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witt.py
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witt.py
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"""
Simple EOS and background opacity package
Coded in python by J. de la Cruz Rodriguez (ISP-SU 2017)
"""
import numpy as np
from math import *
import os
import xdrlib
import witt as this
class dum: # Just a container for the PF
nstage = 0
npi = 0
pf = 0
eion = 0
def __init__(self):
pass
# ----------------------------------------------------------------------------------------
class witt:
"""
EOS described in Mihalas (1970) "Stellar atmospheres"
It considers in detail H, H+, H- and H2, no other molecules.
This particular implementation was taken from Wittmann's routines.
Partition functions from Kurucz.
Coded in python by J. de la Cruz Rodriguez (ISP-SU 2017)
Dependencies: pf_Kurucz.input containing the partition function data.
"""
# Some definitions (from NIST)
BK = 1.3806488E-16 # Boltzmann [erg K]
EE = 4.80320441E-10 # Electron charge
HH = 6.62606957E-27 # Planck [erg s]
PI = 3.14159265358979323846 # PI number
CC = 2.99792458E10 # Speed of light [cm/s]
AMU = 1.660538921E-24 # Atomic mass unit
EV = 1.602176565E-12 # Electron Volt to erg
CM1_TO_EV = HH*CC/EV # CM^-1 to eV
ME = 9.10938188E-28 # mass of electron
saha_fac = ((2.0 * PI * ME * BK) / (HH*HH))**1.5
# Default abundances
ABUND = 10.0**np.float64( [-0.04048,-1.07,-10.95,-10.89, -9.44, -3.48, -3.99,
-3.11, -7.48, -3.95, -5.71, -4.46, -5.57, -4.49, -6.59, -4.83,
-6.54, -5.48, -6.82, -5.68, -8.94, -7.05, -8.04, -6.37, -6.65,
-4.50, -7.12, -5.79, -7.83, -7.44, -9.16, -8.63, -9.67, -8.69,
-9.41, -8.81, -9.44, -9.14, -9.80, -9.54,-10.62,-10.12,-20.00,
-10.20,-10.92,-10.35, -11.10,-10.18,-10.58,-10.04,-11.04, -9.80,
-10.53, -9.81,-10.92, -9.91,-10.82,-10.49,-11.33,-10.54,-20.00,
-11.04,-11.53,-10.92, -11.94,-10.94,-11.78,-11.11,-12.04,-10.96,
-11.28,-11.16,-11.91, -10.93,-11.77,-10.59,-10.69,-10.24,-11.03,
-10.95,-11.14,-10.19, -11.33,-20.00,-20.00,-20.00,-20.00,-20.00,
-20.00,-11.92,-20.00, -12.51,-20.00,-20.00,-20.00,-20.00,-20.00,
-20.00,-20.00])
AMASS = np.float64([1.008, 4.003, 6.941, 9.012, 10.811, 12.011, 14.007, 15.999,
18.998, 20.179, 22.990, 24.305, 26.982, 28.086, 30.974, 32.060,
35.453, 39.948, 39.102, 40.080, 44.956, 47.900, 50.941, 51.996,
54.938, 55.847, 58.933, 58.710, 63.546, 65.370, 69.720, 72.590,
74.922, 78.960, 79.904, 83.800, 85.468, 87.620, 88.906, 91.220,
92.906, 95.940, 98.906,101.070,102.905,106.400,107.868,112.400,
114.820,118.690,121.750,127.600,126.905,131.300,132.905,137.340,
138.906,140.120,140.908,144.240,146.000,150.400,151.960,157.250,
158.925,162.500,164.930,167.260,168.934,170.040,174.970,178.490,
180.948,183.850,186.200,190.200,192.200,195.090,196.967,200.590,
204.370,207.190,208.981,210.000,210.000,222.000,223.000,226.025,
227.000,232.038,230.040,238.029,237.048,242.000,242.000,245.000,
248.000,252.000,253.000])
# Energy of a 6 level H atom in erg and corresponding g-values
eH = np.float64((0.0, 82258.211, 97491.219, 102822.76, 105290.508, 109677.617)) * HH * CC
gH = np.float64((2.0, 8.0, 18.0, 32.0, 50.0, 1.0))
# ----------------------------------------------------------------------------------------
def init_pf_data(self, ifile, to_EV=True):
#
# Reads Kurucz's partition functions and ionization potentials from a file
# Taken from RH (Uitenbroek 2001)
#
ff = open(ifile,'rb')
f = ff.read()
ff.close()
data = xdrlib.Unpacker(f)
npf = data.unpack_uint()
nelem = 99
self.tpf = np.float64(data.unpack_farray(npf, data.unpack_double))
self.el = [None] * nelem
for ii in range(nelem):
pti = data.unpack_uint()
nstage = data.unpack_uint()
self.el[ii] = dum()
self.el[ii].pf = np.float64(data.unpack_farray(npf*nstage, data.unpack_double)).reshape((nstage, npf))
self.el[ii].eion = np.float64(data.unpack_farray(nstage, data.unpack_double)) * self.HH*self.CC
self.el[ii].nstage = nstage
self.el[ii].npf = pti
if(to_EV): self.el[ii].eion /= self.EV
# ----------------------------------------------------------------------------------------
def acota(self, x, x0, x1):
if(x < x0): x = x0
if(x > x1): x = x1
return x
# ----------------------------------------------------------------------------------------
def acotasig(self, x, x0, x1):
if(x < 0):
x = -x
x = self.acota(x, x0, x1)
x = -x
else:
x = self.acota(x, x0, x1)
return x
# ----------------------------------------------------------------------------------------
def sign(self, a, b):
return abs(a) * (b / abs(b))
# ----------------------------------------------------------------------------------------
def __init__(self, abund_init = [], verbose = False, prec = 1.e-5, pf_file='pf_Kurucz.input'):
self.verbose = verbose
self.prec = 1.e-5
self.ncontr = 28 # number of species contributing as electron donnors (sorted)
self.dtype = 'float64'
# Replace default abundances ?
nabund = len(abund_init)
if(nabund > 0):
self.ABUND[0:nabund] = abund_init
if(self.verbose): print('witt::__init__: replacing default abundances with user provided values')
self.abtot = self.ABUND.sum()
self.ABUND /= self.abtot
self.abtot = 1.0
self.ab_others = self.ABUND[1::].sum() / self.ABUND[0]
self.avw = (self.ABUND * self.AMASS).sum()
self.muH = self.avw/ self.AMASS[0] / self.ABUND[0]
self.rho_from_H = self.muH * self.AMASS[0]*self.AMU / self.BK
self.avw *= self.AMU
# init arrays for later
self.alfai = np.zeros(self.ncontr, dtype=self.dtype)
self.chi1 = np.zeros(self.ncontr, dtype=self.dtype)
self.chi2 = np.zeros(self.ncontr, dtype=self.dtype)
self.u0 = np.zeros(self.ncontr, dtype=self.dtype)
self.u1 = np.zeros(self.ncontr, dtype=self.dtype)
self.u2 = np.zeros(self.ncontr, dtype=self.dtype)
# Init PF
this_dir, this_filename = os.path.split(__file__)
DATA_PATH = os.path.join(this_dir, pf_file)
self.init_pf_data(DATA_PATH, True)
# ----------------------------------------------------------------------------------------
def nsaha(self, t, xne, u0, u1, eion):
# operates with t, xne and eion in EV
return 2.0 * self.saha_fac * (u1 / u0) * t**1.5 * exp(-eion*self.EV / (t*self.BK)) / xne
# ----------------------------------------------------------------------------------------
def saha(self, theta, eion, u1, u2, pe):
# Operates with theta, eion in eV and pe
return u2*exp(2.302585093*(9.0804625434325867-theta*eion))/(u1*pe*theta**2.5)
# ----------------------------------------------------------------------------------------
def init_pe_from_pg(self, t, pg):
# Assume that only H is a electron donnor
nu = self.ABUND[0]
saha = 10.0**( -0.4771+2.5*log10(t)-log10(pg)-(13.6*5040.0/t))
aaa = 1.0 + saha
bbb = -(nu-1.0) * saha
ccc = -saha*nu
ybh=(-bbb+sqrt(bbb*bbb-4.*aaa*ccc))/(2.*aaa)
pe=pg*ybh/(1.+ybh)
return pe
# ----------------------------------------------------------------------------------------
def pe_from_pg(self, t, pg, get_fe = False):
dif = 1.1
pe = self.init_pe_from_pg(t, pg) # Init Pe assuming only H and increase it 10%
ope = pe
it = 0
while((abs(dif) > self.prec) and (it < 250)):
pe = (ope + pe)*0.5
ope = pe
pe,fe = self.pe_pg(t, pe, pg, get_fe=True)
dif = 2.0 * abs(pe-ope) / (pe+ope)
it += 1
if(self.verbose): print("witt::pe_from_pg: convergence niter = {0}".format(it-1))
if(get_fe): return pe, fe
return pe
# ----------------------------------------------------------------------------------------
def pe_from_rho(self, t, rho):
# fraction of atoms
xna = rho / self.avw
BKT = self.BK * t
# now estimate Pgas and iterate
if(t > 8000): a = 0.5;
elif(t > 4000): a = 0.1;
elif(t > 2000): a = 0.01;
else: a = 0.001;
xne = a * xna /(1.0 - a)
Pgas = (xna+xne)*BKT
# Iterate
it = 0
dif = 1.0
while((it < 250) and (abs(dif) > self.prec)):
oPgas = Pgas
Pe = self.pe_from_pg(t, Pgas)
xna_guessed = (Pgas-Pe)/BKT
dif = abs(xna-xna_guessed)/xna
Pgas *= xna/xna_guessed
return Pe#, Pgas
# ----------------------------------------------------------------------------------------
def pg_from_rho(self, temp, rho):
xna = (rho / self.avw)
if(temp > 8000): a = 0.5;
elif(temp > 4000): a = 0.1;
elif(temp > 2000): a = 0.01;
else: a = 0.001;
xne = a * xna /(1.0 - a)
pgas = (xna+xne)*self.BK*temp
Pe = self.pe_from_pg(temp, pgas)
irho = self.rho_from_pe(temp, Pe)
dif = 1.0
it = 0
while((dif >= self.prec) and (it<100)):
Pe *= (1.0 + rho / irho)*0.5
irho = self.rho_from_pe(temp, Pe)
dif = np.abs((irho - rho) / (rho))
it+=1
pgas = self.pg_from_pe(temp, Pe)
return pgas
# ----------------------------------------------------------------------------------------
def rho_from_pe(self,temp, pe):
pg, fe_out = self.pg_from_pe(temp, pe, True)
rho = pe * self.rho_from_H / (fe_out * temp)
return rho
# ----------------------------------------------------------------------------------------
def rho_from_pg(self,temp, pg):
pe, fe_out = self.pe_from_pg(temp, pg, True)
rho = pe * self.rho_from_H / (fe_out * temp)
return rho
# ----------------------------------------------------------------------------------------
def molecb(self, X):
Y = np.empty(2, dtype=self.dtype); dy = np.empty(2, dtype=self.dtype)
Y[0]=-11.206998+X*(2.7942767+X*(7.9196803E-2-X*2.4790744E-2)) # H2
Y[1]=-12.533505+X*(4.9251644+X*(-5.6191273E-2+X*3.2687661E-3)) # H
dx=(-X*X)/5040.
dy[0]=dx*(2.7942767+X*(2*7.9196803e-2-X*3*2.4790744e-2))
dy[1]=dx*(4.9251644+X*(-2*5.6191273e-2-X*3*3.2687661e-3))
return Y, dy
# ----------------------------------------------------------------------------------------
def pe_pg(self, t, pe, pgas, get_fe=False):
g1 = 0.; theta = 5040.0/t
# Init some values
if(pe < 0.0):
pe = 1.e-15
g4 = 0.0
g5 = 0.0
else:
cmol, dcmol = self.molecb(theta)
cmol[0] = self.acota(cmol[0], -30., 30.)
cmol[1] = self.acota(cmol[1], -30., 30.)
g4 = pe * 10.0**cmol[0]
g5 = pe * 10.0**cmol[1]
#
# H first
#
u = self.partition_f(0, t, only=3)
g2 = self.saha(theta, self.el[0].eion[0], u[0], u[1], pe) # p(h+)/p(h)
g3 = self.saha(theta, 0.754, 1.0, u[0], pe) # p(h)/p(h-)
g3 = 1.0 / self.acota(g3, 1.e-30, 1.0e30)
#
# Now count electrons contributed by the first
# two ionized stages of all contributing atoms
#
for ii in range(1, self.ncontr):
alfai = self.ABUND[ii] / self.ABUND[0] # relative to H abundance
u = self.partition_f(ii, t, only=3)
a = self.saha(theta, self.el[ii].eion[0], u[0], u[1], pe)
b = self.saha(theta, self.el[ii].eion[1], u[1], u[2], pe)
c = 1.+a*(1.+b)
g1 += alfai/c*a*(1.+2.*b)
# All the math...
a=1.+g2+g3
b=2.*(1.+g2/g5*g4)
c=g5
d=g2-g3
e=g2/g5*g4
a = self.acotasig(a, 1.e-15, 1.e15);
d = self.acotasig(d, 1.e-15, 1.e15);
c1=c*b*b+a*d*b-e*a*a
c2=2.0*a*e-d*b+a*b*g1
c3=-(e+b*g1)
f1=0.5*c2/c1
f1=-f1+self.sign(1.,c1)*sqrt(f1*f1-c3/c1)
f5=(1.-a*f1)/b
f4=e*f5
f3=g3*f1
f2=g2*f1
fe = self.acota(f2-f3+f4+g1, 1.e-30, 1.e30)
phtot = pe/fe
# Refinement by Wittmann, not sure this is needed in
# double prec.
if(f5 <= 1.e-4):
diff = 1.0; const6=g5/pe*f1*f1; const7=f2-f3+g1; it = 0
while((diff > 1.e-5) and (it < 5)):
of5 = f5
f5=phtot*const6
f4=e*f5
fe=const7+f4
phtot=pe/fe
diff = 0.5 * fabs(f5-of5) / (f5 + of5)
it += 1
# Recompute pe
pe = pgas / (1.+(f1+f2+f3+f4+f5+self.ab_others)/fe)
if(pe <= 0.0):
pe = 1.e-15
if(get_fe): return pe, fe
return pe
# ----------------------------------------------------------------------------------------
def Boltzmann(self, t, u, glow, e_pot):
# Gives the ratio between the total population of a ionization stage and a given level
# The energy levels must be in Erg.
return (glow / u) * exp(-(e_pot) / (self.BK*t))
# ----------------------------------------------------------------------------------------
def getH6pop(self, t, pgas, pe):
# Solve ionization for H
n, u = self.getXparts(0, t, pgas, pe, divide_by_u = False, return_u = True)
# Define output array
res = np.empty(6, dtype='float64')
res[-1] = n[1] # number of protons
ratios = np.empty(5, dtype='float64')
# Solve level populations for the 5 first levels of H
for ii in range(5):
ratios[ii] = self.Boltzmann(t, u[0], self.gH[ii], self.eH[ii])
# particle conservation (with 6 levels in H this line has no effect)
#ratios /= ratios.sum()
# Multiply the neutral H population by the ratios of level populations
res[0:5] = n[0] * ratios
return res
# ----------------------------------------------------------------------------------------
def _itep1(self, x, y, xx):
"""
Linear interpolation routine
input:
x: array of input x values
y: array of input y values
xx: scalar x value where the interpolated value of "y must be calculated
"""
if(xx <= x[0]): return y[0]
elif(xx >= x[-1]): return y[-1]
else:
idx=np.where(x>xx)[0]
p0 = idx[0]
p1 = p0-1
dx = x[p1]-x[p0]
u1 = (xx-x[p0]) / dx
u0 = 1.0 - u1
return u0 * y[p0] + u1 * y[p1]
# ----------------------------------------------------------------------------------------
def partition_f(self, n, t, only=0):
"""
Computes the partition function of element "n" for a given temperature
input:
n: Atomic number of the atom -1 (H is 0).
t: Temperature in K.
Keywords:
only: (=int) only return this number first levels of the atom.
The default is to return all the levels
"""
nn = self.el[n].nstage
if(only > 0):
nn = min(nn, only)
res = np.zeros(only, dtype='float64')
else:
res = np.zeros(nn, dtype='float64')
for ii in range(nn):
res[ii] = self._itep1( self.tpf, self.el[n].pf[ii], t)
return res
# ----------------------------------------------------------------------------------------
def pg_from_pe(self, t, pe, get_fe=False):
pg, dum = self.gasc(t, pe)
if(get_fe): return pg, dum[-1]
return pg
# ----------------------------------------------------------------------------------------
def gasc(self, t, pe):
pp = np.zeros(self.ncontr+6, dtype = self.dtype)
theta = 5040. / t
cmol, dmol = self.molecb(theta)
g4 = 10.0**cmol[0]; g5 = 10.0**cmol[1]
# First H
u = self.partition_f(0, t)
g2 = self.saha(theta, self.el[0].eion[0], u[0], u[1], pe) # p(h+)/p(h)
g3 = 1.0 / self.saha(theta, 0.754, 1.0, u[0], pe) # p(h)/p(h-)
g1 = 0.0
# Other contributions
for ii in range(1, self.ncontr):
alfai = self.ABUND[ii] / self.ABUND[0] # relative to H abundance
u = self.partition_f(ii, t, only=3)
a = self.saha(theta, self.el[ii].eion[0], u[0], u[1], pe)
b = self.saha(theta, self.el[ii].eion[1], u[1], u[2], pe)
c=1.+a*(1.+b) # fraction of n0/ntot
pp[ii]=alfai/c # abund /ntot (partial pressure of neutral species ii)
# 1*n1 + 2*n2 + ... j*n_j so we count how many electrons
# come from each ionized species
g1 += pp[ii]*a*(1.+2.*b)
a=1.+g2+g3
e=g2/g5*g4
b=2.0*(1.0 + e)
c=g5
d=g2-g3
c1=c*b*b+a*d*b-e*a*a
c2=2.*a*e-d*b+a*b*g1
c3=-(e+b*g1)
f1=0.5*c2/c1
f1=-f1+self.sign(1.0,c1)*sqrt(f1*f1-c3/c1)
f5=(1.0-a*f1)/b
f4=e*f5
f3=g3*f1
f2=g2*f1
fe=f2-f3+f4+g1
phtot=pe/fe
# Refinement by Wittmann
if(f5 <= 1.e-5):
diff = 1.0; const6=g5/pe*f1*f1; const7=f2-f3+g1; it = 0
while((diff > 1.e-5) and (it < 5)):
of5 = f5
f5=phtot*const6
f4=e*f5
fe=const7+f4
phtot=pe/fe
diff = 0.5 * fabs(f5-of5) / (f5 + of5)
it += 1
pg=pe*(1.0+(f1+f2+f3+f4+f5+self.ab_others)/fe)
# Store the partial pressures of H too
pp[self.ncontr+0] = f1 # p(h)/p(h')
pp[self.ncontr+1] = f2 # p(h+)/p(h')
pp[self.ncontr+2] = f5 # p(h2)/p(h')
pp[self.ncontr+3] = f3 # p(h-)/p(h')
pp[self.ncontr+4] = phtot # p(h') (total hydrogen!)
pp[self.ncontr+5] = fe # p(h') (total hydrogen!)
return pg, pp
# ----------------------------------------------------------------------------------------
def getXparts(self, iatom, t, pg, pe, divide_by_u = False, only = 0, return_u = False):
# Precompute partial densities of atoms, electrons
# and partial density of iatom with the abundance
TBK = t * self.BK; xna = (pg-pe) / TBK; xne = pe / TBK
n_tot = xna * self.ABUND[iatom] / self.abtot
# Partition function
u = self.partition_f(iatom, t, only=only)
nLev = u.size
# Solve saha and get the partial density of each ionized stage
xpa = np.empty(nLev, dtype='float64')
xpa[0] = 1.0
for ii in range(1, nLev):
xpa[ii] = self.nsaha(t, xne, u[ii-1], u[ii], self.el[iatom].eion[ii-1])
for ii in range(nLev-1, 0, -1):
xpa[0] = 1.0 + xpa[0]*xpa[ii]
xpa[0] = 1.0 / xpa[0]
for ii in range(1, nLev):
xpa[ii] *= xpa[ii-1]
# Now that we have the ratios between ionized stages, multiply by the partial
# density of iatom. Divide by the partition function if needed
if(divide_by_u):
xpa[:] *= n_tot / u[:]
else:
xpa *= n_tot
if(return_u): return xpa, u
else: return xpa
# ----------------------------------------------------------------------------------------
def getBackgroundPartials(self, t, pg, pe, divide_by_u = True):
n = np.empty(17, dtype='float64')
tbk = t * self.BK
# --- He/He+/He++ ---
xpa = self.getXparts(1, t, pg, pe, divide_by_u = divide_by_u)
n[3] = xpa[0]; n[4] = xpa[1]; n[5] = xpa[2]
# --- C ---
xpa = self.getXparts(5, t, pg, pe, divide_by_u = divide_by_u)
n[6] = xpa[0]
# --- Al ---
xpa = self.getXparts(12, t, pg, pe, divide_by_u = divide_by_u)
n[7] = xpa[0]
# --- Si/Si+ ---
xpa = self.getXparts(13, t, pg, pe, divide_by_u = divide_by_u)
n[8] = xpa[0]; n[9] = xpa[1]
# --- Ca/Ca+ ---
xpa = self.getXparts(19, t, pg, pe, divide_by_u = divide_by_u)
n[10] = xpa[0]; n[11] = xpa[1]
# --- Mg/Mg+ ---
xpa = self.getXparts(11, t, pg, pe, divide_by_u = divide_by_u)
n[12] = xpa[0]; n[13] = xpa[1]
# --- Fe ---
xpa = self.getXparts(25, t, pg, pe, divide_by_u = divide_by_u)
n[14] = xpa[0]
# --- N ---
xpa = self.getXparts(6, t, pg, pe, divide_by_u = divide_by_u)
n[15] = xpa[0]
# --- O ---
xpa = self.getXparts(7, t, pg, pe, divide_by_u = divide_by_u)
n[16] = xpa[0]
# Get H- and other H densities
if(divide_by_u): pfH = 0.5
else: pfH = 1.0
dum, pp = self.gasc(t, pe)
n[0] = pp[self.ncontr+0]*pp[self.ncontr+4] / tbk * pfH # H / pf[H]
n[1] = pp[self.ncontr+1]*pp[self.ncontr+4] / tbk # H+/ 1.0
n[2] = pp[self.ncontr+3]*pp[self.ncontr+4] / tbk # H-/ 1.0
return n
# ----------------------------------------------------------------------------------------
def contOpacity(self, iT, Pgas, Pe, w):
# Some definitions
TK = iT * self.BK; TKEV = TK / self.EV
HTK = self.HH/TK; TLOG = log(iT);
xna = (Pgas-Pe) / TK; xne = Pe / TK
# Partial densities of background absorvers,
# divided by the partition functions
n = self.getBackgroundPartials(iT, Pgas, Pe, divide_by_u = True)
# get background opacity
opac, scat = this.cop(iT, TKEV, TK, HTK, TLOG, xna, xne, w, n[0], n[1],
n[2], n[3],n[4], n[5], n[6], n[7], n[8], n[9], n[10], n[11],
n[12], n[13], n[14], n[15], n[16])
return opac
# ----------------------------------------------------------------------------------------
#
# All the following functions are used to compute background opacities.
# The main call is done to function "cop", that calls all the other auxiliary
# functions.
#
# ----------------------------------------------------------------------------------------
def SEATON(FREQ0, XSECT, POWER, A, FREQ):
return XSECT*(A+(1.-A)*(FREQ0/FREQ))* (FREQ0/FREQ)**(floor(2.*POWER+0.01)*0.5)
# ----------------------------------------------------------------------------------------
Z4LOG=np.float64((0.,1.20412,1.90849,2.40824,2.79588,3.11261))
A0 = np.float64((
5.53,5.49,5.46,5.43,5.40,5.25,5.00,4.69,4.48,4.16,3.85,
4.91,4.87,4.84,4.80,4.77,4.63,4.40,4.13,3.87,3.52,3.27,
4.29,4.25,4.22,4.18,4.15,4.02,3.80,3.57,3.27,2.98,2.70,
3.64,3.61,3.59,3.56,3.54,3.41,3.22,2.97,2.70,2.45,2.20,
3.00,2.98,2.97,2.95,2.94,2.81,2.65,2.44,2.21,2.01,1.81,
2.41,2.41,2.41,2.41,2.41,2.32,2.19,2.02,1.84,1.67,1.50,
1.87,1.89,1.91,1.93,1.95,1.90,1.80,1.68,1.52,1.41,1.30,
1.33,1.39,1.44,1.49,1.55,1.56,1.51,1.42,1.33,1.25,1.17,
0.90,0.95,1.00,1.08,1.17,1.30,1.32,1.30,1.20,1.15,1.11,
0.55,0.58,0.62,0.70,0.85,1.01,1.15,1.18,1.15,1.11,1.08,
0.33,0.36,0.39,0.46,0.59,0.76,0.97,1.09,1.13,1.10,1.08,
0.19,0.21,0.24,0.28,0.38,0.53,0.76,0.96,1.08,1.09,1.09)).reshape((12,11))
def COULFF(TLOG, FREQLG, NZ):
GAMLOG=10.39638-TLOG/1.15129+Z4LOG[NZ-1]
IGAM=min(int(GAMLOG+7.),10)
if(IGAM<1): IGAM=1
# HVKTLG=2*log10(HVKT) #
HVKTLG=(FREQLG-TLOG)/1.15129-20.63764
IHVKT=min(int(HVKTLG+9.),11)
if(IHVKT<1): IHVKT=1
P=GAMLOG-(IGAM-7);
Q=HVKTLG-(IHVKT-9);
return (1.-P)*((1.-Q)*A0[IHVKT-1,IGAM-1]+Q*A0[IHVKT, IGAM-1])+P*((1.-Q)*A0[IHVKT-1,IGAM]+Q*A0[IHVKT,IGAM])
# ----------------------------------------------------------------------------------------
A1 = np.float64((0.9916,1.105,1.101,1.101,1.102,1.0986))
B1 = np.float64((2.719e3,-2.375e4,-9.863e3,-5.765e3,-3.909e3,-2.704e3))
C1 = np.float64((-2.268e10,4.077e8,1.035e8,4.593e7,2.371e7,1.229e7))
def COULX(N, freq, Z):
n=(N+1.0)**2
if(freq>=(Z*Z*3.28805e15/n)):
FREQ1=freq*1.e-10
CLX=0.2815/FREQ1/FREQ1/FREQ1/n/n/(N+1.0)*Z*Z*Z*Z
if(N>=6):
return CLX
CLX*=(A1[N]+(B1[N]+C1[N]*(Z*Z/FREQ1))*(Z*Z/FREQ1))
return CLX
return 0.0
# ----------------------------------------------------------------------------------------
def HOP( XNE, XH1, XH2, FREQ, FREQLG, T, TLOG, TKEV, STIM, EHVKT):
CONT = np.empty(8, dtype='float64')
BOLT = np.empty(8, dtype='float64')
FREQ3=(FREQ*1.E-10)**3
CFREE=3.6919E-22/FREQ3
n1 = (np.arange(8)+1.0)**2
BOLT = np.exp(-13.595*(1.-1./n1)/TKEV)*2.*n1*XH1
FREET=XNE*CFREE*XH2/sqrt(T)
XR=XH1/13.595*TKEV
BOLTEX=exp(-13.427/TKEV)*XR
EXLIM=exp(-13.595/TKEV)*XR
for N in range(8):
CONT[N]=COULX(N,FREQ,1.0)
C=0.2815/FREQ3;
if(FREQ < 4.05933E13):
BOLTEX=EXLIM/EHVKT
H=(CONT[6]*BOLT[6]+CONT[7]*BOLT[7]+(BOLTEX-EXLIM)*C+
COULFF(TLOG,FREQLG,1)*FREET)*STIM
H += (CONT[0:6]*BOLT[0:6]).sum()*(1.-EHVKT)
return H
# ----------------------------------------------------------------------------------------
def HRAYOP(XH1, FREQ):
WAVE=min(FREQ,2.463e15)
WAVE=2.997925e18/WAVE
WW=WAVE*WAVE
WW2 = WW*WW
SIG=(5.799e-13+1.422e-6/WW+2.784/(WW2))/(WW2)
return SIG*XH1*2.0
# ----------------------------------------------------------------------------------------
def H2PLOP(XH1, XH2, FREQ, FREQLG, FREQ15, TKEV, STIM):
if(FREQ > 3.28805E15):
return 0.0
FR=-3.0233E3+(3.7797E2+(-1.82496E1+(3.9207E-1-3.1672E-3*FREQLG)*
FREQLG)*FREQLG)*FREQLG
ES=-7.342E-3+(-2.409+(1.028+(-0.4230+(0.1224-0.01351*FREQ15)*
FREQ15)*FREQ15)*FREQ15)*FREQ15
return exp(-ES/TKEV+FR)*2.*XH1*XH2*STIM
# ----------------------------------------------------------------------------------------
def HMINOP( XH1, XHMIN, FREQ, T, TKEV, XNE, EHVKT):
FREQ1=FREQ*1.E-10
B=(1.3727E-15+4.3748/FREQ)/FREQ1
C=-2.5993E-7/FREQ1**2
if(FREQ <= 1.8259E14): HMINBF=0.
elif(FREQ >= 2.111E14): HMINBF=6.801E-10+(5.358E-3+(1.481E3+(-5.519E7+4.808E11/FREQ1)/FREQ1)/FREQ1)/FREQ1
else: HMINBF=3.695E-6+(-1.251E-1+1.052E3/FREQ1)/FREQ1
HMINFF=(B+C/T)*XH1*XNE*2.E-20
#
# We use the number density / partition function for H-.
# The partition function for H- is 1
#
if(T < 7730.): HMIN=XHMIN
else: HMIN=exp(0.7552/TKEV)/(2.*2.4148E15*T*sqrt(T))*XH1*XNE
H=HMINBF*(1-EHVKT)*HMIN*1.E-10
return H+HMINFF
# ----------------------------------------------------------------------------------------
G0 = np.float64((1.,3.,1.,9.,3.,3.,1.,9.,20.,3.))
HEFREQ0 = np.float64((5.9452090e15,1.1528440e15,0.9803331e15,.8761076e15,
0.8147100e15,0.4519048e15,0.4030971e15,.8321191e15,
0.3660215e15,0.3627891e15))
CHI0 = np.float64((0.,19.819,20.615,20.964,21.217,22.718,22.920,23.006,
23.073,23.086))
def HE1OP( XHE1, XHE2, XNE, FREQ, FREQLG, T, TKEV, TLOG, EHVKT, STIM):
TRANS = np.zeros(10, dtype='float64')
BOLT=np.exp(-CHI0/TKEV)*G0*XHE1
FREET=XNE*1.E-10*XHE2*1.E-10/sqrt(T)*1.E-10
XRLOG=log(XHE1*(2./13.595)*TKEV)
BOLTEX=exp(-23.730/TKEV+XRLOG)
EXLIM=exp(-24.587/TKEV+XRLOG)
FREQ3=(FREQ*1.E-10)**3
CFREE=3.6919E8/FREQ3
C=2.815E-1/FREQ3
for NMIN in range(10):
if(HEFREQ0[NMIN] <= FREQ): break
dum = np.float64((33.32-2.*FREQLG, -390.026+(21.035-0.318*FREQLG)*FREQLG, 26.83-1.91*FREQLG, 61.21-2.9*FREQLG, 81.35-3.5*FREQLG, 12.69-1.54*FREQLG, 23.85-1.86*FREQLG, 49.30-2.60*FREQLG,85.20-3.69*FREQLG, 58.81-2.89*FREQLG ))
TRANS[NMIN::] = np.exp(dum[NMIN::])
EX = BOLTEX
if(FREQ < 2.055E14): EX=EXLIM/EHVKT
HE1=(EX-EXLIM)*C;
HE1 += (TRANS*BOLT).sum()
return (HE1+COULFF(TLOG,FREQLG,1)*FREET*CFREE)*STIM
# ----------------------------------------------------------------------------------------
def HE2OP( XHE2, XHE3, XNE, FREQ, FREQLG, T, TKEV, TLOG, EHVKT, STIM):
#
# REQUIRES FUNCTIONS COULX AND COULFF
# FREQUENCIES ARE 4X HYDROGEN,CHI ARE FOR ION POT=54.403
#
CONT = np.empty(9, dtype='float64')
N12 = (np.arange(9, dtype='float64')+1.0)**2
BOLT=np.exp(-(54.403-54.403/N12)/TKEV)*2.*N12*XHE2
FREET=XNE*XHE3/sqrt(T)
XR=XHE2/13.595*TKEV
BOLTEX=exp(-53.859/TKEV)*XR
EXLIM=exp(-54.403/TKEV)*XR
for N in range(9): CONT[N]=COULX(N,FREQ,2.0)
FREQ3=(FREQ*1.E-5)**3
CFREE=3.6919E-07/FREQ3*4.0
C=2.815E14*2.0*2.0/FREQ3
EX=BOLTEX
if(FREQ < 1.31522E14): EX=EXLIM/EHVKT
HE2=(EX-EXLIM)*C
HE2 += (CONT*BOLT).sum()
HE2=(HE2+COULFF(TLOG,FREQLG,2)*CFREE*FREET)*STIM
if(HE2 >= 1.E-20): return HE2
else: return 0.0
# ----------------------------------------------------------------------------------------
def HEMIOP( XHE1, FREQ, T, XNE):
A= 3.397E-26+(-5.216E-11+7.039E05/FREQ)/FREQ;
B=-4.116E-22+( 1.067E-06+8.135E09/FREQ)/FREQ;
C= 5.081E-17+(-8.724E-03-5.659E12/FREQ)/FREQ;
return (A*T+B+C/T)*XNE*XHE1*1.E-20;
# ----------------------------------------------------------------------------------------
def HERAOP(XHE1, FREQ):