B.1.9 Distances

Functions for converting between different measures of cosmological distance.

The following parameters are used:

• z: redshift
• H0: Hubble constant in km/sec/Mpc (example value ~70)
• omegaM: Density ratio of the universe (example value 0.3)
• omegaLambda: Normalised cosmological constant (example value 0.7)

For a flat universe, omegaM+omegaLambda=1

The terms and formulae used here are taken from the paper by D.W.Hogg, Distance measures in cosmology, astro-ph/9905116 v4 (2000).

MpcToM( distMpc )

Converts from MegaParsecs to metres.

mToMpc( distM )

Converts from metres to MegaParsecs.

zToDist( z )

Quick and dirty function for converting from redshift to distance.

Warning: this makes some reasonable assumptions about the cosmology and returns the luminosity distance. It is only intended for approximate use. If you care about the details, use one of the more specific functions here.

zToAge( z )

Quick and dirty function for converting from redshift to time.

Warning: this makes some reasonable assumptions about the cosmology. It is only intended for approximate use. If you care about the details use one of the more specific functions here.

comovingDistanceL( z, H0, omegaM, omegaLambda )

Line-of-sight comoving distance.

comovingDistanceT( z, H0, omegaM, omegaLambda )

Transverse comoving distance.

angularDiameterDistance( z, H0, omegaM, omegaLambda )

Angular diameter distance.

luminosityDistance( z, H0, omegaM, omegaLambda )

Luminosity distance.

lookbackTime( z, H0, omegaM, omegaLambda )

Lookback time. This returns the difference between the age of the universe at time of observation (now) and the age of the universe at the time when photons of redshift z were emitted.

comovingVolume( z, H0, omegaM, omegaLambda )

Comoving volume. This returns the all-sky total comoving volume out to a given redshift z.

SPEED_OF_LIGHT

Speed of light in m/s.

METRE_PER_PARSEC

Number of metres in a parsec.

SEC_PER_YEAR

Number of seconds in a year.