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cs.py
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cs.py
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# coding: utf-8
# In[17]:
# timer:
from time import time
time0=time()
def pr(s,gn,message = ''):
print(gn,' :'+message+': ',time()-s)
return time(),gn+1
s,gn=pr(time0,0)
Spectrum={
1:'Compton',
2:'Burst',
3:'Thomson',
0:'FromFile'
}[0]
oblateness='AlGendy'
AtmName='res/B/CR12' # the prefix for all result files related to the set of parameters
PulsName=AtmName+'P2'
computePulse= False
plotAtm=True
plotPulse=False
# In[18]:exit()
#import:
from numpy import linspace, logspace, empty, zeros, ones, array, fromfile
# m=fromfile(AtmName+'m.bin')
# print(m)
# exit()
from numpy import pi, exp, log, sqrt, sin, cos, arccos, arctan2
from numpy import absolute, sign, floor, ceil, argmin
from numpy.polynomial.laguerre import laggauss
from numpy.polynomial.legendre import leggauss
from scipy.interpolate import interp1d,CubicSpline
from scipy.special import kn
from matplotlib.pyplot import *
from bisect import bisect
from time import time
#import numpy as np
#import matplotlib.pyplot as plt
s,gn=pr(s,gn, 'importing')
# In[19]:
colors=['xkcd:brownish red',
'xkcd:red',
'xkcd:orange',
'xkcd:dark yellow',
'xkcd:dark yellow green',
'xkcd:deep green',
'xkcd:dark cyan',
'xkcd:blue',
'xkcd:purple'
] # 'rygcbm' # Rainbow
NColors=len(colors)
#physical constants:
evere=.5109989e6 # electron volts in elecron rest energy
G=13275412528e1 # G*M_sol in km^3/s^2
c=299792458e-3 # speed of light in km/s
# Atmosphere parameters:
tau_T= 1.5 # Thomson optical depth of thermalization
x_l, x_u = -3.7 , .3 # lower and upper bounds of the log_10 energy span
Theta = 0.3 # dimensionless electron gas temperature (Theta = k T_e / m_e c^2) # it's about 0.1
T = 0.002 # 10/evere # dimensionless photon black body temperature T = k T_bb / m_e c^2
#precomputations :
ScatterNum = 15 # total number of scatterings
NGamma= 7# number of Lorenz factor points (\gamma)
NAzimuth= 10 # 12 # numbers of azimuth angles (\phi) [0,pi]
NEnergy = 50 # 50# 101 # number of energy points (x)
NDepth = 100# 101 # number of optical depth levels (\tau)
NMu = 10 # 20# 15 # number of propagation zenith angle cosines (\mu) [0,1]
NZenith = 2*NMu # number of propagation zenith angles (z) [0,pi]
IntGamma = laggauss(NGamma) # sample points and weights for computing thermal matrix
IntAzimuth = leggauss(NAzimuth*2) # sample points and weights for computing azimuth-averaged matrix
IntEnergy = logspace(x_l,x_u,NEnergy), log(1e1)*(x_u-x_l)/(NEnergy-1.) # sample points and weights for integrations over the spectrum computing sorce function
IntDepth = linspace(0,tau_T,num=NDepth,retstep=True) # sample points and weights for integrations over the optical depth computing intencity
IntZenith = leggauss(NZenith) # sample points and weights for integrations over zenith angle in positive and negative directions together
# IntZenith = linspace(1e-6-1,1-1e-6,num=NZenith), array([2.]+[2.]*(NZenith-2)+[2.])/(NZenith)
# IntZenith = linspace(1/NZenith - 1,1 - 1/NZenith,num=NZenith), array([2.]*(NZenith))/(NZenith)
# mu,mu_weight=IntZenith
# mu=array( ([1-1e-7]+list(mu)+[1-1e-7]) )
# mu_weight=array([1e-5]+list(mu_weight)+[1e-5])
# IntZenith=(mu, mu_weight)
# NZenith=NZenith+2
# NMu=NMu+1
K2Y = kn(2,1./Theta) # second modified Bessel function of reversed dimensionless temperature
mu,mu_weight=IntZenith
x,x_weight=IntEnergy
tau,tau_weight=IntDepth
outParams = open(AtmName+'.dat','w')
outParams.write(Spectrum+'\n')
outParams.write(str(tau_T)+' = total depth tau_T\n')
outParams.write(str(x_l)+' '+str(x_u)+' = log_10 energy span from to\n')
outParams.write(str(Theta)+' = dimensionless electron gas temperature in m_ec^2\n')
outParams.write(str(T)+' = dimensionless initial bb photons temperature in m_ec^2\n')
outParams.write(str(ScatterNum)+' = Number of scatterings computed\n')
outParams.write(str(NMu)+' = NMu, NZenith=2 NMu, number of points in mu grid\n')
outParams.write(str(NEnergy)+' = NEnergy, number of points in x grid\n')
outParams.write(str(NGamma)+' '+str(NAzimuth)+' '+str(NDepth)+' = NGamma NAzimuth NDepth parameters\n')
s,gn=pr(s,gn,'precomps')
# In[20]:
def Planck(x):
""" Planck function for Intensity of black body radiation
The only argument x is the energy of a photon in units of electron rest energy ( h \\nu / m_e c^2 )
The photon temperature is given by T also in units of electron rest mass
Planck returns the intensity of BB radiation
"""
e=x/T
C=1. # some dimension constant.
R=C*e*e # Rayleigh Jeans law'
I=.0 if e>5e2 else R*e/(exp(e)-1.) if e > 1e-5 else R
return I
def Delta(x):
C=2e4
I=C*exp(-1e2*(x-T)**2/T/T)
return I
def sigma_cs(x): # not averaged on electron distribution
""" This function compute the Compton scattering cross-section in electron rest frame
x is the energy of the scattering photon in units of electron rest energy
this function approaches the mean compton cross-section when electron gas temperature is small
"""
if x<.1:
a,n,s=3./8.,0.,0.
while(abs(a)*(n+2)**2>1e-11): # Taylor series sum of the formula below
s=s+a*(n+2+2/(n+1)+8/(n+2)-16/(n+3))
n=n+1
a=-2*x*a
return s
else: return 3*(2-(1/x+1-x/2)*log(1+2*x))/4/x/x + 3*(1+x)/4/(1+2*x)**2
def Compton_redistribution_m(x1,x2,mu,gamma):
""" Compton redistribution matrix for monoenergetic electron gas
The arguements are:
x1 and x2 - photon energies in units of electron rest energy ( h \\nu / m_e c^2 )
mu - cosine of a scattering angle
gamma - energy of each electron in the gas in units of the electron rest mass
This fuctions returns (R,RI,RQ,RU)
which are scalar redistribution functions for isotropic monoenergetic gas
and also the are non-zero elements of the matrix: R11,R12=R21,R22,R33 respectively
R44 or RV is also not equal to zero but we never need it
"""
#the next variables' names are adopted from J. Poutanen & O. Vilhu 1993
r = (1.+mu)/(1.-mu)
a1 = sqrt( (gamma-x1)**2 + r )
a2 = sqrt( (gamma+x2)**2 + r )
v = a1*a2
u = a2-a1 #(x1+x2)*(2.*gamma+x2-x1)/(a1+a2) # the formulas probably give always the same numbers
q = x1*x2*(1.-mu)
Q = sqrt( x1*x1 + x2*x2 - 2.*x1*x2*mu ) # sqrt( (x1-x2)**2 +2.*q ) # the formula probably gives the same also
gammaStar = (x1-x2+Q*sqrt( 1. + 2./q ) )/2.
# print( gamma-gammaStar, gammaStar,gamma,Q,u,(u-Q)/(Q+u))
if gamma < gammaStar :
print ('w') # I belive that in the case fucntion just won't be called
return (0.,0.,0.,0.)
else:
Ra = u*( u*u - Q*Q )*( u*u + 5.*v )/2./q/q/v/v/v + u*Q*Q/q/q/v/v
Rb = 2./Q + u/v*( 1. - 2./q )
Rc = u/q/v*( ( u*u - Q*Q )/r/q - 2.)
Rd = 2./Q + 2*(u-Q)/r/q*((u-Q)/r/q*(2.*Q+u) - 4.) + 2.*u/v/q
R = Ra + Rb
RI = Ra + Rc
RU = Rd + 2.*Rc
RQ = RU + Ra
#print(r,v,u,q,Q,gammaStar,Ra,Rb,Rc,R)
#print(x1,x2,mu,gamma,R,RI,RQ,RU)
return (R,RI,RQ,RU)
#the return values of this functon seem to be all right
def Maxwell_r(gamma):
"""The normalized relativistic Maxwellian distribution
the density of particles in the dimensionless momentum volume (4 \pi z^2 dz) is nomalized to unity
Theta is the dimensionless electron gas temperature (Theta = k * T_e / m_e c^2)
gamma is electron energy in units of the electron rest mass
The fuction returns the momentum dencity value ( f(\gamma) )
"""
r = .25/pi/Theta*exp(-gamma/Theta)/K2Y
return r
def Compton_redistribution(x1,x2,mu): # if distribution is not Maxwellian the function must be modified.
""" Thermal Compton redistribution matrix (integrated with electron distribution function)
And the distribution is maxwellian (if it's not the function must be modified)
The arguments are:
x1 and x2 - photon energies in units of electron rest energy ( h \\nu / m_e c^2 )
mu - cosine of a scattering angle
This fuctions returns (R,RI,RQ,RU)
which are scalar redistribution functions for Maxwellian relativistic gas
and also the are non-zero elements of the matrix: R11,R12=R21,R22,R33 respectively
R44 or RV is also not equal to zero but we never need it
"""
q = x1*x2*(1.-mu)
Q = sqrt( x1*x1 + x2*x2 - 2.*x1*x2*mu )
gammaStar = (x1-x2+Q*sqrt( 1. + 2./q ) )/2. # lower bound of integration
C=3./8.*Theta*Maxwell_r(gammaStar)
gamma, gamma_weight = IntGamma
R=[0.,0.,0.,0.]
for i in range(NGamma):
T=Compton_redistribution_m(x1,x2,mu,Theta*gamma[i]+gammaStar)
for j in range(4):
R[j]+=C*gamma_weight[i]*T[j]
return tuple(R)
def Compton_redistribution_aa(x1,x2,mu1,mu2):
""" Azimuth-avereged Compton redistribution matrix
for computing of electron scattering source function
The arguements are:
x1 and x2 are photon energies in units of electron rest energy ( h \\nu / m_e c^2 )
mu1 and mu2 are cosines of angles between photon propagation directions and fixed direction
This function returns R11 R12 R21 R22 matrix elements
We need only 2x2 matrix in the upper left corner of the general matrix,
becouse U and V components on the Stokes vector are zero in this case.
"""
eta1 = 1. - mu1*mu1 # squared sinuses of the angles
eta2 = 1. - mu2*mu2
phi, phi_weight = IntAzimuth
az_c=cos(pi*phi) # array of azimuth cosines
az_s=sin(pi*phi)**2 # array of azimuth square sinuses
sc_c=mu1*mu2-sqrt(eta1*eta2)*az_c # array of scattering angles' cosines
sc_s=1. - sc_c**2 # array of scattering angles' squared sinuses
cos2chi1 = 2.*(mu1*sc_c-mu2)*(mu1*sc_c-mu2)/eta1/sc_s-1. # array[ cos( 2 \chi_1 ) ]
cos2chi2 = 2.*(mu1-mu2*sc_c)*(mu1-mu2*sc_c)/eta2/sc_s-1. # array[ cos( 2 \chi_2 ) ]
sin2chiP = 4.*(mu1-mu2*sc_c)*(mu1*sc_c-mu2)*az_s/sc_s**2 # array[ sin( 2 \chi_1 )*sin( 2 \chi_2 ) ]
R=zeros( (2,2,), )
for i in range(NAzimuth*2):
(C,I,Q,U)=Compton_redistribution(x1,x2,sc_c[i])
R[0,0]+=C*pi*phi_weight[i]
R[0,1]+=I*pi*cos2chi2[i]*phi_weight[i]
R[1,0]+=I*pi*cos2chi1[i]*phi_weight[i]
R[1,1]+=pi*(Q*cos2chi1[i]*cos2chi2[i]+U*sin2chiP[i])*phi_weight[i]
# print(x1,x2,mu1,mu2,R)
return R*x1*x1/x2
# In[21]:
if Spectrum=='Compton' : # checking symmetries #unnecessary
from check import *
print('Angular symmetry: ',CheckAngularSymmetry(Compton_redistribution_aa,0.02,0.02,-0.4,0.5))
s,gn=pr(s,gn,'ang-check')
print('Energy symmetry: ',CheckFrequencySymmetry(Compton_redistribution_aa,0.01,0.02,0.5,0.5,Theta))
s,gn=pr(s,gn,'freq-check')
# exit()
# In[22]:
if Spectrum=='Compton' : # Computing redistribution matrices for all energies and angles
# import FRM
# print(FRM.__doc__)
# print(FRM.fill.__doc__)
# def cr(x1,x2,m1,m2):
# R=Compton_redistribution_aa(x1,x2,m1,m2)
# return 1.0,1.0,2.0,1.0
# # return R[0][0],R[0][1],R[1][0],R[1][1]
# # FRM.cr=Compton_redistribution_aa
# RedistributionMatrix , sigma = FRM.fill( mu_weight,x_weight,x,mu,Theta,cr)
# print('7')
# # print(sigma)
# # exit()
sigma=zeros(NEnergy)
RedistributionMatrix = ones( (NEnergy,NEnergy,NZenith,NZenith,2,2) )
percent=0.0
for e in range(NEnergy): # x [-\infty,\infty]
for e1 in range(e,NEnergy): # x1 [x,\infty]
percent+=200/NEnergy/(NEnergy+1)
npc=int(percent*0.6)
print('||'+'%'*npc+' '*(59-npc)+'|| {:5.3f}%'.format(percent))
for d in range(NMu): # mu [-1,0]
for d1 in range(d,NMu): # mu1 [-1,mu]
md=NZenith-d-1 # -mu
md1=NZenith-d1-1 # -mu1
w=mu_weight[d1]*x_weight*mu_weight[d]
t=d1>d
f=e1>e
r=Compton_redistribution_aa(x[e],x[e1],mu[d],mu[d1])
rm=Compton_redistribution_aa(x[e],x[e1],mu[d],mu[md1])
sigma[e1]+=(r[0,0]+rm[0,0])*w
RedistributionMatrix[e,e1,d,d1]=r
RedistributionMatrix[e,e1,md,md1]=r
RedistributionMatrix[e,e1,d,md1]=rm
RedistributionMatrix[e,e1,md,d1]=rm
if f: # frequency symmetry
m=exp((x[e]-x[e1])/Theta)*x[e1]**3/x[e]**3
rf=r*m # when Maxwellian
rmf=rm*m # or Wein distributions
sigma[e]+=(rf[0,0]+rmf[0,0])*w
RedistributionMatrix[e1,e,d,d1]=rf
RedistributionMatrix[e1,e,md,md1]=rf
RedistributionMatrix[e1,e,d,md1]=rmf
RedistributionMatrix[e1,e,md,d1]=rmf
if t: # angular symmetry
r[0,1],r[1,0]=r[1,0],r[0,1]
rm[0,1],rm[1,0]=rm[1,0],rm[0,1]
sigma[e1]+=(r[0,0]+rm[0,0])*w
RedistributionMatrix[e,e1,d1,d]=r
RedistributionMatrix[e,e1,md1,md]=r
RedistributionMatrix[e,e1,md1,d]=rm
RedistributionMatrix[e,e1,d1,md]=rm
if f: # both symmeties
rf=r*m
rmf=rm*m
sigma[e]+=(rf[0,0]+rmf[0,0])*w
RedistributionMatrix[e1,e,d1,d]=rf
RedistributionMatrix[e1,e,md1,md]=rf
RedistributionMatrix[e1,e,md1,d]=rmf
RedistributionMatrix[e1,e,d1,md]=rmf
s,gn=pr(s,gn,'RMtable')
# In[26]:
if Spectrum=='Compton' : #check cross section
# cro = open('cros.dat','r')
figure(1,figsize=(10,11))
xscale('log')
# fx=[0.0]
# cs=[1.0]
# sgm=[1.0]
# de=lambda X : float (X[:X.find('D')]+'e'+X[X.find('D')+1:])
# for n in range(85):
# line = cro.readline().split()
# fx.append(10**de(line[3]))
# cs.append(de(line[5]))
# sgm.append(sigma_cs(fx[-1]))
# # print x, cs
# cs.append(0)
# fx.append(x[-1])
# sgm.append(sigma_cs(x[-1]))
# fcs=interp1d(fx,cs)
# fcsx=fcs(x)
# plot(fx,cs)
sigam=array(list(map(sigma_cs,x)))
plot(x,sigam,'b')
plot(x,sigma,'r')
# plot(x,fcsx,'k')
# plot(fx,sgm)
# plot(x,sigma2-fcsx)
print(sigma)
print(sigam)
print(sigam-sigma)
print(x)
# savefig('compsigma.png')
# show()
clf()
s,gn=pr(s,gn,'sigmaplot')
# In[27]:
if Spectrum=='Compton' : # Initializing Stokes vectors arrays, computiong scatterings
Iin=Planck # Delta # initial photon distribution
Source=zeros((ScatterNum,NDepth,NEnergy,NZenith,2)) # source function
Stokes=zeros((ScatterNum,NDepth,NEnergy,NZenith,2)) # intensity Stokes vector
Stokes_out=zeros((ScatterNum+1,NEnergy,NZenith,2)) # outgoing Stokes vector of each scattering
Stokes_in=zeros((NDepth,NEnergy,NZenith,2)) # Stokes vector of the initial raiation (0th scattering)
Intensity=zeros((NEnergy,NZenith,2)) # total intensity of all scattering orders from the slab suface
for e in range(NEnergy):
for d in range(NZenith):
for t in range(NDepth):
Stokes_in[t,e,d,0]=Iin(x[e])*exp(-tau[t]*sigma[e]/mu[d]) if mu[d]>0 else 0
Stokes_in[t,e,d,1]=0
else:
Stokes_out[0,e,d,0]=Iin(x[e])*exp(-tau_T*sigma[e]/mu[d]) if mu[d]>0 else 0
Stokes_out[0,e,d,1]=0
s,gn=pr(s,gn,'I0')
# if mod:
try: # Fortran
import FIF
# print(FIF.fill.__doc__)
Stokes=FIF.fill(ScatterNum,Stokes_in,RedistributionMatrix,x_weight,sigma,mu,mu_weight,tau,tau_weight)
s,gn=pr(s,gn,'I')
# else:
except: # python
for k in range(ScatterNum): # do ScatterNum scattering iterations
for t in range(NDepth): # S_k= R I_{k-1}
for e in range(NEnergy):
for d in range(NZenith):
S=zeros(2)
for e1 in range(NEnergy):
for d1 in range(NZenith):
w = mu_weight[d1]*x_weight # total weight
r = RedistributionMatrix[e,e1,d,d1] #
I = Stokes[k-1,t,e1,d1] if k>0 else Stokes_in[t,e1,d1]
S[0]+= w*( I[0]*r[0,0] + I[1]*r[0,1] ) #
S[1]+= w*( I[0]*r[1,0] + I[1]*r[1,1] ) #
Source[k,t,e,d]+=S #
for t in range(NDepth):# I_k= integral S_k
for e in range(NEnergy):
for d in range(NZenith):
I=tau_weight/2*Source[k,t,e,d]
if mu[d]>0:
for t1 in range(t) : #
S=Source[k,t1,e,d] #
I+=tau_weight*S*exp(sigma[e]*(tau[t1]-tau[t])/mu[d])
S=Source[k,0,e,d] #
I-=tau_weight*S*exp(sigma[e]*(-tau[t])/mu[d])
else:
for t1 in range (t+1,NDepth):
S=Source[k,t1,e,d] #
I+=tau_weight*S*exp(sigma[e]*(tau[t1]-tau[t])/mu[d])
S=Source[k,NDepth-1,e,d] #
I-=tau_weight*S*exp(sigma[e]*(tau_T-tau[t])/mu[d])
Stokes[k,t,e,d]+=I/abs(mu[d]) #abs
s,gn=pr(s,gn,'I'+str(1+k))
Intensity += Stokes_out[0]
for k in range(ScatterNum):
Stokes_out[k+1]+=Stokes[k,-1]
Intensity += Stokes[k,-1]
# In[ ]:
if Spectrum=='Thomson':
Iin=Planck # Delta # initial photon distribution
Stokes=zeros((ScatterNum,NDepth,NEnergy,NZenith,2)) # intensity Stokes vector
Stokes_out=zeros((ScatterNum+1,NEnergy,NZenith,2)) # outgoing Stokes vector of each scattering
Intensity=zeros((NEnergy,NZenith,2)) # total intensity of all scattering orders from the slab suface
I_l = zeros((NDepth,NZenith))
I_r = zeros((NDepth,NZenith))
A=zeros(NDepth)
B=zeros(NDepth)
C=zeros(NDepth)
# x_factor=ones(NEnergy)
x_nought=x.copy()
print('Thart')
for d in range(NZenith):
for t in range(NDepth):
I_l[t,d]=exp(-tau[t]/mu[d]) if mu[d]>0 else 0
I_r[t,d]=I_l[t,d]
for e in range(NEnergy):
Stokes_out[0,e,d,0]=Iin(x[e])*(I_l[t,d] + I_r[t,d])
Stokes_out[0,e,d,1]=0
for k in range(ScatterNum): # do ScatterNum scattering iterations
# x_factor *= 1 + 4*Theta #- x
x_nought = (1 + 4*Theta - sqrt(( (1 + 4*Theta)**2-4*x_nought) ))/2
A[:]=0.
B[:]=0.
C[:]=0.
for t in range(NDepth): #
for d in range(NMu):
md=NZenith-d-1
A[t]+=(1. - mu[d]**2)*(I_l[t,d] + I_l[t,md])*mu_weight[d]*3./4./3
B[t]+=(mu[md]**2)*(I_l[t,d] + I_r[t,md])*mu_weight[d]*3./8./3
C[t]+=(I_r[t,md] + I_r[t,d])*mu_weight[d]*3./8./3
I_l[:]=0.
I_r[:]=0.
for t in range(NDepth): #
for d in range(NZenith):
w=tau_weight/abs(mu[d])
I_l[t,d]+=(A[t]*(1 - mu[d]**2) + (B[t] + C[t])*mu[d]**2)*w/2
I_r[t,d]+=(B[t] + C[t])*w/2
if mu[d]>0:
trange=range(t)
t1=0
else:
trange=range(t+1,NDepth)
t1=-1
I_l[t,d]-=exp((tau[t1]-tau[t])/mu[d])*(A[t1]*(1. - mu[d]**2) + (B[t1] + C[t1])*mu[d]**2)*w/2
I_r[t,d]-=exp((tau[t1]-tau[t])/mu[d])*(B[t1] + C[t1])*w/2
for t1 in trange:
I_l[t,d]+=exp((tau[t1] - tau[t])/mu[d])*(A[t1]*(1. - mu[d]**2) + (B[t1] + C[t1])*mu[d]**2)*w
I_r[t,d]+=exp((tau[t1] - tau[t])/mu[d])*(B[t1]+C[t1])*w
for e in range(NEnergy):
Stokes[k,t,e,d,0]=Iin(x_nought[e])*(I_l[t,d] + I_r[t,d])*x[e]/x_nought[e]
Stokes[k,t,e,d,1]=Iin(x_nought[e])*(I_l[t,d] - I_r[t,d])*x[e]/x_nought[e]
# Stokes[k,t,e,d,0]=Iin(x[e]/x_factor[e])*(I_l[t,d] + I_r[t,d])*x_factor[e]
# Stokes[k,t,e,d,1]=Iin(x[e]/x_factor[e])*(I_l[t,d] - I_r[t,d])*x_factor[e]
s,gn=pr(s,gn,'I'+str(k+1))
Intensity += Stokes_out[0]
for k in range(ScatterNum):
Stokes_out[k+1]+=Stokes[k,-1]
Intensity += Stokes[k,-1]
s,gn=pr(s,gn,'I0')
# In[ ]:
if Spectrum=='Burst' : # Initializing Stokes vectors arrays, computing zeroth scattering
Intensity=zeros((NEnergy,NZenith,2)) # total intensity of all scattering orders from the slab suface
for e in range(NEnergy):
# print(e,log(Planck(x[e-1])/Planck(x[e]))/log(x[e]/x[e-1]),' ',log(x[e])/log(10),' ')
for d in range(NZenith):
Intensity[e,d,0]=Planck(x[e])*(1 + 2.06*mu[d])
Intensity[e,d,1]=Intensity[e,d,0]*0.1171*(mu[d] - 1.)/(1. + 3.582*abs(mu[d]))
s,gn=pr(s,gn,'I0')
# exit()
# In[ ]:
if Spectrum=='FromFile' :
inI = open(AtmName+'I.bin')
inx = open(AtmName+'x.bin')
inm = open(AtmName+'m.bin')
x=fromfile(inx)
mu=fromfile(inm)
NEnergy=len(x)
NZenith=len(mu)
NMu=NZenith//2
Intensity=fromfile(inI).reshape((NEnergy,NZenith,2))
s,gn=pr(s,gn,'I is read')
else:
outI = open(AtmName+'I.bin','w')
outx = open(AtmName+'x.bin','w')
outm = open(AtmName+'m.bin','w')
Intensity.tofile(outI,format="%e")
x.tofile(outx,format="%e")
mu.tofile(outm,format="%e")
# In[28]:
if plotAtm: # plot Everything and save All pics and tabs
Iin=Planck # Delta # initial photon distribution
Stokes_defined=Spectrum=='Compton' or Spectrum=='Thomson'
Sangles= range(NMu) if Stokes_defined else [] # list of the angle indeces to be plot a detailed figure
Senergy=[int(0.5+n*log(1+4*Theta)/x_weight) for n in range(NColors) ] if Stokes_defined else []
print(Senergy)
outF = open(AtmName+'Fx.dat','w')
outp = open(AtmName+'Pd.dat','w')
frmt=lambda val, list: '{:>8}'.format(val)+': '+' '.join('{:15.5e}'.format(v) for v in list) +'\n'
outp.write(frmt('Energies',x) )
outF.write(frmt('Energies',x) )
labelsize=20
fontsize=25
figA=figure(1,figsize=(10,11))
figA.clear()
figA.suptitle(r'$\tau_T=$'+str(tau_T)+
r'$,\,T={:5.1f}keV$'.format(T*evere/1e3)+
r'$,\,\Theta=$'+str(Theta),fontsize=fontsize)
plotAF=figA.add_subplot(2,1,1,xscale='log',yscale='log')
plotAp=figA.add_subplot(2,1,2,xscale='log')
xIinx=[(Iin(x[e])*x[e]) for e in range(NEnergy)]
# plotAF.set_xlim([x[0],x[-1]])
plotAF.set_xlim([1e-3,1.])
plotAF.set_ylim([1e-3,1e-2])
plotAF.set_ylabel(r'$xI_x(\tau_T,x)$',fontsize=fontsize)
plotAF.tick_params(axis='both', which='major', labelsize=labelsize)
plotAF.plot(x,xIinx,'k-.')
plotAp.set_xlim([x[0],x[-1]])
plotAp.tick_params(axis='both', which='major', labelsize=labelsize)
plotAp.set_xlabel(r'$x\,[m_ec^2]$',fontsize=fontsize)
plotAp.set_ylabel(r'$p\,[ \% ]$',fontsize=fontsize)
plotAp.plot(x,[.0]*NEnergy,'-.',color='xkcd:brown')
for d in range(NMu):
d1=d+NMu
z=str(int(arccos(mu[d1])*180/pi))
xFx=(Intensity[:,d1,0]*x[:])
plotAF.plot(x,xFx,colors[(d*NColors)//NMu])
outF.write( frmt(z+'deg',xFx) )
p=(Intensity[:,d1,1]/Intensity[:,d1,0]*1e2)
plotAp.plot(x,p,colors[(d*NColors)//NMu])
outp.write( frmt(z+'deg',p) )
if d in Sangles: # Specific angle
figS=figure(2,figsize=(10,13))
figS.suptitle(r'$\tau_T=$'+str(tau_T)+
r'$,\,T={:5.1f}keV$'.format(T*evere*1e-3)+
r'$,\,\Theta=$'+str(Theta)+
r'$,\,\mu={:5.3f}$'.format(mu[d1])+
r'$\,(z\approx$'+z+
r'$^{\circ})$',fontsize=fontsize)
plotSF=figS.add_subplot(3,1,1,xscale='log',yscale='log')
plotSc=figS.add_subplot(3,1,2,xscale='log')
plotSp=figS.add_subplot(3,1,3,xscale='log')
plotSF.set_ylabel(r'$xI_x(\tau_T,x)$',fontsize=fontsize)
plotSF.tick_params(axis='both', which='major', labelsize=labelsize)
plotSF.set_xlim([x[0],x[-1]])
plotSF.set_ylim([1e-6,1e-1])
plotSF.plot(x,xFx,color='k',linewidth=2.1)
plotSF.plot(x,xIinx,'-.',color='xkcd:brown')
outF.write(frmt('Sc.N.0',xFx) )
plotSc.set_xlim([x[0],x[-1]])
plotSc.tick_params(axis='both', which='major', labelsize=labelsize)
plotSc.set_ylabel(r'$c\,[ \% ]$',fontsize=fontsize)
plotSp.set_xlim([x[0],x[-1]])
plotSp.tick_params(axis='both', which='major', labelsize=labelsize)
plotSp.set_xlabel(r'$x\,[m_ec^2]$',fontsize=fontsize)
plotSp.set_ylabel(r'$p\,[ \% ]$',fontsize=fontsize)
plotSp.plot(x,p,color='k',linewidth=2.1)
for k in range(ScatterNum+1):
xFx=(Stokes_out[k,:,d1,0]*x[:])
contribution=(Stokes_out[k,:,d1,0]/Intensity[:,d1,0]*1e2)
p=[.0]*NEnergy if k==0 else (Stokes_out[k,:,d1,1]/Stokes_out[k,:,d1,0]*1e2)
outF.write( frmt('Sc.N.'+str(k),xFx) )
outp.write( frmt('Sc.N.'+str(k),p) )
plotSF.plot(x,xFx,'--',color=colors[(k*NColors)//(ScatterNum+1)])
plotSc.plot(x,contribution,'--',color=colors[(k*NColors)//(ScatterNum+1)])
plotSp.plot(x,p,'--',color=colors[(k*NColors)//(ScatterNum+1)])
figS.savefig(AtmName+'z'+z+'.pdf')
figS.clf()
figA.savefig(AtmName+'zAll.pdf')
figA.clf()
figA.suptitle(r'$\tau_T=$'+str(tau_T)+
r'$,\,T={:5.1f}keV$'.format(T*evere/1e3)+
r'$,\,\Theta=$'+str(Theta),fontsize=fontsize)
plotAF=figA.add_subplot(2,1,1,xscale='linear',yscale='linear')
plotAp=figA.add_subplot(2,1,2,xscale='linear')
plotAF.set_xlim(0,1)
# plotAF.set_ylim()
plotAF.set_ylabel(r'$I_x(\tau_T,\mu)/I_x(\tau_T,1)$',fontsize=fontsize)
plotAF.tick_params(axis='both', which='major', labelsize=labelsize)
plotAp.set_xlim(0,1)
plotAp.tick_params(axis='both', which='major', labelsize=labelsize)
plotAp.set_xlabel(r'$\mu$',fontsize=fontsize)
plotAp.set_ylabel(r'$p\,[ \% ]$',fontsize=fontsize)
plotAp.plot(mu[NMu:NZenith],[.0]*NMu,'-.',color='xkcd:brown')
# show()
outp.write('\n\n' )
outF.write('\n\n' )
outp.write(frmt('Cosines',mu[NMu:]) )
outF.write(frmt('Cosines',mu[NMu:]) )
outp.write(frmt('Angles',arccos(mu[NMu:])*180/pi) )
outF.write(frmt('Angles',arccos(mu[NMu:])*180/pi) )
k=-1
for e in range(NEnergy):
Esp="{:<8.2e}".format(x[e])
Inorm=(Intensity[e,NMu:,0]/Intensity[e,-1,0])
p=(Intensity[e,NMu:,1]/Intensity[e,NMu:,0]*1e2)
outF.write( frmt(Esp,Inorm) )
outp.write( frmt(Esp,p) )
if e in Senergy:
k=k+1
# plotAp.plot(mu[NMu:NZenith],p,'-.',color='xkcd:black')
# plotAF.plot(mu[NMu:NZenith],Inorm,'-.',color='xkcd:black')
Inorm=(Stokes_out[k,e,NMu:,0]/Stokes_out[k,e,-1,0])
p=[.0]*NMu if k==0 else (Stokes_out[k,e,NMu:,1]/Stokes_out[k,e,NMu:,0]*1e2)
plotAp.plot(mu[NMu:],p,'-',color=colors[k])
plotAF.plot(mu[NMu:],Inorm,'-',color=colors[k])
figA.savefig(AtmName+'In.pdf')
outF.close()
outp.close()
s,gn=pr(s,gn,'plap')
# In[30]:
if computePulse:
NPhi = 120 # Number of equidistant phase points
NPhase = 150 # Number of observation phases
NBend= 20 # Number of knots in light bending integrations
NAlpha= 1000 # 10000 # Number of psi/aplha grid points
IntBend = leggauss(NBend)
NZenithBig=100
NRho=4#2#8
NVarphi=6#4
# IntVarphi = linspace(0,2*pi,num=NVarphi,endpoint=False,retstep=True)
IntVarphi = leggauss(NVarphi)
IntRho = leggauss(NRho)
phi=linspace(0,2*pi,num=NPhi,endpoint=False,retstep=False)
phase =linspace(0,1,num=NPhase,endpoint=True,retstep=False)
phase_obs=zeros(NPhi)
nu=600 # star rotation frequency in Hz
M=1.4 # star mass in solar masses
R_g=M*2.95 # gravitational Schwarzschild radius
R_e=12.0 # equatorial radius of the star in kilometers
if oblateness=='AlGendy': # from AlGendy et. al. (2014)
Omega_bar=2*pi*nu*sqrt(2*R_e**3/R_g)/c
print('_O_^2',Omega_bar**2,'_O_',Omega_bar)
flattening=(0.788-0.515*R_g/R_e)*Omega_bar**2
print(R_e*(1-flattening))
elif oblateness=='Sphere':
flattening=0.0
else:
flattening=oblateness
# exit()
print(flattening)
outParams = open(PulsName+'.dat','w')
outParams.write(AtmName+'.dat is the name of file with some corresponding atmosphere model\n')
outParams.write(str(R_e)+' = equatorial radius R_e\n')
outParams.write(str(M)+' = star mass M in solar masses\n')
outParams.write(str(nu)+' = star rotation frequency nu in Hz\n')
outParams.write(str(NPhi)+' '+str(NBend)+' '+str(NAlpha)+' = NPhi NBend NAlpha parameters\n')
def Beloborodov(cos_psi):
"""Beloborodov's approximation for cos_alpha(cos_psi) light bending function
takes the cos psi
returns the cos alpha and its derivative
"""
return 1. + (cos_psi - 1.)/redshift**2 ,1./redshift**2
def Schwarzschild(R,alpha):
"""Schwarzschild exact relation between the \psi and \\alpha angles, where
\\alpha is the angle between radius vector of the spot and the direction of the outgoing photon near the surface
and \psi is the angle between normal and light propagation at the limit of infinite distance.
For given distance from the mass center and the emission angle \\alpha
this function returns two numbers:
the corresponding angle \psi
and the time lag over against the fotons emited with zero impact parameter at the radius.
"""
kx,wx=IntBend
eps=(1+kx[0])/4e2
u=R_g/R
b=sin(alpha)/sqrt(1-u)*R # impact parameter
if 2*alpha>pi+eps:
cos_3eta=sqrt(27)*R_g/2/b
if cos_3eta > 1:
return pi+2*eps,0 # the timelag
closest_approach=-2*b/sqrt(3)*cos(arccos(cos_3eta)/3 + 2*pi/3)
psi_max, lag_max= Schwarzschild(closest_approach,pi/2.)
psi_min, lag_min= Schwarzschild(R,pi-alpha)
psi=2*psi_max - psi_min
lag=2*lag_max - lag_min # + 2*(R - closest_approach + R_g*log((R - R_g)/(closest_approach - R_g)))/c
if psi>pi:
return pi+eps,lag
else:
psi=0
lag=(R_e - R + R_g*log( (R_e - R_g)/(R - R_g) ) )/c
for i in range(NBend):
ex=(kx[i]+1)/2
q=(2. - ex*ex - u*(1 - ex*ex)**2/(1 - u))*sin(alpha)**2
sr=sqrt(cos(alpha)**2+ex*ex*q)
if 2*alpha>pi-eps:
dpsi=b/R/sqrt(q)*wx[i] #*2/2
else:
dpsi=ex*b/R/sr*wx[i] #*2/2
dlag=dpsi*b/c/(1+sr) #*2/2
psi+= dpsi
lag+= dlag
return psi,lag
# flattening=0
NRadius=2 + int(flattening*R_e/1e-1)
print(NRadius)
r, dr = linspace(R_e*(1 - flattening),R_e,num=NRadius,retstep=True)
alpha, dalpha = linspace(0,arccos(-1/sqrt(2*r[0]/R_g/3)),NAlpha,retstep=True)
psi=zeros((NRadius,NAlpha))
dt=zeros((NRadius,NAlpha))
for d in range(NRadius):
print(d)
for a in range(NAlpha):
psi[d,a],dt[d,a]=Schwarzschild(r[d],alpha[a])
s,gn=pr(s,gn,'psidt')
Flux=zeros((NPhase,NEnergy,3))
Flux_obs=zeros((NPhi,NEnergy,3))
i=pi*7/18 # line of sight colatitude
rho_total=0.15 # pi/5 #pi*5/180 # radius of the spot
theta_center=pi/4.1
antipodal = True
NSpots=0
varphi,dvarphi=IntVarphi[0]*pi,IntVarphi[1] *pi
rho,drho=(IntRho[0]+1)*rho_total/2,(IntRho[1])*rho_total/2
# print(IntVarphi)
# print(rho,drho)
l=[]
theta=[]
dS=[]
for v in range(NVarphi):
for rh in range(NRho):
NSpots+=1
cos_theta=cos(theta_center)*cos(rho[rh])+sin(theta_center)*sin(rho[rh])*cos(varphi[v])
sin_l=sin(rho[rh])*sin(varphi[v])/sqrt(1- cos_theta**2)
cos_l=sqrt(1- sin_l**2)
if cos_theta*cos(theta_center)> cos(rho[rh]) :
cos_l=-cos_l
l.append(arctan2(-sin_l,-cos_l) + pi)
theta.append(arccos(cos_theta))
dS.append(drho[rh]*dvarphi[v]*sin(rho[rh]))
print(v,rh,cos_theta,cos_l,sin_l,l[-1],theta[-1],dS[-1])
if antipodal :
NSpots+=1
l.append(arctan2(sin_l,cos_l) + pi)
theta.append(pi- theta[-1])
dS.append(dS[-1])
print(v,rh,cos_theta,cos_l,sin_l,l[-1],theta[-1],dS[-1])
print(NSpots)
outParams.write(str(i)+' = sight colatitude i\n')
outParams.write(str(theta_center)+' = spot colatitudes theta\n')
# outParams.write(str(l)+' = spot longitudes l\n')
outParams.write(str(rho_total)+' = angular radius of the spot rho\n')
sin_i=sin(i)
cos_i=cos(i)
BoloFlux=zeros((NPhase,3))
z=cos(linspace(-pi/2,pi/2,num=NZenithBig))
logIntensity=zeros((NEnergy,NZenithBig,3))
for e in range(NEnergy):
IntInt=CubicSpline(mu,Intensity[e,:,0],extrapolate=True) # interpolate intensity
IQ=CubicSpline(mu,Intensity[e,:,1],extrapolate=True) #
for d in range(NZenithBig):
logIntensity[e,d] = log(max(0,IntInt(z[d]))),log(absolute(IQ(z[d]))),sign(IQ(z[d]))
mu=z.copy()
s,gn=pr(s,gn,'second precomp')
for p in range(NSpots):
sin_theta=sin(theta[p])
cos_theta=cos(theta[p])
R=R_e*(1 - flattening*cos_theta**2)
dR=2*R_e*flattening*cos_theta*sin_theta # dR / d\theta
r1=bisect(r[1:-1],R)
r2=r1 + 1
dr1=(R - r[r1])/dr
dr2=(r[r2] - R)/dr
redshift=1.0/sqrt(1.0 - R_g/R) # 1/sqrt(1-R_g/R) = 1+ z = redshift
f=redshift/R*dR
sin_gamma=f/sqrt(1 + f**2) # angle gamma is positive towards the north pole
cos_gamma=1.0/sqrt(1 + f**2)
beta=2*pi*nu*R*redshift*sin_theta/c
Gamma=1.0/sqrt(1.0 - beta**2)
Gamma1= (1.0-sqrt(1.0 - beta**2) )/ beta
# print(Gamma,beta,Gamma1,'\t\t\t',p/NSpots)
for t in range(NPhi):
if True: # find mu
phi0=phi[t]+l[p]
sin_phi=sin(phi0)
cos_phi=cos(phi0)
cos_psi=cos_i*cos_theta + sin_i*sin_theta*cos_phi
sin_psi=sqrt(1. - cos_psi**2)
psi0=arccos(cos_psi)
a1=bisect(psi[r1], psi0)
a2=bisect(psi[r2], psi0)
psi1=psi[r1, a1]
psi2=psi[r2, a2]
dpsi1=psi1 - psi[r1, a1 - 1]
dpsi2=psi2 - psi[r2, a2 - 1]
dpsi=dpsi1*dr2 + dpsi2*dr1
dalpha1 = dalpha*(psi1 - psi0)/dpsi1
dalpha2 = dalpha*(psi2 - psi0)/dpsi2
alpha1=alpha[a1] - dalpha1
alpha2=alpha[a2] - dalpha2
cos_alpha = cos(alpha2*dr1 + alpha1*dr2) # linear interpolation of alpha(psi)
sin_alpha = sqrt(1. - cos_alpha**2)
sin_alpha_over_sin_psi= sin_alpha/sin_psi if sin_psi > 1e-4 else 1./redshift
dcos_alpha=sin_alpha_over_sin_psi *dalpha/dpsi # d cos\alpha \over d \cos \psi
# cos_alpha, dcos_alpha=Beloborodov(cos_psi) # insert exact formula here
# sin_alpha = sqrt(1. - cos_alpha**2)
# sin_alpha_over_sin_psi= sin_alpha/sin_psi if sin_psi > 1e-4 else 1./redshift
dt1=dt[r1,a1 - 1]*dalpha1/dalpha + dt[r1,a1]*(1. - dalpha1/dalpha)
dt2=dt[r2,a2 - 1]*dalpha2/dalpha + dt[r2,a2]*(1. - dalpha2/dalpha)
dphase=(dt1*dr2 + dt2*dr1)*nu # \delta\phi = \phi_{obs} - \phi
# dphase = 0
phase_obs[t]=( phi[t]/2/pi+dphase)%1.
cos_xi = - sin_alpha_over_sin_psi*sin_i*sin_phi
delta = 1./Gamma/(1.-beta*cos_xi)
cos_sigma = cos_gamma*cos_alpha + sin_alpha_over_sin_psi*sin_gamma*(cos_i*sin_theta - sin_i*cos_theta*cos_phi)
sin_sigma = sqrt(1. - cos_sigma**2)
mu0=delta*cos_sigma # cos(sigma')
Omega=dS[p]*mu0*redshift**2*dcos_alpha #*Gamma*R*R/cos_gamma #
# Omegaarray[t]=max(Omega,0)
# print(t,' : \t',mu0,' \t ',dcos_alpha,'\t',dphi,cos_alpha,cos_psi,Omega)
if mu0<0: # this only for speeding up. the backwards intensity is usually zero
Flux_obs[t]=0
continue