function ismeuv,wave,Hcol,HeIcol,HeIIcol,Fano=fano ;+ ; NAME: ; ISMEUV ; PURPOSE: ; Compute the continuum interstellar EUV optical depth ; ; EXPLANATION: ; The EUV optical depth is computed from the photoionization of ; hydrogen and helium. ; ; CALLING SEQUENCE: ; tau = ISMEUV( wave, Hcol, [ HeIcol, HeIIcol, /Fano ] ; ; INPUTS: ; wave - Vector of wavelength values (in Angstroms). Useful range is ; 40 - 912 A; at shorter wavelengths metal opacity should be ; considered, at longer wavelengths there is no photoionization. ; Hcol - Scalar specifying interstellar hydrogen column density in cm-2. ; Typical values are 1E17 to 1E20. ; ; OUTPUT: ; tau - Vector giving resulting optical depth, same number of elements ; as wave, non-negative values. To obtain the attenuation of ; an input spectrum, multiply by exp(-tau). ; ; OPTIONAL INPUTS: ; HeIcol - Scalar specifying neutral helium column density in cm-2. ; Default is 0.1*Hcol (10% of hydrogen column) ; HeIIcol - Scalar specifying ionized helium column density in cm-2 ; Default is 0 (no HeII) ; ; OPTIONAL INPUT KEYWORDS: ; /FANO - If this keyword is set and non-zero, then the 4 strongest ; auto-ionizing resonances of He I are included. The shape ; of these resonances is given by a Fano profile - see Rumph, ; Bowyer, & Vennes 1994, AJ, 107, 2108. If these resonances are ; included then the input wavelength vector should have ; a fine (>~0.01 A) grid between 190 A and 210 A, since the ; resonances are very narrow. ; EXAMPLE: ; (1) One has a model EUV spectrum with wavelength, w (in Angstroms) and ; flux,f . Plot the model flux after attenuation by 1e18 cm-2 of HI, ; with N(HeI)/N(HI) = N(HeII)/N(HI) = 0.05 ; ; IDL> Hcol = 1e18 ; IDL> plot, w, f*exp(-ismeuv(w, Hcol, .05*Hcol, .05*Hcol)) ; ; (2) Plot the cross-section of HeI from 180 A to 220 A for 1e18 cm-2 ; of HeI, showing the auto-ionizing resonances. This is ; Figure 1 in Rumph et al. (1994) ; ; IDL> w = 180 + findgen(40000)*0.001 ;Need a fine wavelength grid ; IDL> plot, w, ismeuv(w, 0, 1e18, /Fano) ; ; NOTES: ; (1) The more complete program ismtau.pro at ; http://hea-www.harvard.edu/PINTofALE/pro/ extends this work ; to shorter wavelengths and includes metal and molecular hydrogen ; opacities ; (2) This program only compute continuum opacities, and for example, ; the He ionization edges at 504 A and 228 A are blurred by ; converging line absorptions (Dupuis et al. 1995. ApJ, 455, 574) ; ; HISTORY: ; Written, W. Landsman October, 1994 ; Adapted from ism.c at anonymous ftp site cea-ftp.cea.berkeley.edu ; by Pat Jelinsky, Todd Rumph & others. ; Avoid underflow messages, support double prec. W. Landsman October 2003 ; Fix error in He II optical Depth J. Slavin/WL Sep 2013 ;- On_error,2 if N_params() LT 2 then begin print,'Syntax - tau = ISMEUV( wave, Hcol, [ HeIcol, HeIIcol, /FANO] )' return,-1 endif if N_elements( HeIcol) EQ 0 then HeIcol = 0.1*Hcol if N_elements( HeIIcol) EQ 0 then HeIIcol = 0.0*Hcol ; Compute attenuation due to photoionization of hydrogen. See Spitzer ; (Physical processes in the interstellar medium), page 105 if (size(wave,/TNAME) EQ 'DOUBLE') then begin pi = !dpi double = 1b endif else begin pi = !pi double = 0b endelse ratio = wave/911.75 tauh = wave*0. good = where(ratio LT 1, Ngood) minexp = alog((machar(double=double)).xmin) ;Min exponent to avoid underflow if Ngood GT 0 then begin r = ratio[good] z = sqrt( r/(1.0-r) ) denom = replicate(1.0, Ngood) y = -2.*pi*z good1 = where(y GT minexp, Ngood1) if Ngood1 GT 0 then denom[good1] = (1.0 - exp(y[good1])) tauh[good] = Hcol * 3.44e-16 * (r^4)*exp(-4.0*z*atan(1/z)) / denom endif ; Now compute photoionization cross-section of He II; just like hydrogen but ; with a nuclear charge Z = 2 tauheII = wave*0. ratio = 4. * wave/911.75 good = where(ratio LT 1, Ngood) if Ngood GT 0 then begin r = ratio[good] z = sqrt( r/(1.0-r) ) denom = replicate(4.0, Ngood) ;Z^2 Bug fix Sep 13 y = -2*PI*z good1 = where(y GT minexp, Ngood1) if Ngood1 GT 0 then denom[good1] *= (1.0 - exp(y[good1])) tauheII[good] = heiicol * 3.44e-16 * (r^4)*exp(-4.0*z*atan(1/z)) / denom endif ; Polynomial coefficients for He I cross-section taken from experimental ; data by Marr & West (1976) ; c1 for wavelengths greater than 46 A c1 = [-2.953607d+01, 7.083061d+00, 8.678646d-01,-1.221932d+00, $ 4.052997d-02, 1.317109d-01, -3.265795d-02, 2.500933d-03 ] ; c2 for wavelengths less than 46 A. c2 = [ -2.465188d+01, 4.354679d+00, -3.553024d+00, 5.573040d+00, $ -5.872938d+00, 3.720797d+00, -1.226919d+00, 1.576657d-01 ] ; parameters of autoionization resonances for 4 strongest He I resonances ; Numbers are from Oza (1986), Phys Rev. A, 33, 824 -- nu and gamma ; and Fernley et al., J. Phys. B., 20, 6457, 1987 -- q q = [2.81d, 2.51d, 2.45d, 2.44d ] nu = [1.610d, 2.795d, 3.817d, 4.824d ] fano_gamma = [2.64061d-03, 6.20116d-04, 2.56061d-04, 1.320159d-04 ] esubi = 3.0d - 1.0d/nu^2 + 1.807317d tauHeI = wave*0. good = where( wave LT 503.97, Ngood ) if Ngood GT 0 then begin x = alog10(wave[good]) y = x*0. good1 = where(wave LT 46.0, Ngood1 ) if Ngood1 GT 0 then y[good1] = poly( x[good1], c2) good2 = where(wave GE 46.0, Ngood2 ) if Ngood2 GT 0 then begin y[good2] = poly( x[good2], c1) if keyword_set(fano) then begin epsilon = 911.2671/wave for i=0,3 do begin ;Loop over first four HeI resonances x = 2.0 * ((epsilon-esubi[i] )/ fano_gamma[i] ) y = y + alog10( (x - q[i])^2/ (1 + x*x ) ) endfor endif endif tauHeI[good] = HeIcol * 10^y endif ; Total optical depth from HI, HeII and HeI return, tauH + tauHeII + tauHeI end