPopulationModel()
>>> merger_rate_density = cbc.merger_rate_density(zs=0.1)

property merger_rate_density_model_list: Dictionary of available merger rate density functions and its parameters.

z_min

float

Minimum redshift of the source population

z_max

float

Maximum redshift of the source population

event_type

str

Type of event to generate.

e.g. ‘BBH’, ‘BNS’, ‘NSBH’

cosmo

astropy.cosmology

Cosmology to use for the redshift distribution.

e.g. Planck18, WMAP9, FlatLambdaCDM(H0=70, Om0=0.3) etc.

merger_rate_density_param

dict

Dictionary of merger rate density function input parameters

c_n_i

dict

c_n_i stands for ‘create new interpolator’. Dictionary of interpolator creation parameters.

e.g. dict(redshift_distribution=dict(create_new=False, resolution=500), z_to_luminosity_distance=dict(create_new=False, resolution=500), differential_comoving_volume=dict(create_new=False, resolution=500))

normalization_pdf_z

float

Normalization constant of the pdf p(z)

z_to_luminosity_distance

scipy.interpolate.interpolate

Function to convert redshift to luminosity distance

differential_comoving_volume

scipy.interpolate.interpolate

Function to calculate the differential comoving volume

pdf_z(zs, param=None)[source]

Function to compute the pdf p(z). The output is in source frame and is normalized.

Parameters:

zsfloat or numpy.ndarray (1D array of floats): Source redshifts
paramdict: Allows to pass in above parameters as dict. e.g. if the merger_rate_density is merger_rate_density_bbh_popI_II_oguri2018 param = dict(R0=23.9*1e-9, b2=1.6, b3=2.0, b4=30)

Returns:

pdfnumpy.ndarray: 1D array of floats pdf p(z)

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> cbc = SourceGalaxyPopulationModel()
>>> pdf = cbc.pdf_z(zs=0.1)

merger_rate_density_src_frame(zs, param=None)[source]

Function to compute the merger rate density (source frame). The output is in source frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (1D array of floats): Source redshifts
paramdict: Allows to pass in above parameters as dict. e.g. if the merger_rate_density is merger_rate_density_bbh_popI_II_oguri2018 param = dict(R0=23.9*1e-9, b2=1.6, b3=2.0, b4=30)

Returns:

rate_densitynumpy.ndarray: 1D array of floats merger rate density (source frame) (Mpc^-3 yr^-1)

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> cbc = SourceGalaxyPopulationModel()
>>> rate_density = cbc.merger_rate_density_src_frame(zs=0.1)

merger_rate_density_bbh_popI_II_oguri2018(zs, R0=23.9 * 1e-09, b2=1.6, b3=2.0, b4=30, param=None)[source]

Function to compute the merger rate density (PopI/PopII). Reference: Oguri et al. (2018). The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
R0float: local merger rate density at low redshift default: 23.9*1e-9 Mpc^-3 yr^-1
b2float: Fitting paramters default: 1.6
b3float: Fitting paramters default: 2.0
b4float: Fitting paramters default: 30
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(R0=23.9*1e-9, b2=1.6, b3=2.0, b4=30) default: None

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> pop = SourceGalaxyPopulationModel(z_min=0.0, z_max=10, event_type = "BBH", merger_rate_density="merger_rate_density_bbh_popI_II_oguri2018")
>>> rate_density = pop.merger_rate_density(zs=0.1)

star_formation_rate_madau_dickinson2014(zs, af=2.7, bf=5.6, cf=2.9, param=None)[source]

Function to compute star formation rate as given in Eqn. 15 Madau & Dickinson (2014). The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
affloat: Fitting paramters default: 2.7
bffloat: Fitting paramters default: 5.6
cffloat: Fitting paramters default: 2.9
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(af=2.7, bf=5.6, cf=2.9) default: None

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> pop = SourceGalaxyPopulationModel(z_min=5., z_max=40., event_type = "BBH", merger_rate_density="star_formation_rate_madau_dickinson2014")
>>> rate_density = pop.merger_rate_density(zs=10)

merger_rate_density_bbh_popIII_ken2022(zs, n0=19.2 * 1e-09, aIII=0.66, bIII=0.3, zIII=11.6, param=None)[source]

Function to compute the unnormalized merger rate density (PopIII). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
n0float: normalization constant default: 19.2*1e-9
aIIIfloat: Fitting paramters default: 0.66
bIIIfloat: Fitting paramters default: 0.3
zIIIfloat: Fitting paramters default: 11.6
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(aIII=0.66, bIII=0.3, zIII=11.6) default: None

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> pop = SourceGalaxyPopulationModel(z_min=5, z_max=40, event_type = "BBH", merger_rate_density="merger_rate_density_popIII_ken2022")
>>> rate_density = pop.merger_rate_density(zs=10)
>>> rate_density  # Mpc^-3 yr^-1
1.5107979464621443e-08

merger_rate_density_bbh_primordial_ken2022(zs, n0=0.044 * 1e-09, t0=13.786885302009708, param=None)[source]

Function to compute the merger rate density (Primordial). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.

Parameters:

zsfloat: Source redshifts
n0float: normalization constant default: 0.044*1e-9
t0float: Present age of the Universe in Gyr default: 13.786885302009708
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(t0=13.786885302009708)

Returns:

rate_densityfloat: merger rate density

Examples

>>> from ler.gw_source_population import SourceGalaxyPopulationModel
>>> pop = SourceGalaxyPopulationModel(z_min=5, z_max=40, event_type = "BBH", merger_rate_density="merger_rate_density_bbh_primordial_ken2022")
>>> rate_density = pop.merger_rate_density(zs=10)
>>> rate_density  # Mpc^-3 yr^-1
9.78691173794454e-10

create_lookup_table(z_min, z_max, directory)[source]

Function to create a lookup table for the differential comoving volume and luminosity distance wrt redshift.

Parameters:

z_minfloat: Minimum redshift of the source population
z_maxfloat: Maximum redshift of the source population

Attributes:

z_to_luminosity_distancescipy.interpolate.interpolate: Function to convert redshift to luminosity distance
differential_comoving_volumescipy.interpolate.interpolate: Function to calculate the differential comoving volume

ler.gw_source_population.lognormal_distribution_2D(size, m_min=1.0, m_max=100.0, Mc=20.0, sigma=0.3, chunk_size=10000)[source]

Function to sample from a lognormal distribution in 2D space. Reference: Ng et al. 2022. This a helper function for popIII BBH and primordial BBH merger rate density distribution functions.

Parameters:

sizeint: Number of samples to draw
m_minfloat: Minimum mass default: 1.0
m_maxfloat: Maximum mass default: 100.0
Mcfloat: Mass scale default: 20.0
sigmafloat: width of the distribution default: 0.3
chunk_sizeint: Number of samples to draw in each chunk default: 10000

Returns:

m1_samplenumpy.ndarray (1D array of floats): Mass of the primary
m2_samplenumpy.ndarray (1D array of floats): Mass of the secondary

Examples

>>> from ler.gw_source_population import lognormal_distribution_2D
>>> m1_sample, m2_sample = lognormal_distribution_2D(size=1000)

ler.gw_source_population.inverse_transform_sampler_m1m2(size, inv_cdf, x)[source]

Function to sample from a distribution using inverse transform sampling. This is a helper function BNS Alsing mass distribution function.

Parameters:

sizeint: Number of samples to draw
inv_cdfnumpy.ndarray (1D array of floats): Inverse cumulative distribution function
xnumpy.ndarray (1D array of floats): array of mass values for which the inverse cumulative distribution function is computed

Returns:

m1numpy.ndarray (1D array of floats): Mass of the primary
m2numpy.ndarray (1D array of floats): Mass of the secondary

Examples

>>> from ler.gw_source_population import inverse_transform_sampler_m1m2
>>> m1, m2 = inverse_transform_sampler_m1m2(size=1000, inv_cdf=inv_cdf, x=x)

class ler.gw_source_population.CBCSourceParameterDistribution(z_min=0.0, z_max=10.0, event_type='BBH', source_priors=None, source_priors_params=None, cosmology=None, spin_zero=True, spin_precession=False, directory='./interpolator_pickle', create_new_interpolator=False)[source]

Bases: ler.gw_source_population.cbc_source_redshift_distribution.CBCSourceRedshiftDistribution

Class to generate a population of compact binaries. It helps sample all the intrinsic and extrinsic parameters of compact binaries. This daughter class inherits from CBCSourceRedshiftDistribution class.

Parameters:

z_minfloat: Minimum redshift of the source population default: 0.001
z_maxfloat: Maximum redshift of the source population default: 10.
event_typestr: Type of event to generate. e.g. ‘BBH’, ‘BNS’, ‘NSBH’
source_priors, source_priors_paramsdict, dict: Dictionary of prior sampler functions and its input parameters. Check for available priors and corresponding input parameters by running, >>> from ler.gw_source_population import CBCSourceParameterDistribution >>> cbc = CompactBinaryPopulation() >>> cbc.available_gw_prior_list_and_its_params() # To check the current chosen priors and its parameters, run, >>> print(“default priors=”,cbc.gw_param_samplers) >>> print(“default priors’s parameters=”,cbc.gw_param_samplers_params)
cosmologyastropy.cosmology: Cosmology to use default: None/astropy.cosmology.FlatLambdaCDM(H0=70, Om0=0.3)
spin_zerobool: If True, spin parameters are completely ignore in the sampling. default: True
spin_precessionbool: If spin_zero=True and spin_precession=True, spin parameters are sampled for precessing binaries. if spin_zero=True and spin_precession=False, spin parameters are sampled for aligned/anti-aligned spin binaries. default: False
directorystr: Directory to store the interpolator pickle files default: ‘./interpolator_pickle’
create_new_interpolatordict: Dictionary of boolean values and resolution to create new interpolator. default: dict(redshift_distribution=dict(create_new=False, resolution=500), z_to_luminosity_distance=dict(create_new=False, resolution=500), differential_comoving_volume=dict(create_new=False, resolution=500))

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CBCSourceParameterDistribution()
>>> params = cbc.sample_gw_parameters(size=1000)
>>> print("sampled parameters=",list(params.keys()))

Instance Attributes

CompactBinaryPopulation has the following instance attributes:

Instance Methods

CompactBinaryPopulation has the following instance methods:

Methods	Type
`source_priors_categorization()`
	Function to categorize the event priors and its parameters
`lookup_table_luminosity_distance()` Function to create a lookup table for converting redshift to luminosity distance
`sample_gw_parameters()`	Function to sample all the intrinsic and extrinsic parameters of compact binaries
`sample_source_frame_masses()`	Function to sample source mass1 and mass2
`sample_geocent_time()`	Function to sample geocent time
`sample_zs()`	Function to sample source redshift
`sample_ra()`	Function to sample right ascension (sky position)
`sample_dec()`	Function to sample declination (sky position)
`sample_phase()`	Function to sample coalescence phase
`sample_psi()`	Function to sample polarization angle
`sample_theta_jn()`	Function to sample inclination angle
`sample_a1()`	Function to sample spin1 magnitude
`sample_a2()`	Function to sample spin2 magnitude
`sample_tilt_1()`	Function to sample tilt1 angle
`sample_tilt_2()`	Function to sample tilt2 angle
`sample_phi_12()`	Function to sample phi12 angle
`sample_phi_jl()`	Function to sample phi_jl angle
`binary_masses_BBH_popI_II_powerlaw_gaussian()`
	Function to sample source mass1 and mass2 with PowerLaw+PEAK model
`binary_masses_BBH_popIII_lognormal()`
	Function to sample source mass1 and mass2 with popIII orgin from lognormal distribution. Refer to Ng et al. 2022. Eqn. 1 and 4
`binary_masses_BBH_primordial_lognormal()`
	Function to sample source mass1 and mass2 with primordial orgin from lognormal distribution. Refer to Ng et al. 2022. Eqn. 1 and 4
`binary_masses_BNS_gwcosmo()`
	Function to sample source mass1 and mass2 from powerlaw distribution.
`binary_masses_BNS_bimodal()`	Function to sample source mass1 and mass2 from bimodal distribution. Refer to Will M. Farr et al. 2020 Eqn. 6
`constant_values_n_size()`	Function to return array of constant values of size n
`sampler_uniform()`	Function to sample from uniform distribution

property available_gw_prior_list_and_its_params

Dictionary with list all the available priors and it’s corresponding parameters. This is an immutable instance attribute.

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CompactBinaryPopulation()
>>> priors = cbc.available_gw_prior_list_and_its_params
>>> priors.keys()  # type of priors
dict_keys(['merger_rate_density', 'source_frame_masses', 'spin', 'geocent_time', 'ra', 'phase', 'psi', 'theta_jn'])
>>> priors['source_frame_masses'].keys()  # type of source_frame_masses priors
dict_keys(['binary_masses_BBH_popI_II_powerlaw_gaussian', 'binary_masses_BBH_popIII_lognormal', 'binary_masses_BBH_primordial_lognormal', 'binary_masses_BNS_gwcosmo', 'binary_masses_BNS_bimodal'])
>>> priors['source_frame_masses']['binary_masses_BBH_popI_II_powerlaw_gaussian'].keys()  # parameters of binary_masses_BBH_popI_II_powerlaw_gaussian
dict_keys(['mminbh', 'mmaxbh', 'alpha', 'mu_g', 'sigma_g', 'lambda_peak', 'delta_m', 'beta'])

property sample_zs

Function to sample redshifts with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

zsnumpy.ndarray (1D array of floats): Array of redshifts

property sample_source_frame_masses

Function to sample source frame masses (mass1_source, mass2_source) with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

mass_1_sourcenumpy.ndarray (1D array of floats): Array of mass1 in source frame
mass_2_sourcenumpy.ndarray (1D array of floats): Array of mass2 in source frame

property sample_geocent_time

Function to sample geocent time with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

geocent_timenumpy.ndarray (1D array of floats): Array of geocent_time or time of coalescence

property sample_ra

Function to sample right ascension of sky position with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

ranumpy.ndarray (1D array of floats): Array of right ascension of sky position

property sample_dec

Function to sample declination of sky position with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

decnumpy.ndarray (1D array of floats): Array of declination of sky position

property sample_phase

Function to sample coalescence phase with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

phasenumpy.ndarray (1D array of floats): Array of coalescence phase

property sample_psi

Function to sample polarization angle with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

psinumpy.ndarray (1D array of floats): Array of polarization angle

property sample_theta_jn

Function to sample theta_jn with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

theta_jnnumpy.ndarray (1D array of floats): Array of theta_jn

property sample_a_1

Function to sample spin magnitude of the compact binaries (body1) with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

a_1numpy.ndarray (1D array of floats): Array of spin magnitude of the compact binaries (body1)

property sample_a_2

Function to sample spin magnitude of the compact binaries (body2) with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

a_2numpy.ndarray (1D array of floats): Array of spin magnitude of the compact binaries (body2)

property sample_tilt_1

Function to sample tilt angle of the compact binaries (body1) with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

tilt_1numpy.ndarray (1D array of floats): Array of tilt angle of the compact binaries (body1)

property sample_tilt_2

Function to sample tilt angle of the compact binaries (body2) with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

tilt_2numpy.ndarray (1D array of floats): Array of tilt angle of the compact binaries (body2)

property sample_phi_12

Function to sample azimuthal angle between the two spins with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

phi_12numpy.ndarray (1D array of floats): Array of azimuthal angle between the two spins

property sample_phi_jl

Function to sample azimuthal angle between the total angular momentum and the orbital angular momentum with the initialized prior.

Parameters:

sizeint: Number of samples to draw

Returns:

phi_jlnumpy.ndarray (1D array of floats): Array of azimuthal angle between the total angular momentum and the orbital angular momentum

z_min

float

Minimum redshift of the source population

z_max

float

Maximum redshift of the source population

event_type

str

Type of event to generate.

e.g. ‘BBH’, ‘BNS’, ‘NSBH’

source_priors

dict

Dictionary of prior sampler functions.

source_priors_params

dict

Dictionary of prior sampler functions’ input parameters.

cosmo

astropy.cosmology

Cosmology to use.

spin_zero

bool

If True, spin prior is set to zero.

lookup_table_luminosity_distance(z_min, z_max, directory)[source]

Function to create a lookup table for the differential comoving volume and luminosity distance wrt redshift.

Parameters:

z_minfloat: Minimum redshift of the source population
z_maxfloat: Maximum redshift of the source population

Attributes:

z_to_luminosity_distancescipy.interpolate.interpolate: Function to convert redshift to luminosity distance
differential_comoving_volumescipy.interpolate.interpolate: Function to calculate the differential comoving volume

sample_gw_parameters(size=1000, param=None)[source]

Function to sample BBH/BNS/NSBH intrinsic and extrinsics parameters.

Parameters:

sizeint: Number of samples to draw

Returns:

gw_parametersdict: Dictionary of sampled parameters gw_parameters.keys() = [‘mass_1’, ‘mass_2’, ‘mass_1_source’, ‘mass_2_source’, ‘zs’, ‘luminosity_distance’, ‘theta_jn’, ‘psi’, ‘phase’, ‘geocent_time’, ‘ra’, ‘dec’, ‘a_1’, ‘a_2’, ‘tilt_1’, ‘tilt_2’, ‘phi_12’, ‘phi_jl’]

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CBCSourceParameterDistribution()
>>> params = cbc.sample_gw_parameters(size=1000)
>>> print("sampled parameters=",list(params.keys()))

binary_masses_BBH_popI_II_powerlaw_gaussian(size, mminbh=4.98, mmaxbh=112.5, alpha=3.78, mu_g=32.27, sigma_g=3.88, lambda_peak=0.03, delta_m=4.8, beta=0.81, get_attribute=False, param=None)[source]

Function to sample source mass1 and mass2 with PowerLaw+PEAK model

Parameters:

sizeint: Number of samples to draw
mminbhfloat: Minimum mass of the black hole (Msun) default: 4.98
mmaxbhfloat: Maximum mass of the black hole (Msun) default: 86.22
alphafloat: Spectral index for the powerlaw of the primary mass distribution default: 2.63
mu_gfloat: Mean of the Gaussian component in the primary mass distribution default: 33.07
sigma_gfloat: Width of the Gaussian component in the primary mass distribution default: 5.69
lambda_peakfloat: Fraction of the model in the Gaussian component default: 0.10
delta_mfloat: Range of mass tapering on the lower end of the mass distribution default: 4.82
betafloat: Spectral index for the powerlaw of the mass ratio distribution
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(mminbh=4.98, mmaxbh=86.22, alpha=2.63, mu_g=33.07, sigma_g=5.69, lambda_peak=0.10, delta_m=4.82, beta=1.26)

Returns:

mass_1_sourcenumpy.ndarray (1D array of floats): Array of mass1 in source frame (Msun)
mass_2_sourcenumpy.ndarray (1D array of floats): Array of mass2 in source frame (Msun)

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CBCSourceParameterDistribution()
>>> m1_src, m2_src = cbc.binary_masses_BBH_popI_II_powerlaw_gaussian(size=1000)

binary_masses_BBH_popIII_lognormal(size, m_min=5.0, m_max=150.0, Mc=30.0, sigma=0.3, chunk_size=10000, get_attribute=False, param=None)[source]

Function to sample source mass1 and mass2 with pop III origin. Refer to Eqn. 1 and 4 of Ng et al. 2022

Parameters:

sizeint: Number of samples to draw
m_minfloat: Minimum mass of the black hole (popIII) (Msun) default: 10.
m_maxfloat: Maximum mass of the black hole (popIII) (Msun) default: 100.
Mcfloat: Mass scale; the distribution is centered around Mc default: 30.0
sigmafloat: Width of the distribution default: 0.3
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(m_min=10., m_max=100., Mc=30.0, sigma=0.3)

Returns:

mass_1_sourcenumpy.ndarray (1D array of floats): Array of mass1 in source frame (Msun)
mass_2_sourcenumpy.ndarray (1D array of floats): Array of mass2 in source frame (Msun)

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CBCSourceParameterDistribution()
>>> m1_src, m2_src = cbc.binary_masses_BBH_popIII_lognormal(size=1000)

binary_masses_BBH_primordial_lognormal(size, m_min=1.0, m_max=100.0, Mc=20.0, sigma=0.3, chunk_size=10000, get_attribute=False, param=None)[source]

Function to sample source mass1 and mass2 with primordial origin. Refer to Eqn. 1 and 4 of Ng et al. 2022

Parameters:

sizeint: Number of samples to draw
m_minfloat: Minimum mass of the black hole (primordial) (Msun) default: 10.
m_maxfloat: Maximum mass of the black hole (primordial) (Msun) default: 100.
Mc, sigmafloat: Fitting parameters default: Mc=30.0, sigma=0.3
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(m_min=10., m_max=100., Mc=30.0, sigma=0.3)

Returns:

mass_1_sourcenumpy.ndarray (1D array of floats): Array of mass1 in source frame (Msun)
mass_2_sourcenumpy.ndarray (1D array of floats): Array of mass2 in source frame (Msun)

binary_masses_BNS_gwcosmo(size, mminns=1.0, mmaxns=3.0, alphans=0.0, get_attribute=False, param=None)[source]

Function to calculate source mass1 and mass2 of BNS from powerlaw distribution (gwcosmo)

Parameters:

sizeint: Number of samples to draw
mminnsfloat: Minimum mass of the BNS (Msun) default: 1.0
mmaxnsfloat: Maximum mass of the BNS (Msun) default: 3.0
alphansfloat: Power law index default: 0.0

Returns:

mass_1_sourcenumpy.ndarray (1D array of floats): Array of mass1 in source frame (Msun)
mass_2_sourcenumpy.ndarray (1D array of floats): Array of mass2 in source frame (Msun)

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CBCSourceParameterDistribution()
>>> m1_src, m2_src = cbc.binary_masses_BNS_gwcosmo(size=1000)

binary_masses_NSBH_broken_powerlaw(size, mminbh=26, mmaxbh=125, alpha_1=6.75, alpha_2=6.75, b=0.5, delta_m=5, mminns=1.0, mmaxns=3.0, alphans=0.0, get_attribute=False, param=None)[source]

Function to calculate source mass1 and mass2 of NSBH from powerlaw distribution (gwcosmo). Parameters are mminbh=26,mmaxbh=125,alpha_1=6.75,alpha_2=6.75,b=0.5,delta_m=5,mminns=1.0,mmaxns=3.0,alphans=0.0.

Parameters:

sizeint: Number of samples to draw
mminbhfloat: Minimum mass of the black hole (Msun) default: 26
mmaxbhfloat: Maximum mass of the black hole (Msun) default: 125
alpha_1float: Power law index for the primary mass distribution default: 6.75
alpha_2float: Power law index for the secondary mass distribution default: 6.75
bfloat: Break point of the power law default: 0.5
delta_mfloat: Range of mass tapering on default: 5
mminnsfloat: Minimum mass of the neutron star (Msun) default: 1.0
mmaxnsfloat: Maximum mass of the neutron star (Msun) default: 3.0
alphansfloat: Power law index for the neutron star mass distribution default: 0.0
get_attributebool: If True, return a sampler function with size as the only input where parameters are fixed to the given values.
paramdict: Allows to pass in above parameters as dict.

Returns:

mass_1_sourcenumpy.ndarray (1D array of floats): Array of mass1 in source frame (Msun)
mass_2_sourcenumpy.ndarray (1D array of floats): Array of mass2 in source frame (Msun)

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CBCSourceParameterDistribution()
>>> m1_src, m2_src = cbc.binary_masses_NSBH_broken_powerlaw(size=1000)

binary_masses_uniform(size, m_min=1.0, m_max=3.0, get_attribute=False, param=None)[source]

Function to sample source mass1 and mass2 from uniform distribution.

Parameters:

sizeint: Number of samples to draw
m_minfloat: Minimum mass of the BNS default: 1.0
m_maxfloat: Maximum mass of the BNS default: 3.0
get_attributebool: If True, return a sampler function with size as the only input where parameters are fixed to the given values.
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(m_min=1.0, m_max=3.0)

Returns:

mass_1_sourcenumpy.ndarray (1D array of floats): Array of mass1 in source frame (Msun)
mass_2_sourcenumpy.ndarray (1D array of floats): Array of mass2 in source frame (Msun)

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CBCSourceParameterDistribution()
>>> m1_src, m2_src = cbc.binary_masses_uniform(size=1000)

binary_masses_BNS_bimodal(size, w=0.643, muL=1.352, sigmaL=0.08, muR=1.88, sigmaR=0.3, mmin=1.0, mmax=2.3, resolution=500, create_new=False, get_attribute=False, param=None)[source]

Function to sample source mass1 and mass2 from bimodal distribution. Refer to Will M. Farr et al. 2020 Eqn. 6, https://arxiv.org/pdf/2005.00032.pdf .

Parameters:

sizeint: Number of samples to draw
wfloat: Weight of the left peak default: 0.643
muLfloat: Mean of the left peak default: 1.352
sigmaLfloat: Width of the left peak default: 0.08
muRfloat: Mean of the right peak default: 1.88
sigmaRfloat: Width of the right peak default: 0.3
mminfloat: Minimum mass of the BNS default: 1.0
mmaxfloat: Maximum mass of the BNS default: 2.3
resolutionint: Number of points to sample default: 500
create_newbool: If True, create new interpolator default: False
get_attributebool: If True, return a sampler function with size as the only input where parameters are fixed to the given values.
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(w=0.643, muL=1.352, sigmaL=0.08, muR=1.88, sigmaR=0.3, mmin=1.0, mmax=2.3, resolution=500)

Returns:

mass_1_sourcenumpy.ndarray (1D array of floats): Array of mass1 in source frame (Msun)
mass_2_sourcenumpy.ndarray (1D array of floats): Array of mass2 in source frame (Msun)

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CBCSourceParameterDistribution()
>>> m1_src, m2_src = cbc.binary_masses_BNS_bimodal(size=1000)

constant_values_n_size(size=100, value=0.0, get_attribute=False, param=None)[source]

Function to sample constant values of size n.

Parameters:

sizeint: Number of samples to draw
valuefloat: Constant value default: 0.0
get_attributebool: If True, return the njitted sampler function with size as the only input where parameters are fixed to the given values.
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(value=0.0)

Returns:

valuesnumpy.ndarray (1D array of floats): Array of constant values

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CBCSourceParameterDistribution()
>>> value = cbc.constant_values_n_size(size=1000)

sampler_uniform(size, min_=0, max_=np.pi, get_attribute=False, param=None)[source]

Function to sample values from uniform distribution.

Parameters:

sizeint: Number of samples to draw
start_timefloat: Start time of the uniform distribution default: 1238166018
end_timefloat: End time of the uniform distribution default: 1238166018 + 31536000
get_attributebool: If True, return the njitted sampler function with size as the only input where parameters are fixed to the given values.
paramdict: Allows to pass in above parameters as dict.

Returns:

valuesnumpy.ndarray (1D array of floats): Array of uniformly distributed values in the range of [min_, max_]

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CBCSourceParameterDistribution()
>>> value = cbc.sampler_uniform(size=1000)

sampler_cosine(size, get_attribute=False, param=None)[source]

Function to sample from sine distribution at the limit of [-np.pi/2, np.pi/2]

Parameters:

sizeint: Number of samples to draw
get_attributebool: If True, return the njitted sampler function with size as the only input where parameters are fixed to the given values.
paramNone: This parameter is not used. It is only here to make the function signature consistent with other samplers.

Returns:

sinenumpy.ndarray (1D array of floats): Array of values in the range of [-np.pi/2, np.pi/2]

sampler_sine(size, get_attribute=False, param=None)[source]

Function to sample from sine distribution at the limit of [0, np.pi]

Parameters:

sizeint: Number of samples to draw
get_attributebool: If True, return the njitted sampler function with size as the only input where parameters are fixed to the given values.
paramNone: This parameter is not used. It is only here to make the function signature consistent with other samplers.

Returns:

sinenumpy.ndarray (1D array of floats): Array of values in the range of [0, np.pi]

source_priors_categorization(event_type, source_priors, event_prior_params)[source]

Function to categorize the event priors and its parameters.

Parameters:

event_typestr: Type of event to generate. e.g. ‘BBH’, ‘BNS’, ‘BBH_popIII’, ‘BBH_primordial’, ‘NSBH’
source_priorsdict: Dictionary of prior sampler functions for each parameter
event_prior_paramsdict: Dictionary of sampler parameters for each GW parameter

Returns:

source_priors_dict: Dictionary of prior sampler functions for each parameter
event_prior_params_dict: Dictionary of sampler parameters for each parameter
sampler_names_dict: Dictionary of sampler names with description

Examples

>>> from ler.gw_source_population import CBCSourceParameterDistribution
>>> cbc = CBCSourceParameterDistribution()
>>> source_priors, event_prior_params, sampler_names = cbc.source_priors_categorization(event_type='BBH', source_priors=None, event_prior_params=None)
>>> print(source_priors.keys())
>>> print(event_prior_params.keys())
>>> print(sampler_names.keys())

ler.gw_source_population.inverse_transform_sampler(size, cdf, x)[source]

Function to sample from the inverse transform method.

Parameters:

sizeint: number of samples.
cdfnumpy.ndarray: cdf values.
xnumpy.ndarray: x values.

Returns:

samplesnumpy.ndarray: samples from the cdf.

ler.gw_source_population.merger_rate_density_bbh_popI_II_oguri2018(zs, R0=23.9 * 1e-09, b2=1.6, b3=2.0, b4=30)[source]

Function to compute the merger rate density (PopI/PopII). Reference: Oguri et al. (2018). The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
R0float: local merger rate density at low redshift default: 23.9*1e-9 Mpc^-3 yr^-1
b2float: Fitting paramters default: 1.6
b3float: Fitting paramters default: 2.0
b4float: Fitting paramters default: 30

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import merger_rate_density_bbh_popI_II_oguri2018
>>> rate_density = merger_rate_density_bbh_popI_II_oguri2018(zs=0.1)

ler.gw_source_population.merger_rate_density_bbh_popIII_ken2022(zs, n0=19.2 * 1e-09, aIII=0.66, bIII=0.3, zIII=11.6)[source]

Function to compute the unnormalized merger rate density (PopIII). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
n0float: normalization constant default: 19.2*1e-9
aIIIfloat: Fitting paramters default: 0.66
bIIIfloat: Fitting paramters default: 0.3
zIIIfloat: Fitting paramters default: 11.6

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import merger_rate_density_bbh_popIII_ken2022
>>> rate_density = merger_rate_density_bbh_popIII_ken2022(zs=0.1)

ler.gw_source_population.star_formation_rate_madau_dickinson2014(zs, af=2.7, bf=5.6, cf=2.9)[source]

Function to compute star formation rate as given in Eqn. 15 Madau & Dickinson (2014). The output is in detector frame and is unnormalized.

Parameters:

zsfloat or numpy.ndarray (nD array of floats): Source redshifts
affloat: Fitting paramters default: 2.7
bffloat: Fitting paramters default: 5.6
cffloat: Fitting paramters default: 2.9

Returns:

rate_densityfloat or numpy.ndarray (nD array of floats): merger rate density

Examples

>>> from ler.gw_source_population import star_formation_rate_madau_dickinson2014
>>> rate_density = star_formation_rate_madau_dickinson2014(zs=0.1)

ler.gw_source_population.merger_rate_density_bbh_primordial_ken2022(zs, cosmology=cosmo, n0=0.044 * 1e-09, t0=13.786885302009708)[source]

Function to compute the merger rate density (Primordial). Reference: Ng et al. 2022. The output is in detector frame and is unnormalized.

Parameters:

zsfloat: Source redshifts
n0float: normalization constant default: 0.044*1e-9
t0float: Present age of the Universe in Gyr default: 13.786885302009708
paramdict: Allows to pass in above parameters as dict. e.g. param = dict(t0=13.786885302009708)

Returns:

rate_densityfloat: merger rate density

ler.gw_source_population.lognormal_distribution_2D(size, m_min=1.0, m_max=100.0, Mc=20.0, sigma=0.3, chunk_size=10000)[source]

Function to sample from a lognormal distribution in 2D space. Reference: Ng et al. 2022. This a helper function for popIII BBH and primordial BBH merger rate density distribution functions.

Parameters:

sizeint: Number of samples to draw
m_minfloat: Minimum mass default: 1.0
m_maxfloat: Maximum mass default: 100.0
Mcfloat: Mass scale default: 20.0
sigmafloat: width of the distribution default: 0.3
chunk_sizeint: Number of samples to draw in each chunk default: 10000

Returns:

m1_samplenumpy.ndarray (1D array of floats): Mass of the primary
m2_samplenumpy.ndarray (1D array of floats): Mass of the secondary

Examples

>>> from ler.gw_source_population import lognormal_distribution_2D
>>> m1_sample, m2_sample = lognormal_distribution_2D(size=1000)

ler.gw_source_population.inverse_transform_sampler_m1m2(size, inv_cdf, x)[source]

Function to sample from a distribution using inverse transform sampling. This is a helper function BNS Alsing mass distribution function.

Parameters:

sizeint: Number of samples to draw
inv_cdfnumpy.ndarray (1D array of floats): Inverse cumulative distribution function
xnumpy.ndarray (1D array of floats): array of mass values for which the inverse cumulative distribution function is computed

Returns:

m1numpy.ndarray (1D array of floats): Mass of the primary
m2numpy.ndarray (1D array of floats): Mass of the secondary

Examples

>>> from ler.gw_source_population import inverse_transform_sampler_m1m2
>>> m1, m2 = inverse_transform_sampler_m1m2(size=1000, inv_cdf=inv_cdf, x=x)

ler.gw_source_population

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`ler.gw_source_population`