function pottasch,emis,logt,z=z,ion=ion,level=level,wdth=wdth,trange=trange,$_extra=e ;+ ;function pottasch ; returns the Pottasch factor that is a measure of the width of ; the ion emissivity in temperature space over which most of ; the line emission occurs. ; ; the Pottasch factor is the ratio ; {\int [EMIS*ION_BALANCE] dlogT}/{WDTH*max([EMIS*ION_BALANCE])} ; where WDTH is the range in logT where EMIS*ION_BALANCE drops to a ; set fraction of the maximum. ; ; output has as many elements as the 2nd dimension of EMIS, one point ; for each line. ; ;syntax ; pot=pottasch(emis,logt,z=z,ion=ion,level=level,wdth=wdth,$ ; trange=trange,chifil=chifil) ; ;parameters ; emis [INPUT; required] 1- or 2-D array of line intensities as ; a function of temperature ; * if 1D, assumed to be EMIS(Temperature) ; * if 2D, assumed to be EMIS(Temperature,{Z,ION,Wavelength}) ; * if Z is not specified, assumed to be the product of ; line emissivity and ion balance ; logt [INPUT] 1D array of log10(T[K]) ; * WARNING: if not given, or if size does not match 1st dim ; of EMIS, makes a dumb guess ; ;keywords ; Z [INPUT] atomic numbers corresponding to the 2nd dimension ; * if not set, ION is ignored and FOLD_IONEQ is not called ; * if size does not match 2nd dim of EMIS, ; >: ignore extra elements ; <,>1: use as many as specified, take rest to be H (Z=1) ; 1: all are of same element ; ion [INPUT; default: Z+1] ionic state ; level [INPUT; default: 0.1] defines what WDTH means ; wdth [OUTPUT] full width in logT at LEVEL*maximum ; * minimum value at any point is the resolution in LOGT at ; that point. ; trange [OUTPUT] 2-column array of the boundaries of logT that ; define WDTH ; * trange(0,*)=lower bound, trange(1,*)=upper bound ; _extra [INPUT] use to pass defined keywords ; * currently, only CHIFIL to FOLD_IONEQ ; ;subroutines ; FOLD_IONEQ [WHEE, RD_IONEQ [READ_IONEQ]] ; ;history ; vinay kashyap (Apr97) ; changed temperature width calculation to account for bumpy ; emissivities (VK; Oct98) ;- ; usage sze=size(emis) & & nsze=n_elements(sze) & nt=n_elements(logt) if sze(0) eq 0 then begin print,'Usage: b=pottasch(emissivity,logT,Z=Z,ion=ion,wdth=wdth)' print,' return Pottasch factor describing "width" of line emissivity' return,-1L endif ; check input if sze(0) gt 2 then begin message,'Input not understandable',/info & return,-1L endif if sze(1) ne nt then begin ;guess the temperature grid nt=sze(1) logt=findgen(nt)*(4./(nt-1))+4. if nt eq 21 then logt=findgen(nt)*0.1+5 if nt eq 41 then logt=findgen(nt)*0.05+5 endif ; mz=sze(2) & if sze(0) eq 1 then mz=1L & nz=n_elements(z) & zz=intarr(mz)+1 ieq=nz if mz ne nz then begin ;atomic numbers if nz eq 0 then z=[1] else begin if nz lt mz then zz(0:nz-1)=([z])(*) else zz=z(0:mz-1) endelse endif else zz=z ; ni=n_elements(ion) & jon=zz+1 if ni ne mz then begin ;ionic states if ni eq 0 then ion=jon else begin if ni lt mz then jon(0:ni-1)=([ion])(*) else jon=ion(0:mz-1) endelse endif else jon=ion ; fold ion balance if needed if ieq gt 0 then line=fold_ioneq(emis,zz,jon,logt=logt,_extra=e) else line=emis ; integrate over logT numer=dblarr(mz) for i=0,mz-1 do numer(i)=int_tabulated(logt,reform(line(*,i))) ; find maxima & widths lmax=dblarr(mz) & wdth=fltarr(mz) & trange=fltarr(2,mz) & dlogT=logT(1:*)-logT if n_elements(level) eq 0 then dw=0.1 else dw=float(level) for i=0,mz-1 do begin tmp=reform(line(*,i)) tmx=max(tmp,imx) & lmax(i)=tmx oo=where(tmp ge dw*tmx,moo) wdth_min=max([abs(logt([imx-1])-logt(imx)),abs(logt([imx+1])-logt(imx))]) ;{VK: the following used to be the original width calculation, now ;corrected to include the possibility that EMIS may have multiple bumps ; ;wdth(i)=abs(logt(moo-1)-logt(0)) > wdth_min ; if moo gt 0 then wdth(i)=total(dlogT(oo)) else message,'bug!' ; ;VK} trange(0,i)=logt(oo(0)) & trange(1,i)=logt(oo(moo-1)) endfor ; compute Pottasch factor bet=dblarr(mz)+1. denom=wdth*lmax & oo=where(denom gt 0,moo) if moo gt 0 then bet(oo)=numer(oo)/denom(oo) return,bet end