popsynth.distributions package

Submodules

• popsynth.distributions.bpl_distribution module
• popsynth.distributions.cosmological_distribution module
• popsynth.distributions.delta_distribution module
• popsynth.distributions.flatland_distribution module
• popsynth.distributions.log10_normal_distribution module
• popsynth.distributions.log_normal_distribution module
• popsynth.distributions.pareto_distribution module
• popsynth.distributions.schechter_distribution module
• popsynth.distributions.spherical_distribution module
• popsynth.distributions.spiral_galaxy_distribution module

Module contents

class popsynth.distributions.SphericalDistribution(seed: int = 1234, name: str = 'sphere', form: str = None)

Bases: popsynth.distribution.SpatialDistribution

__init__(seed: int = 1234, name: str = 'sphere', form: str = None)

A generic spherical distribution. Can be inherited to form more complex spherical distributions

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• form (str) – Mathematical description of distribution

differential_volume(r)

The differential volume

Parameters:distance – Distance

transform(L, r)

The transform from luminosity to flux for the

Parameters:

• flux –
• distance –

Returns:

class popsynth.distributions.CosmologicalDistribution(seed: int = 1234, name: str = 'cosmo', form: str = None, truth: Dict[str, Any] = {}, is_rate: bool = True)

Bases: popsynth.distribution.SpatialDistribution

__init__(seed: int = 1234, name: str = 'cosmo', form: str = None, truth: Dict[str, Any] = {}, is_rate: bool = True)

Base class for cosmological spatial distributions.

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• form (str) – Mathematical description of distribution
• truth (dict[str, Any]) – True values of parameters
• is_rate (bool) – True if modelling a population of transient events, False if modelling a population of steady-state objects. Affects the time_adjustment method used in cosmo calculations. Default is True.

differential_volume(z)

Differential comoving volume in Gpc^3 sr^-1.

dV/dzdOmega

Parameters:z – Redshift Returns:The differential comoving volume in Gpc^-3 sr^-1.

time_adjustment(z)

Time adjustment factor to handle both transient and steady-state populations.

Parameters:z – Redshift Returns:Appropriate factor depending on is_rate

transform(L, z)

Transformation from luminosity to energy flux.

L / 4 pi dL^2

dL is in cm. Therefore for L in erg s^-1 returns flux in erg cm^-2 s^-1.

Parameters:

• L – Luminosity
• z – Redshift

Returns:

Flux

class popsynth.distributions.SFRDistribution(seed: int = 1234, name: str = 'sfr', is_rate: bool = True)

Bases: popsynth.distributions.cosmological_distribution.CosmologicalDistribution

__init__(seed: int = 1234, name: str = 'sfr', is_rate: bool = True)

A star-formation like distribution of the form presented in Cole et al. 2001.

r0``(``a``+``rise``z)/(1 + (z/``peak)^``decay``)

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• is_rate (bool) – True if modelling a population of transient events, False if modelling a population of steady-state objects. Affects the time_adjustment method used in cosmo calculations. Default is True.
• r0 (DistributionParameter) – The local density in units of Gpc^-3
• a (DistributionParameter) – Offset at z=0
• rise (DistributionParameter) – Rise at low z
• decay (DistributionParameter) – Decay at high z
• peak (DistributionParameter) – Peak of z distribution

a

dNdV(z)

The differential number of objects per volume element

Parameters:distance – Returns:

decay

peak

r0

rise

class popsynth.distributions.ZPowerCosmoDistribution(seed: int = 1234, name: str = 'zpow_cosmo', is_rate: bool = True)

Bases: popsynth.distributions.cosmological_distribution.CosmologicalDistribution

Lambda

__init__(seed: int = 1234, name: str = 'zpow_cosmo', is_rate: bool = True)

A cosmological distribution where the density evolves as a power law.

Lambda (1+z)^``delta``

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• is_rate (bool) – True if modelling a population of transient events, False if modelling a population of steady-state objects. Affects the time_adjustment method used in cosmo calculations. Default is True.
• Lambda (DistributionParameter) – The local density in units of Gpc^-3
• delta (DistributionParameter) – The index of the power law

dNdV(distance)

The differential number of objects per volume element

Parameters:distance – Returns:

delta

class popsynth.distributions.ParetoDistribution(seed: int = 1234, name: str = 'pareto')

Bases: popsynth.distribution.LuminosityDistribution

Lmin

__init__(seed: int = 1234, name: str = 'pareto')

A Pareto luminosity function.

alpha``*``Lmin``^``alpha / L^(``alpha``+1)

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• Lmin (DistributionParameter) – Minimum value of the luminosity
• alpha (DistributionParameter) – Index of the pareto distribution

alpha

draw_luminosity(size: int = 1)

function to draw the luminosity via an alternative method must be implemented in child class

Parameters:size – Returns:

phi(L)

The functional form of the distribution. not required for sampling :param luminosity: Luminosity

class popsynth.distributions.Log10NormalDistribution(seed: int = 1234, name: str = 'log10norm')

Bases: popsynth.distribution.LuminosityDistribution

__init__(seed: int = 1234, name: str = 'log10norm')

A log10-normal luminosity function

Log10Normal(mu, tau)

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• mu (DistributionParameter) – Mean of the log10 normal
• tau (DistributionParameter) – Standard deviation of the log10 normal

draw_luminosity(size=1)

function to draw the luminosity via an alternative method must be implemented in child class

Parameters:size – Returns:

mu

phi(L)

The functional form of the distribution. not required for sampling :param luminosity: Luminosity

tau

class popsynth.distributions.LogNormalDistribution(seed: int = 1234, name: str = 'lognorm')

Bases: popsynth.distribution.LuminosityDistribution

__init__(seed: int = 1234, name: str = 'lognorm')

A log-normal luminosity distribution.

LogNormal(mu, tau)

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• mu (DistributionParameter) – Mean of the log normal
• tau (DistributionParameter) – Standard deviation of the log normal

draw_luminosity(size=1)

function to draw the luminosity via an alternative method must be implemented in child class

Parameters:size – Returns:

mu

phi(L)

The functional form of the distribution. not required for sampling :param luminosity: Luminosity

tau

class popsynth.distributions.SchechterDistribution(seed: int = 1234, name: str = 'schechter')

Bases: popsynth.distribution.LuminosityDistribution

Lmin

__init__(seed: int = 1234, name: str = 'schechter')

A Schechter luminosity function as in Schechter, Astrophysical Journal, Vol. 203, p. 297-306 (1976).

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• Lmin (DistributionParameter) – Minimum value of the luminosity
• alpha (DistributionParameter) – Index of the distribution

alpha

draw_luminosity(size=1)

function to draw the luminosity via an alternative method must be implemented in child class

Parameters:size – Returns:

phi(L)

The functional form of the distribution. not required for sampling :param luminosity: Luminosity

class popsynth.distributions.BPLDistribution(seed: int = 1234, name: str = 'bpl')

Bases: popsynth.distribution.LuminosityDistribution

Lbreak

Lmax

Lmin

__init__(seed: int = 1234, name: str = 'bpl')

A broken power law luminosity distribution.

L ~ L^``alpha`` for L <= Lbreak L ~ L^``beta`` for L > Lbreak

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• Lmin (DistributionParameter) – Minimum value of the luminosity
• alpha (DistributionParameter) – Index of the lower power law
• Lbreak (DistributionParameter) – Luminosity of the power law break
• beta (DistributionParameter) – Index of the upper power law
• Lmax (DistributionParameter) – Maximum value of the luminosity

alpha

beta

draw_luminosity(size=1)

function to draw the luminosity via an alternative method must be implemented in child class

Parameters:size – Returns:

phi(L)

The functional form of the distribution. not required for sampling :param luminosity: Luminosity

class popsynth.distributions.SphericalDistribution(seed: int = 1234, name: str = 'sphere', form: str = None)

Bases: popsynth.distribution.SpatialDistribution

__init__(seed: int = 1234, name: str = 'sphere', form: str = None)

A generic spherical distribution. Can be inherited to form more complex spherical distributions

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• form (str) – Mathematical description of distribution

differential_volume(r)

The differential volume

Parameters:distance – Distance

transform(L, r)

The transform from luminosity to flux for the

Parameters:

• flux –
• distance –

Returns:

class popsynth.distributions.ConstantSphericalDistribution(seed: int = 1234, name: str = 'cons_sphere', form: str = None)

Bases: popsynth.distributions.spherical_distribution.SphericalDistribution

Lambda

__init__(seed: int = 1234, name: str = 'cons_sphere', form: str = None)

A spherical distribution with constant density.

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• form (str) – Mathematical description of distribution
• Lambda (DistributionParameter) – Density per unit volume

dNdV(distance)

The differential number of objects per volume element

Parameters:distance – Returns:

class popsynth.distributions.ZPowerSphericalDistribution(seed: int = 1234, name: str = 'zpow_sphere')

Bases: popsynth.distributions.spherical_distribution.ConstantSphericalDistribution

__init__(seed: int = 1234, name: str = 'zpow_sphere')

A spherical distribution with a power law density profile.

Lambda (1+r)^``delta``

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• form (str) – Mathematical description of distribution
• delta (DistributionParameter) – Index of power law distribution

dNdV(distance)

The differential number of objects per volume element

Parameters:distance – Returns:

delta

class popsynth.distributions.DeltaDistribution(seed: int = 1234, name: str = 'delta')

Bases: popsynth.distribution.LuminosityDistribution

Lp

__init__(seed: int = 1234, name: str = 'delta')

A delta function luminosity distribution, centred on Lp.

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• Lp (DistributionParameter) – The central value

draw_luminosity(size=1)

function to draw the luminosity via an alternative method must be implemented in child class

Parameters:size – Returns:

phi(L)

The functional form of the distribution. not required for sampling :param luminosity: Luminosity

class popsynth.distributions.FlatlandDistribution(seed: int = 1234, name: str = 'flatland', form: str = None)

Bases: popsynth.distribution.SpatialDistribution

Lambda

__init__(seed: int = 1234, name: str = 'flatland', form: str = None)

A flat spatial distribution with only length.

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• form (str) – Mathematical description of distribution
• Lambda (DistributionParameter) – Length

dNdV(distance)

The differential number of objects per volume element

Parameters:distance – Returns:

differential_volume(r)

The differential volume

Parameters:distance – Distance

transform(L, r)

The transform from luminosity to flux for the

Parameters:

• flux –
• distance –

Returns:

class popsynth.distributions.SpiralGalaxyDistribution(seed: int = 1234, name: str = 'spiral_galaxy', form: str = None)

Bases: popsynth.distributions.spherical_distribution.SphericalDistribution

R0

R1

__init__(seed: int = 1234, name: str = 'spiral_galaxy', form: str = None)

A spiral galaxy spatial distribution.

Parameters:

• seed (int) – Random seed
• name (str) – Name of the distribution
• form (str) – Mathematical description of distribution
• rho (DistributionParameter) – Local density
• a (DistributionParameter) – Shape parameter
• b (DistributionParameter) – Shape parameter
• R1 (DistributionParameter) – Scale parameter
• R0 (DistributionParameter) – Scale parameter

a

b

dNdV(r)

The differential number of objects per volume element

Parameters:distance – Returns:

draw_sky_positions(size)

Based on Wainscoat 1992 and Faucher-Giguere 2007.

Code thanks to Mortiz Pleintinger.

rho