four_levels_model.py
21.6 KB
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
# -*- coding: utf-8 -*-
"""
Created on Fri Jul 15 16:47:35 2022
@author: frede
"""
import numpy as np
import radiation_fields as rf
'''
This programme seeks to calculate how a neutral gas subjected to a radiation field
is heated, involving pahs in the ionization of the gas
This program works with the script "radiation_fields.py"
which calculates the scale factor of the radiation field G0
Example of execution of the program for the star of 10 solar radius HD200775,
for a distance to the star at 20pc, for a gas at 750K, an electron density
at 2.4 cm-3 and a size of PAHs à 54 C atoms :
HeatingGas(filename='HD200775_RF.txt', star_radius=10, t_gas=750,
n_e=1.6, n_c=54, parsec=20)
If i consider the Interstellar Radiation Field with
an approach described by Habing (1968), for a gas at 50K and a
fraction of cosmic carbon locked in PAHs at 5%:
HeatingGas('habing1968.txt', 1, t_gas=100, n_e=1.6, n_c=54,
parsec=1, fc_pah=0.05, ISRF=True)
While considering ISRF, the value of the parameters
parsec and star_radius are no longer important
'''
''' Constants '''
h = 6.62607015e-34 #Planck constant in J s
c = 299792458 #Light speed in m s-1
eps_0 = 8.85418782e-12 #epsilon_0, vacuum permitivity in F (Farad) m-1
z_0 = 0 #the charge state of the neutral molecule
z_1 = 1 #the charge state of the ionized 1 molecule
one_in_4_pi_eps_0 = 1/( 4*np.pi*(eps_0/1e9) )
''' Conversions '''
ev = 1.602176634e-19 # 1 ev = 1.60218e-19 J and value of electron charge
erg = 1e-7 # 1 erg = 1e-7 J
ev_to_erg = ev/erg #1 eV in erg
mb = 1e-18 #1Mb = 1e-18cm2, Mb for Megabarn (unit used to express the cross sectional area of nuclei)
''' Saving parameters '''
dust_heating_rate = np.zeros([3])
ionization_rate = np.zeros([2])
recombination_rate = np.zeros([2])
gas_heating_rate = np.zeros([2])
intrinsic_efficiency = np.zeros([2])
class HeatingGas:
"""
----------
Returns total_gas_heating, g_0 , gamma , t_gas, n_e , n_c
total_gas_heating : float,
gas heating rate
g_0 : float,
scaling factor of the radiation field
gamma : float,
( g_0 * sqrt(t_gas) )/n_e ionization parameter
t_gas : float,
gas temperature
n_e : float,
electron density in cm-3
n_c : float,
number of carbon atoms in pah molecules (size of the pah)
-------
"""
def __init__(self, filename, star_radius, t_gas, n_e, n_c, parsec, fc_pah=0.1, ISRF=False):
"""
----------
filename : str,
name of the file containing wavelength in nm and
intensity in erg cm-2 s-1 sr-1 nm-1 of a star or of the interstellar medium
star_radius : float,
star radius, in unit of solar radius
n_e : float,
electron density in cm-3 (n_e = n_h * 1.6e-4, n_h : hydrogene density)
parsec : float,
distance in parsec from the star
fc_pah : float,
fraction of cosmic carbon locked in PAHs (default: 0.1)
ISRF : bool,
Interstellar Radiation Field; if true, then the filename is a file for ISRF
if false, the radiation field of a star is studied (default: False)
-------
"""
''' input parameters '''
self.filename = filename
self.t_gas = t_gas
self.n_e = n_e
self.n_c = n_c
self.parsec = parsec
self.star_radius = star_radius
self.fc_pah = fc_pah
self.ISRF = ISRF
''' parameters to be observed '''
self.g_0 = None
self.distance = None
self.wavelength = None
self.wavelength_intensity = None
self.energy_intensity = None
self.energy = None
self.energy_range = None
self.energy_negative_charged = None
self.energy_neutral = None
self.energy_charged = None
self.energy_double_charged = None
self.pah_cross_a = None
self.pah_cross_n = None
self.pah_cross_c = None
self.pah_cross_dc = None
self.ip_neutral = None
self.ip_charged = None
self.detachment_yield = None
self.yield_of_first_photoionization = None
self.yield_of_second_photoionization = None
self.heating_efficiency = None
self.total_gas_heating = None
self.frac_anion = None
self.frac_neutral = None
self.frac_charged = None
self.frac_double_charged = None
def parameters(self):
''' others parameters to be returned '''
self.g_0, self.distance, self.wavelength, self.wavelength_intensity, self.energy_intensity, self.energy, self.ISRF, RF_list = rf.radiation_field(self.filename, self.star_radius, self.parsec, self.ISRF, RF_list=False)
self.gamma = ( self.g_0 * np.sqrt(self.t_gas) ) / self.n_e #ionization parameter
''' Ionization Potential (IP) estimation '''
a = (self.n_c/468)**(1/3) #molecule diameter, in nm
self.ip_neutral = 3.9 + one_in_4_pi_eps_0 * ( ( z_0 + (1/2) ) * (ev**2/a) + ( z_0 + 2 ) * (ev**2/a) *(0.03/a) ) * (1/ev)
#IP to ionize the molecule : neutral to charged, in ev
self.ip_charged = 3.9 + one_in_4_pi_eps_0 * ( ( z_1 + (1/2) ) * (ev**2/a) + ( z_1 + 2 ) * (ev**2/a) *(0.03/a) ) * (1/ev)
#IP to ionize the charged molecule : charged 1 to charged 2, in ev
'''==========================|building of the cross section|======================='''
''' derives a mean photoabsorption cross section of the molecule considered, in 3 size ranges'''
''' small size '''
self.energy_negative_charged,cross_anion = np.loadtxt('./anions/coronene_anion.txt',unpack=True) #C24
self.energy_negative_charged,crossa_1_case1 = np.loadtxt('./anions/ovalene_anion.txt',unpack=True) #C32
self.energy_neutral,crossn_1_case1 = np.loadtxt('./neutrals/ovalene_neutral.txt',unpack=True) #C32
self.energy_charged,crossc_1_case1 = np.loadtxt('./cations/ovalene_cation.txt',unpack=True) #C32
self.energy_double_charged,crossdc_1_case1 = np.loadtxt('./dications/ovalene_dication.txt',unpack=True) #C32
self.energy_negative_charged,crossa_2_case1 = np.loadtxt('./anions/tetrabenzocoronene_anion.txt',unpack=True) #C36
self.energy_neutral,crossn_2_case1 = np.loadtxt('./neutrals/tetrabenzocoronene_neutral.txt',unpack=True) #C36
self.energy_charged,crossc_2_case1 = np.loadtxt('./cations/tetrabenzocoronene_cation.txt',unpack=True) #C36
self.energy_double_charged,crossdc_2_case1 = np.loadtxt('./dications/tetrabenzocoronene_dication.txt',unpack=True) #C36
self.energy_negative_charged,crossa_3_case1 = np.loadtxt('./anions/circumbiphenyl_anion.txt',unpack=True) #C38
self.energy_neutral,crossn_3_case1 = np.loadtxt('./neutrals/circumbiphenyl_neutral.txt',unpack=True) #C38
self.energy_charged,crossc_3_case1 = np.loadtxt('./cations/circumbiphenyl_cation.txt',unpack=True) #C38
self.energy_double_charged,crossdc_3_case1 = np.loadtxt('./dications/circumbiphenyl_dication.txt',unpack=True) #C38
''' medium size '''
self.energy_negative_charged,crossa_1_case2 = np.loadtxt('./anions/circumanthracene_anion.txt',unpack=True) #C40
self.energy_neutral,crossn_1_case2 = np.loadtxt('./neutrals/circumanthracene_neutral.txt',unpack=True) #C40
self.energy_charged,crossc_1_case2 = np.loadtxt('./cations/circumanthracene_cation.txt',unpack=True) #C40
self.energy_double_charged,crossdc_1_case2 = np.loadtxt('./dications/circumanthracene_dication.txt',unpack=True) #C40
self.energy_negative_charged,crossa_2_case2 = np.loadtxt('./anions/circumpyrene_anion.txt',unpack=True) #C42
self.energy_neutral,crossn_2_case2 = np.loadtxt('./neutrals/circumpyrene_neutral.txt',unpack=True) #C42
self.energy_charged,crossc_2_case2 = np.loadtxt('./cations/circumpyrene_cation.txt',unpack=True) #C42
self.energy_double_charged,crossdc_2_case2 = np.loadtxt('./dications/circumpyrene_dication.txt',unpack=True) #C42
self.energy_negative_charged,crossa_3_case2 = np.loadtxt('./anions/hexabenzocoronene_anion.txt',unpack=True) #C42
self.energy_neutral,crossn_3_case2 = np.loadtxt('./neutrals/hexabenzocoronene_neutral.txt',unpack=True) #C42
self.energy_charged,crossc_3_case2 = np.loadtxt('./cations/hexabenzocoronene_cation.txt',unpack=True) #C42
self.energy_double_charged,crossdc_3_case2 = np.loadtxt('./dications/hexabenzocoronene_dication.txt',unpack=True) #C42
''' large size '''
self.energy_negative_charged,crossa_1_case3 = np.loadtxt('./anions/dicoronylene_anion.txt',unpack=True) #C48
self.energy_neutral,crossn_1_case3 = np.loadtxt('./neutrals/dicoronylene_neutral.txt',unpack=True) #C48
self.energy_charged,crossc_1_case3 = np.loadtxt('./cations/dicoronylene_cation.txt',unpack=True) #C48
self.energy_double_charged,crossdc_1_case3 = np.loadtxt('./dications/dicoronylene_dication.txt',unpack=True) #C48
self.energy_negative_charged,crossa_2_case3 = np.loadtxt('./anions/circumcoronene_anion.txt',unpack=True) #C54
self.energy_neutral,crossn_2_case3 = np.loadtxt('./neutrals/circumcoronene_neutral.txt',unpack=True) #C54
self.energy_charged,crossc_2_case3 = np.loadtxt('./cations/circumcoronene_cation.txt',unpack=True) #C54
self.energy_double_charged,crossdc_2_case3 = np.loadtxt('./dications/circumcoronene_dication.txt',unpack=True) #C54
self.energy_negative_charged,crossa_3_case3 = np.loadtxt('./anions/circumovalene_anion.txt',unpack=True) #C66
self.energy_neutral,crossn_3_case3 = np.loadtxt('./neutrals/circumovalene_neutral.txt',unpack=True) #C66
self.energy_charged,crossc_3_case3 = np.loadtxt('./cations/circumovalene_cation.txt',unpack=True) #C66
self.energy_double_charged,crossdc_3_case3 = np.loadtxt('./dications/circumovalene_dication.txt',unpack=True) #C66
#for each cross section for each state of the molecule, we have an associated energy
self.energy_range = np.where(self.energy_neutral<13.6)[0]
self.pah_cross_a = ( ( (cross_anion/24) +(crossa_1_case1/32)+(crossa_2_case1/36) +\
(crossa_3_case1/38)+(crossa_1_case2/40)+(crossa_2_case2/42) +\
(crossa_3_case2/42)+(crossa_1_case3/48)+(crossa_2_case3/54) +\
(crossa_3_case3/66) )/10 ) * self.n_c
self.pah_cross_n = ( ( (crossn_1_case1/32)+(crossn_2_case1/36)+(crossn_3_case1/38) +\
(crossn_1_case2/40)+(crossn_2_case2/42)+(crossn_3_case2/42) +\
(crossn_1_case3/48)+(crossn_2_case3/54)+(crossn_3_case3/66) )/9 ) * self.n_c
self.pah_cross_c = ( ( (crossc_1_case1/32)+(crossc_2_case1/36)+(crossc_3_case1/38) +\
(crossc_1_case2/40)+(crossc_2_case2/42)+(crossc_3_case2/42) +\
(crossc_1_case3/48)+(crossc_2_case3/54)+(crossc_3_case3/66) )/9 ) * self.n_c
self.pah_cross_dc = ( ((crossdc_1_case1/32)+(crossdc_2_case1/36)+(crossdc_3_case1/38) +\
(crossdc_1_case2/40)+(crossdc_2_case2/42)+(crossdc_3_case2/42) +\
(crossdc_1_case3/48)+(crossdc_2_case3/54)+(crossdc_3_case3/66) )/9 ) * self.n_c
#cross_n is the average cross section of a pah of all types of size
''' Ranges imposed '''
self.energy_negative_charged = self.energy_negative_charged[self.energy_range]
self.energy_neutral = self.energy_neutral[self.energy_range]
self.energy_charged = self.energy_charged[self.energy_range]
self.energy_double_charged = self.energy_double_charged[self.energy_range]
self.pah_cross_a = self.pah_cross_a[self.energy_range]
self.pah_cross_n = self.pah_cross_n[self.energy_range]
self.pah_cross_c = self.pah_cross_c[self.energy_range]
self.pah_cross_dc = self.pah_cross_dc[self.energy_range]
''' yield from anion to neutral '''
part = np.where(self.energy_negative_charged >= 0)[0]
self.detachment_yield = np.full(len(part), 1)
#the anion being unstable, any energy is enough to detach the electron
''' yield from neutral to the first photoionization '''
first_part = np.where(self.energy_neutral<self.ip_neutral)[0]
second_part = np.where( (self.energy_neutral>=self.ip_neutral) & (self.energy_neutral<(self.ip_neutral+9.2) ) )[0]
third_part = np.where((self.energy_neutral>self.ip_neutral+9.2))[0]
y_1 = np.zeros([len(first_part)])
y_2 = ( self.energy_neutral[second_part]-self.ip_neutral )/9.2
y_3 = np.full(len(third_part), 1)
self.yield_of_first_photoionization = np.concatenate( (y_1,y_2,y_3) )
''' yield from the first photoionization to the second photoionization '''
alpha = 0.3 #teepness coefficient, see Wenzel et al. 2020
if (self.n_c >= 32) & (self.n_c < 50):
beta = 0.59 + 8.1e-3 * self.n_c
if self.n_c >= 50:
beta = 1
first_part = np.where( self.energy_charged<self.ip_charged )[0]
second_part = np.where( ( self.energy_charged>=self.ip_charged ) & ( self.energy_charged<11.3 ) )[0]
third_part = np.where( ( self.energy_charged>=11.3 ) & ( self.energy_charged<12.9 ) )[0]
fourth_part = np.where( ( self.energy_charged>=12.9 ) & ( self.energy_charged<13.6 ) )[0]
y_1 = np.zeros([len(first_part)])
y_2 = ( alpha/(11.3-self.ip_charged) ) * (self.energy_charged[second_part]-self.ip_charged)
y_3 = np.full(len(third_part), alpha)
y_4 = ( (beta-alpha)/2.1 ) * (self.energy_charged[fourth_part]-12.9) + alpha
self.yield_of_second_photoionization = np.concatenate( (y_1,y_2,y_3,y_4) )
''' adaptating the cross section from 0 to 13.6eV'''
pah_crossa = np.interp(self.energy,self.energy_negative_charged,self.pah_cross_a)*mb #in cm2/Carbon (from Mb/C to cm2/C)
pah_crossn = np.interp(self.energy,self.energy_neutral,self.pah_cross_n)*mb #in cm2/Carbon (from Mb/C to cm2/C)
pah_crossc = np.interp(self.energy,self.energy_charged,self.pah_cross_c)*mb #in cm2/Carbon (from Mb/C to cm2/C)
pah_crossdc = np.interp(self.energy,self.energy_double_charged,self.pah_cross_dc)*mb #in cm2/Carbon (from Mb/C to cm2/C)
yield_a = np.interp(self.energy,self.energy_negative_charged,self.detachment_yield)
yield_n = np.interp(self.energy,self.energy_neutral,self.yield_of_first_photoionization)
yield_c = np.interp(self.energy,self.energy_charged,self.yield_of_second_photoionization)
#interpolation
'''===================== dust and gas heating calculation ==================='''
energy_range_power_absorbed = np.where(self.energy<=13.6)[0]
energy_range_anion = np.where(self.energy<=13.6)[0]
energy_range_neutral = np.where(np.logical_and(self.energy >= self.ip_neutral, self.energy <= 13.6))[0]
energy_range_charged = np.where(np.logical_and(self.energy >= self.ip_charged, self.energy <= 13.6))[0]
''' photoabsorption of the neutrals, cations and dications molecules '''
photo_absorption_a = self.energy_intensity*pah_crossa*2*np.pi #erg s-1 eV-1 /!\ the 2*np.pi is the solid angle considered => the RF comes from the star only
photo_absorption_n = self.energy_intensity*pah_crossn*2*np.pi #erg s-1 eV-1
photo_absorption_c = self.energy_intensity*pah_crossc*2*np.pi #erg s-1 eV-1
photo_absorption_dc = self.energy_intensity*pah_crossdc*2*np.pi #erg s-1 eV-1
''' power density absorbed for ionization '''
ionization_absorption_a = yield_a*photo_absorption_a #erg s-1 eV-1
ionization_absorption_n = yield_n*photo_absorption_n #erg s-1 eV-1
ionization_absorption_c = yield_c*photo_absorption_c #erg s-1 eV-1
''' number of ionizations '''
number_ionization_absorption_a = ionization_absorption_a/(self.energy*ev_to_erg)
number_ionization_absorption_n = ionization_absorption_n/(self.energy*ev_to_erg)
number_ionization_absorption_c = ionization_absorption_c/(self.energy*ev_to_erg)
#number of ionizations per s per eV for a charge state
''' detachment rate '''
kdet = np.trapz(number_ionization_absorption_a[energy_range_anion], self.energy[energy_range_anion])
#in s-1
''' photoemission rate '''
kpe_neutral = np.trapz(number_ionization_absorption_n[energy_range_neutral], (self.energy-self.ip_neutral)[energy_range_neutral])
kpe_charged = np.trapz(number_ionization_absorption_c[energy_range_charged], (self.energy-self.ip_charged)[energy_range_charged])
#in s-1
''' attachment rate ''' #for coronene
katt = self.n_e * 2.74e-9 * (self.t_gas/300)**(0.11) * np.exp(-(-1.12)/self.t_gas)
#in s-1
''' recombination rate '''
phi = ( 1.85*1e5 )/( self.t_gas*np.sqrt(self.n_c) ) #dimensionless
krec_neutral = self.n_e * 1.28e-10 * self.n_c * np.sqrt(self.t_gas) * ( 1 + phi )
krec_charged = self.n_e * 1.28e-10 * self.n_c * np.sqrt(self.t_gas) * ( 1 + phi * (1 + z_1) )
#in s-1
''' population fraction computation '''
#anions
self.frac_anion = 1/(1 + (kdet/katt) + (kdet*kpe_neutral)/(katt*krec_neutral) + (kdet*kpe_neutral*kpe_charged)/(katt*krec_neutral*krec_charged))
#neutrals
self.frac_neutral = 1/(1 + (katt/kdet) + (kpe_neutral/krec_neutral) + (kpe_neutral*kpe_charged)/(krec_neutral*krec_charged))
#cations
self.frac_charged = 1/(1 + (krec_neutral/kpe_neutral) + (krec_neutral*katt)/(kdet*kpe_neutral) + (kpe_charged/krec_charged))
#dications
self.frac_double_charged = 1/(1 + (krec_charged/kpe_charged) + (krec_neutral*krec_charged)/(kpe_neutral*kpe_charged) + (katt*krec_neutral*krec_charged)/(kdet*kpe_neutral*kpe_charged) )
''' selection of the partition coefficient '''
partition_coeff = 0.46 #pah parameter, 0.46 + or - 0.06
''' spectrum of the gas heating per charge state '''
anion_heating_rate_spectrum = 1 * (self.energy-0) *\
number_ionization_absorption_a * ev_to_erg #erg s-1 eV-1
neutral_heating_rate_spectrum = partition_coeff * (self.energy-self.ip_neutral) *\
number_ionization_absorption_n * ev_to_erg #erg s-1 eV-1
charged_heating_rate_spectrum = partition_coeff * (self.energy-self.ip_charged) *\
number_ionization_absorption_c * ev_to_erg #erg s-1 eV-1
#partition_coeff * (E-IP) is the kinetic energy of the photoelectron following absorption of a UV photon of energy E
''' gas heating rate per charge state '''
anion_gas_heating_rate = np.trapz(anion_heating_rate_spectrum[energy_range_anion],\
self.energy[energy_range_anion] ) #erg s-1 molecule-1
neutral_gas_heating_rate = np.trapz(neutral_heating_rate_spectrum[energy_range_neutral],\
(self.energy-self.ip_neutral)[energy_range_neutral] ) #erg s-1 molecule-1
charged_gas_heating_rate = np.trapz(charged_heating_rate_spectrum[energy_range_charged],\
(self.energy-self.ip_charged)[energy_range_charged] ) #erg s-1 molecule-1
#powers injected in the gas by photoelectrons ejected from
#anionic neutral and cationic PAHs
'''======================== heating efficiencies ========================'''
''' total power injected into the gas via the photoelectrons from pahs '''
total_injected_power = self.frac_anion * anion_gas_heating_rate +\
self.frac_neutral * neutral_gas_heating_rate +\
self.frac_charged * charged_gas_heating_rate
#erg s-1 /(molecule of size n_c)
''' heating rate of the molecule itself '''
heating_pah_a = np.trapz(photo_absorption_a,\
self.energy) #erg s-1
heating_pah_n = np.trapz(photo_absorption_n[energy_range_power_absorbed],\
self.energy[energy_range_power_absorbed]) #erg s-1
heating_pah_c = np.trapz(photo_absorption_c[energy_range_power_absorbed],\
self.energy[energy_range_power_absorbed]) #erg s-1
heating_pah_dc = np.trapz(photo_absorption_dc[energy_range_power_absorbed],\
self.energy[energy_range_power_absorbed]) #erg s-1
''' total power of the radiation absorbed by pahs '''
total_absorbed_radiation_power = self.frac_anion * heating_pah_a +\
self.frac_neutral * heating_pah_n +\
self.frac_charged * heating_pah_c +\
self.frac_double_charged * heating_pah_dc
#erg s-1 /(molecule of size n_c)
''' heating efficiency '''
self.heating_efficiency = total_injected_power/total_absorbed_radiation_power
''' gas heating '''
self.total_gas_heating = total_injected_power * (self.fc_pah/self.n_c) * 2.7e-4
#2.7e-4 : elemental abundance of C relative to H (Tielens 2021)
return self.total_gas_heating, self.g_0 , self.gamma, self.t_gas, self.n_e, self.n_c