constants – physical constants and cosmological calculations¶

The constants module contains attributes storing physical constants and conversion factors. Most of these are at the package level and should be imported as:

from astropysics.constants import c,G,ergperev

The following constants are included (all in cgs units):

G: Newton’s gravitational constant
mp: proton mass
me: electron mass
e: electron charge
Ms: solar mass
Mj: jupiter mass
Me: earth mass
Rs: solar radius
Rj: jupiter radius
Re: mean earth radius
Rea: equatorial earth radius (as defined by WGS84)
Reb: polar earth radius (as defined by WGS84)
Lsun: solar luminosity
kb: boltzmann’s constant
Rb: gas constant
c: speed of light - exact
h: planck’s constant
hbar: reduced planck’s constant
g0: mean earth gravitational acceleration at sea level

The following unit conversion factors are also provided:

ergperev
secperday
secperyr
secpergyr
cmperpc
pcpercm
lyperpc
pcperly
cmperau
aupercm
asecperrad
auperpc (same as asecperrad)

Additional, convinience or derived values include:

GMskm: Standard gravitational parameter for the sun in km^3 s^-2
GMsau: Standard gravitational parameter for the sun in AU km^2 s^-2
GMspc: Standard gravitational parameter for the sun in pc km^2 s^-2

The package also includes classes representing various cosmologies that are used to derive relevant cosmological parameters. The current default is the WMAP7Cosmology, based on the LCDM cosmology with parameters favored by WMAP7 .

The cosmological parameters for the builtin cosmologies are:

H0: Hubble’s constant (all cosmologies)
h: H0/100 (all cosmologies)
h7: H0/70 (all cosmologies)
omega: Total energy density as a fraction of the critical density (any FRW)
omegaR: radiataion desnity (any FRW)
omegaM: total matter density (any FRW)
omegaL: dark energy/cosmological constant density (any FRW)
omegaK: curvature density (any FRW)
sigma8: rmc density fluctuation amplitude at 8 Mpc/h (WMAP)
omegaB: Baryon density (WMAP)
omegaC: dark/non-baryonic matter density (WMAP)
ns: primordial power spectrum index (WMAP)
t0: Age of universe in Gyr (WMAP)

The currently active cosmology will export it’s parameters so they should be used in other modules as:

from astropysics.constants import H0,omega

Classes and Inheritance Structure¶

Inheritance diagram of astropysics.constants

Module API¶

class astropysics.constants.Cosmology¶

Bases: object

A base class for a cosmology - intended to be subclassed, as this cosmology only has a hubble constant.

Subclassing

All cosmologies should have a hubble constant (H0) in km/s/Mpc
Subclasses should also define a class variable _params with a list of strings that specify the names of the cosmological parameters for the subclasses cosmology. These will be exported to the constants module.
Error bars for parameters in _params can optional be specified as a class variable <paramname>_err. These should be a tuple (lowererr,uppererr)

H0 = 0¶: Hubble constant $H_0$ for this cosmology in units of km s^-1/Mpc.

getParamWithError(parname)¶

Returns the requested parameter’s value and its associated errors.

Parameters:	parname – The name of the parameter to be retrieved.
Returns:	A tuple `(parval,lowererr,uppererr)`

h¶: Reduced Hubble constant: $H_0/100$ .

h7¶: Reduced Hubble constant: $H_0/70$ .

h70¶: Reduced Hubble constant: $H_0/70$ .

params¶: Names of the cosmological parameters for this Cosmology.

class astropysics.constants.FRWCosmology¶

Bases: astropysics.constants.Cosmology

A cosmology based on the FRW metric with a global density, a matter density, and a radiation density, and a comological constant as specified at z=0

default values are approximately LambdaCDM

H(z)¶

H0 = 72¶

computeOmegaKz(z, units='cgs')¶: compute curvature density at arbitrary redshift

computeOmegaLz(z)¶: compute cosmological constant density at arbitrary redshift

computeOmegaMz(z)¶: compute matter density at arbitrary redshift

computeOmegaRz(z)¶: compute radiation density at arbitrary redshift

deltavir(z=0)¶

Virial overdensity asparamaterized in Bryan&Norman 98 for a given redshift.

Good to 1% for omega(z) = 0.1-1, requires either omega = 1 (flat universe) or omega_lambda = 0.

omega¶

omegaK¶

omegaL = 0.7¶

omegaM = 0.3¶

omegaR = 0¶

rho(z=0, units='cgs')¶

mean density in this cosmology

units can be ‘cgs’ or ‘cosmological’ (Mpc,Msun)

rhoC(z=0, units='cgs')¶

Computes the critical density at a given redshift, e.g.

$\rho_c = \frac{3 H(z)^2}{8 \pi G}$

Raises ValueError:
Parameters:	z (scalar or array) – redshift at which to compute critical density units (string) – ‘cgs’: g/cm^3 ‘cosmological’: Msun/Mpc^3
Returns:	Critical density in the requested units
	if an unrecognized units string is given

class astropysics.constants.SCDMCosmology¶

Bases: astropysics.constants.FRWCosmology

“Standard” CDM – flat, with no cosmological constant.

omegaL = 0¶

omegaM = 1.0¶

omegaR = 0¶

class astropysics.constants.WMAP3AllCosmology¶

Bases: astropysics.constants.FRWCosmology

WMAP3+all (http://lambda.gsfc.nasa.gov/product/map/dr2/params/lcdm_all.cfm)

H0 = 70.4¶

H0_err = (1.6, 1.5)¶

ns = 0.947¶

ns_err = 0.015¶

omegaB = 0.04266666666666667¶

omegaB_err = 0.0013¶

omegaC = 0.19766666666666668¶

omegaC_err = (0.0079, 0.0077)¶

omegaL = 0.7596666666666667¶

omegaL_err = 0.018¶

omegaM¶

omegaM_err¶

sigma8 = 0.776¶

sigma8_err = (0.032, 0.031)¶

class astropysics.constants.WMAP3Cosmology¶

Bases: astropysics.constants.FRWCosmology

WMAP3 only (http://lambda.gsfc.nasa.gov/product/map/dr2/params/lcdm_wmap.cfm)

H0 = 73.2¶

H0_err = (3.2, 3.1)¶

ns = 0.958¶

ns_err = 0.016¶

omegaB = 0.044¶

omegaB_err = 0.0014¶

omegaC = 0.224¶

omegaC_err = 0.014¶

omegaL = 0.732¶

omegaL_err = 0.034¶

omegaM¶

omegaM_err¶

sigma8 = 0.761¶

sigma8_err = (0.048, 0.049)¶

class astropysics.constants.WMAP5BAOSNCosmology¶

Bases: astropysics.constants.FRWCosmology

WMAP5+BAO+SN (http://lambda.gsfc.nasa.gov/product/map/dr3/parameters_summary.cfm)

H0 = 70.1¶

H0_err = 1.3¶

ns = 0.96¶

ns_err = (0.013, 0.014)¶

omegaB = 0.046¶

omegaB_err = 0.0015¶

omegaC = 0.233¶

omegaC_err = 0.013¶

omegaL = 0.721¶

omegaL_err = 0.015¶

omegaM¶

omegaM_err¶

sigma8 = 0.817¶

sigma8_err = 0.026¶

t0 = 13.73¶

t0_err = 0.12¶

class astropysics.constants.WMAP5Cosmology¶

Bases: astropysics.constants.FRWCosmology

WMAP5-only (http://lambda.gsfc.nasa.gov/product/map/dr3/parameters_summary.cfm)

H0 = 71.9¶

H0_err = (2.7, 2.6)¶

ns = 0.963¶

ns_err = (0.015, 0.014)¶

omegaB = 0.044¶

omegaB_err = 0.003¶

omegaC = 0.214¶

omegaC_err = 0.027¶

omegaL = 0.742¶

omegaL_err = 0.03¶

omegaM¶

omegaM_err¶

sigma8 = 0.796¶

sigma8_err = 0.036¶

t0 = 13.69¶

t0_err = 0.13¶

class astropysics.constants.WMAP7BAOH0Cosmology¶

Bases: astropysics.constants.FRWCosmology

WMAP7+BAO+H0 (http://lambda.gsfc.nasa.gov/product/map/dr4/params/lcdm_sz_lens_wmap7_bao_h0.cfm)

H0 = 70.4¶

H0_err = (1.4, 1.3)¶

ns = 0.963¶

ns_err = 0.012¶

omegaB = 0.045¶

omegaB_err = 0.0016¶

omegaC = 0.227¶

omegaC_err = 0.014¶

omegaL = 0.728¶

omegaL_err = (0.016, 0.015)¶

omegaM¶

omegaM_err¶

sigma8 = 0.809¶

sigma8_err = 0.024¶

t0 = 13.78¶

t0_err = 0.11¶

class astropysics.constants.WMAP7Cosmology¶

Bases: astropysics.constants.FRWCosmology

WMAP7-only (http://lambda.gsfc.nasa.gov/product/map/dr4/params/lcdm_sz_lens_wmap7.cfm)

H0 = 71.0¶

H0_err = 2.5¶

ns = 0.963¶

ns_err = 0.014¶

omegaB = 0.044¶

omegaB_err = 0.0028¶

omegaC = 0.222¶

omegaC_err = 0.026¶

omegaL = 0.734¶

omegaL_err = 0.029¶

omegaM¶

omegaM_err¶

sigma8 = 0.801¶

sigma8_err = 0.03¶

t0 = 13.71¶

t0_err = 0.13¶

astropysics.constants.choose_cosmology(nameorobj, autoupdate=True, args=None, kwargs=None)¶

Change the currently active cosmology and export its cosmological parameters into the package namespace.

Parameters:

nameorobj (string or Cosmology object) – the new cosmology to use
autoupdate (bool) – If True, the cosmology object will automatically propogate changes to its parameters up to the module variables. Otherwise, update_cosmology() must be called explicitly to have this behavior occur.
args (dictionary or None) – If nameorobj is a string, these are passed in as positional arguments to the object initializer (if not None). Otherwise it is ignored.
args – If nameorobj is a string, these are passed in as keyword arguments to the object initializer (if not None). Otherwise it is ignored.

Returns:

the Cosmology object after being assigned as current.

astropysics.constants.flambda_to_fnu_l(flambda, lamb)¶

astropysics.constants.flambda_to_fnu_n(flambda, nu)¶

astropysics.constants.fnu_to_flambda_l(fnu, lamb)¶

astropysics.constants.fnu_to_flambda_n(fnu, nu)¶

astropysics.constants.get_cosmology(name=None)¶: If name is None, will retreive the currently in use Cosmology instance. Otherwise, returns the subclass of Cosmology with the provided name.

astropysics.constants.get_registry_names()¶: Returns the names of all cosmology types in the registry

astropysics.constants.register_cosmology(cosmocls, name=None)¶

Add the provided subclass of Cosmology to the cosmology registry

if name is None, the name will be inferred from the class name, otherwise

astropysics.constants.update_cosmology()¶: updates the package-level variables for changes in the current Cosmology object

constants – physical constants and cosmological calculations¶

Classes and Inheritance Structure¶

Module API¶

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constants – physical constants and cosmological calculations¶

Classes and Inheritance Structure¶

Module API¶

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