celestial (version 1.3)

cosdist: 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

z

Redshift, where z must be > -1 (can be a vector).

H0

Hubble constant as defined at z=0 (default is H0=100 (km/s)/Mpc).

OmegaM

Omega matter (default is 0.3).

OmegaL

Omega Lambda (default is for a flat Universe with OmegaL = 1-OmegaM = 0.7).

age

Flag for cosdist function to return age or not- this slows calculation, so is by default turned off.

ref

The name of a reference cosmology to use, one of 137 / 737 / Planck / WMAP9 / WMAP7 / WMAP5 / WMAP3 / WMAP1 / Millennium / GiggleZ. See cosref for details. This overrides any other settings for H0/ OmegaM and OmegaL.

error

Flag for cosdist to calculate the relative error for distance/age values.

Value

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

z	Requested redshift
a	Universe expansion factor, as given by a=1/(1+z)
CoDist	Line-of-sight (i.e. radial) comoving distance in units of Mpc
LumDist	Luminosity distance in units of Mpc
AngDist	Angular diameter distance in units of Mpc
CoDistTran	Transverse comoving distance in units of Mpc
DistMod	The distance modulus used where AbsMag = ApMag - DistMod, and DistMod = 5log10(LumDist)+25 in units of mag
AngSize	Physical projected size of an object at z in units of kpc/arcsec
CoVol	Comoving volume of Universe within z in units of Gpc^3

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

HubTime	Approximate Hubble age of the Universe in units of Gyrs
UniAgeNow	Age of the Universe now in units of Gyrs
UniAgeAtz	Age of the Universe at the specified redshift (z) in units of Gyrs
TravelTime	Light travel time from the specified redshift (AKA look back time) in units of Gyrs

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

RelError

Relative error of the distance/age integrals (this is the main source of error in the calculations)

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).

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.

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

# NOT RUN {
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')
# }