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LUMDIST

LUMDIST

## Purpose

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

## Explanation

The luminosity distance in the Friedmann-Robertson-Walker model is
taken from Caroll, Press, and Turner (1992, ARAA, 30, 499), p. 511
Uses a closed form (Mattig equation) to compute the distance when the
cosmological constant is zero. Otherwise integrates the function using
QSIMP.

## Calling Sequence

result = lumdist(z, [H0 = , k = , Omega_M =, Lambda0 = , q0 = ,/SILENT])

## Inputs

z = redshift, positive scalar or vector

## Optional Keyword Inputs

/SILENT - If set, the program will not display adopted cosmological
parameters at the terminal.
H0: Hubble parameter in km/s/Mpc, default is 70
No more than two of the following four parameters should be
specified. None of them need be specified -- the adopted defaults
are given.
k - curvature constant, normalized to the closure density. Default is
0, indicating a flat universe
Omega_m - Matter density, normalized to the closure density, default
is 0.3. Must be non-negative
Lambda0 - Cosmological constant, normalized to the closure density,
default is 0.7
q0 - Deceleration parameter, numeric scalar = -R*(R'')/(R')^2, default
is -0.55

## Outputs

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

## Example

(1) 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)
IDL> z = findgen(50)/10.
IDL> plot,z,lumdist(z),xtit='z',ytit='Distance (Mpc)'
Now overplot the relation for zero cosmological constant and
Omega_m=0.3
IDL> oplot,z,lumdist(z,lambda=0,omega=0.3),linestyle=1

(1) Integrates using the IDL Astronomy Version procedure QSIMP. (The
intrinsic IDL QSIMP function is not called because of its ridiculous
restriction that only scalar arguments can be passed to the integrating
function.)
(2) Can fail to converge at high redshift for closed universes with
non-zero lambda. This can presumably be fixed by replacing QSIMP with
an integrator that can handle a singularity

## Procedures Called

COSMO_PARAM, QSIMP

## Revision History

Written W. Landsman Raytheon ITSS April 2000
Avoid integer overflow for more than 32767 redshifts July 2001
Use double precision J. Moustakas/W. Landsman April 2008

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