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cs_ts2_comp_pa.py
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cs_ts2_comp_pa.py
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#!/usr/bin/python
# 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
# return time0,gn+1
#s,gn=pr(time0,0)
Spectrum={
1:'Compton',
2:'Burst',
3:'Thomson',
4:'Bbody',
0:'FromFile'
}[0]
#}[4]
#}[2]
oblateness='AlGendy'
AtmName='res/B/B0'#_new' # the prefix for all result files related to the set of parameters
#PulsName=AtmName+'P2'
#PulsName='res/B/B0P1'
PulsName='res/B/B0Ptest'
#PulsName='res/B/B0Prho10'
computePulse= True
plotAtm=False#True
plotPulse=True
# 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, arctan, tan
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.interpolate import CubicSpline
from scipy.special import kn
from matplotlib.pyplot import *
from bisect import bisect
#import numpy as np
#import matplotlib.pyplot as plt
#s,gn=pr(s,gn, 'importing')
rdg = 180.0/pi
def Planck(x,T):
""" 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 compf(mass,eqrad,incl_deg,theta_deg,rho_deg,freq,spherical=False):
# 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= .6 # Thomson optical depth of thermalization
x_l, x_u = -3.7 , .3 # lower and upper bounds of the log_10 energy span
Theta = 0.1 # 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 #~ 1.0219978 keV
#precomputations :
ScatterNum = 23 # total number of scatterings
NGamma= 7# number of Lorenz factor points (\gamma)
NAzimuth= 10 # 12 # numbers of azimuth angles (\phi) [0,pi]
NEnergy = 281 # 50# 101 # number of energy points (x)
NDepth = 100# 101 # number of optical depth levels (\tau)
NMu = 22 # 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[ ]:
if Spectrum=='Bbody' : # 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("energy, T =", x[e]*evere/1e3,T*evere/1e3)
E=x[e]/T
for d in range(NZenith):
constbb= 5.039617e22
ex=exp(-x[e]/T)
Intensity[e][d][0]=constbb*x[e]**3*ex/(1.0-ex)
Intensity[e][d][1]=0.0
#s,gn=pr(s,gn,'I0')
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],T)#*(1 + 2.06*mu[d])#TS TESTING BLACKBODY energy spectrum with burst-beaming only in polarization
#Intensity[e,d,1]=Intensity[e,d,0]*0.1171*(mu[d] - 1.)/(1. + 3.582*abs(mu[d]))
Intensity[e,d,1]=Intensity[e,d,0]#*0.1171*(mu[d] - 1.)/(1. + 3.82*abs(mu[d]))
#s,gn=pr(s,gn,'I0')
# exit()
# In[ ]:
if Spectrum=='FromFile' :
print("reading from file: ", AtmName)
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: #Make sure this save wont overwrite your old tables!
print("Not saving the spectrum")
#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 computePulse:
NPhi = 120 #500 #120 # Number of equidistant phase points
NPhase = 150 #500# 150 # Number of observation phases
NBend= 20 # Number of knots in light bending integrations
NAlpha= 200#1000 # 10000 # Number of psi/aplha grid points
IntBend = leggauss(NBend)
NZenithBig=100
#NZenithBig = NZenith
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=freq #600.0#1.0#100 #600 # star rotation frequency in Hz
#M=1.4 # star mass in solar masses
M=mass #input param
R_g=M*2.95325 # gravitational Schwarzschild radius #TS: Made this more accurate
#R_e=12.0 # equatorial radius of the star in kilometers
R_e=eqrad #input param
NRho= 1#40#20#4#2#8
NVarphi=1 #40#20#6#4
# IntVarphi = linspace(0,2*pi,num=NVarphi,endpoint=False,retstep=True)
IntVarphi = leggauss(NVarphi)
IntRho = leggauss(NRho)
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)
if(spherical):#TS: from input param, 0.0 not working in this code
print("spherical star")
flattening = 1e-10
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)
NRadius=4+ int(flattening*R_e/1e-1)#4#
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/180.0*incl_deg#pi*7/18 # line of sight colatitude
intgspot_version = "sinlgepoint" #"new"
#Even newer version for integration over spot from Vlad:
if(intgspot_version=="new"):
#i=pi*7/18 # line of sight colatitude
#rho_total=0.15 # pi/5 #pi*5/180 # radius of the spot
rho_total=rho_deg*pi/180.0#pi/5 #pi*5/180 # radius of the spot
theta_center=pi/180.0*theta_deg#pi/4.1
antipodal = False#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)
#New version for integration over spot from Vlad:
if(intgspot_version=="old"):
rho=rho_deg*pi/180.0#pi/5 #pi*5/180 # radius of the spot
Nrho = 10#12#4#15#4#10#4
drho=rho/Nrho
antipodal = True#False#True
l=[0]
theta=[pi/180.0*theta_deg]#[pi/4.1]
NSpots=1
if antipodal :
l.append(pi)
theta.append(pi- theta[0])
NSpots+=1
for tr in range(Nrho):
for tph in range(8*tr):
varphi=(2*tph+1)*pi/8/tr
cos_theta=cos(theta[0])*cos(drho*tr)+sin(theta[0])*sin(drho*tr)*cos(varphi)
sin_l=sin(drho*tr)*sin(varphi)/sqrt(1- cos_theta**2)
cos_l=sqrt(1- sin_l**2)
if cos_theta*cos(theta[0])> cos(drho*tr) :
cos_l=-cos_l
# print(tr,(2*tph+1)*pi/8/tr,l[-1])
l.append(arctan2(-sin_l,-cos_l) + pi)
theta.append(arccos(cos_theta))
NSpots+=1
if antipodal :
l.append(arctan2(sin_l,cos_l) + pi)
theta.append(pi- theta[-1])
NSpots+=1
###############################
#NSpots= 2*4 # * somewhat
## theta = [pi/3,2*pi/3] # spot colatitude
## l=[0,pi] # spot longitude
## dS=[1,1] # some arbitrary units
#little=10.0*pi/180.0#1e-8#1e-2 #TS: made this smaller to match better infitesimal spot
dS=[1]*NSpots
#l=[0,0,little,little,pi,pi,pi+little,pi+little]
## pi*=2/3
#theta=[pi/3,pi/3+little,pi/3,pi/3+little,2*pi/3,2*pi/3+little,2*pi/3,2*pi/3+little]
## pi*=3/2
###############################
#i=pi/180.0*incl_deg#40.0
thettta = pi/180.0*theta_deg#60.0
#theta=[thettta,thettta+little,thettta,thettta+little,2*thettta,2*thettta+little,2*thettta,2*thettta+little]
#In case of 1 spot:
####i=pi*4/18#1.5 # line of sight colatitude #in radians
###i=pi/180.0*40.0
NSpots= 1 #2 # * somewhat
###theta = [pi/3,pi-pi/3] # spot colatitude
theta = [thettta,pi-thettta] # spot colatitude
l=[0,pi] # spot longitude
dS=[1,1] # some arbitrary units
###############################
outParams.write(str(i)+' = sight colatitude i\n')
outParams.write(str(theta)+' = spot colatitudes theta\n')
outParams.write(str(l)+' = spot longitudes l\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
#IntInt = interp1d(mu,Intensity[e,:,0])#,fill_value="extrapolate")
IQ=CubicSpline(mu,Intensity[e,:,1],extrapolate=True) #
#IQ=interp1d(mu,Intensity[e,:,1])#,fill_value="extrapolate") #
for d in range(NZenithBig):
#TS: Prevent the code from computing log(0):
#log0 = -100.0
#if(IntInt(z[d])< 1e-8 or absolute(IQ(z[d])) < 1e-8):
# if(absolute(IQ(z[d])) < 1e-8):
# if(IntInt(z[d]) < 1e-8):
# logIntensity[e,d] = log0,log0,sign(IQ(z[d]))
# else:
# logIntensity[e,d] = log(max(0,IntInt(z[d]))),log0,sign(IQ(z[d]))
# else:
# if(IntInt(z[d]) < 1e-8):
# logIntensity[e,d] = log0,log(absolute(IQ(z[d]))),sign(IQ(z[d]))
#else:
# logIntensity[e,d] = log(max(0,IntInt(z[d]))),log(absolute(IQ(z[d]))),sign(IQ(z[d]))
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):
print(theta[p]*rdg, " ",p)
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
#print("Flattening:",f, " ",dR," ",flattening)
#exit()
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
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)
#print(psi0)
#print(len(psi[r1]),a1,a2)
#TS: bug correction ....#####
if(a1 >= len(psi[r1])):
a1=len(psi[r1])-1
if(a2 >= len(psi[r2])):
a2=len(psi[r2])-1
########
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 #without time delay
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',cos_alpha,cos_psi,Omega)
if mu0<0: # this only for speeding up. the backwards intensity is usually zero
Flux_obs[t]=0
#continue
if True: # find chi
sin_chi_0= - sin_theta*sin_phi # times sin psi
cos_chi_0=sin_i*cos_theta - sin_theta*cos_i*cos_phi # times sin psi
chi_0=arctan2(sin_chi_0,cos_chi_0)
sin_chi_1=sin_gamma*sin_i*sin_phi*sin_alpha_over_sin_psi #times sin alpha sin sigma
cos_chi_1=cos_gamma - cos_alpha*cos_sigma #times sin alpha sin sigma
chi_1=arctan2(sin_chi_1,cos_chi_1)
sin_lambda=sin_theta*cos_gamma - sin_gamma*cos_theta
cos_lambda=cos_theta*cos_gamma + sin_theta*sin_gamma
cos_eps = sin_alpha_over_sin_psi*(cos_i*sin_lambda - sin_i*cos_lambda*cos_phi + cos_psi*sin_gamma) - cos_alpha*sin_gamma
# this line is the longest one
# alt_cos_eps=(cos_sigma*cos_gamma - cos_alpha)/sin_gamma # legit! thanks God I checked it!
# sin_chi_prime=cos_eps*mu0*Gamma*beta # times something
#sin_chi_prime=cos_eps*mu0*delta*Gamma*beta*(1-Gamma1*cos_xi)# times something
# cos_chi_prime=1. - cos_sigma**2 /(1. - beta*cos_xi) # times the samething
#cos_chi_prime=sin_sigma**2 - Gamma*mu0**2*beta*cos_xi*(1 - Gamma1*cos_xi) # times the samething
#OR THE ORIGINAL VERSION:
sin_chi_prime=cos_eps*mu0*Gamma*beta#*the_thing#*delta**3#*delta
cos_chi_prime=(1. - cos_sigma**2 /(1. - beta*cos_xi))#*the_thing
chi_prime=arctan2(sin_chi_prime,cos_chi_prime)
tan_chi_prime_sph = beta*cos_alpha*(cos_i*sin_theta-sin_i*cos_theta*cos_phi)/(sin_alpha*sin_psi+beta*sin_i*sin_phi)
chi_prime_sph=arctan(tan_chi_prime_sph)
chi=chi_0 + chi_1 + chi_prime
#print(chi,'\t',chi_0/chi,'\t',chi_1/chi ,'\t', chi_prime/chi )
#print(phase_obs[t], ' ', chi*rdg,' ',chi_0*rdg,' ',chi_1*rdg ,' ', chi_prime*rdg, chi_prime_sph*rdg)
#params = "Sph"+str(spherical)+"_t"+str(int(theta_deg))+"i"+str(int(incl_deg))+"nu"+str(int(freq))
#save_pa=open("res/B/pa_eqs_figs/pa_"+params+".txt","a+")
#save_pa.write(str(phase_obs[t])+', '+str(chi*rdg)+', '+str(chi_0*rdg)+', '+str(chi_1*rdg)+', '+str(chi_prime*rdg)+', '+str(chi_prime_sph*rdg)+"\n")
#save_pa.close()
sin_2chi=sin(2*chi)
cos_2chi=cos(2*chi)
# print(chi_prime,' \t',cos_chi_prime )
#testing my new formulas:
cos_lambd = cos_theta*cos_gamma+sin_theta*sin_gamma#cos(theta-gamma)
sin_lambd = sin_theta*cos_gamma-cos_theta*sin_gamma#sin(theta-gamma)
bigS = sin_alpha*(sin_i*cos_lambd*cos_phi-cos_i*sin_lambd)+sin_gamma*(sin_psi*cos_alpha-cos_psi*sin_alpha)
dn1 = -bigS**2-cos_sigma**2*sin_psi**2
dn2 = (bigS**2/sin_sigma**2)+(cos_sigma**2*sin_i**2*sin_phi**2*sin_alpha**2/sin_sigma**2)
nom = sin_alpha*sin_i**2*sin_phi**2-(sin_psi**2/sin_alpha)
nom0 = beta*(sin_alpha/sin_psi)*bigS*cos_sigma
cos_ksi = -(sin_alpha/sin_psi)*sin_i*sin_phi
dntot = beta*cos_ksi*dn1+sin_sigma**2*dn2
tanchi_p20 = nom0*nom/dntot
tanchi_vlad = tan(chi_prime)
sin_ksi = sqrt(1-cos_ksi**2)
tanchi_juri_app = (-beta*cos_sigma*(bigS/sin_psi)*sin_ksi**2)/((bigS/sin_psi)**2+cos_sigma**2*cos_ksi**2-beta*cos_ksi*((bigS/sin_psi)**2+cos_sigma**2))
#print(sin_ksi**2, (bigS/sin_psi)**2+cos_sigma**2)
tanchi_pmdot = ((cos_ksi-beta)/(1-beta*cos_ksi))*(cos_sigma*sin_psi/bigS)
tanchi_pm = sin_i*sin_phi*cos_sigma*sin_alpha/bigS
tanchi_cgr= (tanchi_pmdot+tanchi_pm)/(1.0-tanchi_pmdot*tanchi_pm)
tanchi_pmdot_sph = ((cos_ksi-beta)/(1-beta*cos_ksi))*(cos_alpha*sin_psi/(sin_alpha*(sin_i*cos_theta*cos_phi-cos_i*sin_theta)))
tanchi_pm_sph = sin_i*sin_phi*cos_alpha/(sin_i*cos_theta*cos_phi-cos_i*sin_theta)
tanchi_cgr_sph= (tanchi_pmdot_sph+tanchi_pm_sph)/(1.0-tanchi_pmdot_sph*tanchi_pm_sph)
#print("tanchi_cgr, tan_pout, tan_vlad, tan_sph =", tanchi_cgr, tanchi_p20, tanchi_vlad, tan_chi_prime_sph) #it seesm tanchi_cgr=tan_pout but it differs from tan_vlad if the star is not spherical...
print("tanchi_p20, tan_vlad, tan_juri_app =", tanchi_p20, tanchi_vlad, tanchi_juri_app)
#print("nom, dn1, dn2 = ", nom*sin_alpha, dn1, -1.0*dn2)
#testing a direct formula for oblate corrected chi_0:
sin_chi_0_obl= - sin_lambda*sin_phi # times sin psi
cos_chi_0_obl=sin_i*cos_lambda - sin_lambda*cos_i*cos_phi # times sin psi
chi_0_obl=arctan2(sin_chi_0_obl,cos_chi_0_obl)
bA = -sin_theta*sin_phi*sin_psi*(cos_gamma-cos_alpha*cos_sigma)+sin_gamma*sin_alpha*sin_i*sin_phi*(sin_i*cos_theta-cos_i*sin_theta*cos_phi)
bB = sin_psi*(sin_i*cos_theta-cos_i*sin_theta*cos_phi)*(cos_gamma-cos_alpha*cos_sigma)
bC = sin_theta*sin_phi*sin_gamma*sin_alpha*sin_i*sin_phi
chi_01 = arctan2(bA,bB+bC)
chi_0_cr = chi_0_obl-chi_0
#print("chi0+chi1=",chi_0+chi_1,"chi0_obl=",chi_0_obl)#, "chi_01=",chi_01)
#print("chi_new?=",(chi_0_obl+chi_prime)*rdg,"chi_current=",(chi_0+chi_1+chi_prime)*rdg)#, "chi_01=",chi_01)
d2=bisect(mu[:-1],mu0)
d1=d2-1
# print(mu0,mu[d2],mu[d1],d2,d1,' ')
mu1,mu2=mu[d1],mu[d2]
dmu, dmu1, dmu2 = mu2 - mu1, mu0 - mu1, mu2 - mu0
shift=delta/redshift
for e in range(NEnergy):
x0=x[e]/shift
e1=bisect(x[1:-1],x0) # not the fastest way? anybody cares? ## seems, that light bending is more time consuming anyways
e2=e1+1
x1, x2 = x[e1], x[e2]
dx, dx1, dx2 = x2 - x1, x0 - x1, x2 - x0
logIQ = (
dx2*dmu2*logIntensity[e1, d1] +
dx2*dmu1*logIntensity[e1, d2] +
dx1*dmu2*logIntensity[e2, d1] +
dx1*dmu1*logIntensity[e2, d2] # bilinear interpolation of the Stokes parameters
)/dx/dmu
I,Q=exp(logIQ[:2])* shift**3 * Omega
Q*=logIQ[2]
if I<0: ############
print('never')
Flux_obs[t,e]=[I, Q*cos_2chi, Q*sin_2chi]
#Flux_obs[t,e]=[I, -I*0.1171*cos_2chi*(1.0 - mu0)/(1.0 + 3.82*abs(mu0)),-0.1171*I*sin_2chi*(1.0 - mu0)/(1.0 + 3.82*abs(mu0))]
#Flux_obs[t,e]=[I, (1.0 - cos_alpha),(1.0 - cos_alpha)]
#print(t,mu0,-0.1171*(1.0 - mu0)/(1.0 + 3.82*abs(mu0)))
#Flux_obs[t,e]=[I, cos_2chi, sin_2chi]
for t in range(NPhase):
phase0=phase[t]
for t2 in range(NPhi):
t1=t2-1
phase2=phase_obs[t2]
phase1=phase_obs[t1]
if phase0>phase1 and phase0<phase2:
break
else :
phase0=0
t2=argmin(phase_obs)
t1=t2-1
phase2=phase_obs[t2]
phase1=phase_obs[t1]-1
dphase1=phase0-phase1
dphase2=phase2-phase0
dphase=phase2-phase1
Flux[t-1]+=(Flux_obs[t2]*dphase1+Flux_obs[t1]*dphase2)/dphase #TS: changed here t to t-1 to match the phaseshift to my fortran results
#print(Flux[t,0], t, NPhi)
#s,gn=pr(s,gn,'curves done ')
# In[31]:
savePulse = False #True
if savePulse:
outF = open(PulsName + 'FF.bin','w')
outf = open(PulsName + 'ff.bin','w')
Flux.tofile(outF,format="%e")
phase.tofile(outf,format="%e")
#for e in range(0,NEnergy,20): # too many pictures
# I=zeros(NPhase)
# Q=zeros(NPhase)
# U=zeros(NPhase)
# for t in range(NPhase):
# I[t],Q[t],U[t]=Flux[t,e]
# p=sqrt(Q**2+U**2)/I*100
# PA=arctan2(-U,-Q)*90/pi+90
# print(Q[0], U[0], Flux[0,0], x[e]*evere/1e3)
#print('end')
return Flux
#compf(1.0,1.0,1.0,1.0)