;+ ; 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