;+ ; NAME: ; GALAGE ; ; PURPOSE: ; Determine the age of a galaxy given its redshift and a formation redshift. ; ; CALLING SEQUENCE: ; age = galage(z, [zform, H0 =, k=, lambda0 =, Omega_m= , q0 =, /SILENT])' ; ; INPUTS: ; z - positive numeric vector or scalar of measured redshifts ; zform - redshift of galaxy formation (> z), numeric positive scalar ; To determine the age of the universe at a given redshift, set zform ; to a large number (e.g. ~1000). ; ; OPTIONAL KEYWORD INPUTS: ; H0 - Hubble constant in km/s/Mpc, positive scalar, default is 70 ; /SILENT - If set, then the adopted cosmological parameters are not ; displayed at the terminal. ; ; 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: ; age - age of galaxy in years, will have the same number of elements ; as the input Z vector ; ; EXAMPLE: ; (1) Determine the age of a galaxy observed at z = 1.5 in a cosmology with ; Omega_matter = 0.3 and Lambda = 0.0. Assume the formation redshift was ; at z = 25, and use the default Hubble constant (=70 km/s/Mpc) ; ; IDL> print,galage(1.5,25,Omega_m=0.3, Lambda = 0) ; ===> 3.35 Gyr ; ; (2) Plot the age of a galaxy in Gyr out to a redshift of z = 5, assuming ; the default cosmology (omega_m=0.3, lambda=0.7), and zform = 100 ; ; IDL> z = findgen(50)/10. ; IDL> plot,z,galage(z,100)/1e9,xtit='z',ytit = 'Age (Gyr)' ; ; PROCEDURE: ; For a given formation time zform and a measured z, integrate dt/dz from ; zform to z. Analytic formula of dt/dz in Gardner, PASP 110:291-305, 1998 ; March (eq. 7) ; ; COMMENTS: ; (1) Integrates using the IDL Astronomy Library 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.) The function 'dtdz' is defined at the beginning of the ; routine (so it can compile first). ; ; (2) Should probably be fixed to use a different integrator from QSIMP when ; computing age from an "infinite" redshift of formation. But using a ; large value of zform seems to work adequately. ; ; (3) An alternative set of IDL procedures for computing cosmological ; parameters is available at ; https://github.com/jlfischer/red-idl-cosmology ; PROCEDURES CALLED: ; COSMO_PARAM, QSIMP ; HISTORY: ; STIS version by P. Plait (ACC) June 1999 ; IDL Astro Version W. Landsman (Raytheon ITSS) April 2000 ; Avoid integer overflow for more than 32767 redshifts July 2001 ;- ; ; define function dtdz ; function dtdz, z, lambda0 = lambda0, q0 = q0 term1 = (1.0d + z) term2 = 2.0d * (q0 + lambda0) * z + 1.0d - lambda0 term3 = (1.0d + z) * (1.0d +z) return, 1.0 / (term1 * sqrt(term2 * term3 + lambda0)) end ;;;;;;;;;;;;;;;;;;;;;;;;; function galage, z, zform, h0 = h0, Omega_m=omega_m, lambda0 = lambda0, k = k, \$ q0 = q0, SILENT = silent if N_params() LE 1 then begin print,\$ 'Syntax: age = GALAGE(z, zform, [H0= , Omega_M = ,lambda0 =, k= , q0=, /SIL]' return, 0 endif ; ; initialize numbers ; if N_elements(h0) EQ 0 then h0 = 70.0 COSMO_PARAM, Omega_m, lambda0, k, q0 if not keyword_set(silent) then \$ print,'GALAGE: 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)' nz = N_elements(z) age = z*0. ;Return same dimensions and data type as Z ; ; use qsimp to integrate dt/dz to get age for each z ; watch out for null case of z >= zform ; for i= 0L, nz-1 do begin if (z[i] ge zform) then age_z = 0 else \$ qsimp,'dtdz', z[i], zform, age_z, q0 = q0, lambda0 = lambda0 age[i] = age_z endfor ; convert units of age: km/s/Mpc to years, divide by H0 ; 3.085678e19 km --> 1 Mpc ; 3.15567e+07 sec --> 1 year return, age * 3.085678e+19 / 3.15567e+7/ H0 end