lumdist.pro

basic median filter simulation

;+
; NAME: 
;    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
; COMMENTS:
;    (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
;-                                   
 function ldist, z, q0 = q0, lambda0 = lambda0
   term1 = (1.+z)^2
   term2 =  1.+2.*(q0+lambda0)*z
   term3 = z*(2.+z)*lambda0
   denom = (term1*term2 - term3)
   out = z*0.  
   good = where(denom GT 0.0, Ngood)
   if Ngood GT 0 then out[good] = 1./sqrt(denom[good])
   return, out
 end 

 FUNCTION  lumdist, z, h0=h0, k = k, Lambda0 = lambda0, Omega_m = Omega_m, $
                    q0 = q0, Silent = silent

 compile_opt idl2
 if N_params() eq 0 then begin
	print,'Syntax: result = lumdist(z, H0 = ,k=, Lambda0 = ])'
	print,'Returns luminosity distance in Mpc'
	return, 0.
  endif

 n = N_elements(z)
 cosmo_param,Omega_m,Lambda0, k, q0 

; Check keywords 
  c = 2.99792458D5                  ;  speed of light in km/s
  if N_elements(H0) EQ 0 then H0 = 70
  if not keyword_set(silent) then $
     print,'LUMDIST: H0:', h0, ' Omega_m:', omega_m, ' Lambda0',lambda0, $
        ' q0: ',q0, ' k: ', k, f='(A,I3,A,f5.2,A,f5.2,A,f5.2,A,F5.2)' 
 
; For the case of Lambda = 0, we use the closed form from equation 5.238 of
; Astrophysical Formulae (Lang 1998).   This avoids terms that almost cancel
; at small q0*z better than the more familiar Mattig formula.
;
 if lambda0 EQ  0 then begin
    denom = sqrt(1+2*q0*z) + 1 + q0*z 
    dlum = (c*z/h0)*(1 + z*(1-q0)/denom)
    return,dlum
 
; For non-zero lambda 
endif else begin 
    dlum = z*0.0 
    for  i=0L,N-1 do begin
         if z[i] LE 0.0 then dlum[i] = 0.0 else begin
         qsimp,'LDIST',0,z[i], lz,q0 = q0, Lambda0 = lambda0
         dlum[i] = lz
         endelse
    endfor

    if k GT 0 then $
         dlum = sinh(sqrt(k)*dlum)/sqrt(k) $
    else if k LT 0 then $
          dlum = sin(sqrt(-k)*dlum)/sqrt(-k) > 0 
    return, c*(1+z)*dlum/h0
 endelse   

 end