1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
|
! Copyright (C) 2005 Barbara Ercolano
!
! Version 2.02
module ionization_mod
use common_mod ! common variables
use constants_mod ! physical constants
use xSec_mod ! x sections module
! common variables
real, allocatable :: contBoltz(:) ! Boltzman factors for the continuum array
real, allocatable :: FFOpacity(:) ! FF opacity
real, allocatable :: log10nuArray(:) ! log10(nu) at this cell
real, allocatable &
&:: density(:,:) ! abundance*ionDensity*HDen [cm^-3]
real, save :: log10Ne ! log10(Ne) at this cell
real, save :: log10Te ! log10(Te) at this cell
real, save :: sqrTeUsed ! sqr(Te) at this cell
real, save :: eDenFFSum=0. ! sum of heavy elements free electrons
contains
! main routine to drive ionization solution for all species
subroutine ionizationDriver(grid, ix, iy, iz)
implicit none
integer, intent(in) :: ix, iy, iz ! pointers to cell in the x,y,z grid
logical, save :: firstLg=.true. ! first time?
type(grid_type), intent(inout) :: grid
! local variables
integer :: err ! allocation error status
integer :: i, n ! counter
! check whether this cell is outside the nebula
if (grid%active(ix,iy,iz) <= 0) return
if (firstLg) then
allocate(density(nElements, nStages), stat=err)
if (err /= 0) then
print*, "! ionizationDriver: can't allocate grid memory"
stop
end if
end if
density=0.
! find the physical properties of this cell
ionDenUsed = grid%ionDen(grid%active(ix, iy, iz), :,:)
log10Ne = log10(grid%Ne(grid%active(ix, iy, iz)))
log10Te = log10(grid%Te(grid%active(ix, iy, iz)))
NeUsed = grid%Ne(grid%active(ix, iy, iz))
TeUsed = grid%Te(grid%active(ix, iy, iz))
sqrTeUsed = sqrt(TeUsed)
density = 0.
! find the ion number density [cm^-3] at this cell
do n = 1, nElements
do i= 1, min(n, nstages)
! check this element is present
if (.not.lgElementOn(n)) exit
if (grid%abFileIndex(ix,iy,iz)<=0) then
print*, '! ionizationDriver: abundance file index has value: ', grid%abFileIndex(ix,iy,iz)
print*, 'Cell: ', ix,iy,iz, grid%active(ix,iy,iz)
print*, 'Abundance file index array: ', grid%abFileIndex
stop
end if
density(n, i) = ionDenUsed(elementXref(n), i)*grid%elemAbun(grid%abFileIndex(ix,iy,iz),n)*&
& grid%Hden(grid%active(ix, iy, iz))
end do
end do
! initialize arrays if this is the first time the procedure is called
if (firstLg) then
allocate(log10nuArray(nbins), stat = err)
if (err /= 0) then
print*, "! ionizationDriver: can't allocate grid memory"
stop
end if
allocate(contBoltz(nbins), stat = err)
if (err /= 0) then
print*, "! ionizationDriver: can't allocate grid memory"
stop
end if
allocate(gauntFF(nbins), stat = err)
if (err /= 0) then
print*, "! ionizationDriver: can't allocate grid memory"
stop
end if
allocate(gauntFFHeII(nbins), stat = err)
if (err /= 0) then
print*, "! ionizationDriver: can't allocate grid memory"
stop
end if
allocate(FFOpacity(nbins), stat = err)
if (err /= 0) then
print*, "! ionizationDriver: can't allocate grid memory"
stop
end if
contBoltz = 0.
FFOpacity = 0.
gauntFF = 0.
gauntFFHeII = 0.
log10nuArray = log10(nuArray)
firstLg = .false.
end if
! re-evaluate gaunt factors and boltzmann factors
call BoltGaunt()
! (re)evauate the sum of heavy elements free electrons density
call eDenSum()
! reevaluate all opacities if new ionization
call addOpacity(grid%opacity(grid%active(ix, iy, iz), :))
end subroutine ionizationDriver
! this subroutine evaluates boltzmann factors for the continuum
! and related variables
subroutine BoltGaunt()
implicit none
! local variables
integer :: i ! counter
integer :: iflag ! status flag returned by getGauntFF
integer :: max ! upper nu limit given by 0 exp
real :: exponent ! exponenent
real, save :: TeOld1=-1., TeOld2=-1. ! te on last run of sub
! correction factors for induced recombination
! are also used as Boltzmann factors.
! check for temperature changes or for first evaluation
if ( (TeOld1 /= TeUsed) .or. (contBoltz(1) <= 0.) ) then
TeOld1 = TeUsed
do i = 1, nbins
exponent = (Te1Ryd / TeUsed) + nuArray(i)
if( exponent > 84.) exit
contBoltz(i) = exp(-exponent)
end do
! set max
max = i
! zero out the remainder
do i = max, nbins
contBoltz(i) = 0.
end do
end if
! find the Gaunt factors
! check if temperature has changed by much
if ( abs(1. - TeOld2/TeUsed) > 0.10 ) then
call getGauntFF(0., log10Te, log10nuArray, gauntFF, iflag)
! following is for ionized helium
call getGauntFF(0.30103, log10Te, log10nuArray, gauntFFHeII, iflag)
TeOld2 = TeUsed
end if
end subroutine BoltGaunt
! this subroutine computes the gaunt factors for any charge
! it generates thermally averaged free-free non-relativistic gaunt
! factor for a hydrogenic ion of charge z, with a maximum relative
! error of 0.007, (rms fitting error = 0.001) for tmps and freqs in
! intervals:
! 10^-4 <= U <= 10^1.5
! 10^-3 <= Gams <= 10^3~
! where U = h*nu/k*T and gams = Z^2 * Ryd / k*T. To obtain the stated
! accuracy the full number of significant figures must be retained.
!
! this subroutine uses a two-dimensional chebyshev epansion computed
! from expressions given bu Karzas and Latter (ApJSuppl., V.6, P.167,
! 1961) augmented by various limiting forms of energy-specific gaunt-
! factors.
! D.G.Hummer, Jila, May 1987. ApJ 327, 477
! modified with correct limits, J Ferguson, July 94
! modified for MOCASSIN by B Ercolano (Ercolano et al 2003, MNRAS 340, 1136)
subroutine getGauntFF(z, log10Te, xlf, g, iflag)
implicit none
integer, intent(out) :: iflag ! explanation given in each area
real, intent(in) :: log10Te ! log10(Te)
real, intent(in) :: z ! log10 of nuclear charge
real, dimension(:), intent(in) :: xlf ! array of log10(h*nu/Ryd)
real, dimension(size(xlf)), intent(out) :: g ! array of values of g
! local variables
integer :: i, ir, j
real, dimension(11) :: b
real, dimension(8) :: c
real :: con
real(kind=8), dimension(88) :: dd
real(kind=8), dimension(8, 11) :: d
real :: gamma2 ! gamma^2 (gams = Z^2 * Ryd / k*T)
real :: slope ! slope
real :: txg ! hummer variable related to gamma^2
real :: txu ! hummer variable related to U
real :: u ! U = h*nu/k*T
real :: xlrkt ! log(ryd/kt)
dd = (/8.986940175e+00, -4.009515855e+00, 8.808871266e-01,&
& 2.640245111e-02, -4.580645915e-02, -3.568055702e-03,&
& 2.827798067e-03, 3.365860195e-04, -8.006936989e-01,&
& 9.466021705e-01, 9.043402532e-02, -9.608451450e-02,&
& -1.885629865e-02, 1.050313890e-02, 2.800889961e-03,&
& -1.078209202e-03, -3.781305103e-01, 1.102726332e-01,&
& -1.543619180e-02, 8.310561114e-03, 2.179620525e-02,&
& 4.259726289e-03, -4.181588794e-03, -1.770208330e-03,&
& 1.877213132e-02, -1.004885705e-01, -5.483366378e-02,&
& -4.520154409e-03, 8.366530426e-03, 3.700273930e-03,&
& 6.889320423e-04, 9.460313195e-05, 7.300158392e-02,&
& 3.576785497e-03, -4.545307025e-03, -1.017965604e-02,&
& -9.530211924e-03, -3.450186162e-03, 1.040482914e-03,&
& 1.407073544e-03, -1.744671550e-03, 2.864013856e-02,&
& 1.903394837e-02, 7.091074494e-03, -9.668371391e-04,&
& -2.999107465e-03, -1.820642230e-03, -3.874082085e-04,&
& -1.707268366e-02, -4.694254776e-03, 1.311691517e-03,&
& 5.316703136e-03, 5.178193095e-03, 2.451228935e-03,&
& -2.277321615e-05, -8.182359057e-04, 2.567331664e-04,&
& -9.155339970e-03, -6.997479192e-03, -3.571518641e-03,&
& -2.096101038e-04, 1.553822487e-03, 1.509584686e-03,&
& 6.212627837e-04, 4.098322531e-03, 1.635218463e-03,&
& -5.918883504e-04, -2.333091048e-03, -2.484138313e-03,&
& -1.359996060e-03, -5.371426147e-05, 5.553549563e-04,&
& 3.837562402e-05, 2.938325230e-03, 2.393747064e-03,&
& 1.328839809e-03, 9.135013312e-05, -7.137252303e-04,&
& -7.656848158e-04, -3.504683798e-04, -8.491991820e-04,&
& -3.615327726e-04, 3.148015257e-04, 8.909207650e-04,&
& 9.869737522e-04, 6.134671184e-04, 1.068883394e-04,&
& -2.046080100e-04/)
d = reshape( dd, (/8, 11/) )
! compute temperature dependent coeffcients for U expansion
! xlrxt is log(ryd/kt), code note valid for Te > 10^8
! xlrxt is log(ryd/kt), code note valid for Te < 10^2.5
if ( log10Te < 2.5 ) then
xlrkt = 5.1983649 - 2.5
else if ( log10Te > 8. ) then
xlrkt = 5.1983649 - 8.
else
xlrkt = 5.1983649 - log10Te
end if
! set txg
txg = 0.66666667*(2.0*z+xlrkt)
gamma2 = 10**(txg*1.5)
con = 0.72727273*xlrkt+0.90909091
do j=1,8
ir = 9
b(11) = real(d(j,11))
b(10) = real(txg*b(11)+d(j,10))
do i=1,9
b(ir) = real(txg*b(ir+1)-b(ir+2)+d(j,ir))
ir = ir-1
end do
c(j) = 0.25*(b(1)-b(3))
end do
! sum U expansion
! loop through energy at fixed temperature
do i = 1, size(xlf)
txu = 0.72727273*xlf(i)+con
u = 10**((txu - .90909091)/.72727273)
! criteria set by hummer limits. it is a wedge from
! log(hnu),log(T)) =
! (-5,2.5) to (-5,4) to (-1,8) to (4,8) to (-1.5,2.5).
! these limits correspond to the gamma^2 and U limits
! given above
if(abs(txu)<=2.0) then
ir = 6
b(8) = c(8)
b(7) = txu*b(8)+c(7)
do j=1,6
b(ir) = txu*b(ir+1)-b(ir+2)+c(ir)
ir = ir-1
end do
g(i) = b(1)-b(3)
if( (log10Te>=2.5) .and. (log10Te<=8.0)) iflag = 0
! On the bottom side of the hummer box,u<-4 and gamma2>.33
else if( (log10(u)<-4.0) .and. (gamma2<0.3) ) then
g(i) = 0.551329 * log(2.24593/u)
if( (log10Te>=2.5) .and. (log10Te<=8.0) ) iflag = 2
! On the bottom side of the box,u<-4 and gamma2<.33
else if( (log10(u)<-4.0) .and. (gamma2>=0.3) ) then
g(i) = 0.551329 * alog( 0.944931/u/sqrt(gamma2) )
if( (log10Te>=2.5) .and.( log10Te<=8.0) ) iflag = 3
! Now on the bottom side of the box
else if (txu>2.0) then
! Top of the box high T first
if (log10(gamma2)<-3.) then
g(i) = sqrt(0.9549297/u)
if(log10Te>=2.5.and.log10Te<=8.0) iflag = 4
! Must interpolate between two asymptotes
else if(log10(gamma2)<0.0) then
slope = ( sqrt(12*gamma2/u) - sqrt(0.9549297/u) ) / 3.0
g(i) = sqrt(12*gamma2/u) + slope * log10(gamma2)
if((log10Te>=2.5) .and. (log10Te<=8.0)) iflag = 7
else
! The top side with wedge of 1.05 where region 6 fails
g(i) = sqrt(12. * gamma2 / u)
g(i) = min(1.05,g(i))
if( (g(i)==1.05) .and. (log10Te>=2.5) .and. (log10Te<=8.0)) &
& iflag = 5
if( (g(i)<1.05) .and. (log10Te>=2.5) .and. (log10Te<=8.0)) &
& iflag = 6
end if
end if
u = 0.0
end do
end subroutine getGauntFF
! this subroutine sums up the free electron density over all species
subroutine eDenSum()
implicit none
! local variables
integer :: n, i ! counters
! sum the heavy metal free electron density
eDenFFSum = 0.
do n = 3, nElements
do i = 1, min(n, nstages-1)
eDenFFSum = eDenFFSum + float(i*i)*density(n, i+1)
end do
end do
end subroutine eDenSum
subroutine addOpacity(opacity)
implicit none
real, dimension(:), intent(out) :: opacity ! opacity
! local variables
integer :: i ! counters
real :: fac1, fac2, fac3 ! factors to be used in calculations
! (re) initialize opacity arrays
opacity = 0.
! hydrogen helium and heavy element brems (free-free) opacity,
! assuming hydrogen ff gaunt factors
! xSecArray is missing factor of 1.e-20 to avoid underflow.
fac1 = (NeUsed/1.e10) * ( (density(1,2) + density(2, 2) + &
& 4.*density(2, 3) + eDenFFSum)/1.e10 ) / sqrTeUsed
fac2 = fac1 * Te1Ryd / TeUsed
do i = 1, nbins
if (i>1) then
if (FFOpacity(i-1)<1.e-35) then
FFOpacity(i) = 0.
end if
else
if (contBoltz(i) < 0.995 ) then
! 1-exp(hn/kT) is used only is exp is small
! the last term is scaled h minus free-free absorption
fac3 = xSecArray(i-1+bremsXSecP)*(1.-contBoltz(i))*gauntFF(i)
FFOpacity(i) = fac3 * fac1
else
fac3 = xSecArray(i-1+bremsXSecP)*nuArray(i)*gauntFF(i)
FFOpacity(i) = fac3 * fac2
end if
end if
opacity(i) = opacity(i) + FFOpacity(i)
end do
! hydrogen lyman continuum photoelectric opacity
call inOpacity(HlevXSecP(1), HlevNuP(1), nbins, density(1,1), 0.)
! NOTE: the opacity due to the excited levels of HI, HeI and HeII is
! neglected for now as it requires calculations of the densities of
! the excited levels populations -> 4th argument in inOpacity is density
! of the lower level [cm^-3]
! helium singlets HeI (ground special because it extends to the high energy limit)
call inOpacity(HeISingXSecP(1), HeIlevNuP(1), nbins, density(2, 1), 0.)
! ionized helium HeII (ground special because it extends to the high energy limit)
call inOpacity(HeIIXSecP(1), HeIIlevNuP(1), nbins, density(2, 2), 0.)
do i = 3, nElements
if ( lgElementOn(i) ) call putOpacity(i)
end do
contains
! this subroutine enters the total phoo cross section
! for all subshells into opacity array. it drives inOpacity
! to put in total opacities
subroutine putOpacity(nElem)
implicit none
integer, intent(in) :: nElem
! local variables
integer :: nIon ! counter
integer :: nuLowP, nuHighP ! pointers to lower and highert limit of energy range
integer :: nShell ! counter
integer :: xSecP ! pointer to x scetion in xSecArray
do nIon = 1, min(nElem, nstages)
if ( density(nElem, nIon) > 0. ) then
! number of bound electrons
do nShell = 1, nShells(nElem, nIon)
nuLowP = elementP(nElem, nIon, nShell, 1)
nuHighP = elementP(nElem, nIon, nShell, 2)
xSecP = elementP(nElem, nIon, nShell, 3)
call inOpacity(xSecP, nuLowP, nuHighP, density(nElem, nIon), 0.)
end do
end if
end do
end subroutine putOpacity
! this subroutine adds the opacity of individual species,
! it can include stimulated emission. the departure coefficient b
! can be set to zero.
subroutine inOpacity(xSecP, nuLowP, nuHighP, den, b)
implicit none
integer, intent(in) :: nuLowP, nuHighP ! pointers to lower and higher limits in nuArray
integer, intent(in) :: xSecP ! x section pointer
real, intent(in) :: b ! departure coefficient
real, intent(in) :: den ! density of the lower level [cm^-3]
! local variables
integer :: i ! counter
integer :: iup ! upper limit
integer :: k ! offset
real :: bInv ! 1./b
k = xSecP - nuLowP
iup = min(nuHighP, nbins)
iup = max(nuLowP, iup)
if (b > 1e-35) then
bInv = 1./b
do i = nuLowP, iup
opacity(i) = opacity(i) + xSecArray(i+k)*den*&
& max(0., 1.-contBoltz(i)*bInv)
end do
else
do i = nuLowP, iup
opacity(i) = opacity(i) + xSecArray(i+k)*den
end do
end if
end subroutine inOpacity
end subroutine addOpacity
end module ionization_mod
|
