Package astLib :: Module astCalc

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Module astCalc

module for performing common calculations

(c) 2007-2009 Matt Hilton

http://astlib.sourceforge.net

The focus in this module is at present on calculations of distances in a given cosmology. The parameters for the cosmological model are set using the variables OMEGA_M, OMEGA_L, H0 in the module namespace (see below for details).

Functions

float

dl(z)
Calculates the luminosity distance in Mpc at redshift z.

source code

float

da(z)
Calculates the angular diameter distance in Mpc at redshift z.

source code

float

dm(z)
Calculates the transverse comoving distance (proper motion distance) in Mpc at redshift z.

source code

float

dc(z)
Calculates the line of sight comoving distance in Mpc at redshift z.

source code

float

dl2z(distanceMpc)
Calculates the redshift z corresponding to the luminosity distance given in Mpc.

source code

float

dc2z(distanceMpc)
Calculates the redshift z corresponding to the comoving distance given in Mpc.

source code

float

t0()
Calculates the age of the universe in Gyr at z=0 for the current set of cosmological parameters.

source code

float

tl(z)
Calculates the lookback time in Gyr to redshift z for the current set of cosmological parameters.

source code

float

tz(z)
Calculates the age of the universe at redshift z for the current set of cosmological parameters.

source code

float

tl2z(tlGyr)
Calculates the redshift z corresponding to lookback time tlGyr given in Gyr.

source code

float

tz2z(tzGyr)
Calculates the redshift z corresponding to age of the universe tzGyr given in Gyr.

source code

float

absMag(appMag, distMpc)
Calculates the absolute magnitude of an object at given luminosity distance in Mpc.

source code

float

Ez2(z)
Calculates the value of E(z)^2, which describes evolution of the Hubble parameter with redshift, at redshift z for the current set of cosmological parameters.

source code

float

OmegaMz(z)
Calculates the matter density of the universe at redshift z.

source code

float

DeltaVz(z)
Calculates the density contrast of a virialised region ΔV(z), assuming a ΛCDM-type flat cosmology.

source code

float

RVirialXRayCluster(kT, z, betaT)
Calculates the virial radius (in Mpc) of a galaxy cluster at redshift z with X-ray temperature kT, assuming self-similar evolution and a flat cosmology.

source code

Variables

float OMEGA_M0 = 0.3
The matter density parameter at z=0.

float OMEGA_L = 0.7
The dark energy density (in the form of a cosmological constant) at z=0.

float H0 = 70.0
The Hubble parameter (in km/s/Mpc) at z=0.

float C_LIGHT = 3.0e5
The speed of light in km/s.

Function Details

dl(z)

Calculates the luminosity distance in Mpc at redshift z.

Parameters:

z (float) - redshift

Returns: float

luminosity distance in Mpc

da(z)

Calculates the angular diameter distance in Mpc at redshift z.

Parameters:

z (float) - redshift

Returns: float

angular diameter distance in Mpc

dm(z)

Calculates the transverse comoving distance (proper motion distance) in Mpc at redshift z.

Parameters:

z (float) - redshift

Returns: float

transverse comoving distance (proper motion distance) in Mpc

dc(z)

Calculates the line of sight comoving distance in Mpc at redshift z.

Parameters:

z (float) - redshift

Returns: float

transverse comoving distance (proper motion distance) in Mpc

dl2z(distanceMpc)

Calculates the redshift z corresponding to the luminosity distance given in Mpc.

Parameters:

distanceMpc (float) - distance in Mpc

Returns: float

redshift

dc2z(distanceMpc)

Calculates the redshift z corresponding to the comoving distance given in Mpc.

Parameters:

distanceMpc (float) - distance in Mpc

Returns: float

redshift

t0()	source code

Calculates the age of the universe in Gyr at z=0 for the current set of cosmological parameters.

Returns: float: age of the universe in Gyr at z=0

tl(z)

Calculates the lookback time in Gyr to redshift z for the current set of cosmological parameters.

Parameters:

z (float) - redshift

Returns: float

lookback time in Gyr to redshift z

tz(z)

Calculates the age of the universe at redshift z for the current set of cosmological parameters.

Parameters:

z (float) - redshift

Returns: float

age of the universe in Gyr at redshift z

tl2z(tlGyr)

Calculates the redshift z corresponding to lookback time tlGyr given in Gyr.

Parameters:

tlGyr (float) - lookback time in Gyr

Returns: float

redshift

tz2z(tzGyr)

Calculates the redshift z corresponding to age of the universe tzGyr given in Gyr.

Parameters:

tzGyr (float) - age of the universe in Gyr

Returns: float

redshift

absMag(appMag, distMpc)

Calculates the absolute magnitude of an object at given luminosity distance in Mpc.

Parameters:

appMag (float) - apparent magnitude of object
distMpc (float) - distance to object in Mpc

Returns: float

absolute magnitude of object

Ez2(z)

Calculates the value of E(z)^2, which describes evolution of the Hubble parameter with redshift, at redshift z for the current set of cosmological parameters. See, e.g., Bryan & Norman 1998 (ApJ, 495, 80).

Parameters:

z (float) - redshift

Returns: float

value of E(z)^2 at redshift z

OmegaMz(z)

Calculates the matter density of the universe at redshift z. See, e.g., Bryan & Norman 1998 (ApJ, 495, 80).

Parameters:

z (float) - redshift

Returns: float

matter density of universe at redshift z

DeltaVz(z)

Calculates the density contrast of a virialised region ΔV(z), assuming a ΛCDM-type flat cosmology. See, e.g., Bryan & Norman 1998 (ApJ, 495, 80).

Parameters:

z (float) - redshift

Returns: float

density contrast of a virialised region at redshift z

Note: If OMEGA_M0+OMEGA_L is not equal to 1, this routine exits and prints an error message to the console.

RVirialXRayCluster(kT, z, betaT)

Calculates the virial radius (in Mpc) of a galaxy cluster at redshift z with X-ray temperature kT, assuming self-similar evolution and a flat cosmology. See Arnaud et al. 2002 (A&A, 389, 1) and Bryan & Norman 1998 (ApJ, 495, 80). A flat ΛCDM-type flat cosmology is assumed.

Parameters:

kT (float) - cluster X-ray temperature in keV
z (float) - redshift
betaT (float) - the normalisation of the virial relation, for which Evrard et al. 1996 (ApJ,469, 494) find a value of 1.05

Returns: float

virial radius of cluster in Mpc

Note: If OMEGA_M0+OMEGA_L is not equal to 1, this routine exits and prints an error message to the console.