Name

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    LUMDIST
     

Purpose

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

Explanation

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    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

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

Inputs

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    z = redshift, positive scalar or vector

Optional Keyword Inputs

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    /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

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

Example

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    (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

Comments

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    (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

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    COSMO_PARAM, QSIMP

Revision History

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    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