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Package astLib :: Module astCalc
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Module astCalc

source code

module for performing common calculations

(c) 2007-2011 Matt Hilton

(c) 2013-2014 Matt Hilton & Steven Boada

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_M0, OMEGA_L0, OMEGA_R0, H0 in the module namespace (see below for details).

Functions [hide private]
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
dVcdz(z)
Calculates the line of sight comoving volume element per steradian dV/dz 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
Ez(z)
Calculates the value of E(z), which describes evolution of the Hubble parameter with redshift, at redshift z for the current set of cosmological parameters.		 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
OmegaLz(z)
Calculates the dark energy density of the universe at redshift z.		 source code
float
OmegaRz(z)
Calculates the radiation 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 [hide private]
float OMEGA_M0 = 0.3
The matter density parameter at z=0.
float OMEGA_L0 = 0.7
The dark energy density (in the form of a cosmological constant) at z=0.
float OMEGA_R0 = 8.24e-05
The radiation density at z=0 (note this is only used currently in calculation of Ez).
float H0 = 70.0
The Hubble parameter (in km/s/Mpc) at z=0.
float C_LIGHT = 300000.0
The speed of light in km/s.
  __package__ = 'astLib'
Function Details [hide private]

dl(z)

source code 

Calculates the luminosity distance in Mpc at redshift z.

Parameters:
  • z (float) - redshift
Returns: float
luminosity distance in Mpc

da(z)

source code 

Calculates the angular diameter distance in Mpc at redshift z.

Parameters:
  • z (float) - redshift
Returns: float
angular diameter distance in Mpc

dm(z)

source code 

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)

source code 

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

dVcdz(z)

source code 

Calculates the line of sight comoving volume element per steradian dV/dz at redshift z. The unit is Mpc^3/sr. To find the total volume of the universe integrate this function between two redshifts and multiply by the total area of the sky, 4pi steradians.

Parameters:
  • z (float) - redshift
Returns: float
comoving volume element per steradian

dl2z(distanceMpc)

source code 

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

Parameters:
  • distanceMpc (float) - distance in Mpc
Returns: float
redshift

dc2z(distanceMpc)

source code 

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)

source code 

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)

source code 

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)

source code 

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

Parameters:
  • tlGyr (float) - lookback time in Gyr
Returns: float
redshift

Note: Raises ValueError if tlGyr is not positive.

tz2z(tzGyr)

source code 

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

Note: Raises ValueError if Universe age not positive

absMag(appMag, distMpc)

source code 

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

Ez(z)

source code 

Calculates the value of E(z), 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) at redshift z

Ez2(z)

source code 

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)

source code 

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

OmegaLz(z)

source code 

Calculates the dark energy density of the universe at redshift z.

Parameters:
  • z (float) - redshift
Returns: float
dark energy density of universe at redshift z

OmegaRz(z)

source code 

Calculates the radiation density of the universe at redshift z.

Parameters:
  • z (float) - redshift
Returns: float
radiation density of universe at redshift z

DeltaVz(z)

source code 

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_L0 is not equal to 1, this routine exits and prints an error message to the console.

RVirialXRayCluster(kT, z, betaT)

source code 

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_L0 is not equal to 1, this routine exits and prints an error message to the console.


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