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1 | -# -*- coding: utf-8 -*- | |
2 | -""" | |
3 | -Created on Tue Jun 14 10:48:49 2022 | |
4 | - | |
5 | -@author: frede | |
6 | -""" | |
7 | -import numpy as np | |
8 | -import radiation_fields as rf | |
9 | - | |
10 | -''' | |
11 | - | |
12 | -This programme seeks to calculate how a neutral gas subjected to a radiation field | |
13 | -is heated, involving PAHs in the ionization of the gas | |
14 | - | |
15 | -This program works with the script "radiation_fields.py" | |
16 | -which calculates the scale factor of the radiation field G0 | |
17 | - | |
18 | -Example of execution of the program for the star of 10 solar radius HD200775, | |
19 | -for a distance to the star at 20pc, for a gas at 750K, an electron density | |
20 | -at 2.4 cm-3 and a size of PAHs à 54 C atoms : | |
21 | - | |
22 | -HeatingGas(filename='HD200775_RF.txt', star_radius=10, t_gas=750, | |
23 | - n_e=1.6, n_c=54, parsec=20) | |
24 | - | |
25 | -If i consider the Interstellar Radiation Field with | |
26 | -an approach described by Habing (1968), for a gas at 50K and a | |
27 | -fraction of cosmic carbon locked in PAHs at 5%: | |
28 | - | |
29 | -HeatingGas('habing1968.txt', 1, t_gas=100, n_e=1.6, n_c=54, | |
30 | - parsec=1, fc_pah=0.05, ISRF=True) | |
31 | - | |
32 | -While considering ISRF, the value of the parameters | |
33 | -parsec and star_radius are no longer important | |
34 | - | |
35 | -''' | |
36 | - | |
37 | -''' Constants ''' | |
38 | -h = 6.62607015e-34 #Planck constant in J s | |
39 | -c = 299792458 #Light speed in m s-1 | |
40 | -eps_0 = 8.85418782e-12 #epsilon_0, vacuum permitivity in F (Farad) m-1 | |
41 | -z_0 = 0 #the charge state of the neutral molecule | |
42 | -z_1 = 1 #the charge state of the ionized 1 molecule | |
43 | -one_in_4_pi_eps_0 = 1/( 4*np.pi*(eps_0/1e9) ) | |
44 | - | |
45 | -''' Conversions ''' | |
46 | -ev = 1.602176634e-19 # 1 ev = 1.60218e-19 J and value of electron charge | |
47 | -erg = 1e-7 # 1 erg = 1e-7 J | |
48 | -ev_to_erg = ev/erg #1 eV in erg | |
49 | -mb = 1e-18 #1Mb = 1e-18cm2, Mb for Megabarn (unit used to express the cross sectional area of nuclei) | |
50 | - | |
51 | -''' Saving parameters ''' | |
52 | -dust_heating_rate = np.zeros([3]) | |
53 | -ionization_rate = np.zeros([2]) | |
54 | -recombination_rate = np.zeros([2]) | |
55 | -gas_heating_rate = np.zeros([2]) | |
56 | -intrinsic_efficiency = np.zeros([2]) | |
57 | - | |
58 | -class HeatingGas: | |
59 | - | |
60 | - """ | |
61 | - | |
62 | - ---------- | |
63 | - | |
64 | - Returns total_gas_heating, g_0 , gamma , t_gas, n_e , n_c | |
65 | - | |
66 | - total_gas_heating : float, | |
67 | - gas heating rate | |
68 | - g_0 : float, | |
69 | - scaling factor of the radiation field | |
70 | - gamma : float, | |
71 | - ( g_0 * sqrt(t_gas) )/n_e ionization parameter | |
72 | - t_gas : float, | |
73 | - gas temperature | |
74 | - n_e : float, | |
75 | - electron density in cm-3 | |
76 | - n_c : float, | |
77 | - number of carbon atoms in pah molecules (size of the pah) | |
78 | - | |
79 | - ------- | |
80 | - | |
81 | - """ | |
82 | - | |
83 | - def __init__(self, filename, star_radius, t_gas, n_e, n_c, parsec, fc_pah=0.1, ISRF=False): | |
84 | - | |
85 | - """ | |
86 | - | |
87 | - ---------- | |
88 | - filename : str, | |
89 | - name of the file containing wavelength in nm and | |
90 | - intensity in erg cm-2 s-1 sr-1 nm-1 of a star or of the interstellar medium | |
91 | - star_radius : float, | |
92 | - star radius, in unit of solar radius | |
93 | - n_e : float, | |
94 | - electron density in cm-3 (n_e = n_h * 1.6e-4, n_h : hydrogen density) | |
95 | - parsec : float, | |
96 | - distance in parsec from the star | |
97 | - fc_pah : float, | |
98 | - fraction of cosmic carbon locked in PAHs (default: 0.1) | |
99 | - ISRF : bool, | |
100 | - Interstellar Radiation Field; if true, then the filename is a file for ISRF | |
101 | - if false, the radiation field of a star is studied (default: False) | |
102 | - ------- | |
103 | - | |
104 | - """ | |
105 | - | |
106 | - ''' input parameters ''' | |
107 | - self.filename = filename | |
108 | - self.t_gas = t_gas | |
109 | - self.n_e = n_e | |
110 | - self.n_c = n_c | |
111 | - self.parsec = parsec | |
112 | - self.star_radius = star_radius | |
113 | - self.fc_pah = fc_pah | |
114 | - self.ISRF = ISRF | |
115 | - | |
116 | - ''' parameters to be observed ''' | |
117 | - self.g_0 = None | |
118 | - self.distance = None | |
119 | - self.wavelength = None | |
120 | - self.wavelength_intensity = None | |
121 | - self.energy_intensity = None | |
122 | - self.energy = None | |
123 | - self.energy_range = None | |
124 | - self.energy_neutral = None | |
125 | - self.energy_charged = None | |
126 | - self.energy_double_charged = None | |
127 | - self.pah_cross_n = None | |
128 | - self.pah_cross_c = None | |
129 | - self.pah_cross_dc = None | |
130 | - self.ip_neutral = None | |
131 | - self.ip_charged = None | |
132 | - self.yield_of_first_photoionization = None | |
133 | - self.yield_of_second_photoionization = None | |
134 | - self.heating_efficiency = None | |
135 | - self.total_gas_heating = None | |
136 | - self.frac_neutral = None | |
137 | - self.frac_charged = None | |
138 | - self.frac_double_charged = None | |
139 | - | |
140 | - def parameters(self): | |
141 | - | |
142 | - ''' others parameters to be returned ''' | |
143 | - 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) | |
144 | - self.gamma = ( self.g_0 * np.sqrt(self.t_gas) ) / self.n_e #ionization parameter | |
145 | - | |
146 | - ''' Ionization Potential (IP) estimation ''' | |
147 | - a = (self.n_c/468)**(1/3) #molecule diameter, in nm | |
148 | - 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) | |
149 | - #IP to ionize the molecule : neutral to charged, in ev | |
150 | - 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) | |
151 | - #IP to ionize the charged molecule : charged 1 to charged 2, in ev | |
152 | - | |
153 | - '''==========================|building of the cross section|=======================''' | |
154 | - ''' derives a mean photoabsorption cross section of the molecule considered, in 3 size ranges''' | |
155 | - | |
156 | - ''' small size ''' | |
157 | - self.energy_neutral,crossn_1_case1 = np.loadtxt('./neutrals/ovalene_neutral.txt',unpack=True) #C32 | |
158 | - self.energy_charged,crossc_1_case1 = np.loadtxt('./cations/ovalene_cation.txt',unpack=True) #C32 | |
159 | - self.energy_double_charged,crossdc_1_case1 = np.loadtxt('./dications/ovalene_dication.txt',unpack=True) #C32 | |
160 | - | |
161 | - self.energy_neutral,crossn_2_case1 = np.loadtxt('./neutrals/tetrabenzocoronene_neutral.txt',unpack=True) #C36 | |
162 | - self.energy_charged,crossc_2_case1 = np.loadtxt('./cations/tetrabenzocoronene_cation.txt',unpack=True) #C36 | |
163 | - self.energy_double_charged,crossdc_2_case1 = np.loadtxt('./dications/tetrabenzocoronene_dication.txt',unpack=True) #C36 | |
164 | - | |
165 | - self.energy_neutral,crossn_3_case1 = np.loadtxt('./neutrals/circumbiphenyl_neutral.txt',unpack=True) #C38 | |
166 | - self.energy_charged,crossc_3_case1 = np.loadtxt('./cations/circumbiphenyl_cation.txt',unpack=True) #C38 | |
167 | - self.energy_double_charged,crossdc_3_case1 = np.loadtxt('./dications/circumbiphenyl_dication.txt',unpack=True) #C38 | |
168 | - | |
169 | - ''' medium size ''' | |
170 | - self.energy_neutral,crossn_1_case2=np.loadtxt('./neutrals/circumanthracene_neutral.txt',unpack=True) #C40 | |
171 | - self.energy_charged,crossc_1_case2=np.loadtxt('./cations/circumanthracene_cation.txt',unpack=True) #C40 | |
172 | - self.energy_double_charged,crossdc_1_case2=np.loadtxt('./dications/circumanthracene_dication.txt',unpack=True) #C40 | |
173 | - | |
174 | - self.energy_neutral,crossn_2_case2 = np.loadtxt('./neutrals/circumpyrene_neutral.txt',unpack=True) #C42 | |
175 | - self.energy_charged,crossc_2_case2 = np.loadtxt('./cations/circumpyrene_cation.txt',unpack=True) #C42 | |
176 | - self.energy_double_charged,crossdc_2_case2 = np.loadtxt('./dications/circumpyrene_dication.txt',unpack=True) #C42 | |
177 | - | |
178 | - self.energy_neutral,crossn_3_case2 = np.loadtxt('./neutrals/hexabenzocoronene_neutral.txt',unpack=True) #C42 | |
179 | - self.energy_charged,crossc_3_case2 = np.loadtxt('./cations/hexabenzocoronene_cation.txt',unpack=True) #C42 | |
180 | - self.energy_double_charged,crossdc_3_case2 = np.loadtxt('./dications/hexabenzocoronene_dication.txt',unpack=True) #C42 | |
181 | - | |
182 | - ''' large size ''' | |
183 | - self.energy_neutral,crossn_1_case3 = np.loadtxt('./neutrals/dicoronylene_neutral.txt',unpack=True) #C48 | |
184 | - self.energy_charged,crossc_1_case3 = np.loadtxt('./cations/dicoronylene_cation.txt',unpack=True) #C48 | |
185 | - self.energy_double_charged,crossdc_1_case3 = np.loadtxt('./dications/dicoronylene_dication.txt',unpack=True) #C48 | |
186 | - | |
187 | - self.energy_neutral,crossn_2_case3 = np.loadtxt('./neutrals/circumcoronene_neutral.txt',unpack=True) #C54 | |
188 | - self.energy_charged,crossc_2_case3 = np.loadtxt('./cations/circumcoronene_cation.txt',unpack=True) #C54 | |
189 | - self.energy_double_charged,crossdc_2_case3 = np.loadtxt('./dications/circumcoronene_dication.txt',unpack=True) #C54 | |
190 | - | |
191 | - self.energy_neutral,crossn_3_case3 = np.loadtxt('./neutrals/circumovalene_neutral.txt',unpack=True) #C66 | |
192 | - self.energy_charged,crossc_3_case3 = np.loadtxt('./cations/circumovalene_cation.txt',unpack=True) #C66 | |
193 | - self.energy_double_charged,crossdc_3_case3 = np.loadtxt('./dications/circumovalene_dication.txt',unpack=True) #C66 | |
194 | - #for each cross section for each state of the molecule, we have an associated energy | |
195 | - | |
196 | - self.energy_range = np.where(self.energy_neutral<13.6)[0] | |
197 | - #energy_neutral|charged|double_charged are the same | |
198 | - | |
199 | - self.pah_cross_n = ( ( (crossn_1_case1/32)+(crossn_2_case1/36)+(crossn_3_case1/38) +\ | |
200 | - (crossn_1_case2/40)+(crossn_2_case2/42)+(crossn_3_case2/42) +\ | |
201 | - (crossn_1_case3/48)+(crossn_2_case3/54)+(crossn_3_case3/66) )/9 ) * self.n_c | |
202 | - self.pah_cross_c = ( ( (crossc_1_case1/32)+(crossc_2_case1/36)+(crossc_3_case1/38) +\ | |
203 | - (crossc_1_case2/40)+(crossc_2_case2/42)+(crossc_3_case2/42) +\ | |
204 | - (crossc_1_case3/48)+(crossc_2_case3/54)+(crossc_3_case3/66) )/9 ) * self.n_c | |
205 | - self.pah_cross_dc = ( ((crossdc_1_case1/32)+(crossdc_2_case1/36)+(crossdc_3_case1/38) +\ | |
206 | - (crossdc_1_case2/40)+(crossdc_2_case2/42)+(crossdc_3_case2/42) +\ | |
207 | - (crossdc_1_case3/48)+(crossdc_2_case3/54)+(crossdc_3_case3/66) )/9 ) * self.n_c | |
208 | - #cross_n is the average cross section of a pah of all types of size | |
209 | - | |
210 | - ''' Ranges imposed ''' | |
211 | - self.energy_neutral = self.energy_neutral[self.energy_range] | |
212 | - self.energy_charged = self.energy_charged[self.energy_range] | |
213 | - self.energy_double_charged = self.energy_double_charged[self.energy_range] | |
214 | - self.pah_cross_n = self.pah_cross_n[self.energy_range] | |
215 | - self.pah_cross_c = self.pah_cross_c[self.energy_range] | |
216 | - self.pah_cross_dc = self.pah_cross_dc[self.energy_range] | |
217 | - | |
218 | - ''' yield from neutral to the first photoionization ''' | |
219 | - first_part = np.where(self.energy_neutral<self.ip_neutral)[0] | |
220 | - | |
221 | - second_part = np.where( (self.energy_neutral>=self.ip_neutral) & (self.energy_neutral<(self.ip_neutral+9.2) ) )[0] | |
222 | - third_part = np.where((self.energy_neutral>self.ip_neutral+9.2))[0] | |
223 | - | |
224 | - y_1 = np.zeros([len(first_part)]) | |
225 | - y_2 = ( self.energy_neutral[second_part]-self.ip_neutral )/9.2 | |
226 | - y_3 = np.full(len(third_part), 1) | |
227 | - | |
228 | - self.yield_of_first_photoionization = np.concatenate( (y_1,y_2,y_3) ) | |
229 | - | |
230 | - ''' yield from the first photoionization to the second photoionization ''' | |
231 | - alpha = 0.3 #teepness coefficient, see Wenzel et al. 2020 | |
232 | - if (self.n_c >= 32) & (self.n_c < 50): | |
233 | - beta = 0.59 + 8.1e-3 * self.n_c | |
234 | - if self.n_c >= 50: | |
235 | - beta = 1 | |
236 | - | |
237 | - first_part = np.where( self.energy_charged<self.ip_charged )[0] | |
238 | - second_part = np.where( ( self.energy_charged>=self.ip_charged ) & ( self.energy_charged<11.3 ) )[0] | |
239 | - third_part = np.where( ( self.energy_charged>=11.3 ) & ( self.energy_charged<12.9 ) )[0] | |
240 | - fourth_part = np.where( ( self.energy_charged>=12.9 ) & ( self.energy_charged<13.6 ) )[0] | |
241 | - | |
242 | - y_1 = np.zeros([len(first_part)]) | |
243 | - y_2 = ( alpha/(11.3-self.ip_charged) ) * (self.energy_charged[second_part]-self.ip_charged) | |
244 | - y_3 = np.full(len(third_part), alpha) | |
245 | - y_4 = ( (beta-alpha)/2.1 ) * (self.energy_charged[fourth_part]-12.9) + alpha | |
246 | - | |
247 | - self.yield_of_second_photoionization = np.concatenate( (y_1,y_2,y_3,y_4) ) | |
248 | - | |
249 | - ''' adaptating the cross section from 0 to 13.6eV''' | |
250 | - pah_crossn = np.interp(self.energy,self.energy_neutral,self.pah_cross_n)*mb #in cm2/Carbon (from Mb/C to cm2/C) | |
251 | - pah_crossc = np.interp(self.energy,self.energy_charged,self.pah_cross_c)*mb #in cm2/Carbon (from Mb/C to cm2/C) | |
252 | - pah_crossdc = np.interp(self.energy,self.energy_double_charged,self.pah_cross_dc)*mb #in cm2/Carbon (from Mb/C to cm2/C) | |
253 | - | |
254 | - yield_n = np.interp(self.energy,self.energy_neutral,self.yield_of_first_photoionization) | |
255 | - yield_c = np.interp(self.energy,self.energy_charged,self.yield_of_second_photoionization) | |
256 | - #interpolation | |
257 | - | |
258 | - '''===================== dust and gas heating calculation ===================''' | |
259 | - energy_range_power_absorbed = np.where(self.energy<=13.6)[0] | |
260 | - energy_range_neutral = np.where(np.logical_and(self.energy >= self.ip_neutral, self.energy <= 13.6))[0] | |
261 | - energy_range_charged = np.where(np.logical_and(self.energy >= self.ip_charged, self.energy <= 13.6))[0] | |
262 | - | |
263 | - ''' photoabsorption of the neutrals, cations and dications molecules ''' | |
264 | - photo_absorption_n = self.energy_intensity*pah_crossn*2*np.pi #erg s-1 eV-1 /!\ the 2*np.pi is the solid angle considered => the RF comes from the star only | |
265 | - photo_absorption_c = self.energy_intensity*pah_crossc*2*np.pi #erg s-1 eV-1 | |
266 | - photo_absorption_dc = self.energy_intensity*pah_crossdc*2*np.pi #erg s-1 eV-1 | |
267 | - | |
268 | - ''' power density absorbed for ionization ''' | |
269 | - ionization_absorption_n = yield_n*photo_absorption_n #erg s-1 eV-1 | |
270 | - ionization_absorption_c = yield_c*photo_absorption_c #erg s-1 eV-1 | |
271 | - | |
272 | - ''' number of ionizations ''' | |
273 | - number_ionization_absorption_n = ionization_absorption_n/(self.energy*ev_to_erg) | |
274 | - number_ionization_absorption_c = ionization_absorption_c/(self.energy*ev_to_erg) | |
275 | - #number of ionizations per s per eV for a charge state | |
276 | - | |
277 | - ''' photoemission rate ''' | |
278 | - kpe_neutral = np.trapz(number_ionization_absorption_n[energy_range_neutral], (self.energy-self.ip_neutral)[energy_range_neutral]) | |
279 | - kpe_charged = np.trapz(number_ionization_absorption_c[energy_range_charged], (self.energy-self.ip_charged)[energy_range_charged]) | |
280 | - #in s-1 | |
281 | - | |
282 | - ''' recombination rate ''' | |
283 | - phi = ( 1.85*1e5 )/( self.t_gas*np.sqrt(self.n_c) ) #dimensionless | |
284 | - krec_neutral = self.n_e * 1.28e-10 * self.n_c * np.sqrt(self.t_gas) * ( 1 + phi ) | |
285 | - krec_charged = self.n_e * 1.28e-10 * self.n_c * np.sqrt(self.t_gas) * ( 1 + phi * (1 + z_1) ) | |
286 | - #in s-1 | |
287 | - | |
288 | - ''' population fraction computation ''' | |
289 | - #cations | |
290 | - self.frac_charged = 1/( 1+( krec_neutral/kpe_neutral) + (kpe_charged/krec_charged) ) | |
291 | - #neutrals | |
292 | - self.frac_neutral = (1 - self.frac_charged * (kpe_charged/krec_charged) )/( 1 + (kpe_neutral/krec_neutral) ) | |
293 | - #dications | |
294 | - self.frac_double_charged = (1 - self.frac_neutral)/( 1 + (krec_charged/kpe_charged) ) | |
295 | - | |
296 | - ''' selection of the partition coefficient ''' | |
297 | - partition_coeff = 0.46 #PAH parameter, 0.46 + or - 0.06 | |
298 | - | |
299 | - ''' spectrum of the gas heating per charge state ''' | |
300 | - neutral_heating_rate_spectrum = partition_coeff * (self.energy-self.ip_neutral) *\ | |
301 | - number_ionization_absorption_n * ev_to_erg #erg s-1 eV-1 | |
302 | - charged_heating_rate_spectrum = partition_coeff * (self.energy-self.ip_charged) *\ | |
303 | - number_ionization_absorption_c * ev_to_erg #erg s-1 eV-1 | |
304 | - #partition_coeff * (E-IP) is the kinetic energy of the photoelectron following absorption of a UV photon of energy E | |
305 | - | |
306 | - ''' gas heating rate per charge state ''' | |
307 | - neutral_gas_heating_rate = np.trapz(neutral_heating_rate_spectrum[energy_range_neutral],\ | |
308 | - (self.energy-self.ip_neutral)[energy_range_neutral] ) #erg s-1 molecule-1 | |
309 | - charged_gas_heating_rate = np.trapz(charged_heating_rate_spectrum[energy_range_charged],\ | |
310 | - (self.energy-self.ip_charged)[energy_range_charged] ) #erg s-1 molecule-1 | |
311 | - #powers injected in the gas by photoelectrons ejected from | |
312 | - #neutral and cationic PAHs | |
313 | - | |
314 | - '''======================== heating efficiencies ========================''' | |
315 | - | |
316 | - ''' total power injected into the gas via the photoelectrons from pahs ''' | |
317 | - total_injected_power = self.frac_neutral * neutral_gas_heating_rate +\ | |
318 | - self.frac_charged * charged_gas_heating_rate | |
319 | - #erg s-1 /(molecule of size n_c) | |
320 | - | |
321 | - ''' heating rate of the molecule itself ''' | |
322 | - heating_pah_n = np.trapz(photo_absorption_n[energy_range_power_absorbed],\ | |
323 | - self.energy[energy_range_power_absorbed]) #erg s-1 | |
324 | - heating_pah_c = np.trapz(photo_absorption_c[energy_range_power_absorbed],\ | |
325 | - self.energy[energy_range_power_absorbed]) #erg s-1 | |
326 | - heating_pah_dc = np.trapz(photo_absorption_dc[energy_range_power_absorbed],\ | |
327 | - self.energy[energy_range_power_absorbed]) #erg s-1 | |
328 | - #power absorbed by each PAH charge state | |
329 | - | |
330 | - ''' total power of the radiation absorbed by PAHs ''' | |
331 | - total_absorbed_radiation_power = self.frac_neutral * heating_pah_n +\ | |
332 | - self.frac_charged * heating_pah_c +\ | |
333 | - self.frac_double_charged * heating_pah_dc | |
334 | - #erg s-1 /(molecule of size n_c) | |
335 | - | |
336 | - ''' heating efficiency ''' | |
337 | - self.heating_efficiency = total_injected_power/total_absorbed_radiation_power | |
338 | - | |
339 | - ''' gas heating ''' | |
340 | - self.total_gas_heating = total_injected_power * (self.fc_pah/self.n_c) * 2.7e-4 | |
341 | - #2.7e-4 : elemental abundance of C relative to H (Tielens 2021) | |
342 | - | |
343 | - return self.total_gas_heating, self.g_0 , self.gamma , self.t_gas, self.n_e, self.n_c | |
344 | 0 | \ No newline at end of file |