Cosmological Distance Calculations

Description

These functions allows comoving, angular size and luminosity distances to be calculated for a given redshift, it can also return look back time. They use curvature correctly, calculated internally using the relation OmegaM+OmegaL+OmegaK=1, but by default they assume a flat Universe where only OmegaM needs to be specified.

Usage

cosdist(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, age=FALSE, ref, error=FALSE)
cosdistz(z=1)
cosdista(z=1)
cosdistCoDist(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosdistLumDist(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosdistAngDist(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosdistCoDistTran(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosdistDistMod(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosdistAngSize(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosdistCoVol(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosdistHubTime(H0=100)
cosdistUniAgeNow(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosdistUniAgeAtz(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosdistTravelTime(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosdistRelError(z=1, OmegaM=0.3, OmegaL=1-OmegaM, ref)

Arguments

Details

Function is largely based on D. W. Hogg et al. 1999 and Wright et al 2006.

Negative value of z> -1 are allowed, which produces future predictions based on present day cosmology.

Value

cosdist function returns a data.frame (even if only 1 redshift if requested) with the following columns:

If age=TRUE is set then additional age-related information is calculated for each z as extra columns:

If error=TRUE is set then the relative error for distance/age values is calculated for each z as an extra column:

cosdistz function returns the input redshift (only included for clarity).

cosdista function returns the Universe expansion factor, as given by a=1/(1+z).

cosdistCoDist function returns the line-of-sight (i.e. radial) comoving distance in units of Mpc.

cosdistLumDist function returns the luminosity distance in units of Mpc.

cosdistAngDist function returns the angular diameter distance in units of Mpc.

cosdistCoDistTran function returns the transverse comoving distance in units of Mpc.

cosdistDistMod function returns the distance modulus used where AbsMag = ApMag - DistMod, and DistMod = 5log10(LumDist)+25 in units of mag.

cosdistAngSize function returns the physical projected size of an object at z in units of kpc/arcsec.

cosdistCoVol function returns the comoving volume of Universe within z in units of Gpc^3.

cosdistHubTime function returns the approximate Hubble age of the Universe in units of Gyrs.

cosdistUniAgeNow function returns the age of the Universe now in units of Gyrs.

cosdistUniAgeAtz function returns the age of the Universe at the specified redshift (z) in units of Gyrs.

cosdistTravelTime function returns the light travel time from the specified redshift (AKA look back time) in units of Gyrs.

cosdistRelError function returns the relative error of the distance/age integrals (this is the main source of error in the calculations).

Author(s)

Aaron Robotham

References

Based on the equations in:

Hogg D.W., 1999, arXiv, 9905116 Wright E.L., 2006, PASP, 118, 1711

See Also

cosvol, cosmap, cosgrow, cosref

Examples

cosdist(0.3,70,age=TRUE)
cosdist(0.3,70,age=TRUE,ref='Planck')
cosdistz(0.3)
cosdista(0.3)
cosdistCoDist(0.3,70)
cosdistLumDist(0.3,70)
cosdistAngDist(0.3,70)
cosdistCoDistTran(0.3,70)
cosdistDistMod(0.3,70)
cosdistAngSize(0.3,70)
cosdistCoVol(0.3,70)
cosdistHubTime(70)
cosdistUniAgeNow(0.3,70)
cosdistUniAgeAtz(0.3,70)
cosdistTravelTime(0.3,70)
cosdistRelError(0.3)

redshifts=seq(0,3,by=0.01)
plot(redshifts, cosdist(redshifts, 70)[,'CoDist'], type='l', col='darkgreen', xlab='Redshift / z',
ylab='Distance / Mpc')
lines(redshifts, cosdist(redshifts, 70)[,'LumDist'], col='red')
lines(redshifts, cosdist(redshifts, 70)[,'AngDist'], col='blue')
legend('topleft', legend=c('Comoving Distance', 'Luminosity Distance', 'Angular Diameter Distance'),
col=c('darkgreen', 'red', 'blue'),lty=1)

plot(redshifts, cosdist(redshifts, 70, age=TRUE)[,'TravelTime'], type='l', xlab='Redshift / z',
ylab='Light travel time / Yrs')

Results