Sources

kHz

From Earth we can detect following systems: stellar mass black hole mergers, binary neutron star mergers, stellar mass black hole - neutron star mergers. Each system is represented by its own class.

class gwtoolbox.sources_kHz.BHB(cosmos)[source]

This is a class to describe stellar mass black hole black hole mergers.

Parameters:cosmos – define cosmological model
MCMCsample(n_sources, inits, ranges, T, rho_cri, ant_fun, noise_tab)[source]

The Markov-chain-Monte-Carlo sampling according to the distribution ndet(M, eta, z).

Parameters:
  • n_sources (int) – number of sources to detect
  • inits (list of floats) – initial values of z, m1, m2, chi
  • ranges (list of list of floats) – parameter ranges
  • rho_cri (float) – The detection SNR threshold
  • ant_fun (function) – antenna pattern
  • noise_tab (array of dtype float) – noise function for detector
Returns:

samples of parameters Mchirp,z,m1,m2,chi,D
Return type:

(list of arrays of dtype float)
cos_mer_rate(z, m1, m2, chi)[source]

The cosmic merger rate density of the stellar-mass BHB mergers.

Parameters:
  • z (float) – The red-shift of the GW source
  • m1 (float) – Red-shifted masses of the BHB
  • m2 (float) – Red-shifted masses of the BHB
  • chi (float) – spin
Returns:

The number of mergers per year per Gpc3
Return type:

(float)
density_det(T, z, m1, m2, chi, rho_cri, ant_fun, noise_tab)[source]

The parameter distribution of detected sources.

Parameters:
  • T (float) – Observation time, in unit of minute
  • z (float) – The redshift of the GW source
  • m1 (float) – Red-shifted masses of the BHB
  • m2 (float) – Red-shifted masses of the BHB
  • chi (float) – spin
  • rho_cri (float) – The detection SNR threshold
  • ant_fun (function) – antenna pattern
  • noise_tab (array of dtype float) – noise function for detector
Returns:

Number density of detection
Return type:

(float)
errors_FIM(n_sources, samples, noise_tab)[source]

Return errors of parameters from Fisher Information Matrix

Parameters:
  • n_sources (int) – number of sources to detect
  • samples (list of arrays of dtype float) – sampled parameters
  • noise_tab (array of dtype float) – noise function for detector
Returns:

errors of sampled parameters m1,m2,chi
Return type:

(list of arrays of dtype float)
freq_limit(m1, m2, chi)[source]

The frequency upper limit of the waveform.

Parameters:
  • m1 (float) – The Red-shifted individual masses
  • m2 (float) – The Red-shifted individual masses
Returns:

The upper limit of the frequency
Return type:

(float)
mod_norm(Mch, F, iota, z)[source]

The normalization constant of the modulus of the GW waveform from stellar-mass binary black holes (BHB) mergers in frequency domain.

Parameters:
  • Mch (float) – Red-shifted chirp mass of the BHB in solar masses
  • F (array of dtype float) – The Antenna Patterns of the observatory
  • iota (float) – The inclination of the BHB orbit
  • z (float) – The redshift of the GW source
Returns:

The normalization of the GW strain
Return type:

(float)
mod_shape(f)[source]

The frequency dependence of the modulus of the GW waveform of BHB mergers.

Parameters:f (float or array of dtype float) – Frequencies of GW
Returns:The modulus of the waveform corresponds to each frequency in f
Return type:(float or array of dtype float)
partial(A, m1, m2, chi, t0, phi0)[source]

The matrix of partial derivatives of waveform as function of f

Parameters:
  • A (float or array of dtype float) – The modulus of h(f)
  • m1 (float) – Red-shifted masses of the BHB
  • m2 (float) – Red-shifted masses of the BHB
  • chi (float) – spin
  • t0 (float) – The time of coalescence
  • phi0 (float) – The phase of coalescence
Returns:

matrix of partial derivatives of (f,i,j), Pij(f)
Return type:

(function)
phase(f, m1, m2, chi, t0, phi0)[source]

The phase of the waveform of the stellar-mass BHB mergers in the frequency domain.

Parameters:
  • f (float or array of dtype float) – Frequencies of GW
  • m1 (float) – Red-shifted mass of the prime BH
  • m2 (float) – Red-shifted mass of the second BH
  • chi (float) – spin
  • t0 (float) – The time of coalescence
  • phi0 (float) – The phase of coalescence
Returns:

The phase psi(f) of the waveform as in exp^{−ipsi(f)}
Return type:

(array of dtype float)
set_model_theta(new_theta=None)[source]

The function to change theta from fiducial to user-defined in cosmic merger rate

Parameters:new_theta (Optional[list of floats]) – new parameter values
Returns:theta with new values, if new_theta=None return theta to fiducial
Return type:(list of floats)
tel_fun(z, m1, m2, chi, rho_cri, ant_fun, noise_tab)[source]

The telescope function of Laser Interferometers and kHz sources.

Parameters:
  • z (float) – The redshift of the GW source
  • m1 (float) – Red-shifted masses of the BHB
  • m2 (float) – Red-shifted masses of the BHB
  • chi (float) – spin
  • rho_cri (float) – The detection SNR threshold
  • ant_fun (function) – antenna pattern
  • noise_tab (array of dtype float) – noise function for detector
Returns:

The probability of detection
Return type:

(float)
tot_num(T, rho_cri, ant_fun, noise_tab, ranges)[source]

The total number of sources detected.

Parameters:
  • T (float) – Observation time, in unit of minutes
  • rho_cri (float) – The detection SNR threshold
  • ant_fun (function) – antenna pattern
  • noise_tab (array of dtype float) – noise function for detector
  • ranges (list) – parameter ranges
Returns:

The total number of sources detected
Return type:

(float)
class gwtoolbox.sources_kHz.DNS(cosmos)[source]

This is a class to describe double neutron stars mergers. It inherits all functions from BHB class except set_model_theta and cos_mer_rate.

Attributes: cosmos: define cosmological model

cos_mer_rate(z, m1, m2, chi)[source]

The cosmic merger rate density of the stellar-mass DNS mergers.

Parameters:
  • z (float) – The redshift of the GW source
  • m1 (float) – Red-shifted masses of the NS
  • m2 (float) – Red-shifted masses of the NS
  • chi (float) – spin
Returns:

The number of mergers per year per Gpc3
Return type:

(float)
set_model_theta(new_theta=None)[source]

The function to change theta from fiducial to user-defined.

Parameters:new_theta (Optional[list of floats]) – new parameter values
Returns:theta with new values, if new_theta=None return theta to fiducial
Return type:(list of floats)
class gwtoolbox.sources_kHz.BHNS(cosmos)[source]

This is a class to describe stellar mass black hole neutron stars mergers. It inherits all functions from BHB class except set_model_theta and cos_mer_rate.

Attributes: cosmos: define cosmological model

cos_mer_rate(z, M, m, chi)[source]

The cosmic merger rate density of the stellar-mass BHB mergers.

Parameters:
  • z (float) – The redshift of the GW source
  • M (float) – Red-shifted mass of the BH
  • m (float) – Red-shifted mass of the NS
  • chi (float) – spin
Returns:

The number of mergers per year per Gpc3
Return type:

(float)
set_model_theta(new_theta=None)[source]

The function to change theta from fiducial to user-defined.

Parameters:new_theta (Optional[list of floats]) – new parameter values
Returns:theta with new values, if new_theta=None return theta to fiducial
Return type:(list of floats)

mHz

From space we can observe: super massive black hole mergers, inspirals of binary stellar black hole mergers, inspirals of double neutron star mergers, inspirals of stellar black hole-neutron star mergers, and extreme mass ratio inspirals.

class gwtoolbox.sources_mHz.SMBHB(cosmos)[source]

This is a class to describe super massive black hole black hole mergers.

Parameters:cosmos – define cosmological model
class gwtoolbox.sources_mHz.EMRI(cosmos)[source]

This is a class to describe extreme mass ratio inspirals.

Parameters:cosmos – define cosmological model
class gwtoolbox.sources_mHz.Insp(cosmos)[source]

This is a class to describe inspirals

Parameters:cosmos – define cosmological model

nHz