def dBdT(temp, lambda2):
"""// Computes the first partial derivative of B(T) wrt T, dB/dT:"""
#double logdBdTlam;
#//double c = Useful.c; //linear
logC = Useful.logC() #//log
#//double k = Useful.k #//linear
logK = Useful.logK() #//log
#//double h = Useful.h #//linear
logH = Useful.logH() #//log
logPreFac = math.log(2.0) + logH + 2.0 * logC #//log
logExpFac = logH + logC - logK #//log
#//Declare scratch variables:
#double logLam, logTemp, logPreLamFac, logExpLamFac, expon, logExpon, eTerm, denom, logDenom; //log
#//lambda = lambda * 1.0E-7; // convert nm to cm
logLam = math.log(lambda2) #// Do the call to log for lambda once //log
logTemp = math.log(temp)
logPreLamFac = logPreFac + logExpFac - 6.0 * logLam - 2.0 * logTemp #//log
logExpLamFac = logExpFac - logLam #//log
#//This is very subtle and dangerous!
logExpon = logExpLamFac - logTemp #// log of hc/kTlambda
expon = math.exp(logExpon) #// hc/kTlambda
eTerm = math.exp(expon) #// e^hc/ktlambda
denom = eTerm - 1.0 #// e^hc/ktlambda - 1
logDenom = math.log(denom) #// log(e^hc/ktlambda - 1)
logdBdTlam = logPreLamFac + expon - 2.0 * logDenom #//log
return logdBdTlam;
#} //end method dBdT
def masterMetal(numDeps, numLams, temp, lambdaScale, stagePops):
"""/* Metal b-f opacity routines taken from Moog (moogjul2014/, MOOGJUL2014.tar)
Chris Sneden (Universtiy of Texas at Austin) and collaborators
http://www.as.utexas.edu/~chris/moog.html
//From Moog source file Opacitymetals.f
*/"""
#//System.out.println("masterMetal called...");
#//From Moog source file Opacitymetals.f
#// From how values such as aC1[] are used in Moog file Opacit.f to compute the total opacity
#// and then the optical depth scale, I infer that they are extinction coefficients
#// in cm^-1
#// There does not seem to be any correction for stimulated emission
logE = math.log10(math.e)
masterBF = [[0.0 for i in range(numDeps)] for j in range(numLams)]
logUC1 = [0.0 for i in range(5)]
logUMg1 = [0.0 for i in range(5)]
logUMg2 = [0.0 for i in range(5)]
logUAl1 = [0.0 for i in range(5)]
logUSi1 = [0.0 for i in range(5)]
logUSi2 = [0.0 for i in range(5)]
logUFe1 = [0.0 for i in range(5)]
logStatWC1 = 0.0
logStatWMg1 = 0.0
logStatWMg2 = 0.0
logStatWAl1 = 0.0
logStatWSi1 = 0.0
logStatWSi2 = 0.0
logStatWFe1 = 0.0
theta = 1.0
species = ""
logGroundPopsC1 = [0.0 for i in range(numDeps)]
logGroundPopsMg1 = [0.0 for i in range(numDeps)]
logGroundPopsMg2 = [0.0 for i in range(numDeps)]
logGroundPopsAl1 = [0.0 for i in range(numDeps)]
logGroundPopsSi1 = [0.0 for i in range(numDeps)]
logGroundPopsSi2 = [0.0 for i in range(numDeps)]
logGroundPopsFe1 = [0.0 for i in range(numDeps)]
#//
#// C I: Z=6 --> iZ=5:
aC1 = [0.0 for i in range(numDeps)]
#// Mg I: Z=12 --> iZ=11:
aMg1 = [0.0 for i in range(numDeps)]
#// Mg II: Z=12 --> iZ=11:
aMg2 = [0.0 for i in range(numDeps)]
#// Al I: Z=13 --> iZ=12:
aAl1 = [0.0 for i in range(numDeps)]
#// Si I: Z=14 --> iZ=13:
aSi1 = [0.0 for i in range(numDeps)]
#// Si II: Z=14 --> iZ =13:
aSi2 = [0.0 for i in range(numDeps)]
#// Fe I: Z=26 --> iZ=25
aFe1 = [0.0 for i in range(numDeps)]
species = "CI"
logUC1 = PartitionFn.getPartFn2(species)
species = "MgI"
logUMg1 = PartitionFn.getPartFn2(species)
species = "MgII"
logUMg2 = PartitionFn.getPartFn2(species)
species = "AlI"
logUAl1 = PartitionFn.getPartFn2(species)
species = "SiI"
logUSi1 = PartitionFn.getPartFn2(species)
species = "SiII"
logUSi2 = PartitionFn.getPartFn2(species)
species = "FeI"
logUFe1 = PartitionFn.getPartFn2(species)
#//System.out.println("iD PpC1 PpMg1 PpMg2 PpAl1 PpSi1 PpSi2 PpFe1");
for iD in range(numDeps):
#//neutral stage
#//Assumes ground state stat weight, g_1, is 1.0
#theta = 5040.0 / temp[0][iD]
#// U[0]: theta = 1.0, U[1]: theta = 0.5
"""
if (theta <= 0.5):
logStatWC1 = logUC1[1]
logStatWMg1 = logUMg1[1]
logStatWMg2 = logUMg2[1]
logStatWAl1 = logUAl1[1]
logStatWSi1 = logUSi1[1]
logStatWSi2 = logUSi2[1]
logStatWFe1 = logUFe1[1]
elif ( (theta < 1.0) and (theta > 0.5) ):
logStatWC1 = ( (theta-0.5) * logUC1[0] ) + ( (1.0-theta) * logUC1[1] )
#//divide by common factor of interpolation interval of 0.5 = (1.0 - 0.5):
logStatWC1 = 2.0 * logStatWC1
logStatWMg1 = ( (theta-0.5) * logUMg1[0] ) + ( (1.0-theta) * logUMg1[1] );
logStatWMg1 = 2.0 * logStatWMg1;
logStatWMg2 = ( (theta-0.5) * logUMg2[0] ) + ( (1.0-theta) * logUMg2[1] );
logStatWMg2 = 2.0 * logStatWMg2;
logStatWAl1 = ( (theta-0.5) * logUAl1[0] ) + ( (1.0-theta) * logUAl1[1] );
logStatWAl1 = 2.0 * logStatWAl1;
logStatWSi1 = ( (theta-0.5) * logUSi1[0] ) + ( (1.0-theta) * logUSi1[1] );
logStatWSi1 = 2.0 * logStatWSi1;
logStatWSi2 = ( (theta-0.5) * logUSi2[0] ) + ( (1.0-theta) * logUSi2[1] );
logStatWSi2 = 2.0 * logStatWSi2;
logStatWFe1 = ( (theta-0.5) * logUFe1[0] ) + ( (1.0-theta) * logUFe1[1] );
logStatWFe1 = 2.0 * logStatWFe1;
else:
logStatWC1 = logUC1[0]
logStatWMg1 = logUMg1[0]
logStatWMg2 = logUMg2[0]
logStatWAl1 = logUAl1[0]
logStatWSi1 = logUSi1[0]
logStatWSi2 = logUSi2[0]
logStatWFe1 = logUFe1[0]
"""
#// NEW Interpolation involving temperature for new partition function: lburns
thisTemp = temp[0][iD]
if (thisTemp <= 130):
logStatWC1 = logUC1[0]
logStatWMg1 = logUMg1[0]
logStatWMg2 = logUMg2[0]
logStatWAl1 = logUAl1[0]
logStatWSi1 = logUSi1[0]
logStatWSi2 = logUSi2[0]
logStatWFe1 = logUFe1[0]
elif (thisTemp > 130 and thisTemp <= 500):
#// Add in interpolation here lburns
logStatWC1 = logUC1[1] * (thisTemp - 130)/(500 - 130) \
+ logUC1[0] * (500 - thisTemp)/(500 - 130)
logStatWMg1 = logUMg1[1] * (thisTemp - 130)/(500 - 130) \
+ logUMg1[0] * (500 - thisTemp)/(500 - 130)
logStatWMg2 = logUMg2[1] * (thisTemp - 130)/(500 - 130) \
+ logUMg2[0] * (500 - thisTemp)/(500 - 130)
logStatWAl1 = logUAl1[1] * (thisTemp - 130)/(500 - 130) \
+ logUAl1[0] * (500 - thisTemp)/(500 - 130)
logStatWSi1 = logUSi1[1] * (thisTemp - 130)/(500 - 130) \
+ logUSi1[0] * (500 - thisTemp)/(500 - 130)
logStatWSi2 = logUSi2[1] * (thisTemp - 130)/(500 - 130) \
+ logUSi2[0] * (500 - thisTemp)/(500 - 130)
logStatWFe1 = logUFe1[1] * (thisTemp - 130)/(500 - 130) \
+ logUFe1[0] * (500 - thisTemp)/(500 - 130)
elif (thisTemp > 500 and thisTemp <= 3000):
logStatWC1 = logUC1[2] * (thisTemp - 500)/(3000 - 500) \
+ logUC1[1] * (3000 - thisTemp)/(3000 - 500)
logStatWMg1 = logUMg1[2] * (thisTemp - 500)/(3000 - 500) \
+ logUMg1[1] * (3000 - thisTemp)/(3000 - 500)
logStatWMg2 = logUMg2[2] * (thisTemp - 500)/(3000 - 500) \
+ logUMg2[1] * (3000 - thisTemp)/(3000 - 500)
logStatWAl1 = logUAl1[2] * (thisTemp - 500)/(3000 - 500) \
+ logUAl1[1] * (3000 - thisTemp)/(3000 - 500)
logStatWSi1 = logUSi1[2] * (thisTemp - 500)/(3000 - 500) \
+ logUSi1[1] * (3000 - thisTemp)/(3000 - 500)
logStatWSi2 = logUSi2[2] * (thisTemp - 500)/(3000 - 500) \
+ logUSi2[1] * (3000 - thisTemp)/(3000 - 500)
logStatWFe1 = logUFe1[2] * (thisTemp - 500)/(3000 - 500) \
+ logUFe1[1] * (3000 - thisTemp)/(3000 - 500)
elif (thisTemp > 3000 and thisTemp <= 8000):
logStatWC1 = logUC1[3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUC1[2] * (8000 - thisTemp)/(8000 - 3000)
logStatWMg1 = logUMg1[3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUMg1[2] * (8000 - thisTemp)/(8000 - 3000)
logStatWMg2 = logUMg2[3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUMg2[2] * (8000 - thisTemp)/(8000 - 3000)
logStatWAl1 = logUAl1[3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUAl1[2] * (8000 - thisTemp)/(8000 - 3000)
logStatWSi1 = logUSi1[3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUSi1[2] * (8000 - thisTemp)/(8000 - 3000)
logStatWSi2 = logUSi2[3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUSi2[2] * (8000 - thisTemp)/(8000 - 3000)
logStatWFe1 = logUFe1[3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUFe1[2] * (8000 - thisTemp)/(8000 - 3000)
elif (thisTemp > 8000 and thisTemp < 10000):
logStatWC1 = logUC1[4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUC1[3] * (10000 - thisTemp)/(10000 - 8000)
logStatWMg1 = logUMg1[4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUMg1[3] * (10000 - thisTemp)/(10000 - 8000)
logStatWMg2 = logUMg2[4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUMg2[3] * (10000 - thisTemp)/(10000 - 8000)
logStatWAl1 = logUAl1[4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUAl1[3] * (10000 - thisTemp)/(10000 - 8000)
logStatWSi1 = logUSi1[4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUSi1[3] * (10000 - thisTemp)/(10000 - 8000)
logStatWSi2 = logUSi2[4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUSi2[3] * (10000 - thisTemp)/(10000 - 8000)
logStatWFe1 = logUFe1[4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUFe1[3] * (10000 - thisTemp)/(10000 - 8000)
else:
#// for temperatures greater than or equal to 10000
logStatWC1 = logUC1[4]
logStatWMg1 = logUMg1[4]
logStatWMg2 = logUMg2[4]
logStatWAl1 = logUAl1[4]
logStatWSi1 = logUSi1[4]
logStatWSi2 = logUSi2[4]
logStatWFe1 = logUFe1[4]
logGroundPopsC1[iD] = stagePops[5][0][iD] - logStatWC1
logGroundPopsMg1[iD] = stagePops[11][0][iD] - logStatWMg1
logGroundPopsMg2[iD] = stagePops[11][1][iD] - logStatWMg2
logGroundPopsAl1[iD] = stagePops[12][0][iD] - logStatWAl1
logGroundPopsSi1[iD] = stagePops[13][0][iD] - logStatWSi1
logGroundPopsSi2[iD] = stagePops[13][1][iD] - logStatWSi2
logGroundPopsFe1[iD] = stagePops[25][0][iD] - logStatWFe1
#// if (iD%5 == 1){
#// System.out.format("%03d, %21.15f, %21.15f, %21.15f, %21.15f, %21.15f, %21.15f, %21.15f %n",
#// iD, logE*(logGroundPopsC1[iD]+temp[1][iD]+Useful.logK()),
#// logE*(logGroundPopsMg1[iD]+temp[1][iD]+Useful.logK()),
#// logE*(logGroundPopsMg2[iD]+temp[1][iD]+Useful.logK()),
#// logE*(logGroundPopsAl1[iD]+temp[1][iD]+Useful.logK()),
#// logE*(logGroundPopsSi1[iD]+temp[1][iD]+Useful.logK()),
#// logE*(logGroundPopsSi2[iD]+temp[1][iD]+Useful.logK()),
#// logE*(logGroundPopsFe1[iD]+temp[1][iD]+Useful.logK()));
#id loop// }
#double waveno; //cm??
#double freq, logFreq, kapBF;
#double stimEmExp, stimEmLogExp, stimEmLogExpHelp, stimEm;
#//System.out.println("iD iL lambda stimEm aC1 aMg1 aMg2 aAl1 aSi1 aSi2 aFe1 ");
for iL in range(numLams):
#print("iL ", iL)
#//
#//initialization:
for i in range(numDeps):
aC1[i] = 0.0
aMg1[i] = 0.0
aMg2[i] = 0.0
aAl1[i] = 0.0
aSi1[i] = 0.0
aSi2[i] = 0.0
aFe1[i] = 0.0
waveno = 1.0 / lambdaScale[iL] #//cm^-1??
logFreq = Useful.logC() - math.log(lambdaScale[iL])
freq = math.exp(logFreq)
#if (iL%20 == 1):
# print("freq ", freq)
stimEmLogExpHelp = Useful.logH() + logFreq - Useful.logK()
#//System.out.println("Calling opacC1 from masterMetal...");
if (freq >= 2.0761e15):
aC1 = opacC1(numDeps, temp, lambdaScale[iL], logGroundPopsC1)
if (freq >= 2.997925e+14):
#print("opacMg1 called")
aMg1 = opacMg1(numDeps, temp, lambdaScale[iL], logGroundPopsMg1)
if (freq >= 2.564306e15):
aMg2 = opacMg2(numDeps, temp, lambdaScale[iL], logGroundPopsMg2)
if (freq >= 1.443e15):
aAl1 = opacAl1(numDeps, temp, lambdaScale[iL], logGroundPopsAl1)
if (freq >= 2.997925e+14):
#print("opacSi1 called")
aSi1 = opacSi1(numDeps, temp, lambdaScale[iL], logGroundPopsSi1)
if (freq >= 7.6869872e14):
aSi2 = opacSi2(numDeps, temp, lambdaScale[iL], logGroundPopsSi2)
if (waveno >= 21000.0):
aFe1 = opacFe1(numDeps, temp, lambdaScale[iL], logGroundPopsFe1)
for iD in range(numDeps):
kapBF = 1.0e-99 #minimum safe value
stimEmLogExp = stimEmLogExpHelp - temp[1][iD]
stimEmExp = -1.0 * math.exp(stimEmLogExp)
stimEm = (1.0 - math.exp(stimEmExp)
) #//LTE correction for stimulated emission
kapBF = kapBF + aC1[iD] + aMg1[iD] + aMg2[iD] + aAl1[iD] + aSi1[
iD] + aSi2[iD] + aFe1[iD]
#kapBF = aC1[iD] + aMg2[iD] + aAl1[iD] + aSi2[iD] + aFe1[iD]
#if ( (iL%20 == 1) and (iD%10 == 1) ):
#print("iL ", iL, " iD ", iD, " stimEm ", stimEm, " kapBF ", kapBF)
# print("aMg1 ", aMg1[iD], " aSi1 ", aSi1[iD])
masterBF[iL][iD] = math.log(kapBF) + math.log(stimEm)
#// if ( (iD%10 == 0) && (iL%10 == 0) ) {
#// System.out.format("%03d, %03d, %21.15f, %21.15f, %21.15f, %21.15f, %21.15f, %21.15f, %21.15f, %21.15f, %21.15f, %n",
#// iD, iL, lambdaScale[iL], Math.log10(stimEm), Math.log10(aC1[iD]), Math.log10(aMg1[iD]), Math.log10(aMg2[iD]), Math.log10(aAl1[iD]), Math.log10(aSi1[iD]), Math.log10(aSi2[iD]), Math.log10(aFe1[iD]));
#// }
#} //iD
#} //iL
return masterBF
def planck(temp, lambda2):
""" /**
* Inputs: lambda: a single scalar wavelength in cm temp: a single scalar
* temperature in K Returns log of Plank function in logBBlam - B_lambda
* distribution in pure cgs units: ergs/s/cm^2/ster/cm
*/"""
#//int numLams = (int) (( lamSetup[1] - lamSetup[0] ) / lamSetup[2]) + 1;
#double logBBlam; //, BBlam;
#//double c = Useful.c; //linear
logC = Useful.logC() # //log
#//double k = Useful.k; //linear
logK = Useful.logK() #//log
#//double h = Useful.h; //linear
logH = Useful.logH() #//log
logPreFac = math.log(2.0) + logH + 2.0 * logC #//log
logExpFac = logH + logC - logK #//log
#//double preFac = 2.0 * h * ( c * c ); //linear
#//double expFac = ( h / k ) * c; //linear
#//System.out.println("logC " + logC + " logK " + logK + " logH " + logH);
#//System.out.println("logPreFac " + logPreFac + " logExpFac " + logExpFac);
#//Declare scratch variables:
#double logLam, logPreLamFac, logExpLamFac, expon, logExpon, eTerm, denom, logDenom; //log
#//double preLamFac, expLamFac, expon, denom; //linear
#//for (int il = 0; il < numLams; il++){
#//lambda = lambda[il] * 1.0E-7; // convert nm to cm
#//lambda = lambda * 1.0E-7; // convert nm to cm
logLam = math.log(lambda2) #// Do the call to log for lambda once //log
#//System.out.println("lambda " + lambda + " logLam " + logLam);
logPreLamFac = logPreFac - 5.0 * logLam #//log
logExpLamFac = logExpFac - logLam #//log
#//System.out.println("logPreLamFac " + logPreLamFac + " logExpLamFac " + logExpLamFac);
#// Be VERY careful about how we divide by lambda^5:
#//preLamFac = preFac / ( lambda * lambda ); //linear
#//preLamFac = preLamFac / ( lambda * lambda ); //linear
#//preLamFac = preLamFac / lambda; //linear
#//expLamFac = expFac / lambda;
#//for (int id = 0; id < numDeps; id++){
#//logExpon = logExpLamFac - temp[1][id];
#//This is very subtle and dangerous!
logExpon = logExpLamFac - math.log(temp) #// log of hc/kTlambda
#//System.out.println("temp " + temp + " logTemp " + Math.log(temp));
expon = math.exp(logExpon) #// hc/kTlambda
#//System.out.println("logExpon " + logExpon + " expon " + expon + " denom " + denom);
#// expon = expLamFac / temp; //linear
eTerm = math.exp(expon) #// e^hc/ktlambda
denom = eTerm - 1.0 #// e^hc/ktlambda - 1
logDenom = math.log(denom) #// log(e^hc/ktlambda - 1)
#//BBlam[1][id][il] = logPreLamFac - logDenom;
#//BBlam[0][id][il] = Math.exp(BBlam[1][id][il]);
logBBlam = logPreLamFac - logDenom #//log
#// Not needed? BBlam = math.exp(logBBlam) #//log
#//BBlam = preLamFac / denom; //linear
#// } //id loop - depths
#// } //il loop - lambdas
return logBBlam;
def jolaProfilePR(omega0, logf, vibConst, jolaPoints, alphP, alphR, numDeps,
temp):
"""//
//JOLA profile for P (Delta J = 1) and R (Delta J = -1) branches
//Equation 19 from Zeidler & Koestler"""
nm2cm = 1.0e-7
log10E = math.log10(math.e)
numPoints = len(jolaPoints)
#// derivative of rotational-line oscillator strength with respect to frequency
dfBydw = [[0.0 for i in range(numDeps)] for j in range(numPoints)]
fvv = math.exp(logf)
logHcBbyK = Useful.logH() + Useful.logC() + math.log(vibConst[0]) \
- Useful.logK()
#//System.out.println("omega0 " + omega0 + " logf " + log10E*logf + " vibConst " + vibConst[0] + " " + vibConst[1] + " alphP " + alphP + " alphR " + alphR);
Bsum = vibConst[1] + vibConst[0]
Bdiff = vibConst[1] - vibConst[0]
#//value of J-related "m" at band-head:
mH = -1.0 * Bsum / (2.0 * Bdiff) #//Eq. 14
#//Frequency (or wavenumber??) at band head:
wH = (-1.0 * Bdiff * mH * mH) + omega0 #//Eq. 15
#//System.out.println("1.0/wH " + 1.0/wH + " 1.0/omega0 " + 1.0/omega0);
mTheta1 = 1.0 #//R branch?
mTheta2 = 1.0 #//P branch?
#double m1, m2; // related to J, for R & P branches, respectively
alpha1 = 1.0
alpha2 = 1.0
#//value of m is closely related to rotational quantum number J,
#//Near band origin, frequency, w, range should correspond to -1 <= m <= 1 - ???:
#//double wMin = Useful.c / (1.0e-7*jolaPoints[numPoints-1]); //first frequency omega
#//double wMax = Useful.c / (1.0e-7*jolaPoints[0]); //last frequency omega
#//double deltaW = 0.02;
#double w, logW, m1Fctr, m2Fctr, mHelp, wMinuswHOverBDiff;
#double denom1, denom2, m1Term, m2Term;
#double help1, logHcBbyKt, hcBbyKt;
#//Outer loop over frequency omega
#// for (int iW = -1; iW <= 1; iW++){
#for (int iW = numPoints-1; iW >= 0; iW--){
for iW in range(numPoints - 1, 0, -1):
#//dW = (double) iW;
#//w = wMin + (dW*deltaW);
#//logW = Useful.logC() - Math.log(1.0e-7*jolaPoints[iW]); //if w is freq in Hz
logW = 0.0 - math.log(
nm2cm * jolaPoints[iW]) #//if w is waveno in cm^-1
w = math.exp(logW)
#//System.out.println("logW " + log10E*logW);
#//I have no idea if this is right...
wMinuswHOverBDiff = (w - wH) / Bdiff
mHelp = math.sqrt(abs(wMinuswHOverBDiff)) #//Eq. 17
m1 = mH + mHelp
m2 = mH - mHelp #//Eq. 18
#//System.out.println("mH " + mH + " m1 " + m1 + " m2 " + m2);
m1Fctr = (m1 * m1 - m1)
m2Fctr = (m2 * m2 - m2)
#//The following association between the sign of m1 or m2 and whether
#//it's the P or the R branch might be backwards:
if (m1 < 0):
alpha1 = alphP
if (m1 >= 0):
alpha1 = alphR
if (m2 < 0):
alpha2 = alphP
if (m2 >= 0):
alpha2 = alphR
denom1 = abs(Bsum + 2.0 * m1 * Bdiff)
denom2 = abs(Bsum + 2.0 * m2 * Bdiff)
for iD in range(numDeps):
if (wMinuswHOverBDiff > 0):
logHcBbyKt = logHcBbyK - temp[1][iD]
hcBbyKt = math.exp(logHcBbyKt)
help1 = -1.0 * hcBbyKt * m1Fctr
m1Term = alpha1 * mTheta1 * math.exp(help1) / denom1
help1 = -1.0 * hcBbyKt * m2Fctr
m2Term = alpha2 * mTheta2 * math.exp(help1) / denom2
#//Can this be used like a differential cross-section (once converted to sigma)?
#// System.out.println("fvv " + fvv + " hcBbyKt " + hcBbyKt + " m1Term " + m1Term + " m2Term " + m2Term);
dfBydw[iW][iD] = fvv * hcBbyKt * (m1Term + m2Term) #// Eq. 19
else:
dfBydw[iW][iD] = 0.0
#}
#// if (iD%10 == 1){
#// System.out.println("PR iD " + iD + " iW " + iW + " dfBydw " + dfBydw[iW][iD]);
#// }
#} //iD - depth loop
#} //iW - frequency loop
return dfBydw
def kappas2(numDeps, pe, zScale, temp, rho, numLams, lambdas, logAHe, \
logNH1, logNH2, logNHe1, logNHe2, Ne, teff, logKapFudge):
"""/* Compute opacities properly from scratch with real physical cross-sections
*/ // *** CAUTION:
//
// This return's "kappa" as defined by Gray 3rd Ed. - cm^2 per *relelvant particle* where the "releveant particle"
// depends on *which* kappa """
#//
#// *** CAUTION:
#//
#// This return's "kappa" as defined by Gray 3rd Ed. - cm^2 per *relelvant particle* where the "releveant particle"
#// depends on *which* kappa
log10E = math.log10(math.e) #//needed for g_ff
logLog10E = math.log(log10E)
logE10 = math.log(10.0)
logNH = [0.0 for i in range(numDeps)] #//Total H particle number density cm^-3
#double logPH1, logPH2, logPHe1, logPHe2;
for i in range(numDeps):
logNH[i] = math.exp(logNH1[i]) + math.exp(logNH2[i])
logNH[i] = math.log(logNH[i])
#//System.out.println("i " + i + " logNH1 " + log10E*logNH1[i] + " logNH2 " + log10E*logNH2[i]
#//+ " logNHe1 " + log10E*logNHe1[i] + " logNHe2 " + log10E*logNHe2[i] + " logPe " + log10E*pe[1][i]);
#// logPH1 = logNH1[i] + temp[1][i] + Useful.logK();
#// logPH2 = logNH2[i] + temp[1][i] + Useful.logK();
#// logPHe1 = logNHe1[i] + temp[1][i] + Useful.logK();
#// logPHe2 = logNHe2[i] + temp[1][i] + Useful.logK();
#//System.out.println("i " + i + " logPH1 " + log10E*logPH1 + " logPH2 " + log10E*logPH2
#//+ " logPHe1 " + log10E*logPHe1 + " logPHe2 " + log10E*logPHe2 + " logPe " + log10E*pe[1][i]);
#double[][] logKappa = new double[numLams][numDeps];
logKappa = [ [0.0 for i in range(numDeps)] for j in range(numLams) ]
#double kappa; //helper
#double stimEm; //temperature- and wavelength-dependent stimulated emission correction
#double stimHelp, logStimEm;
#double ii; //useful for converting integer loop counter, i, to float
#//
#//
#//Input data and variable declarations:
#//
#//
#// H I b-f & f-f
chiIH = 13.598433 #//eV
Rydberg = 1.0968e-2 #// "R" in nm^-1
#//Generate threshold wavelengths and b-f Gaunt (g_bf) helper factors up to n=10:
#double n; //principle quantum number of Bohr atom E-level
numHlevs = 10
#double logChiHlev;
invThresh = [0.0 for i in range(numHlevs)] #//also serves as g_bf helper factor
threshLambs = [0.0 for i in range(numHlevs)]
chiHlev = [0.0 for i in range(numHlevs)]
for i in range(numHlevs):
n = 1.0 + float(i)
invThresh[i] = Rydberg / n / n #//nm^-1; also serves as g_bf helper factor
threshLambs[i] = 1.0 / invThresh[i] #//nm
logChiHlev = Useful.logH() + Useful.logC() + math.log(invThresh[i]) + 7.0*logE10 #// ergs
chiHlev[i] = math.exp(logChiHlev - Useful.logEv()) #//eV
chiHlev[i] = chiIH - chiHlev[i]
#// System.out.println("i " + i + " n " + n + " invThresh " + invThresh[i] + " threshLambs[i] " + threshLambs[i] + " chiHlev " + chiHlev[i]);
logGauntPrefac = math.log(0.3456) - 0.333333*math.log(Rydberg)
#// **** Caution: this will require lamba in A!:
a0 = 1.0449e-26 #//if lambda in A
logA0 = math.log(a0)
#// Boltzmann const "k" in eV/K - needed for "theta"
logKeV = Useful.logK() - Useful.logEv()
#//g_bf Gaunt factor - depends on lower E-level, n:
loggbf = [0.0 for i in range(numHlevs)]
#//initialize quantities that depend on lowest E-level contributing to opacity at current wavelength:
for iThresh in range(numHlevs):
loggbf[iThresh] = 0.0
#double logGauntHelp, gauntHelp;
#double gbf, gbfHelp, loggbfHelp;
#double gff, gffHelp, loggffHelp, logffHelp, loggff;
#double help, logHelp3;
#double chiLambda, logChiLambda;
#double bfTerm, logbfTerm, bfSum, logKapH1bf, logKapH1ff;
#//initial defaults:
gbf = 1.0
gff = 1.0
loggff = 0.0
logChiFac = math.log(1.2398e3) #// eV per lambda, for lambda in nm
#// Needed for kappa_ff:
#double ffBracket;
logffHelp = logLog10E - math.log(chiIH) - math.log(2.0)
#//logHelp = logffHelp - math.log(2.0)
#//
#//Hminus:
#//
#// H^- b-f
#//This is for the sixth order polynomial fit to the cross-section's wavelength dependence
numHmTerms = 7
logAHm = [0.0 for i in range(numHmTerms)]
signAHm = [0.0 for i in range(numHmTerms)]
aHmbf = 4.158e-10
#//double logAHmbf = Math.log(aHmbf);
#//Is the factor of 10^-18cm^2 from the polynomial fit to alpha_Hmbf missing in Eq. 8.12 on p. 156 of Gray 3rd Ed??
logAHmbf = math.log(aHmbf) - 18.0*logE10
#double alphaHmbf, logAlphaHmbf, logTermHmbf, logKapHmbf;
#//Computing each polynomial term logarithmically
logAHm[0] = math.log(1.99654)
signAHm[0] = 1.0
logAHm[1] = math.log(1.18267e-5)
signAHm[1] = -1.0
logAHm[2] = math.log(2.64243e-6)
signAHm[2] = 1.0
logAHm[3] = math.log(4.40524e-10)
signAHm[3] = -1.0
logAHm[4] = math.log(3.23992e-14)
signAHm[4] = 1.0
logAHm[5] = math.log(1.39568e-18)
signAHm[5] = -1.0
logAHm[6] = math.log(2.78701e-23)
signAHm[6] = 1.0
alphaHmbf = math.exp(logAHm[0]) #//initialize accumulator
#// H^- f-f:
logAHmff = -26.0*logE10
numHmffTerms = 5
#double fPoly, logKapHmff, logLambdaAFac;
fHmTerms = [ [ 0.0 for i in range(numHmffTerms) ] for j in range(3) ]
fHm = [0.0 for i in range(3)]
fHmTerms[0][0] = -2.2763
fHmTerms[0][1] = -1.6850
fHmTerms[0][2] = 0.76661
fHmTerms[0][3] = -0.053346
fHmTerms[0][4] = 0.0
fHmTerms[1][0] = 15.2827
fHmTerms[1][1] = -9.2846
fHmTerms[1][2] = 1.99381
fHmTerms[1][3] = -0.142631
fHmTerms[1][4] = 0.0
fHmTerms[2][0] = -197.789
fHmTerms[2][1] = 190.266
fHmTerms[2][2] = -67.9775
fHmTerms[2][3] = 10.6913
fHmTerms[2][4] = -0.625151
#//
#//H_2^+ molecular opacity - cool stars
#// scasles with proton density (H^+)
#//This is for the third order polynomial fit to the "sigma_l(lambda)" and "U_l(lambda)"
#//terms in the cross-section
numH2pTerms = 4
sigmaH2pTerm = [0.0 for i in range(numH2pTerms)]
UH2pTerm = [0.0 for i in range(numH2pTerms)]
#double logSigmaH2p, sigmaH2p, UH2p, logKapH2p;
aH2p = 2.51e-42
logAH2p = math.log(aH2p)
sigmaH2pTerm[0] = -1040.54
sigmaH2pTerm[1] = 1345.71
sigmaH2pTerm[2] = -547.628
sigmaH2pTerm[3] = 71.9684
#//UH2pTerm[0] = 54.0532
#//UH2pTerm[1] = -32.713
#//UH2pTerm[2] = 6.6699
#//UH2pTerm[3] = -0.4574
#//Reverse signs on U_1 polynomial expansion co-efficients - Dave Gray private communcation
#//based on Bates (1952)
UH2pTerm[0] = -54.0532
UH2pTerm[1] = 32.713
UH2pTerm[2] = -6.6699
UH2pTerm[3] = 0.4574
#// He I b-f & ff:
#double totalH1Kap, logTotalH1Kap, helpHe, logKapHe;
#//
#//He^- f-f
AHe = math.exp(logAHe)
#double logKapHemff, nHe, logNHe, thisTerm, thisLogTerm, alphaHemff, log10AlphaHemff;
#// Gray does not have this pre-factor, but PHOENIX seems to and without it
#// the He opacity is about 10^26 too high!:
logAHemff = -26.0*logE10
numHemffTerms = 5
logC0HemffTerm = [0.0 for i in range(numHemffTerms)]
logC1HemffTerm = [0.0 for i in range(numHemffTerms)]
logC2HemffTerm = [0.0 for i in range(numHemffTerms)]
logC3HemffTerm = [0.0 for i in range(numHemffTerms)]
signC0HemffTerm = [0.0 for i in range(numHemffTerms)]
signC1HemffTerm = [0.0 for i in range(numHemffTerms)]
signC2HemffTerm = [0.0 for i in range(numHemffTerms)]
signC3HemffTerm = [0.0 for i in range(numHemffTerms)]
#//we'll be evaluating the polynominal in theta logarithmically by adding logarithmic terms -
logC0HemffTerm[0] = math.log(9.66736)
signC0HemffTerm[0] = 1.0
logC0HemffTerm[1] = math.log(71.76242)
signC0HemffTerm[1] = -1.0
logC0HemffTerm[2] = math.log(105.29576)
signC0HemffTerm[2] = 1.0
logC0HemffTerm[3] = math.log(56.49259)
signC0HemffTerm[3] = -1.0
logC0HemffTerm[4] = math.log(10.69206)
signC0HemffTerm[4] = 1.0
logC1HemffTerm[0] = math.log(10.50614)
signC1HemffTerm[0] = -1.0
logC1HemffTerm[1] = math.log(48.28802)
signC1HemffTerm[1] = 1.0
logC1HemffTerm[2] = math.log(70.43363)
signC1HemffTerm[2] = -1.0
logC1HemffTerm[3] = math.log(37.80099)
signC1HemffTerm[3] = 1.0
logC1HemffTerm[4] = math.log(7.15445)
signC1HemffTerm[4] = -1.0
logC2HemffTerm[0] = math.log(2.74020)
signC2HemffTerm[0] = 1.0
logC2HemffTerm[1] = math.log(10.62144)
signC2HemffTerm[1] = -1.0
logC2HemffTerm[2] = math.log(15.50518)
signC2HemffTerm[2] = 1.0
logC2HemffTerm[3] = math.log(8.33845)
signC2HemffTerm[3] = -1.0
logC2HemffTerm[4] = math.log(1.57960)
signC2HemffTerm[4] = 1.0
logC3HemffTerm[0] = math.log(0.19923)
signC3HemffTerm[0] = -1.0
logC3HemffTerm[1] = math.log(0.77485)
signC3HemffTerm[1] = 1.0
logC3HemffTerm[2] = math.log(1.13200)
signC3HemffTerm[2] = -1.0
logC3HemffTerm[3] = math.log(0.60994)
signC3HemffTerm[3] = 1.0
logC3HemffTerm[4] = math.log(0.11564)
signC3HemffTerm[4] = -1.0
# //initialize accumulators:
cHemff = [0.0 for i in range(4)]
cHemff[0] = signC0HemffTerm[0] * math.exp(logC0HemffTerm[0]);
cHemff[1] = signC1HemffTerm[0] * math.exp(logC1HemffTerm[0]);
cHemff[2] = signC2HemffTerm[0] * math.exp(logC2HemffTerm[0]);
cHemff[3] = signC3HemffTerm[0] * math.exp(logC3HemffTerm[0]);
#//
#//Should the polynomial expansion for the Cs by in 10g10Theta?? No! Doesn't help:
#//double[] C0HemffTerm = new double[numHemffTerms];
#//double[] C1HemffTerm = new double[numHemffTerms];
#//double[] C2HemffTerm = new double[numHemffTerms];
#//double[] C3HemffTerm = new double[numHemffTerms];
#//
#//C0HemffTerm[0] = 9.66736;
#//C0HemffTerm[1] = -71.76242;
#//C0HemffTerm[2] = 105.29576;
#//C0HemffTerm[3] = -56.49259;
#//C0HemffTerm[4] = 10.69206;
#//C1HemffTerm[0] = -10.50614;
#//C1HemffTerm[1] = 48.28802;
#//C1HemffTerm[2] = -70.43363;
#//C1HemffTerm[3] = 37.80099;
#//C1HemffTerm[4] = -7.15445;
#//C2HemffTerm[0] = 2.74020;
#//C2HemffTerm[1] = -10.62144;
#//C2HemffTerm[2] = 15.50518;
#//C2HemffTerm[3] = -8.33845;
#//C2HemffTerm[4] = 1.57960;
#//C3HemffTerm[0] = -0.19923;
#//C3HemffTerm[1] = 0.77485;
#//C3HemffTerm[2] = -1.13200;
#//C3HemffTerm[3] = 0.60994;
#//C3HemffTerm[4] = -0.11564;
#//initialize accumulators:
#// double[] cHemff = new double[4];
#// cHemff[0] = C0HemffTerm[0];
#// cHemff[1] = C1HemffTerm[0];
#// cHemff[2] = C2HemffTerm[0];
#// cHemff[3] = C3HemffTerm[0];
#//
#// electron (e^-1) scattering (Thomson scattering)
#double kapE, logKapE;
alphaE = 0.6648e-24 #//cm^2/e^-1
logAlphaE = math.log(0.6648e-24)
#//Universal:
#//
# double theta, logTheta, log10Theta, log10ThetaFac;
# double logLambda, lambdaA, logLambdaA, log10LambdaA, lambdanm, logLambdanm;
#//Okay - here we go:
#//Make the wavelength loop the outer loop - lots of depth-independnet lambda-dependent quantities:
#//
#//
# //System.out.println("Kappas called...");
#//
#// **** START WAVELENGTH LOOP iLam
#//
#//
#//
for iLam in range(numLams):
#//
#//Re-initialize all accumulators to be on safe side:
kappa = 0.0
logKapH1bf = -99.0
logKapH1ff = -99.0
logKapHmbf = -99.0
logKapHmff = -99.0
logKapH2p = -99.0
logKapHe = -99.0
logKapHemff = -99.0
logKapE = -99.0
#//
#//*** CAUTION: lambda MUST be in nm here for consistency with Rydbeg
logLambda = math.log(lambdas[iLam]) #//log cm
lambdanm = 1.0e7 * lambdas[iLam]
logLambdanm = math.log(lambdanm)
lambdaA = 1.0e8 * lambdas[iLam] #//Angstroms
logLambdaA = math.log(lambdaA)
log10LambdaA = log10E * logLambdaA
logChiLambda = logChiFac - logLambdanm
chiLambda = math.exp(logChiLambda) #//eV
#// Needed for both g_bf AND g_ff:
logGauntHelp = logGauntPrefac - 0.333333*logLambdanm #//lambda in nm here
gauntHelp = math.exp(logGauntHelp)
#// if (iLam == 142){
#// System.out.println("lambdaA " + lambdaA);
#// }
#//HI b-f depth independent factors:
#//Start at largest threshold wavelength and break out of loop when next threshold lambda is less than current lambda:
#for (iThresh = numHlevs-1; iThresh >= 0; iThresh--){
for iThresh in range(0, numHlevs-1, -1):
if (threshLambs[iThresh] < lambdanm):
break
if (lambdanm <= threshLambs[iThresh]):
#//this E-level contributes
loggbfHelp = logLambdanm + math.log(invThresh[iThresh]) # //lambda in nm here; invThresh here as R/n^2
gbfHelp = math.exp(loggbfHelp)
gbf = 1.0 - (gauntHelp * (gbfHelp - 0.5))
#// if (iLam == 1){}
#// System.out.println("iThresh " + iThresh + " threshLambs " + threshLambs[iThresh] + " gbf " + gbf);
#// }
loggbf[iThresh] = math.log(gbf)
#//end iThresh loop
#//HI f-f depth independent factors:
# //logChi = logLog10E + logLambdanm - logChiFac; //lambda in nm here
# //chi = Math.exp(logChi);
loggffHelp = logLog10E - logChiLambda
#//
#//
#//
#// ****** Start depth loop iTau ******
#//
#//
#//
#//
for iTau in range(numDeps):
#//
# //Re-initialize all accumulators to be on safe side:
kappa = 0.0
logKapH1bf = -99.0
logKapH1ff = -99.0
logKapHmbf = -99.0
logKapHmff = -99.0
logKapH2p = -99.0
logKapHe = -99.0
logKapHemff = -99.0
logKapE = -99.0
#//
#//
#//if (iTau == 36 && iLam == 142){
#// System.out.println("lambdanm[142] " + lambdanm + " temp[0][iTau=36] " + temp[0][iTau=36]);
#// }
#//This is "theta" ~ 5040/T:
logTheta = logLog10E - logKeV - temp[1][iTau]
log10Theta = log10E * logTheta
theta = math.exp(logTheta)
#//System.out.println("theta " + theta + " logTheta " + logTheta);
#// temperature- and wavelength-dependent stimulated emission coefficient:
stimHelp = -1.0 * theta * chiLambda * logE10
stimEm = 1.0 - math.exp(stimHelp)
logStimEm = math.log(stimEm)
# // if (iTau == 36 && iLam == 142){
# // System.out.println("stimEm " + stimEm);
# //}
ffBracket = math.exp(loggffHelp - logTheta) + 0.5
gff = 1.0 + (gauntHelp*ffBracket)
#//if (iTau == 36 && iLam == 1){
#// System.out.println("gff " + gff);
#// }
loggff = math.log(gff)
#//H I b-f:
#//Start at largest threshold wavelength and break out of loop when next threshold lambda is less than current lambda:
bfSum = 0.0 #//initialize accumulator
logHelp3 = logA0 + 3.0*logLambdaA #//lambda in A here
#for (int iThresh = numHlevs-1; iThresh >= 0; iThresh--){
for iThresh in range(0, numHlevs-1, -1):
if (threshLambs[iThresh] < lambdanm):
break
n = 1.0 + float(iThresh)
if (lambdanm <= threshLambs[iThresh]):
#//this E-level contributes
logbfTerm = loggbf[iThresh] - 3.0*math.log(n)
logbfTerm = logbfTerm - (theta*chiHlev[iThresh])*logE10
bfSum = bfSum + math.exp(logbfTerm)
#//if (iTau == 36 && iLam == 142){
# //System.out.println("lambdanm " + lambdanm + " iThresh " + iThresh + " threshLambs[iThresh] " + threshLambs[iThresh]);
# //System.out.println("loggbf " + loggbf[iThresh] + " theta " + theta + " chiHlev " + chiHlev[iThresh]);
# //System.out.println("bfSum " + bfSum + " logbfTerm " + logbfTerm);
#// }
#//end iThresh loop
#// cm^2 per *neutral* H atom
logKapH1bf = logHelp3 + math.log(bfSum)
#//Stimulated emission correction
logKapH1bf = logKapH1bf + logStimEm
#//System.out.println("lambda " + lambdas[iLam] + "iTau " + iTau + " sigma " + Math.exp(logKapH1bf));
#//Add it in to total - opacity per neutral HI atom, so multiply by logNH1
#// This is now linear opacity in cm^-1
logKapH1bf = logKapH1bf + logNH1[iTau]
#//System.out.println(" aH1 " + Math.exp(logKapH1bf));
#////Nasty fix to make Balmer lines show up in A0 stars!
#// if (teff > 8000){
#// logKapH1bf = logKapH1bf - logE10*1.5;
#//
kappa = math.exp(logKapH1bf)
#//System.out.println("HIbf " + log10E*logKapH1bf);
#//if (iTau == 36 && iLam == 142){
#// System.out.println("lambdaA " + lambdaA + " logKapH1bf " + log10E*(logKapH1bf)); //-rho[1][iTau]));
#//}
#//H I f-f:
#// cm^2 per *neutral* H atom
logKapH1ff = logHelp3 + loggff + logffHelp - logTheta - (theta*chiIH)*logE10
#//Stimulated emission correction
logKapH1ff = logKapH1ff + logStimEm
#//Add it in to total - opacity per neutral HI atom, so multiply by logNH1
#// This is now linear opacity in cm^-1
logKapH1ff = logKapH1ff + logNH1[iTau]
#////Nasty fix to make Balmer lines show up in A0 stars!
#// if (teff > 8000){
#// logKapH1ff = logKapH1ff - logE10*1.5;
#//
kappa = kappa + math.exp(logKapH1ff);
#//System.out.println("HIff " + log10E*logKapH1ff);
#//if (iTau == 36 && iLam == 142){
#// System.out.println("logKapH1ff " + log10E*(logKapH1ff)); //-rho[1][iTau]));
#//}
#//
#//Hminus:
#//
#// H^- b-f:
#//if (iTau == 36 && iLam == 142){
# // System.out.println("temp " + temp[0][iTau] + " lambdanm " + lambdanm);
# // }
logKapHmbf = -99.0 #//initialize default
#//if ( (temp[0][iTau] > 2500.0) && (temp[0][iTau] < 10000.0) ){
#//if ( (temp[0][iTau] > 2500.0) && (temp[0][iTau] < 8000.0) ){
#//Try lowering lower Teff limit to avoid oapcity collapse in outer layers of late-type stars
if ( (temp[0][iTau] > 1000.0) and (temp[0][iTau] < 10000.0) ):
if ((lambdanm > 225.0) and (lambdanm < 1500.0) ): # //nm
#//if (iTau == 36 && iLam == 142){
# // System.out.println("In KapHmbf condition...");
#//}
ii = 0.0
alphaHmbf = signAHm[0]*math.exp(logAHm[0]) #//initialize accumulator
#for (int i = 1; i < numHmTerms; i++){
for i in range(1, numHmTerms):
ii = float(i)
#//if (iTau == 36 && iLam == 142){
#// System.out.println("ii " + ii);
#//}
logTermHmbf = logAHm[i] + ii*logLambdaA
alphaHmbf = alphaHmbf + signAHm[i]*math.exp(logTermHmbf)
#//if (iTau == 36 && iLam == 142){
#// System.out.println("logTermHmbf " + log10E*logTermHmbf + " i " + i + " logAHm " + log10E*logAHm[i]);
#//}
logAlphaHmbf = math.log(alphaHmbf)
#// cm^2 per neutral H atom
logKapHmbf = logAHmbf + logAlphaHmbf + pe[1][iTau] + 2.5*logTheta + (0.754*theta)*logE10
#//Stimulated emission correction
logKapHmbf = logKapHmbf + logStimEm
#//if (iTau == 36 && iLam == 142){
#// System.out.println("alphaHmbf " + alphaHmbf);
#// System.out.println("logKapHmbf " + log10E*logKapHmbf + " logAHmbf " + log10E*logAHmbf + " logAlphaHmbf " + log10E*logAlphaHmbf);
#// }
#//Add it in to total - opacity per neutral HI atom, so multiply by logNH1
#// This is now linear opacity in cm^-1
logKapHmbf = logKapHmbf + logNH1[iTau]
kappa = kappa + math.exp(logKapHmbf)
#//System.out.println("Hmbf " + log10E*logKapHmbf);
#//if (iTau == 36 && iLam == 142){
#// System.out.println("logKapHmbf " + log10E*(logKapHmbf)); //-rho[1][iTau]));
#//}
#//wavelength condition
#// temperature condition
#// H^- f-f:
logKapHmff = -99.0 #//initialize default
#//if ( (temp[0][iTau] > 2500.0) && (temp[0][iTau] < 10000.0) ){
#//Try lowering lower Teff limit to avoid oapcity collapse in outer layers of late-type stars
#//if ( (temp[0][iTau] > 2500.0) && (temp[0][iTau] < 8000.0) ){
if ( (temp[0][iTau] > 1000.0) and (temp[0][iTau] < 10000.0) ):
if ((lambdanm > 260.0) and (lambdanm < 11390.0) ): #//nm
#//construct "f_n" polynomials in log(lambda)
for j in range(3):
fHm[j] = fHmTerms[j][0] #//initialize accumulators
ii = 0.0
for i in range(1, numHmffTerms):
ii = float(i)
logLambdaAFac = math.pow(log10LambdaA, ii)
for j in range(3):
fHm[j] = fHm[j] + (fHmTerms[j][i]*logLambdaAFac)
#} #// i
#} #// j
#//
fPoly = fHm[0] + fHm[1]*log10Theta + fHm[2]*log10Theta*log10Theta
#// In cm^2 per neutral H atom:
#// Stimulated emission alreadya ccounted for
logKapHmff = logAHmff + pe[1][iTau] + fPoly*logE10
#//Add it in to total - opacity per neutral HI atom, so multiply by logNH1
#// This is now linear opacity in cm^-1
logKapHmff = logKapHmff + logNH1[iTau]
kappa = kappa + math.exp(logKapHmff)
#//System.out.println("Hmff " + log10E*logKapHmff);
#//if (iTau == 36 && iLam == 142){
#// System.out.println("logKapHmff " + log10E*(logKapHmff)); //-rho[1][iTau]));
#//}
#//wavelength condition
#// temperature condition
#// H^+_2:
#//
logKapH2p = -99.0 #//initialize default
if ( temp[0][iTau] < 4000.0 ):
if ((lambdanm > 380.0) and (lambdanm < 2500.0) ): # //nm
sigmaH2p = sigmaH2pTerm[0] #//initialize accumulator
UH2p = UH2pTerm[0] #//initialize accumulator
ii = 0.0#
for i in range(1, numH2pTerms):
ii = float(i)
logLambdaAFac = math.pow(log10LambdaA, ii)
#// kapH2p way too large with lambda in A - try cm: No! - leads to negative logs
#//logLambdaAFac = Math.pow(logLambda, ii);
sigmaH2p = sigmaH2p + sigmaH2pTerm[i] * logLambdaAFac
UH2p = UH2p + UH2pTerm[i] * logLambdaAFac
logSigmaH2p = math.log(sigmaH2p)
logKapH2p = logAH2p + logSigmaH2p - (UH2p*theta)*logE10 + logNH2[iTau]
#//Stimulated emission correction
logKapH2p = logKapH2p + logStimEm
#//Add it in to total - opacity per neutral HI atom, so multiply by logNH1
#// This is now linear opacity in cm^-1
logKapH2p = logKapH2p + logNH1[iTau]
kappa = kappa + math.exp(logKapH2p)
#//System.out.println("H2p " + log10E*logKapH2p);
#//if (iTau == 16 && iLam == 142){
# //System.out.println("logKapH2p " + log10E*(logKapH2p-rho[1][iTau]) + " logAH2p " + log10E*logAH2p
#// + " logSigmaH2p " + log10E*logSigmaH2p + " (UH2p*theta)*logE10 " + log10E*((UH2p*theta)*logE10) + " logNH2[iTau] " + log10E*logNH2[iTau]);
#//}
#//wavelength condition
#// temperature condition
#//He I
#//
#// HeI b-f + f-f
#//Scale sum of He b-f and f-f with sum of HI b-f and f-f
#//wavelength condition comes from requirement that lower E level be greater than n=2 (edge at 22.78 nm)
logKapHe = -99.0 #//default intialization
if ( temp[0][iTau] > 10000.0 ):
if (lambdanm > 22.8): #//nm
totalH1Kap = math.exp(logKapH1bf) + math.exp(logKapH1ff)
logTotalH1Kap = math.log(totalH1Kap)
helpHe = Useful.k() * temp[0][iTau]
#// cm^2 per neutral H atom (after all, it's scaled wrt kappHI
#// Stimulated emission already accounted for
#//
#// *** CAUTION: Is this *really* the right thing to do???
#// - we're re-scaling the final H I kappa in cm^2/g corrected for stim em, NOT the raw cross section
logKapHe = math.log(4.0) - (10.92 / helpHe) + logTotalH1Kap
#//Add it in to total - opacity per neutral HI atom, so multiply by logNH1
#// This is now linear opacity in cm^-1
logKapHe = logKapHe + logNH1[iTau]
kappa = kappa + math.exp(logKapHe)
#//System.out.println("He " + log10E*logKapHe);
#//if (iTau == 36 && iLam == 142){
#// System.out.println("logKapHe " + log10E*(logKapHe)); //-rho[1][iTau]));
#//}
#//wavelength condition
#// temperature condition
#//
#//He^- f-f:
logKapHemff = -99.0 #//default initialization
if ( (theta > 0.5) and (theta < 2.0) ):
if ((lambdanm > 500.0) and (lambdanm < 15000.0) ):
#// initialize accumulators:
cHemff[0] = signC0HemffTerm[0]*math.exp(logC0HemffTerm[0]);
#//System.out.println("C0HemffTerm " + signC0HemffTerm[0]*Math.exp(logC0HemffTerm[0]));
cHemff[1] = signC1HemffTerm[0]*math.exp(logC1HemffTerm[0]);
#//System.out.println("C1HemffTerm " + signC1HemffTerm[0]*Math.exp(logC1HemffTerm[0]));
cHemff[2] = signC2HemffTerm[0]*math.exp(logC2HemffTerm[0]);
#//System.out.println("C2HemffTerm " + signC2HemffTerm[0]*Math.exp(logC2HemffTerm[0]));
cHemff[3] = signC3HemffTerm[0]*math.exp(logC3HemffTerm[0]);
#//System.out.println("C3HemffTerm " + signC3HemffTerm[0]*Math.exp(logC3HemffTerm[0]));
#//build the theta polynomial coefficients
ii = 0.0
for i in range(1, numHemffTerms):
ii = float(i)
thisLogTerm = ii*logTheta + logC0HemffTerm[i]
cHemff[0] = cHemff[0] + signC0HemffTerm[i]*math.exp(thisLogTerm)
#//System.out.println("i " + i + " ii " + ii + " C0HemffTerm " + signC0HemffTerm[i]*Math.exp(logC0HemffTerm[i]));
thisLogTerm = ii*logTheta + logC1HemffTerm[i]
cHemff[1] = cHemff[1] + signC1HemffTerm[i]*math.exp(thisLogTerm)
#//System.out.println("i " + i + " ii " + ii + " C1HemffTerm " + signC1HemffTerm[i]*Math.exp(logC1HemffTerm[i]));
thisLogTerm = ii*logTheta + logC2HemffTerm[i]
cHemff[2] = cHemff[2] + signC2HemffTerm[i]*math.exp(thisLogTerm)
#//System.out.println("i " + i + " ii " + ii + " C2HemffTerm " + signC2HemffTerm[i]*Math.exp(logC2HemffTerm[i]));
thisLogTerm = ii*logTheta + logC3HemffTerm[i]
cHemff[3] = cHemff[3] + signC3HemffTerm[i]*math.exp(thisLogTerm)
#//System.out.println("i " + i + " ii " + ii + " C3HemffTerm " + signC3HemffTerm[i]*Math.exp(logC3HemffTerm[i]));
#//// Should polynomial expansion for Cs be in log10Theta??: - No! Doesn't help
#// initialize accumulators:
#// cHemff[0] = C0HemffTerm[0];
#// cHemff[1] = C1HemffTerm[0];
#// cHemff[2] = C2HemffTerm[0];
#// cHemff[3] = C3HemffTerm[0];
#// ii = 0.0;
#// for (int i = 1; i < numHemffTerms; i++){
#// ii = (double) i;
#// log10ThetaFac = Math.pow(log10Theta, ii);
#// thisTerm = log10ThetaFac * C0HemffTerm[i];
#// cHemff[0] = cHemff[0] + thisTerm;
#// thisTerm = log10ThetaFac * C1HemffTerm[i];
#// cHemff[1] = cHemff[1] + thisTerm;
#// thisTerm = log10ThetaFac * C2HemffTerm[i];
#// cHemff[2] = cHemff[2] + thisTerm;
#// thisTerm = log10ThetaFac * C3HemffTerm[i];
#// cHemff[3] = cHemff[3] + thisTerm;
#// }
#//Build polynomial in logLambda for alpha(He^1_ff):
log10AlphaHemff = cHemff[0] #//initialize accumulation
#//System.out.println("cHemff[0] " + cHemff[0]);
ii = 0.0
for i in range(1, 3+1):
#//System.out.println("i " + i + " cHemff[i] " + cHemff[i]);
ii = float(i)
thisTerm = cHemff[i] * math.pow(log10LambdaA, ii)
log10AlphaHemff = log10AlphaHemff + thisTerm
#//System.out.println("log10AlphaHemff " + log10AlphaHemff);
alphaHemff = math.pow(10.0, log10AlphaHemff) #//gives infinite alphas!
#// alphaHemff = log10AlphaHemff; // ?????!!!!!
#//System.out.println("alphaHemff " + alphaHemff);
#// Note: this is the extinction coefficient per *Hydrogen* particle (NOT He- particle!)
# //nHe = Math.exp(logNHe1[iTau]) + Math.exp(logNHe2[iTau]);
# //logNHe = Math.log(nHe);
# //logKapHemff = Math.log(alphaHemff) + Math.log(AHe) + pe[1][iTau] + logNHe1[iTau] - logNHe;
logKapHemff = logAHemff + math.log(alphaHemff) + pe[1][iTau] + logNHe1[iTau] - logNH[iTau]
#//Stimulated emission already accounted for
#//Add it in to total - opacity per H particle, so multiply by logNH
#// This is now linear opacity in cm^-1
logKapHemff = logKapHemff + logNH[iTau]
kappa = kappa + math.exp(logKapHemff)
#//System.out.println("Hemff " + log10E*logKapHemff);
#//if (iTau == 36 && iLam == 155){
#//if (iLam == 155){
#// System.out.println("logKapHemff " + log10E*(logKapHemff)); //-rho[1][iTau]));
#//}
#//wavelength condition
#// temperature condition
#//
#// electron (e^-1) scattering (Thomson scattering)
#//coefficient per *"hydrogen atom"* (NOT per e^-!!) (neutral or total H??):
logKapE = logAlphaE + Ne[1][iTau] - logNH[iTau]
#//Stimulated emission not relevent
#//Add it in to total - opacity per H particle, so multiply by logNH
#// This is now linear opacity in cm^-1
#//I know, we're adding logNH right back in after subtracting it off, but this is for dlarity and consistency for now... :
logKapE = logKapE + logNH[iTau]
kappa = kappa + math.exp(logKapE)
#//System.out.println("E " + log10E*logKapE);
#//if (iTau == 36 && iLam == 142){
#// System.out.println("logKapE " + log10E*(logKapE)); //-rho[1][iTau]));
#//}
#//Metal b-f
#//Fig. 8.6 Gray 3rd Ed.
#//
#//
#// This is now linear opacity in cm^-1
#// Divide by mass density
#// This is now mass extinction in cm^2/g
#//
logKappa[iLam][iTau] = math.log(kappa) - rho[1][iTau]
#// Fudge is in cm^2/g: Converto to natural log:
logEKapFudge = logE10 * logKapFudge
logKappa[iLam][iTau] = logKappa[iLam][iTau] + logEKapFudge
#//if (iTau == 36 && iLam == 142){
#//System.out.println(" " + log10E*(logKappa[iLam][iTau]+rho[1][iTau]));
#//}
#// close iTau depth loop
#//
#//close iLam wavelength loop
return logKappa
def jolaProfileQ(omega0, logf, vibConst, jolaPoints, alphQ, numDeps, temp):
"""//JOLA profile for Q (Delta J = 0) branch
//Equation 24 from Zeidler & Koestler"""
nm2cm = 1.0e-7
numPoints = len(jolaPoints)
#// derivative of rotational-line oscillator strength with respect to frequency
dfBydw = [[0.0 for i in range(numDeps)] for j in range(numPoints)]
fvv = math.exp(logf)
logHcBbyK = Useful.logH() + Useful.logC() + math.log(vibConst[0]) \
- Useful.logK()
Bsum = vibConst[1] + vibConst[0]
Bdiff = vibConst[1] - vibConst[0]
#double mQ; #// related to J, for R & P branches, respectively
#//value of m is closely related to rotational quantum number J,
#//Near band origin, frequency, w, range should correspond to -1 <= m <= 1 - ???:
#// double wMin = Useful.c / (1.0e-7*lambda[1]); //first frequency omega
#// double wMax = Useful.c / (1.0e-7*lambda[0]); //last frequency omega
#// double deltaW = 0.02;
#double w, logW, mQFctr, mHelp;
#double denom, mQTerm, wMinusw0OverBDiff;
#double help1, logHcBbyKt, hcBbyKt;
#//Outer loop over frequency omega
#//for (int iW = -1; iW <= 1; iW++){
#for (int iW = numPoints-1; iW >= 0; iW--){
for iW in range(numPoints - 1, 0, -1):
#//dW = (double) iW;
#//w = wMin + (dW*deltaW);
#//logW = Useful.logC() - Math.log(1.0e-7*jolaPoints[iW]); //if w is freq in Hz
logW = 0.0 - math.log(
nm2cm * jolaPoints[iW]) #//if w is waveno in cm^-1
w = math.exp(logW)
#//I have no idea if this is right...
wMinusw0OverBDiff = (w - omega0) / Bdiff
mHelp = 0.25 + math.abs(wMinusw0OverBDiff)
mHelp = math.sqrt(mHelp) #//Eq. 17
mQ = -0.5 + mHelp
mQFctr = (mQ * mQ - mQ)
denom = math.abs(Bdiff)
for iD in range(numDeps):
if (wMinusw0OverBDiff > 0):
logHcBbyKt = logHcBbyK - temp[1][iD]
hcBbyKt = math.exp(logHcBbyKt)
help1 = -1.0 * hcBbyKt * mQFctr
mQTerm = math.exp(help1) / denom
#//Can this be used like a differential cross-section (once converted to sigma)?
#//System.out.println("alphQ " + alphQ + " fvv " + " logHcBbyKt " + logHcBbyKt + " mQTerm " + mQTerm);
dfBydw[iW][iD] = alphQ * fvv * hcBbyKt * mQTerm #// Eq. 24
else:
dfBydw[iW][iD] = 0.0
#//if (iD%10 == 1){
#//System.out.println("Q iD " + iD + " iW " + iW + " dfBydw " + dfBydw[iW][iD]);
#//}
#//iD - depth loop
#} //iW - frequency loop
return dfBydw
def jolaKap(jolaLogNums, dfBydw, jolaPoints, numDeps, temp, rho):
log10E = math.log10(math.e)
nm2cm = 1.0e-7
numPoints = len(jolaPoints)
logKappaJola = [[0.0 for i in range(numDeps)] for j in range(numPoints)]
#//Initialize this carefully:
for iD in range(numDeps):
for iW in range(numPoints):
logKappaJola[iW][iD] = -999.0
#double stimEmExp, stimEmLogExp, stimEmLogExpHelp, stimEm;
#double freq, lastFreq, w, lastW, deltaW, thisDeltaF;
logSigma = -999.0
logFreq = Useful.logC() - math.log(nm2cm * jolaPoints[0])
logW = 0.0 - math.log(nm2cm * jolaPoints[0]) #//if w is waveno in cm^-1
#//lastFreq = Math.exp(logFreq)
lastW = math.exp(logW)
#//try accumulating oscillator strenth, f, across band - assumes f = 0 at first (largest) lambda- ??
thisF = 0.0
#//If f is cumulative in wavenumber, then we have to make the wavenumber loop the inner one even if it
#//means re-calculating depth-independent quantities each time:
for iD in range(numDeps):
thisF = 0.0 #//re-set accumulator
#//loop in order of *increasing* wavenumber
#for (int iW = numPoints-1; iW >=1; iW--){
for iW in range(numPoints - 1, 1, -1):
#//df/dv is a differential oscillator strength in *frequency* space:
logFreq = Useful.logC() - math.log(nm2cm * jolaPoints[iW])
freq = math.exp(logFreq)
logW = 0.0 - math.log(
nm2cm * jolaPoints[iW]) #//if w is waveno in cm^-1
w = math.exp(logW) #//if w is waveno in cm^-1
#//System.out.println("w " + w);
#//deltaW = Math.abs(freq - lastFreq);
deltaW = abs(w - lastW)
#//For LTE stimulated emission correction:
stimEmLogExpHelp = Useful.logH() + logFreq - Useful.logK()
#// for (int iD = 0; iD < numDeps; iD++){
thisDeltaF = deltaW * dfBydw[iW][iD]
if (thisDeltaF > 0.0):
#thisF += thisDeltaF #//cumulative version
thisF = thisDeltaF
#//non-cumulative version
logSigma = math.log(thisF) + math.log(
math.pi) + 2.0 * Useful.logEe() - Useful.logMe(
) - Useful.logC()
else:
logSigma = -999.0
#// LTE stimulated emission correction:
stimEmLogExp = stimEmLogExpHelp - temp[1][iD]
stimEmExp = -1.0 * math.exp(stimEmLogExp)
stimEm = (1.0 - math.exp(stimEmExp))
#//extinction coefficient in cm^2 g^-1:
logKappaJola[iW][iD] = logSigma + jolaLogNums[iD] - rho[1][
iD] + math.log(stimEm)
#//logKappaJola[iW][iD] = -999.0;
#//if (iD%10 == 1){
#//System.out.println("iD " + iD + " iW " + iW + " logFreq " + log10E*logFreq + " logW " + log10E*logW + " logStimEm " + log10E*Math.log(stimEm));
#//System.out.println("iD " + iD + " iW " + iW + " thisDeltaF " + thisDeltaF + " logSigma " + log10E*logSigma + " jolaLogNums " + log10E*jolaLogNums[iD] + " rho " + log10E*rho[1][iD] + " logKappaJola " + log10E*logKappaJola[iW][iD]);
#//}
#// } //iD loop - depths
lastFreq = freq
#} //iW loop - wavelength
#} //iD loop - depths
return logKappaJola
def molPops(nmrtrLogNumB, nmrtrDissE, logUwA, nmrtrLogUwB, nmrtrLogQwAB, nmrtrLogMuAB, \
numMolsB, logNumB, dissEArr, logUwB, logQwABArr, logMuABArr, \
logGroundRatio, numDeps, temp):
# line 1: //species A data - ionization equilibrium of A
# //data for set of species "B" - molecular equlibrium for set {AB}
"""Diatomic molecular equilibrium routine that accounts for molecule formation:
// Returns depth distribution of molecular population
// Input parameters:
// logNum - array with depth-dependent total element number densities (cm^-3)
// chiI1 - ground state ionization energy of neutral stage
// chiI2 - ground state ionization energy of singly ionized stage
// Also needs atsmopheric structure information:
// numDeps
// temp structure
// rho structure
//
// Atomic element "A" is the one kept on the LHS of the master fraction, whose ionization fractions are included
// in the denominator of the master fraction
// Element "B" refers to array of other sintpecies with which A forms molecules "AB" """
logE = math.log10(math.e) #// for debug output
#//System.out.println("molPops: nmrtrDissE " + nmrtrDissE + " log10UwA " + log10UwA[0] + " " + log10UwA[1] + " nmrtrLog10UwB " +
#// nmrtrLog10UwB[0] + " " + nmrtrLog10UwB[1] + " nmrtrLog10QwAB " + logE*nmrtrLogQwAB[2] + " nmrtrLogMuAB " + logE*nmrtrLogMuAB
#// + " numMolsB " + numMolsB + " dissEArr " + dissEArr[0] + " log10UwBArr " + log10UwBArr[0][0] + " " + log10UwBArr[0][1] + " log10QwABArr " +
#// logE*logQwABArr[0][2] + " logMuABArr " + logE*logMuABArr[0]);
#//System.out.println("Line: nmrtrLog10UwB[0] " + logE*nmrtrLog10UwB[0] + " nmrtrLog10UwB[1] " + logE*nmrtrLog10UwB[1]);
ln10 = math.log(10.0)
log2pi = math.log(2.0 * math.pi)
log2 = math.log(2.0)
logE10 = math.log(10.0)
#// Convert to natural logs:
#double Ttheta, thisTemp;
#//Treat at least one molecule - if there are really no molecules for an atomic species,
#//there will be one phantom molecule in the denominator of the ionization fraction
#//with an impossibly high dissociation energy
if (numMolsB == 0):
numMolsB = 1
#//This should be inherited, but let's make sure:
dissEArr[0] = 29.0 #//eV
#//var molPops = function(logNum, numeratorLogNumB, numeratorDissE, numeratorLog10UwA, numeratorLog10QwAB, numeratorLogMuAB, //species A data - ionization equilibrium of A
#//Molecular partition functions - default initialization:
thisLogUwB = [0.0 for i in range(numMolsB)]
for iMol in range(numMolsB):
thisLogUwB[
iMol] = 0.0 #// variable for temp-dependent computed partn fn of array element B
thisLogUwA = 0.0 #// element A
nmrtrThisLogUwB = 0.0 #// element A
thisLogQwAB = math.log(300.0)
nmrtrThisLogQwAB = math.log(300.0)
#//For clarity: neutral stage of atom whose ionization equilibrium is being computed is element A
#// for molecule formation:
#logUwA = [0.0 for i in range(5)]
#nmrtrLogUwB = [0.0 for i in range(5)]
#for kk in range(len(logUwA)):
#logUwA[kk] = logE10*log10UwA[kk]
#nmrtrLogUwB[kk] = logE10*nmrtrLog10UwB[kk]
#// lburns
#// Array of elements B for all molecular species AB:
#double[][] logUwB = new double[numMolsB][2];
#logUwB = [ [ 0.0 for i in range(5) ] for j in range(numMolsB) ]
#//if (numMolsB > 0){
#for iMol in range(numMolsB):
# for kk in range(5):
# logUwB[iMol][kk] = logE10*log10UwBArr[iMol][kk]
# // lburns new loop
#//}
#// Molecular partition functions:
#// double nmrtrLogQwAB = logE10*nmrtrLog10QwAB;
#// double[] logQwAB = new double[numMolsB];
#// //if (numMolsB > 0){
#// for (int iMol = 0; iMol < numMolsB; iMol++){
#// logQwAB[iMol] = logE10*log10QwABArr[iMol];
#// }
# //}
#//Molecular dissociation Boltzmann factors:
nmrtrBoltzFacIAB = 0.0
nmrtrLogMolSahaFac = 0.0
logDissE = math.log(nmrtrDissE) + Useful.logEv()
#//System.out.println("logDissE " + logE*logDissE)
logBoltzFacIAB = logDissE - Useful.logK()
#//System.out.println("logBoltzFacIAB " + logE*logBoltzFacIAB);
nmrtrBoltzFacIAB = math.exp(logBoltzFacIAB)
nmrtrLogMolSahaFac = (3.0 / 2.0) * (log2pi + nmrtrLogMuAB + Useful.logK() -
2.0 * Useful.logH())
#//System.out.println("nmrtrLogMolSahaFac " + logE*nmrtrLogMolSahaFac);
#//System.out.println("nmrtrDissE " + nmrtrDissE + " logDissE " + logE*logDissE + " logBoltzFacIAB " + logE*logBoltzFacIAB + " nmrtrBoltzFacIAB " + nmrtrBoltzFacIAB + " nmrtrLogMuAB " + logE*nmrtrLogMuAB + " nmrtrLogMolSahaFac " + logE*nmrtrLogMolSahaFac);
boltzFacIAB = [0.0 for i in range(numMolsB)]
logMolSahaFac = [0.0 for i in range(numMolsB)]
#//if (numMolsB > 0){
for iMol in range(numMolsB):
logDissE = math.log(dissEArr[iMol]) + Useful.logEv()
logBoltzFacIAB = logDissE - Useful.logK()
boltzFacIAB[iMol] = math.exp(logBoltzFacIAB)
logMolSahaFac[iMol] = (3.0 / 2.0) * (
log2pi + logMuABArr[iMol] + Useful.logK() - 2.0 * Useful.logH())
#//System.out.println("logMolSahaFac[iMol] " + logE*logMolSahaFac[iMol]);
#//System.out.println("iMol " + iMol + " dissEArr[iMol] " + dissEArr[iMol] + " logDissE " + logE*logDissE + " logBoltzFacIAB " + logE*logBoltzFacIAB + " boltzFacIAB[iMol] " + boltzFacIAB[iMol] + " logMuABArr " + logE*logMuABArr[iMol] + " logMolSahaFac " + logE*logMolSahaFac[iMol]);
#//double[] logNums = new double[numDeps]
#//}
#// For molecular species:
#double nmrtrSaha, nmrtrLogSahaMol, nmrtrLogInvSahaMol; //, nmrtrInvSahaMol;
logMolFrac = [0.0 for i in range(numDeps)]
logSahaMol = [0.0 for i in range(numMolsB)]
invSahaMol = [0.0 for i in range(numMolsB)]
#//
#// System.out.println("molPops: id nmrtrLogNumB logNumBArr[0] logGroundRatio");
for id in range(numDeps):
#//System.out.format("%03d, %21.15f, %21.15f, %21.15f, %n", id, logE*nmrtrLogNumB[id], logE*logNumB[0][id], logE*logGroundRatio[id]);
#//// reduce or enhance number density by over-all Rosseland opcity scale parameter
#//Determine temparature dependent partition functions Uw:
thisTemp = temp[0][id]
#Ttheta = 5040.0 / thisTemp
"""
if (Ttheta >= 1.0):
thisLogUwA = logUwA[0]
nmrtrThisLogUwB = nmrtrLogUwB[0]
for iMol in range(numMolsB):
thisLogUwB[iMol] = logUwB[iMol][0]
if (Ttheta <= 0.5):
thisLogUwA = logUwA[1]
nmrtrThisLogUwB = nmrtrLogUwB[1]
for iMol in range(numMolsB):
thisLogUwB[iMol] = logUwB[iMol][1]
if (Ttheta > 0.5 and Ttheta < 1.0):
thisLogUwA = ( logUwA[1] * ((Ttheta - 0.5)/(1.0 - 0.5)) ) \
+ ( logUwA[0] * ((1.0 - Ttheta)/(1.0 - 0.5)) )
nmrtrThisLogUwB = ( nmrtrLogUwB[1] * ((Ttheta - 0.5)/(1.0 - 0.5)) ) \
+ ( nmrtrLogUwB[0] * ((1.0 - Ttheta)/(1.0 - 0.5)) )
for iMol in range(numMolsB):
thisLogUwB[iMol] = ( logUwB[iMol][1] * ((Ttheta - 0.5)/(1.0 - 0.5)) ) \
+ ( logUwB[iMol][0] * ((1.0 - Ttheta)/(1.0 - 0.5)) )
"""
#// NEW Determine temperature dependent partition functions Uw: lburns
thisTemp = temp[0][id]
if (thisTemp <= 130):
thisLogUwA = logUwA[0]
nmrtrThisLogUwB = nmrtrLogUwB[0]
for iMol in range(numMolsB):
thisLogUwB[iMol] = logUwB[iMol][0]
if (thisTemp > 130 and thisTemp <= 500):
thisLogUwA = logUwA[1] * (thisTemp - 130)/(500 - 130) \
+ logUwA[0] * (500 - thisTemp)/(500 - 130)
nmrtrThisLogUwB = nmrtrLogUwB[1] * (thisTemp - 130)/(500 - 130) \
+ nmrtrLogUwB[0] * (500 - thisTemp)/(500 - 130)
for iMol in range(numMolsB):
thisLogUwB[iMol] = logUwB[iMol][1] * (thisTemp - 130)/(500 - 130) \
+ logUwB[iMol][0] * (500 - thisTemp)/(500 - 130)
if (thisTemp > 500 and thisTemp <= 3000):
thisLogUwA = logUwA[2] * (thisTemp - 500)/(3000 - 500) \
+ logUwA[1] * (3000 - thisTemp)/(3000 - 500)
nmrtrThisLogUwB = nmrtrLogUwB[2] * (thisTemp - 500)/(3000 - 500) \
+ nmrtrLogUwB[1] * (3000 - thisTemp)/(3000 - 500)
for iMol in range(numMolsB):
thisLogUwB[iMol] = logUwB[iMol][2] * (thisTemp - 500)/(3000 - 500) \
+ logUwB[iMol][1] * (3000 - thisTemp)/(3000 - 500)
if (thisTemp > 3000 and thisTemp <= 8000):
thisLogUwA = logUwA[3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUwA[2] * (8000 - thisTemp)/(8000 - 3000)
nmrtrThisLogUwB = nmrtrLogUwB[3] * (thisTemp - 3000)/(8000 - 3000) \
+ nmrtrLogUwB[2] * (8000 - thisTemp)/(8000 - 3000)
for iMol in range(numMolsB):
thisLogUwB[iMol] = logUwB[iMol][3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUwB[iMol][2] * (8000 - thisTemp)/(8000 - 3000)
if (thisTemp > 8000 and thisTemp < 10000):
thisLogUwA = logUwA[4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUwA[3] * (10000 - thisTemp)/(10000 - 8000)
nmrtrThisLogUwB = nmrtrLogUwB[4] * (thisTemp - 8000)/(10000 - 8000) \
+ nmrtrLogUwB[3] * (10000 - thisTemp)/(10000 - 8000)
for iMol in range(numMolsB):
thisLogUwB[iMol] = logUwB[iMol][4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUwB[iMol][3] * (10000 - thisTemp)/(10000 - 8000)
if (thisTemp >= 10000):
thisLogUwA = logUwA[4]
nmrtrThisLogUwB = nmrtrLogUwB[4]
for iMol in range(numMolsB):
thisLogUwB[iMol] = logUwB[iMol][4]
for iMol in range(numMolsB):
if (thisTemp < 3000.0):
thisLogQwAB = ( logQwABArr[iMol][1] * (3000.0 - thisTemp)/(3000.0 - 500.0) ) \
+ ( logQwABArr[iMol][2] * (thisTemp - 500.0)/(3000.0 - 500.0) )
if ((thisTemp >= 3000.0) and (thisTemp <= 8000.0)):
thisLogQwAB = ( logQwABArr[iMol][2] * (8000.0 - thisTemp)/(8000.0 - 3000.0) ) \
+ ( logQwABArr[iMol][3] * (thisTemp - 3000.0)/(8000.0 - 3000.0) )
if (thisTemp > 8000.0):
thisLogQwAB = ( logQwABArr[iMol][3] * (10000.0 - thisTemp)/(10000.0 - 8000.0) ) \
+ ( logQwABArr[iMol][4] * (thisTemp - 8000.0)/(10000.0 - 8000.0) )
if (thisTemp < 3000.0):
nmrtrThisLogQwAB = ( nmrtrLogQwAB[1] * (3000.0 - thisTemp)/(3000.0 - 500.0) ) \
+ ( nmrtrLogQwAB[2] * (thisTemp - 500.0)/(3000.0 - 500.0) )
if ((thisTemp >= 3000.0) and (thisTemp <= 8000.0)):
nmrtrThisLogQwAB = ( nmrtrLogQwAB[2] * (8000.0 - thisTemp)/(8000.0 - 3000.0) ) \
+ ( nmrtrLogQwAB[3] * (thisTemp - 3000.0)/(8000.0 - 3000.0) )
if (thisTemp > 8000.0):
nmrtrThisLogQwAB = ( nmrtrLogQwAB[3] * (10000.0 - thisTemp)/(10000.0 - 8000.0) ) \
+ ( nmrtrLogQwAB[4] * (thisTemp - 8000.0)/(10000.0 - 8000.0) )
#//For clarity: neutral stage of atom whose ionization equilibrium is being computed is element A
#// for molecule formation:
# //Ionization stage Saha factors:
#//System.out.println("id " + id + " nmrtrLogNumB[id] " + logE*nmrtrLogNumB[id]);
# // if (id == 16){
# // System.out.println("id " + id + " nmrtrLogNumB[id] " + logE*nmrtrLogNumB[id] + " pp nmrtB " + (logE*(nmrtrLogNumB[id]+temp[1][id]+Useful.logK())) + " nmrtrThisLogUwB " + logE*nmrtrThisLogUwB + " thisLogUwA " + logE*thisLogUwA + " nmrtrLogQwAB " + logE*nmrtrThisLogQwAB);
# //System.out.println("nmrtrThisLogUwB " + logE*nmrtrThisLogUwB + " thisLogUwA " + logE*thisLogUwA + " nmrtrThisLogQwAB " + logE*nmrtrThisLogQwAB);
# // }
nmrtrLogSahaMol = nmrtrLogMolSahaFac - nmrtrLogNumB[id] - (
nmrtrBoltzFacIAB / temp[0][id]) + (
3.0 * temp[1][id] /
2.0) + nmrtrThisLogUwB + thisLogUwA - nmrtrThisLogQwAB
nmrtrLogInvSahaMol = -1.0 * nmrtrLogSahaMol
#//System.out.println("nmrtrLogInvSahaMol " + logE*nmrtrLogInvSahaMol);
#//nmrtrInvSahaMol = Math.exp(nmrtrLogSahaMol);
#// if (id == 16){
#// System.out.println("nmrtrLogInvSahaMol " + logE*nmrtrLogInvSahaMol);
#// }
#// if (id == 16){
#// System.out.println("nmrtrBoltzFacIAB " + nmrtrBoltzFacIAB + " nmrtrThisLogUwB " + logE*nmrtrThisLogUwB + " thisLogUwA " + logE*thisLogUwA + " nmrtrThisLogQwAB " + nmrtrThisLogQwAB);
#// System.out.println("nmrtrLogSahaMol " + logE*nmrtrLogSahaMol); // + " nmrtrInvSahaMol " + nmrtrInvSahaMol);
#// }
#//Molecular Saha factors:
for iMol in range(numMolsB):
#//System.out.println("iMol " + iMol + " id " + id + " logNumB[iMol][id] " + logE*nmrtrLogNumB[id]);
#//System.out.println("iMol " + iMol + " thisLogUwB[iMol] " + logE*thisLogUwB[iMol] + " thisLogUwA " + logE*thisLogUwA + " thisLogQwAB " + logE*thisLogQwAB);
logSahaMol[iMol] = logMolSahaFac[iMol] - logNumB[iMol][id] - (
boltzFacIAB[iMol] / temp[0][id]) + (
3.0 * temp[1][id] /
2.0) + thisLogUwB[iMol] + thisLogUwA - thisLogQwAB
#//For denominator of ionization fraction, we need *inverse* molecular Saha factors (N_AB/NI):
logSahaMol[iMol] = -1.0 * logSahaMol[iMol]
invSahaMol[iMol] = math.exp(logSahaMol[iMol])
#//TEST invSahaMol[iMol] = 1.0e-99; //test
#// if (id == 16){
#// System.out.println("iMol " + iMol + " boltzFacIAB[iMol] " + boltzFacIAB[iMol] + " thisLogUwB[iMol] " + logE*thisLogUwB[iMol] + " logQwAB[iMol] " + logE*thisLogQwAB + " logNumB[iMol][id] " + logE*logNumB[iMol][id] + " logMolSahaFac[iMol] " + logE*logMolSahaFac[iMol]);
#// System.out.println("iMol " + iMol + " logSahaMol " + logE*logSahaMol[iMol] + " invSahaMol[iMol] " + invSahaMol[iMol]);
#// }
#//Compute log of denominator is ionization fraction, f_stage
# //default initialization
# // - ratio of total atomic particles in all ionization stages to number in ground state:
denominator = math.exp(
logGroundRatio[id]
) #//default initialization - ratio of total atomic particles in all ionization stages to number in ground state
#//molecular contribution
for iMol in range(numMolsB):
#// if (id == 16){
#// System.out.println("invSahaMol[iMol] " + invSahaMol[iMol] + " denominator " + denominator);
#// }
denominator = denominator + invSahaMol[iMol]
#//
logDenominator = math.log(denominator)
#//System.out.println("logGroundRatio[id] " + logE*logGroundRatio[id] + " logDenominator " + logE*logDenominator);
#// if (id == 16){
#// System.out.println("id " + id + " logGroundRatio " + logGroundRatio[id] + " logDenominator " + logDenominator);
#// }
#//if (id == 36){
#// System.out.println("logDenominator " + logE*logDenominator);
#// }
#//var logDenominator = Math.log( 1.0 + saha21 + (saha32 * saha21) + (saha43 * saha32 * saha21) + (saha54 * saha43 * saha32 * saha21) );
logMolFrac[id] = nmrtrLogInvSahaMol - logDenominator
#// if (id == 16){
#// System.out.println("id " + id + " logMolFrac[id] " + logE*logMolFrac[id]);
#// }
#//logNums[id] = logNum[id] + logMolFrac;
#} //id loop
return logMolFrac
def sahaRHS(chiI, logUwU, logUwL, temp):
"""RHS of partial pressure formulation of Saha equation in standard form (N_U*P_e/N_L on LHS)
// Returns depth distribution of LHS: Phi(T) === N_U*P_e/N_L (David Gray notation)
// Input parameters:
// chiI - ground state ionization energy of lower stage
// log10UwUArr, log10UwLArr - array of temperature-dependent partition function for upper and lower ionization stage
// Also needs atsmopheric structure information:
// numDeps
// temp structure
//
// Atomic element "A" is the one whose ionization fractions are being computed
// Element "B" refers to array of other species with which A forms molecules "AB" """
ln10 = math.log(10.0)
logE = math.log10(math.e) #// for debug output
log2pi = math.log(2.0 * math.pi)
log2 = math.log(2.0)
#// var numMols = dissEArr.length;
#// Parition functions passed in are 2-element vectore with remperature-dependent base 10 log Us
#// Convert to natural logs:
#double Ttheta, thisTemp;
#//Default initializations:
#//We need one more stage in size of saha factor than number of stages we're actualy populating
thisLogUwU = 0.0
thisLogUwL = 0.0
logE10 = math.log(10.0)
#//We need one more stage in size of saha factor than number of stages we're actualy populating
#logUwU = [0.0 for i in range(5)]
#logUwL = [0.0 for i in range(5)]
for kk in range(len(logUwL)):
logUwU[kk] = logUwL[kk]
# logUwL[kk] = logE10*log10UwLArr[kk]
#//System.out.println("chiL before: " + chiL);
#// If we need to subtract chiI from chiL, do so *before* converting to tiny numbers in ergs!
#//atomic ionization stage Boltzmann factors:
#double logChiI, logBoltzFacI;
#double boltzFacI;
logChiI = math.log(chiI) + Useful.logEv()
logBoltzFacI = logChiI - Useful.logK()
boltzFacI = math.exp(logBoltzFacI)
#//Extra factor of k to get k^5/2 in the P_e formulation of Saha Eq.
logSahaFac = log2 + (3.0 / 2.0) * (log2pi + Useful.logMe() + Useful.logK()
- 2.0 * Useful.logH()) + Useful.logK()
#//double[] logLHS = new double[numDeps];
#double logLHS;
#// For atomic ionization stages:
#double logSaha, saha, expFac;
#// for (int id = 0; id < numDeps; id++) {
#//
#//Determine temperature dependent partition functions Uw:
thisTemp = temp[0]
#Ttheta = 5040.0 / thisTemp
"""
if (Ttheta >= 1.0):
thisLogUwU = logUwU[0]
thisLogUwL = logUwL[0]
if (Ttheta <= 0.5):
thisLogUwU = logUwU[1]
thisLogUwL = logUwL[1]
if (Ttheta > 0.5 and Ttheta < 1.0):
thisLogUwU = ( logUwU[1] * (Ttheta - 0.5)/(1.0 - 0.5) )
+ ( logUwU[0] * (1.0 - Ttheta)/(1.0 - 0.5) )
thisLogUwL = ( logUwL[1] * (Ttheta - 0.5)/(1.0 - 0.5) )
+ ( logUwL[0] * (1.0 - Ttheta)/(1.0 - 0.5) )
"""
if (thisTemp <= 130):
thisLogUwU = logUwU[0]
thisLogUwL = logUwL[0]
if (thisTemp > 130 and thisTemp <= 500):
thisLogUwU = logUwU[1] * (thisTemp - 130)/(500 - 130) \
+ logUwU[0] * (500 - thisTemp)/(500 - 130)
thisLogUwL = logUwL[1] * (thisTemp - 130)/(500 - 130) \
+ logUwL[0] * (500 - thisTemp)/(500 - 130)
if (thisTemp > 500 and thisTemp <= 3000):
thisLogUwU = logUwU[2] * (thisTemp - 500)/(3000 - 500) \
+ logUwU[1] * (3000 - thisTemp)/(3000 - 500)
thisLogUwL = logUwL[2] * (thisTemp - 500)/(3000 - 500) \
+ logUwL[1] * (3000 - thisTemp)/(3000 - 500)
if (thisTemp > 3000 and thisTemp <= 8000):
thisLogUwU = logUwU[3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUwU[2] * (8000 - thisTemp)/(8000 - 3000)
thisLogUwL = logUwL[3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUwL[2] * (8000 - thisTemp)/(8000 - 3000)
if (thisTemp > 8000 and thisTemp < 10000):
thisLogUwU = logUwU[4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUwU[3] * (10000 - thisTemp)/(10000 - 8000)
thisLogUwL = logUwL[4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUwL[3] * (10000 - thisTemp)/(10000 - 8000)
if (thisTemp >= 10000):
thisLogUwU = logUwU[4]
thisLogUwL = logUwL[4]
#//Ionization stage Saha factors:
#//Need T_kin^5/2 in the P_e formulation of Saha Eq.
logSaha = logSahaFac - (boltzFacI / temp[0]) + (
5.0 * temp[1] / 2.0) + thisLogUwU - thisLogUwL
#// saha = Math.exp(logSaha);
#//logLHS[id] = logSaha;
logLHS = logSaha
#// } //id loop
return logLHS
def stagePops2(logNum, Ne, chiIArr, logUw, \
numMols, logNumB, dissEArr, logUwB, logQwABArr, logMuABArr, \
numDeps, temp):
#line 1: //species A data - ionization equilibrium of A
#line 2: //data for set of species "B" - molecular equlibrium for set {AB}
"""Ionization equilibrium routine that accounts for molecule formation:
// Returns depth distribution of ionization stage populations
// Input parameters:
// logNum - array with depth-dependent total element number densities (cm^-3)
// chiI1 - ground state ionization energy of neutral stage
// chiI2 - ground state ionization energy of singly ionized stage
// Also needs atsmopheric structure information:
// numDeps
// temp structure
// rho structure
// Atomic element A is the one whose ionization fractions are being computed
// Element B refers to array of other species with which A forms molecules AB """
ln10 = math.log(10.0)
logE = math.log10(math.e) #// for debug output
log2pi = math.log(2.0 * math.pi)
log2 = math.log(2.0)
numStages = len(
chiIArr
) #// + 1; //need one more stage above the highest stage to be populated
#// var numMols = dissEArr.length;
#// Parition functions passed in are 2-element vectore with remperature-dependent base 10 log Us
#// Convert to natural logs:
#double Ttheta, thisTemp;
#//Default initializations:
#//We need one more stage in size of saha factor than number of stages we're actualy populating
thisLogUw = [0.0 for i in range(numStages + 1)]
for i in range(numStages + 1):
thisLogUw[i] = 0.0
logE10 = math.log(10.0)
#//We need one more stage in size of saha factor than number of stages we're actualy populating
#double[][] logUw = new double[numStages+1][2];
#logUw = [ [ 0.0 for i in range(5) ] for j in range(numStages+1) ]
#for i in range(numStages):
# for kk in range(5):
# logUw[i][kk] = logE10*log10UwAArr[i][kk]
#// lburns- what variable can we use instead of 5?
#//Assume ground state statistical weight (or partition fn) of highest stage is 1.0;
#//var logGw5 = 0.0;
#for kk in range(5):
# logUw[numStages][kk] = 0.0
#// lburns
#//System.out.println("chiL before: " + chiL);
#// If we need to subtract chiI from chiL, do so *before* converting to tiny numbers in ergs!
#//atomic ionization stage Boltzmann factors:
#double logChiI, logBoltzFacI;
boltzFacI = [0.0 for i in range(numStages)]
#print("numStages ", numStages, " Useful.logEv ", Useful.logEv())
for i in range(numStages):
#print("i ", i, " chiIArr ", chiIArr[i])
logChiI = math.log(chiIArr[i]) + Useful.logEv()
logBoltzFacI = logChiI - Useful.logK()
boltzFacI[i] = math.exp(logBoltzFacI)
logSahaFac = log2 + (3.0 / 2.0) * (log2pi + Useful.logMe() +
Useful.logK() - 2.0 * Useful.logH())
#// return a 2D 5 x numDeps array of logarithmic number densities
#// Row 0: neutral stage ground state population
#// Row 1: singly ionized stage ground state population
#// Row 2: doubly ionized stage ground state population
#// Row 3: triply ionized stage ground state population
#// Row 4: quadruply ionized stage ground state population
#double[][] logNums = new double[numStages][numDeps];
logNums = [[0.0 for i in range(numDeps)] for j in range(numStages)]
#//We need one more stage in size of saha factor than number of stages we're actualy populating
#// for index accounting pirposes
#// For atomic ionization stages:
# double[][] logSaha = new double[numStages+1][numStages+1];
# double[][] saha = new double[numStages+1][numStages+1];
logSaha = [[0.0 for i in range(numStages + 1)]
for j in range(numStages + 1)]
saha = [[0.0 for i in range(numStages + 1)] for j in range(numStages + 1)]
#//
logIonFrac = [0.0 for i in range(numStages)]
#double expFac, logNe;
#// Now - molecular variables:
#//Treat at least one molecule - if there are really no molecules for an atomic species,
#//there will be one phantom molecule in the denominator of the ionization fraction
#//with an impossibly high dissociation energy
ifMols = True
if (numMols == 0):
ifMols = False
numMols = 1
#//This should be inherited, but let's make sure:
dissEArr[0] = 19.0 #//eV
#//Molecular partition functions - default initialization:
#double[] thisLogUwB = new double[numMols];
thisLogUwB = [0.0 for i in range(numMols)]
for iMol in range(numMols):
thisLogUwB[
iMol] = 0.0 #// variable for temp-dependent computed partn fn of array element B
thisLogUwA = 0.0 #// element A
thisLogQwAB = math.log(300.0)
#//For clarity: neutral stage of atom whose ionization equilibrium is being computed is element A
#// for molecule formation:
logUwA = [0.0 for i in range(5)]
if (numMols > 0):
for kk in range(len(logUwA)):
logUwA[kk] = logUw[0][kk]
#// lburns
#// Array of elements B for all molecular species AB:
#double[][] logUwB = new double[numMols][2];
#logUwB = [ [ 0.0 for i in range(5) ] for j in range(numMols) ]
#//if (numMols > 0){
#for iMol in range(numMols):
# for kk in range(5):
# #print("iMol ", iMol, " kk ", kk)
# logUwB[iMol][kk] = logE10*log10UwBArr[iMol][kk]
#// lburns new loop
#//}
#//// Molecular partition functions:
#// double[] logQwAB = new double[numMols];
#// //if (numMols > 0){
#// for (int iMol = 0; iMol < numMols; iMol++){
#// logQwAB[iMol] = logE10*log10QwABArr[iMol];
#// }
# //}
#//Molecular dissociation Boltzmann factors:
boltzFacIAB = [0.0 for i in range(numMols)]
logMolSahaFac = [0.0 for i in range(numMols)]
#//if (numMols > 0){
#double logDissE, logBoltzFacIAB;
for iMol in range(numMols):
logDissE = math.log(dissEArr[iMol]) + Useful.logEv()
logBoltzFacIAB = logDissE - Useful.logK()
boltzFacIAB[iMol] = math.exp(logBoltzFacIAB)
logMolSahaFac[iMol] = (3.0 / 2.0) * (
log2pi + logMuABArr[iMol] + Useful.logK() - 2.0 * Useful.logH())
#//console.log("iMol " + iMol + " dissEArr[iMol] " + dissEArr[iMol] + " logDissE " + logE*logDissE + " logBoltzFacIAB " + logE*logBoltzFacIAB + " boltzFacIAB[iMol] " + boltzFacIAB[iMol] + " logMuABArr " + logE*logMuABArr[iMol] + " logMolSahaFac " + logE*logMolSahaFac[iMol]);
#//}
#// For molecular species:
logSahaMol = [0.0 for i in range(numMols)]
invSahaMol = [0.0 for i in range(numMols)]
for id in range(numDeps):
#//// reduce or enhance number density by over-all Rosseland opcity scale parameter
#//
#//Row 1 of Ne is log_e Ne in cm^-3
logNe = Ne[1][id]
#//Determine temperature dependent partition functions Uw:
thisTemp = temp[0][id]
#Ttheta = 5040.0 / thisTemp
"""
if (Ttheta >= 1.0):
for iStg in range(numStages):
thisLogUw[iStg] = logUw[iStg][0]
for iMol in range(numMols):
thisLogUwB[iMol] = logUwB[iMol][0]
if (Ttheta <= 0.5):
for iStg in range(numStages):
thisLogUw[iStg] = logUw[iStg][1]
for iMol in range(numMols):
thisLogUwB[iMol] = logUwB[iMol][1]
if (Ttheta > 0.5 and Ttheta < 1.0):
for iStg in range(numStages):
thisLogUw[iStg] = ( logUw[iStg][1] * (Ttheta - 0.5)/(1.0 - 0.5) ) \
+ ( logUw[iStg][0] * (1.0 - Ttheta)/(1.0 - 0.5) )
"""
#// NEW Determine temperature dependent partition functions Uw: lburns
if (thisTemp <= 130):
for iStg in range(numStages):
thisLogUw[iStg] = logUw[iStg][0]
for iMol in range(numMols):
thisLogUwB[iMol] = logUwB[iMol][0]
if (thisTemp > 130 and thisTemp <= 500):
for iStg in range(numStages):
thisLogUw[iStg] = logUw[iStg][1] * (thisTemp - 130)/(500 - 130) \
+ logUw[iStg][0] * (500 - thisTemp)/(500 - 130)
for iMol in range(numMols):
thisLogUwB[iMol] = logUwB[iMol][1] * (thisTemp - 130)/(500 - 130) \
+ logUwB[iMol][0] * (500 - thisTemp)/(500 - 130)
if (thisTemp > 500 and thisTemp <= 3000):
for iStg in range(numStages):
thisLogUw[iStg] = logUw[iStg][2] * (thisTemp - 500)/(3000 - 500) \
+ logUw[iStg][1] * (3000 - thisTemp)/(3000 - 500)
for iMol in range(numMols):
thisLogUwB[iMol] = logUwB[iMol][2] * (thisTemp - 500)/(3000 - 500) \
+ logUwB[iMol][1] * (3000 - thisTemp)/(3000 - 500)
if (thisTemp > 3000 and thisTemp <= 8000):
for iStg in range(numStages):
thisLogUw[iStg] = logUw[iStg][3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUw[iStg][2] * (8000 - thisTemp)/(8000 - 3000)
for iMol in range(numMols):
thisLogUwB[iMol] = logUwB[iMol][3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUwB[iMol][2] * (8000 - thisTemp)/(8000 - 3000)
if (thisTemp > 8000 and thisTemp < 10000):
for iStg in range(numStages):
thisLogUw[iStg] = logUw[iStg][4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUw[iStg][3] * (10000 - thisTemp)/(10000 - 8000)
for iMol in range(numMols):
thisLogUwB[iMol] = logUwB[iMol][4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUwB[iMol][3] * (10000 - thisTemp)/(10000 - 8000)
if (thisTemp >= 10000):
for iStg in range(numStages):
thisLogUw[iStg] = logUw[iStg][4]
for iMol in range(numMols):
thisLogUwB[iMol] = logUwB[iMol][4]
thisLogUw[numStages] = 0.0
for iMol in range(numMols):
if (thisTemp < 3000.0):
thisLogQwAB = ( logQwABArr[iMol][1] * (3000.0 - thisTemp)/(3000.0 - 500.0) ) \
+ ( logQwABArr[iMol][2] * (thisTemp - 500.0)/(3000.0 - 500.0) )
if ((thisTemp >= 3000.0) and (thisTemp <= 8000.0)):
thisLogQwAB = ( logQwABArr[iMol][2] * (8000.0 - thisTemp)/(8000.0 - 3000.0) ) \
+ ( logQwABArr[iMol][3] * (thisTemp - 3000.0)/(8000.0 - 3000.0) )
if (thisTemp > 8000.0):
thisLogQwAB = ( logQwABArr[iMol][3] * (10000.0 - thisTemp)/(10000.0 - 8000.0) ) \
+ ( logQwABArr[iMol][4] * (thisTemp - 8000.0)/(10000.0 - 8000.0) )
#// iMol loop
#//For clarity: neutral stage of atom whose ionization equilibrium is being computed is element A
#// for molecule formation:
thisLogUwA = thisLogUw[0]
#//Ionization stage Saha factors:
for iStg in range(numStages):
#print("iStg ", iStg)
#stop
logSaha[iStg + 1][iStg] = logSahaFac - logNe - (
boltzFacI[iStg] /
temp[0][id]) + (3.0 * temp[1][id] /
2.0) + thisLogUw[iStg + 1] - thisLogUw[iStg]
saha[iStg + 1][iStg] = math.exp(logSaha[iStg + 1][iStg])
#// if (id == 36){
#// console.log("iStg " + iStg + " boltzFacI[iStg] " + boltzFacI[iStg] + " thisLogUw[iStg] " + logE*thisLogUw[iStg] + " thisLogUw[iStg+1] " + logE*thisLogUw[iStg+1]);
#// console.log("iStg+1 " + (iStg+1) + " iStg " + iStg + " logSahaji " + logE*logSaha[iStg+1][iStg] + " saha[iStg+1][iStg] " + saha[iStg+1][iStg]);
#// }
#//Molecular Saha factors:
for iMol in range(numMols):
logSahaMol[iMol] = logMolSahaFac[iMol] - logNumB[iMol][id] - (
boltzFacIAB[iMol] / temp[0][id]) + (
3.0 * temp[1][id] /
2.0) + thisLogUwB[iMol] + thisLogUwA - thisLogQwAB
#//For denominator of ionization fraction, we need *inverse* molecular Saha factors (N_AB/NI):
logSahaMol[iMol] = -1.0 * logSahaMol[iMol]
invSahaMol[iMol] = math.exp(logSahaMol[iMol])
#//TEST invSahaMol[iMol] = 1.0e-99; //test
#// if (id == 36){
#// console.log("iMol " + iMol + " boltzFacIAB[iMol] " + boltzFacIAB[iMol] + " thisLogUwB[iMol] " + logE*thisLogUwB[iMol] + " logNumB[iMol][id] " + logE*logNumB[iMol][id] + " logMolSahaFac[iMol] " + logMolSahaFac[iMol]);
#// console.log("iMol " + iMol + " logSahaMol " + logE*logSahaMol[iMol] + " invSahaMol[iMol] " + invSahaMol[iMol]);
#// }
#//logSaha32 = logSahaFac - logNe - (boltzFacI2 / temp[0][id]) + (3.0 * temp[1][id] / 2.0) + thisLogUw3 - thisLogUw2; // log(RHS) of standard Saha equation
#//saha32 = Math.exp(logSaha32); //RHS of standard Saha equation
#//Compute log of denominator is ionization fraction, f_stage
denominator = 1.0 #//default initialization - leading term is always unity
#//ion stage contributions:
for jStg in range(1, numStages + 1):
addend = 1.0 #//default initialization for product series
for iStg in range(jStg):
#//console.log("jStg " + jStg + " saha[][] indices " + (iStg+1) + " " + iStg);
addend = addend * saha[iStg + 1][iStg]
denominator = denominator + addend
#//molecular contribution
if (ifMols == True):
for iMol in range(numMols):
denominator = denominator + invSahaMol[iMol]
#//
logDenominator = math.log(denominator)
#//if (id == 36){
#// console.log("logDenominator " + logE*logDenominator);
#// }
#//var logDenominator = Math.log( 1.0 + saha21 + (saha32 * saha21) + (saha43 * saha32 * saha21) + (saha54 * saha43 * saha32 * saha21) );
logIonFrac[
0] = -1.0 * logDenominator #// log ionization fraction in stage I
#//if (id == 36){
# //console.log("jStg 0 " + " logIonFrac[jStg] " + logE*logIonFrac[0]);
#//}
for jStg in range(1, numStages):
addend = 0.0 #//default initialization for product series
for iStg in range(jStg):
#//console.log("jStg " + jStg + " saha[][] indices " + (iStg+1) + " " + iStg);
addend = addend + logSaha[iStg + 1][iStg]
logIonFrac[jStg] = addend - logDenominator
#//if (id == 36){
#// console.log("jStg " + jStg + " logIonFrac[jStg] " + logE*logIonFrac[jStg]);
#//}
#//logIonFracI = -1.0 * logDenominator; // log ionization fraction in stage I
#//logIonFracII = logSaha21 - logDenominator; // log ionization fraction in stage II
#//logIonFracIII = logSaha32 + logSaha21 - logDenominator; //log ionization fraction in stage III
#//logIonFracIV = logSaha43 + logSaha32 + logSaha21 - logDenominator; //log ionization fraction in stage III
#//if (id == 36) {
#// System.out.println("logSaha21 " + logE*logSaha21 + " logSaha32 " + logE*logSaha32);
#// System.out.println("IonFracII " + Math.exp(logIonFracII) + " IonFracI " + Math.exp(logIonFracI) + " logNe " + logE*logNe);
#//}
#//System.out.println("LevelPops: id, ionFracI, ionFracII: " + id + " " + Math.exp(logIonFracI) + " " + Math.exp(logIonFracII) );
# //System.out.println("LevPops: ionized branch taken, ionized = " + ionized);
for iStg in range(numStages):
logNums[iStg][id] = logNum[id] + logIonFrac[iStg]
#//id loop
return logNums
def levelPops(lam0In, logNStage, chiL, logUw, gwL, numDeps, temp):
""" Returns depth distribution of occupation numbers in lower level of b-b transition,
// Input parameters:
// lam0 - line centre wavelength in nm
// logNStage - log_e density of absorbers in relevent ion stage (cm^-3)
// logFlu - log_10 oscillator strength (unitless)
// chiL - energy of lower atomic E-level of b-b transition in eV
// Also needs atsmopheric structure information:
// numDeps
// temp structure """
c = Useful.c()
logC = Useful.logC()
k = Useful.k()
logK = Useful.logK()
logH = Useful.logH()
logEe = Useful.logEe()
logMe = Useful.logMe()
ln10 = math.log(10.0)
logE = math.log10(math.e)
#// for debug output
log2pi = math.log(2.0 * math.pi)
log2 = math.log(2.0)
#//double logNl = logNlIn * ln10; // Convert to base e
#// Parition functions passed in are 2-element vectore with remperature-dependent base 10 log Us
#// Convert to natural logs:
#double thisLogUw, Ttheta;
thisLogUw = 0.0 # //default initialization
#logUw = [ 0.0 for i in range(5) ]
logE10 = math.log(10.0)
#print("log10UwStage ", log10UwStage)
#for kk in range(len(logUw)):
# logUw[kk] = logE10*log10UwStage[kk] #// lburns new loop
logGwL = math.log(gwL)
#//System.out.println("chiL before: " + chiL);
#// If we need to subtract chiI from chiL, do so *before* converting to tiny numbers in ergs!
#////For testing with Ca II lines using gS3 internal line list only:
#//boolean ionized = true;
#//if (ionized) {
#// //System.out.println("ionized, doing chiL - chiI: " + ionized);
#// // chiL = chiL - chiI;
#// chiL = chiL - 6.113;
#// }
#// //
#//Log of line-center wavelength in cm
logLam0 = math.log(lam0In) #// * 1.0e-7);
#// energy of b-b transition
logTransE = logH + logC - logLam0 #//ergs
if (chiL <= 0.0):
chiL = 1.0e-49
logChiL = math.log(
chiL) + Useful.logEv() #// Convert lower E-level from eV to ergs
logBoltzFacL = logChiL - Useful.logK(
) #// Pre-factor for exponent of excitation Boltzmann factor
boltzFacL = math.exp(logBoltzFacL)
boltzFacGround = 0.0 / k #//I know - its zero, but let's do it this way anyway'
#// return a 1D numDeps array of logarithmic number densities
#// level population of lower level of bb transition (could be in either stage I or II!)
logNums = [0.0 for i in range(numDeps)]
#double num, logNum, expFac;
for id in range(numDeps):
#//Determine temperature dependenet partition functions Uw:
#Ttheta = 5040.0 / temp[0][id]
#//NEW Determine temperature dependent partition functions Uw: lburns
thisTemp = temp[0][id]
"""
if (Ttheta >= 1.0):
thisLogUw = logUw[0]
if (Ttheta <= 0.5):
thisLogUw = logUw[1]
if (Ttheta > 0.5 and Ttheta < 1.0):
thisLogUw = ( logUw[1] * (Ttheta - 0.5)/(1.0 - 0.5) ) \
+ ( logUw[0] * (1.0 - Ttheta)/(1.0 - 0.5) )
"""
if (thisTemp >= 10000):
thisLogUw = logUw[4]
if (thisTemp <= 130):
thisLogUw = logUw[0]
if (thisTemp > 130 and thisTemp <= 500):
thisLogUw = logUw[1] * (thisTemp - 130)/(500 - 130) \
+ logUw[0] * (500 - thisTemp)/(500 - 130)
if (thisTemp > 500 and thisTemp <= 3000):
thisLogUw = logUw[2] * (thisTemp - 500)/(3000 - 500) \
+ logUw[1] * (3000 - thisTemp)/(3000 - 500)
if (thisTemp > 3000 and thisTemp <= 8000):
thisLogUw = logUw[3] * (thisTemp - 3000)/(8000 - 3000) \
+ logUw[2] * (8000 - thisTemp)/(8000 - 3000)
if (thisTemp > 8000 and thisTemp < 10000):
thisLogUw = logUw[4] * (thisTemp - 8000)/(10000 - 8000) \
+ logUw[3] * (10000 - thisTemp)/(10000 - 8000)
#print("logUw ", logUw, " thisLogUw ", thisLogUw)
#//System.out.println("LevPops: ionized branch taken, ionized = " + ionized);
#// Take stat weight of ground state as partition function:
logNums[id] = logNStage[id] - boltzFacL / temp[0][
id] + logGwL - thisLogUw #// lower level of b-b transition
#print("LevelPopsServer.stagePops id ", id, " logNStage[id] ", logNStage[id], " boltzFacL ", boltzFacL, " temp[0][id] ", temp[0][id], " logGwL ", logGwL, " thisLogUw ", thisLogUw, " logNums[id] ", logNums[id]);
#// System.out.println("LevelPops: id, logNums[0][id], logNums[1][id], logNums[2][id], logNums[3][id]: " + id + " "
#// + Math.exp(logNums[0][id]) + " "
#// + Math.exp(logNums[1][id]) + " "
#// + Math.exp(logNums[2][id]) + " "
#// + Math.exp(logNums[3][id]));
#//System.out.println("LevelPops: id, logNums[0][id], logNums[1][id], logNums[2][id], logNums[3][id], logNums[4][id]: " + id + " "
#// + logE * (logNums[0][id]) + " "
#// + logE * (logNums[1][id]) + " "
#// + logE * (logNums[2][id]) + " "
# // + logE * (logNums[3][id]) + " "
#// + logE * (logNums[4][id]) );
#//System.out.println("LevelPops: id, logIonFracI, logIonFracII: " + id + " " + logE*logIonFracI + " " + logE*logIonFracII
#// + "logNum, logNumI, logNums[0][id], logNums[1][id] "
#// + logE*logNum + " " + logE*logNumI + " " + logE*logNums[0][id] + " " + logE*logNums[1][id]);
#//System.out.println("LevelPops: id, logIonFracI: " + id + " " + logE*logIonFracI
#// + "logNums[0][id], boltzFacL/temp[0][id], logNums[2][id]: "
#// + logNums[0][id] + " " + boltzFacL/temp[0][id] + " " + logNums[2][id]);
#//id loop
#stop
return logNums
def lineKap(lam0In, logNums, logFluIn, linePoints, lineProf, numDeps, zScale,
tauRos, temp, rho, logFudgeTune):
logE10 = math.log(10.0) #//natural log of 10
c = Useful.c()
logC = Useful.logC()
k = Useful.k()
logK = Useful.logK()
logH = Useful.logH()
logEe = Useful.logEe()
logMe = Useful.logMe()
ln10 = math.log(10.0)
logE = math.log10(math.e) #// for debug output
log2pi = math.log(2.0 * math.pi)
log2 = math.log(2.0)
lam0 = lam0In #// * 1.0E-7; //nm to cm
logLam0 = math.log(lam0)
#//double logNl = logNlIn * ln10; // Convert to base e
logFlu = logFluIn * ln10 #// Convert to base e
logKScale = math.log10(zScale)
#//chiI = chiI * Useful.eV; // Convert lower E-level from eV to ergs
#//double boltzFacI = chiI / k; // Pre-factor for exponent of excitation Boltzmann factor
#//double logSahaFac = log2 + (3.0/2.0) * ( log2pi + logMe + logK - 2.0*logH);
#//chiL = chiL * Useful.eV; // Convert lower E-level from eV to ergs
#//double boltzFac = chiL / k; // Pre-factor for exponent of excitation Boltzmann factor
numPoints = len(linePoints[0])
#//System.out.println("LineKappa: numPoints: " + numPoints);
#double logPreFac;
#//This converts f_lu to a volume extinction coefficient per particle - Rutten, p. 23
logPreFac = logFlu + math.log(math.pi) + 2.0 * logEe - logMe - logC
#//System.out.println("LINEKAPPA: logPreFac " + logPreFac);
#//Assume wavelength, lambda, is constant throughout line profile for purpose
#// of computing the stimulated emission correction
#double logExpFac;
logExpFac = logH + logC - logK - logLam0
#//System.out.println("LINEKAPPA: logExpFac " + logExpFac);
#// int refRhoIndx = TauPoint.tauPoint(numDeps, tauRos, 1.0);
#// double refLogRho = rho[1][refRhoIndx];
#//System.out.println("LINEKAPPA: refRhoIndx, refRho " + refRhoIndx + " " + logE*refRho);
#// return a 2D numPoints x numDeps array of monochromatic *LINE* extinction line profiles
logKappaL = [[0.0 for i in range(numDeps)] for j in range(numPoints)]
#double num, logNum, logExpFac2, expFac, stimEm, logStimEm, logSaha, saha, logIonFrac;
#double logNe;
for id in range(numDeps):
logExpFac2 = logExpFac - temp[1][id]
expFac = -1.0 * math.exp(logExpFac2)
stimEm = 1.0 - math.exp(expFac)
logStimEm = math.log(stimEm)
logNum = logNums[id]
#//if (id == refRhoIndx) {
#// System.out.println("LINEKAPPA: logStimEm " + logE*logStimEm);
#//}
for il in range(numPoints):
#// From Radiative Transfer in Stellar Atmospheres (Rutten), p.31
#// This is a *volume* co-efficient ("alpha_lambda") in cm^-1:
logKappaL[il][id] = logPreFac + logStimEm + logNum + math.log(
lineProf[il][id])
#//if (id == 36) {
#// System.out.println("il " + il + " logNum " + logE*logNum + " Math.log(lineProf[il][id]) " + logE*Math.log(lineProf[il][id]));
#//// //System.out.println("logPreFac " + logPreFac + " logStimEm " + logStimEm);
#//}
#//System.out.println("LINEKAPPA: id, il " + id + " " + il + " logKappaL " + logE * logKappaL[il][id]);
#//Convert to mass co-efficient in g/cm^2:
#// This direct approach won't work - is not consistent with fake Kramer's law scaling of Kapp_Ros with g instead of rho
logKappaL[il][id] = logKappaL[il][id] - rho[1][id]
#//Try something:
#//
#// **********************
#// Opacity problem #2
#//
#//Line opacity needs to be enhanced by same factor as the conitnuum opacity
#// - related to Opacity problem #1 (logFudgeTune in GrayStarServer3.java) - ??
#//
logKappaL[il][id] = logKappaL[il][id] + logE10 * logFudgeTune
#//if (id == 12) {
#// System.out.println("LINEKAPPA: id, il " + id + " " + il + " logKappaL " + logE * logKappaL[il][id]
#// + " logPreFac " + logE*logPreFac + " logStimEm " + logE*logStimEm + " logNum " + logE*logNum
#// + " log(lineProf[il]) " + logE*Math.log(lineProf[il][id]) + " rho[1][id] " + logE * rho[1][id]);
#// }
#//if (id == refRhoIndx-45) {
#// System.out.println("LINEKAPPA: id, il " + id + " " + il + " logKappaL " + logE*logKappaL[il][id]
#// + " logPreFac " + logE*logPreFac + " logStimEm " + logE*logStimEm + " logNum " + logE*logNum + " logRho " + logE*rho[1][id]
#// + " log(lineProf[1]) " + logE*Math.log(lineProf[1][il]) );
#//}
#} // il - lambda loop
#} // id - depth loop
return logKappaL
