astrolibR (version 0.1)

lumdist: Calculate luminosity distance (in Mpc) of an object given its redshift

Description

Calculate luminosity distance (in Mpc) of an object given its redshift

Usage

lumdist(z, h0=70, k, lambda0, omega_m, q0)

Arguments

z

redshift, positive scalar or vector

h0

Hubble expansion parameter, in km/s/Mpc (default = 70.0)

k

curvature constant normalized to the closure density (default = 0.0 corresponding to a flat universe)

omega_m

matter density normalized to the closure density (default = 0.3)

lambda0

cosmological constant normalized to the closure density (default = 0.7)

q0

deceleration parameter, scalar (default = 0.55)

Value

lumdist

The result of the function is the luminosity distance (in Mpc) for each input value of z

Details

The luminosity distance in the Friedmann-Robertson-Walker model is taken from Carroll et al. (1992, p.511). It uses a closed form (Mattig equation) to compute the distance when the cosmological constant is zero, and otherwise computes the partial integral using the R function integrate. The integration can fail to converge at high redshift for closed universes with non-zero lambda.

No more than two of the four parameters (k, omega_M, lambda0, q0) should be specified. None of them need be specified if the default values are adopted.

References

Carroll, S. M., Press, W. H. and Turner, E. L., 1992, The cosmological constant, Ann. Rev. Astron. Astrophys., 30, 499-542

Examples

# Plot the distance of a galaxy in Mpc as a function of redshift out 
#  to z = 5.0, assuming the default cosmology (Omega_m=0.3, Lambda = 0.7,
#  H0 = 70 km/s/Mpc)

z <- seq(0,5,length=51)
plot(z, lumdist(z), type='l', lwd=2, xlab='z', ylab='Distance (Mpc)') 

# Now overplot the relation for zero cosmological constant and 
# Omega_m=0.3

lines(z,lumdist(z, lambda=0, omega_m=0.3), lty=2, lwd=2)