def log_likelihood(e_cutoff, data, amplitude, alpha, B, Eemin, Eemax):
crab_distance = 2.2 * u.kpc
ECPL = ExponentialCutoffPowerLaw(amplitude=amplitude / u.eV,
e_0=1 * u.TeV,
alpha=alpha,
e_cutoff=abs(e_cutoff) * u.erg)
SYN = Synchrotron(ECPL, B=B, Eemin=Eemin, Eemax=Eemax)
model = SYN.sed(data['energy'].quantity, distance=crab_distance)
sigma = (data['flux_error_lo'].quantity +
data['flux_error_hi'].quantity) / 2
sigma2 = np.where(sigma != 0, sigma, np.ones_like(sigma))
loglik = np.sum(np.log((model.value - data['flux'].data)**2))
return loglik - 2 * np.sum(np.log(sigma2))
def do_fit(
periods, # [0, 1],
ThetaIC, # np.array([90, 90]),
Pos3D, # [[1, 1, 1], [1, 1, 1]],
Dist, # np.array([2, 2]),
Alpha, # np.array([2.58, 2.16])
label='',
do_abs=True,
lgEdot_min=31,
lgEdot_max=37.5,
lgEdot_bins=10,
lgSigma_min=-3,
lgSigma_max=-1,
lgSigma_bins=10,
Tstar=pars.TSTAR,
Rstar=pars.RSTAR,
AlphaSigma=1,
Mdot=1e-8,
Vw=1500
):
logging.info('Starting fitting')
OutFit = open('fit_results/fit_results_' + label + '.txt', 'w')
NEdot = (lgEdot_max - lgEdot_min) * lgEdot_bins
NSigma = (lgSigma_max - lgSigma_min) * lgSigma_bins
Edot_list = np.logspace(lgEdot_min, lgEdot_max, int(NEdot))
Sigma_list = np.logspace(lgSigma_min, lgSigma_max, int(NSigma))
logging.info('{} iterations'.format(NEdot * NSigma))
print(Edot_list)
print(Sigma_list)
n_periods = len(periods)
if len(ThetaIC) != n_periods:
logging.error('Argument with wrong dimensions - aborting')
return None
# Absorption
if not do_abs:
logging.info('Skipping absorption')
else:
# Computing Taus
logging.info('Computing absorption')
start = time.time()
Obs = np.array([0, 0, -1])
Abs = abso.Absorption(Tstar=Tstar, Rstar=Rstar)
data_en, data_fl, data_fl_er = list(), list(), list()
Tau = list()
DistTau = list()
for iper in periods:
en, fl, fl_er = data.get_data(iper, GT=True)
data_en.append(en)
data_fl.append(fl)
data_fl_er.append(fl_er)
DistTau.append(list())
tt = dict()
for i in range(len(en)):
tt[i] = list()
Tau.append(tt)
DistFrac = np.linspace(0.01, 1, 50)
for ff in DistFrac:
for i_per in range(n_periods):
dist = ff * norm(Pos3D[i_per])
PosStar = Pos3D[i_per] * dist / norm(Pos3D[i_per])
for i_en in range(len(data_en[i_per])):
tau = Abs.TauGG(en=data_en[i_per][i_en] * u.keV.to(u.TeV), obs=Obs, pos=PosStar)
Tau[i_per][i_en].append(tau)
DistTau[i_per].append(dist)
logging.info('Abs done, dt/s = {}'.format(time.time() - start))
# # Ploting tau vs dist
# plt.figure(figsize=(8, 6), tight_layout=True)
# ax = plt.gca()
# ax.set_yscale('log')
# ax.set_ylabel(r'$\tau_{\gamma \gamma}$')
# ax.set_xlabel(r'$D$ [AU]')
# ax.plot(DistTau0, Tau0[92], marker='o', linestyle='-')
# ax.plot(DistTau0, Tau0[95], marker='o', linestyle='-')
# plt.show()
for (Edot, Sigma) in itertools.product(Edot_list, Sigma_list):
logging.debug('Starting Edot={}, Sigma={}'.format(Edot, Sigma))
# Computed parameters
DistPulsar = [psr.Rshock(Edot=Edot, Mdot=Mdot, Vw=Vw, D=d) for d in Dist]
DistStar = Dist - DistPulsar
DistRef = 4.
# SigmaFac = [pow(Dist[0] / d, AlphaSigma) for d in Dist]
SigmaFac = [pow(DistRef / d, AlphaSigma) for d in Dist]
SigmaShock = [Sigma * f for f in SigmaFac]
Bfield = [psr.B2_KC(Edot=Edot, Rs=dp, sigma=s) for (dp, s) in zip(DistPulsar, SigmaShock)]
Density = [psr.PhotonDensity(Tstar=Tstar, Rstar=Rstar, d=d) for d in DistStar]
if 0 in Bfield:
logging.info('Bfield is 0 - skipping')
continue
# Normalization
Norm0 = np.array([1e24 / b for b in Bfield])
# Fitting
fix_n = [True for p in range(pars.MAX_PERIOD)]
fit_n = [Norm0[0] for p in range(pars.MAX_PERIOD)]
for idx, iper in enumerate(periods):
fix_n[iper] = False
fit_n[iper] = Norm0[idx]
logging.info('fix_n:')
logging.info(fix_n)
logging.info('fit_n:')
logging.info(fit_n)
npar = 5 - sum([int(f) for f in fix_n])
####################
# Further parameters
Eref = 1 * u.TeV
Ecut = 50 * u.TeV
Emax = 20 * u.PeV
Emin = 10 * u.GeV
SourceDist = pars.SRC_DIST * u.kpc
EnergyToPlot = np.logspace(-2, 11, 500) * u.keV
######################
# Loading data
data_en, data_fl, data_fl_er = list(), list(), list()
tau = list()
model = list()
for ii in range(pars.MAX_PERIOD):
idx = periods.index(ii) if (ii in periods) else 0
en, fl, fl_er = data.get_data(ii, GT=True)
data_en.append(en)
data_fl.append(fl)
data_fl_er.append(fl_er)
thisTau = list()
if do_abs and (ii in periods):
for ien in range(len(en)):
thisTau.append(np.interp(DistStar[idx], xp=DistTau[idx], fp=Tau[idx][ien]))
else:
thisTau = [0] * len(en)
tau.append(thisTau)
ECPL = ExponentialCutoffPowerLaw(
amplitude=1e20 / u.eV,
e_0=Eref,
alpha=Alpha[idx],
e_cutoff=Ecut
)
SYN = Synchrotron(
particle_distribution=ECPL,
B=Bfield[idx] * u.G,
Eemax=Emax,
Eemin=Emin
)
IC = InverseCompton(
particle_distribution=ECPL,
seed_photon_fields=[[
'STAR',
Tstar * u.K,
Density[idx] * u.erg / u.cm**3,
ThetaIC[idx] * u.deg
]],
Eemax=Emax,
Eemin=Emin
)
thisModel = (
SYN.sed(photon_energy=[e * u.keV for e in en], distance=SourceDist) +
IC.sed(photon_energy=[e * u.keV for e in en], distance=SourceDist)
)
if do_abs:
thisModel = [math.exp(-t) * m for (m, t) in zip(thisModel, thisTau)]
model.append(thisModel)
# END for
def least_square(n0, n1, n2, n3, n4):
chisq = 0
for ii, nn in enumerate([n0, n1, n2, n3, n4]):
if fix_n[ii]:
continue
chisq += sum(util.vecChiSq(
[(nn / 1e20) * m.value for m in model[ii]],
data_fl[ii],
data_fl_er[ii])
)
return chisq
minuit = Minuit(
least_square,
n0=fit_n[0], fix_n0=fix_n[0],
n1=fit_n[1], fix_n1=fix_n[1],
n2=fit_n[2], fix_n2=fix_n[2],
n3=fit_n[3], fix_n3=fix_n[3],
n4=fit_n[4], fix_n4=fix_n[4],
limit_n0=(fit_n[0] * 0.001, fit_n[0] * 1000),
limit_n1=(fit_n[1] * 0.001, fit_n[1] * 1000),
limit_n2=(fit_n[2] * 0.001, fit_n[2] * 1000),
limit_n3=(fit_n[3] * 0.001, fit_n[3] * 1000),
limit_n4=(fit_n[4] * 0.001, fit_n[4] * 1000)
)
fmin, param = minuit.migrad()
logging.info(minuit.matrix(correlation=True))
chisq_min = minuit.fval
n_fit, n_err = list(), list()
ndf = 0
for ii in range(pars.MAX_PERIOD):
n_fit.append(param[ii]['value'])
n_err.append(param[ii]['error'])
if not fix_n[ii]:
ndf += len(data_en[ii])
ndf -= npar
# p_value = 1 - stats.chi2.cdf(chisq_min, ndf)
logging.info('Fit')
logging.info('ChiSq/ndf = {}'.format(chisq_min / ndf))
logging.info('ChiSq - ndf = {}'.format(chisq_min - ndf))
# # plot testing
# for ii, nn in enumerate(n_fit):
# if fix_n[ii]:
# continue
# plt.figure(figsize=(8, 6), tight_layout=True)
# ax = plt.gca()
# ax.set_xscale('log')
# ax.set_yscale('log')
# ax.set_title(ii)
# ax.errorbar(
# data_en[ii],
# data_fl[ii],
# yerr=data_fl_er[ii],
# marker='o',
# linestyle='none'
# )
# ax.plot(
# data_en[ii],
# [(nn / 1e20) * m.value for m in model[ii]],
# marker='o',
# linestyle='none'
# )
# plt.show()
# print('p-value', p_value)
# if do_abs:
# TauPrint0 = [tau0[len(data_en0) - 4], tau0[len(data_en0) - 1]]
# TauPrint1 = [tau1[len(data_en1) - 3], tau1[len(data_en1) - 1]]
# else:
# TauPrint0 = [0, 0]
# TauPrint1 = [0, 0]
if chisq_min - ndf < 1e3:
OutFit.write(str(chisq_min) + ' ')
OutFit.write(str(ndf) + ' ')
for ii in range(pars.MAX_PERIOD):
if not fix_n[ii]:
OutFit.write(str(math.log10(n_fit[ii])) + ' ')
OutFit.write(str(math.log10(Edot)) + ' ')
OutFit.write(str(math.log10(Sigma)) + ' ')
for ii in range(pars.MAX_PERIOD):
if not fix_n[ii]:
idx = periods.index(ii)
OutFit.write(str(Dist[idx]) + ' ')
OutFit.write(str(DistPulsar[idx]) + ' ')
OutFit.write(str(Bfield[idx]) + ' ')
# OutFit.write(str(TauPrint0[0]) + ' ')
# OutFit.write(str(TauPrint0[1]) + ' ')
# OutFit.write(str(TauPrint1[0]) + ' ')
# OutFit.write(str(TauPrint1[1]) + '\n')
OutFit.write('\n')
OutFit.close()
["SSC", Esy, phn_sy],
],
Eemax=50 * u.PeV,
Eemin=0.1 * u.GeV,
)
# Use plot_data from naima to plot the observed spectra
data = ascii.read("CrabNebula_spectrum.ecsv")
figure = naima.plot_data(data, e_unit=u.eV)
ax = figure.axes[0]
# Plot the computed model emission
energy = np.logspace(-7, 15, 100) * u.eV
ax.loglog(
energy,
IC.sed(energy, 2 * u.kpc) + SYN.sed(energy, 2 * u.kpc),
lw=3,
c="k",
label="Total",
)
for i, seed, ls in zip(range(4), ["CMB", "FIR", "NIR", "SSC"],
["--", "-.", ":", "-"]):
ax.loglog(
energy,
IC.sed(energy, 2 * u.kpc, seed=seed),
lw=2,
c=naima.plot.color_cycle[i + 1],
label=seed,
ls=ls,
)
# Synchroton luminosity by setting distance to 0.
Esy = np.logspace(-6, 6, 100) * u.eV
Lsy = SYN.flux(Esy, distance=0 * u.cm)
# Define source radius and compute photon density
R = 2 * u.pc
phn_sy = Lsy / (4 * np.pi * R**2 * c) * 2.26
# Create IC instance with CMB and synchrotron seed photon fields:
IC = InverseCompton(
ECPL, seed_photon_fields=['CMB', 'FIR', 'NIR', ['SSC', Esy, phn_sy]])
# Compute SEDs
spectrum_energy = np.logspace(-8, 14, 100) * u.eV
sed_IC = IC.sed(spectrum_energy, distance=1.5 * u.kpc)
sed_SYN = SYN.sed(spectrum_energy, distance=1.5 * u.kpc)
# Plot
plt.figure(figsize=(8, 5))
#plt.rc('font', family='sans')
#plt.rc('mathtext', fontset='custom')
ssc = IC.sed(spectrum_energy, seed='SSC', distance=1.5 * u.kpc)
plt.loglog(spectrum_energy,
ssc,
lw=1.5,
ls='-',
label='IC (SSC)',
c=naima.plot.color_cycle[2])
for seed, ls in zip(['CMB', 'FIR', 'NIR'], ['-', '--', ':']):
sed = IC.sed(spectrum_energy, seed=seed, distance=1.5 * u.kpc)
plt.loglog(spectrum_energy, sed, lw=1, ls=ls,
Esy = np.logspace(-7, 9, 100) * u.eV
Lsy = SYN.flux(Esy, distance=0 * u.cm) # use distance 0 to get luminosity
phn_sy = Lsy / (4 * np.pi * Rpwn**2 * c) * 2.24
IC = InverseCompton(ECBPL,
seed_photon_fields=['CMB',
['FIR', 70 * u.K, 0.5 * u.eV / u.cm**3],
['NIR', 5000 * u.K, 1 * u.eV / u.cm**3],
['SSC', Esy, phn_sy]],
Eemax=50 * u.PeV, Eemin=0.1 * u.GeV)
# Use plot_data from naima to plot the observed spectra
data = ascii.read('CrabNebula_spectrum.ecsv')
figure = naima.plot_data(data, e_unit=u.eV)
ax = figure.axes[0]
# Plot the computed model emission
energy = np.logspace(-7, 15, 100) * u.eV
ax.loglog(energy, IC.sed(energy, 2 * u.kpc) + SYN.sed(energy, 2 * u.kpc),
lw=3, c='k', label='Total')
for i, seed, ls in zip(
range(4), ['CMB', 'FIR', 'NIR', 'SSC'], ['--', '-.', ':', '-']):
ax.loglog(energy, IC.sed(energy, 2 * u.kpc, seed=seed),
lw=2, c=naima.plot.color_cycle[i + 1], label=seed, ls=ls)
ax.set_ylim(1e-12, 1e-7)
ax.legend(loc='upper right', frameon=False)
figure.tight_layout()
figure.savefig('CrabNebula_SynSSC.png')
EIC = InverseCompton(
lab,
seed_photon_fields=[
"CMB",
["BLR", T, w],
],
Eemax=Emax * delta,
Eemin=Emin * delta,
)
# Use matplotlib to plot the spectra
figure, ax = plt.subplots()
# Plot the computed model emission
energy = np.logspace(-3, 13, 100) * u.eV
SYN_plot = SYN.sed(energy / delta, distance=0 * u.cm) * delta**2
SSC_plot = SSC.sed(energy / delta, distance=0 * u.cm) * delta**2
EIC_plot = EIC.sed(energy, distance=0 * u.cm)
ylim_max = max(SYN_plot.max().value,
SSC_plot.max().value,
EIC_plot.max().value)
ax.set_ylim(ylim_max / 1.e10, ylim_max * 5)
for i, seed, ls in zip(range(2), ["CMB", "BLR"], ["--", "-."]):
ax.loglog(
energy,
EIC.sed(energy, distance=0 * u.cm, seed=seed),
lw=1,
c=naima.plot.color_cycle[i + 1],
label=seed,
ls=ls,
def do_fit(
ThetaIC, # np.array([90, 90]),
Pos3D, # [[1, 1, 1], [1, 1, 1]],
Dist, # np.array([2, 2]),
label='',
do_abs=True,
lgEdot_min=31,
lgEdot_max=37.5,
lgEdot_bins=10,
lgSigma_min=-3,
lgSigma_max=-1,
lgSigma_bins=10,
Tstar=pars.TSTAR_LS,
Rstar=pars.RSTAR_LS,
AlphaSigma=1,
Mdot=pars.MDOT_LS,
Vw=pars.VW_LS):
logging.info('Starting fitting')
OutFit = open('fit_results/fit_results_ls5039_' + label + '.txt', 'w')
# Loading data
phaseData, fluxSuzaku, fluxErrSuzaku, gammaSuzaku, gammaErrSuzaku = get_data_ls5039(
'SUZAKU')
phaseData, fluxHESS, fluxErrHESS, gammaHESS, gammaErrHESS = get_data_ls5039(
'HESS')
logging.debug('PhaseData')
logging.debug(phaseData)
# Loading energy
energyXrays = np.logspace(0, 1, 5)
energyGamma = np.logspace(math.log10(0.2e9), math.log10(5e9), 10)
energyAll = np.concatenate((energyXrays, energyGamma))
logging.debug('Energies')
logging.debug(energyXrays)
logging.debug(energyGamma)
logging.debug(energyAll)
# Loading grid
NEdot = int((lgEdot_max - lgEdot_min) * lgEdot_bins)
NSigma = int((lgSigma_max - lgSigma_min) * lgSigma_bins)
Edot_list = np.logspace(lgEdot_min, lgEdot_max, int(NEdot))
Sigma_list = np.logspace(lgSigma_min, lgSigma_max, int(NSigma))
logging.info('{} iterations'.format(len(Edot_list) * len(Sigma_list)))
if (len(ThetaIC) != len(phaseData) or len(Pos3D) != len(phaseData)
or len(Dist) != len(phaseData)):
logging.error('Argument with wrong dimensions - aborting')
return None
# Absorption
if not do_abs:
logging.info('Skipping absorption')
else:
if Path('abs_pars.json').exists():
logging.debug('Reading abs pars')
with open('abs_pars.json', 'r') as file:
data = json.load(file)
DistFrac = data['DistFrac']
DistTau = data['DistTau']
Tau = data['Tau']
else:
# Computing Taus
logging.info('Computing absorption')
start = time.time()
Obs = np.array([0, 0, -1])
Abs = abso.Absorption(Tstar=Tstar,
Rstar=Rstar,
name_table='absorption_table_ls5039.dat')
Tau = list()
DistTau = list()
for iph in range(len(phaseData)):
DistTau.append(list())
tt = dict()
for i in range(len(energyAll)):
tt[i] = list()
Tau.append(tt)
DistFrac = np.concatenate(
(np.linspace(0.005, 0.2, 20), np.linspace(0.201, 1.0, 10)))
for ff in DistFrac:
for iph in range(len(phaseData)):
dist = ff * norm(Pos3D[iph])
PosStar = Pos3D[iph] * dist / norm(Pos3D[iph])
for ien in range(len(energyAll)):
tau = Abs.TauGG(en=energyAll[ien] * u.keV.to(u.TeV),
obs=Obs,
pos=PosStar)
Tau[iph][ien].append(tau)
DistTau[iph].append(dist)
logging.info('Abs done, dt/s = {}'.format(time.time() - start))
absToSave = dict()
absToSave['DistFrac'] = list(DistFrac)
absToSave['DistTau'] = list(DistTau)
absToSave['Tau'] = list(Tau)
logging.debug('Writing abs to json file')
with open('abs_pars.json', 'w') as file:
json.dump(absToSave, file)
# # Ploting tau vs dist
# plt.figure(figsize=(8, 6), tight_layout=True)
# ax = plt.gca()
# ax.set_yscale('log')
# ax.set_ylabel(r'$\tau_{\gamma \gamma}$')
# ax.set_xlabel(r'$D$ [AU]')
# ax.plot(DistTau[7], Tau[7][str(5)], marker='o', linestyle='-')
# ax.plot(DistTau[7], Tau[7][str(13)], marker='o', linestyle='-')
# plt.show()
chisqMin = 1e10
minEdot = 0
minSigma = 0
for (Edot, Sigma) in itertools.product(Edot_list, Sigma_list):
print('Starting Edot={}, Sigma={}'.format(Edot, Sigma))
# Computed parameters
DistPulsar = [
psr.Rshock(Edot=Edot, Mdot=Mdot, Vw=Vw, D=d) for d in Dist
]
DistStar = Dist - DistPulsar
SigmaFac = [pow(0.1 / d, AlphaSigma) for d in DistPulsar]
SigmaShock = [Sigma * f for f in SigmaFac]
Bfield = [
psr.B2_KC(Edot=Edot, Rs=dp, sigma=s)
for (dp, s) in zip(DistPulsar, SigmaShock)
]
Density = [
psr.PhotonDensity(Tstar=Tstar, Rstar=Rstar, d=d) for d in DistStar
]
# plt.figure(figsize=(8, 6), tight_layout=True)
# ax = plt.gca()
# ax.set_yscale('log')
# ax.set_ylabel(r'$\tau_{\gamma \gamma}$')
# ax.set_xlabel(r'$D$ [AU]')
# ax.plot(DistPulsar, SigmaShock, marker='o', linestyle='-')
# plt.show()
# logging.debug('DistPulsar')
# logging.debug(DistPulsar)
# logging.debug('DistStar')
# logging.debug(DistStar)
# logging.debug('SigmaShock')
# logging.debug(SigmaShock)
# logging.debug('SigmaFac')
# logging.debug(SigmaFac)
logging.debug('Bfield')
logging.debug(Bfield)
logging.debug('MeanBfield')
logging.debug(sum(Bfield) / len(Bfield))
if 0 in Bfield:
logging.info('Bfield is 0 - skipping')
continue
# Normalization
NormStart = np.array([1e23 / b for b in Bfield])
npar = len(phaseData)
# Further parameters
Ecut = [rad.Emax(b, 1) * u.TeV for b in Bfield]
Eref = 1 * u.TeV
Emax = 100 * u.PeV
Emin = 10 * u.GeV
SourceDist = pars.SRC_DIST_LS * u.kpc
# Computing Alpha
Alpha = [2 * g - 1 for g in gammaSuzaku]
# print('Alpha')
# print(Alpha)
# print('gamma')
# print(gammaSuzaku)
# Computing Model
tau = list()
modelAll = list()
for iph in range(len(phaseData)):
thisTau = list()
if do_abs:
for ien in range(len(energyAll)):
thisTau.append(
np.interp(DistStar[iph],
xp=DistTau[iph],
fp=Tau[iph][str(ien)]))
else:
thisTau = [0] * len(energyAll)
tau.append(thisTau)
ECPL = ExponentialCutoffPowerLaw(amplitude=1e20 / u.eV,
e_0=Eref,
alpha=Alpha[iph],
e_cutoff=Ecut[iph])
SYN = Synchrotron(particle_distribution=ECPL,
B=Bfield[iph] * u.G,
Eemax=Emax,
Eemin=Emin)
IC = InverseCompton(particle_distribution=ECPL,
seed_photon_fields=[[
'STAR', Tstar * u.K,
Density[iph] * u.erg / u.cm**3,
ThetaIC[iph] * u.deg
]],
Eemax=Emax,
Eemin=Emin)
thisModel = (SYN.sed(photon_energy=[e * u.keV for e in energyAll],
distance=SourceDist) +
IC.sed(photon_energy=[e * u.keV for e in energyAll],
distance=SourceDist))
if do_abs:
thisModel = [
math.exp(-t) * m for (m, t) in zip(thisModel, thisTau)
]
# Ploting tau vs dist
# plt.figure(figsize=(8, 6), tight_layout=True)
# ax = plt.gca()
# ax.set_yscale('log')
# ax.set_xscale('log')
# ax.set_ylabel(r'$\tau_{\gamma \gamma}$')
# ax.set_xlabel(r'$E$ [keV]')
# print(energyAll)
# print(thisTau)
# ax.plot(energyAll[5:], thisTau[5:], marker='o', linestyle='-')
# ax.set_xlim(1e8, 1e10)
# plt.show()
modelAll.append(thisModel)
# END for
fluxModelSuzaku, fluxModelHESS, gammaModelHESS = list(), list(), list()
for thisModel in modelAll:
sedSuzaku = [f for (f, e) in zip(thisModel, energyAll) if e < 1e3]
energySuzaku = [e for e in energyAll if e < 1e3]
sedHESS = [f for (f, e) in zip(thisModel, energyAll) if e > 1e3]
energyHESS = [e for e in energyAll if e > 1e3]
fluxModelSuzaku.append(getSuzakuFlux(sedSuzaku, energySuzaku))
n, g = getHESSFluxAndGamma(sedHESS, energyHESS)
fluxModelHESS.append(n)
gammaModelHESS.append(g)
def computeModelPars(N, model, energy):
thisModel = [(N / 1e20) * m for m in model]
sedSuzaku = [f for (f, e) in zip(thisModel, energy) if e < 1e3]
energySuzaku = [e for e in energyAll if e < 1e3]
sedHESS = [f for (f, e) in zip(thisModel, energy) if e > 1e3]
energyHESS = [e for e in energyAll if e > 1e3]
thisFluxModelSuzaku = getSuzakuFlux(sedSuzaku, energySuzaku)
thisFluxModelHESS, thisGammaModelHESS = getHESSFluxAndGamma(
sedHESS, energyHESS)
return thisFluxModelSuzaku, thisFluxModelHESS, thisGammaModelHESS
chisqFit, nFit = list(), list()
fluxFitSuzaku, fluxFitHESS, gammaFitHESS = list(), list(), list()
for ii in range(len(phaseData)):
def least_square(n):
chisq = 0
fitFluxModelSuzaku, fitFluxModelHESS, fitGammaModelHESS = computeModelPars(
n, modelAll[ii], energyAll)
chisq += ((fitFluxModelSuzaku.value * 1e12 - fluxSuzaku[ii]) /
fluxErrSuzaku[ii])**2
chisq += ((fitFluxModelHESS.value * 1e12 - fluxHESS[ii]) /
fluxErrHESS[ii])**2
# chisq += ((fitGammaModelHESS - gammaHESS[ii]) / gammaErrHESS[ii])**2
return chisq
minuit = Minuit(least_square,
n=NormStart[ii],
fix_n=False,
limit_n=(NormStart[ii] * 0.0001,
NormStart[ii] * 10000),
errordef=1.)
fmin, param = minuit.migrad()
chisqFit.append(minuit.fval)
nFit.append(param[0]['value'])
fitFS, fitFH, fitGH = computeModelPars(param[0]['value'],
modelAll[ii], energyAll)
fluxFitSuzaku.append(fitFS)
fluxFitHESS.append(fitFH)
gammaFitHESS.append(fitGH)
# print('N*B')
# print([n * b for (n,b) in zip(nFit, Bfield)])
# print([c / 2 for c in chisqFit])
totalChiSq = sum(chisqFit) / 10.
if totalChiSq < chisqMin:
chisqMin = totalChiSq
minEdot = Edot
minSigma = Sigma
print('ChiSq = {}'.format(totalChiSq))
if totalChiSq < 1e20:
plotResults(phaseData=phaseData,
nFit=nFit,
fluxFitSuzaku=fluxFitSuzaku,
fluxSuzaku=fluxSuzaku,
fluxErrSuzaku=fluxErrSuzaku,
fluxFitHESS=fluxFitHESS,
fluxHESS=fluxHESS,
fluxErrHESS=fluxErrHESS,
gammaFitHESS=gammaFitHESS,
gammaHESS=gammaHESS,
gammaErrHESS=gammaErrHESS,
modelAll=modelAll,
energyAll=energyAll)
continue
# logging.info('Fit')
# logging.info('ChiSq/ndf = {}'.format(chisq_min / ndf))
# logging.info('ChiSq - ndf = {}'.format(chisq_min - ndf))
# # plot testing
# for ii, nn in enumerate(n_fit):
# if fix_n[ii]:
# continue
# plt.figure(figsize=(8, 6), tight_layout=True)
# ax = plt.gca()
# ax.set_xscale('log')
# ax.set_yscale('log')
# ax.set_title(ii)
# ax.errorbar(
# data_en[ii],
# data_fl[ii],
# yerr=data_fl_er[ii],
# marker='o',
# linestyle='none'
# )
# ax.plot(
# data_en[ii],
# [(nn / 1e20) * m.value for m in model[ii]],
# marker='o',
# linestyle='none'
# )
# plt.show()
# print('p-value', p_value)
# if do_abs:
# TauPrint0 = [tau0[len(data_en0) - 4], tau0[len(data_en0) - 1]]
# TauPrint1 = [tau1[len(data_en1) - 3], tau1[len(data_en1) - 1]]
# else:
# TauPrint0 = [0, 0]
# TauPrint1 = [0, 0]
if chisq_min - ndf < 1e3:
OutFit.write(str(chisq_min) + ' ')
OutFit.write(str(ndf) + ' ')
for ii in range(pars.MAX_PERIOD):
if not fix_n[ii]:
OutFit.write(str(math.log10(n_fit[ii])) + ' ')
OutFit.write(str(math.log10(Edot)) + ' ')
OutFit.write(str(math.log10(Sigma)) + ' ')
for ii in range(pars.MAX_PERIOD):
if not fix_n[ii]:
idx = periods.index(ii)
OutFit.write(str(Dist[idx]) + ' ')
OutFit.write(str(DistPulsar[idx]) + ' ')
OutFit.write(str(Bfield[idx]) + ' ')
# OutFit.write(str(TauPrint0[0]) + ' ')
# OutFit.write(str(TauPrint0[1]) + ' ')
# OutFit.write(str(TauPrint1[0]) + ' ')
# OutFit.write(str(TauPrint1[1]) + '\n')
OutFit.write('\n')
print('ChiSqMin {}'.format(chisqMin))
print('lgEdot {}'.format(math.log10(minEdot)))
print('Sigma {}'.format(minSigma))
OutFit.close()
synch = Synchrotron(electrons, B=3*u.uG,
Eemin = 1*u.GeV, Eemax = 510*u.TeV, nEed = 100)
IC = InverseCompton(electrons, seed_photon_fields=["CMB", "NIR", "FIR"],
Eemin = 1*u.GeV, Eemax = 510*u.TeV, nEed = 300)
brems = Bremsstrahlung(electrons, n0=1.0/u.cm**3,
Eemin = 1*u.GeV, Eemax = 510*u.TeV, nEed = 100)
#set normalization by fixing the total electron energy. For some reason, this is done
#via the emission spectrum.
synch.set_We(10**50 * u.erg)
#units check...
print "Flux dN/dE:", synch.flux([1]*u.keV, distance=2*u.kpc)
print "SED E^2dN/dE:", synch.sed([1]*u.keV, distance=2*u.kpc)
# In[47]:
#gamma-ray flux dN/dE
#energies at which we want to evaluate the spectrum
Egamma = np.logspace(-6, 5, 100) * u.GeV
#source distance
D=2*u.kpc
#get_ipython().magic(u'matplotlib inline')
plt.clf()
Eemax=510 * u.TeV,
nEed=300)
brems = Bremsstrahlung(electrons,
n0=1.0 / u.cm**3,
Eemin=1 * u.GeV,
Eemax=510 * u.TeV,
nEed=100)
#set normalization by fixing the total electron energy. For some reason, this is done
#via the emission spectrum.
synch.set_We(10**50 * u.erg)
#units check...
print "Flux dN/dE:", synch.flux([1] * u.keV, distance=2 * u.kpc)
print "SED E^2dN/dE:", synch.sed([1] * u.keV, distance=2 * u.kpc)
# In[47]:
#gamma-ray flux dN/dE
#energies at which we want to evaluate the spectrum
Egamma = np.logspace(-6, 5, 100) * u.GeV
#source distance
D = 2 * u.kpc
#get_ipython().magic(u'matplotlib inline')
plt.clf()
plt.loglog(Egamma,
def plot_sed(
self,
iperiod=0,
period=0,
best_solution=True,
Edot=1e36,
theta_ic=90,
dist=2,
pos=np.array([1, 1, 1]),
ls='-',
lw=1,
label='None',
Tstar=pars.TSTAR,
Rstar=pars.RSTAR,
emin=0.1,
ecut=50,
fast=False
):
Alpha = pars.ELEC_SPEC_INDEX[period]
Eref = 1 * u.TeV
Ecut = ecut * u.TeV
Emax = 20 * u.PeV
Emin = emin * u.TeV
SourceDist = pars.SRC_DIST * u.kpc
n_en = 1 if fast else 2
Obs = np.array([0, 0, -1])
Abs = absorption.Absorption(Tstar=Tstar, Rstar=Rstar)
if best_solution:
b_sed = self.bMin[iperiod]
norm_sed = self.normMin[iperiod]
dist_sed = self.distPulsarMin[iperiod]
dist_star = dist - dist_sed
density_sed = psr.PhotonDensity(Tstar=Tstar, Rstar=Rstar, d=dist_star)
else:
idx = np.argmin(np.array([math.fabs(l - math.log10(Edot)) for l in self.lgEdotLine]))
b_sed = self.bLine[iperiod][idx]
norm_sed = 10**self.lgNormLine[iperiod][idx]
dist_sed = self.distPulsarLine[iperiod][idx]
dist_star = dist * (1 - dist_sed)
density_sed = psr.PhotonDensity(Tstar=Tstar, Rstar=Rstar, d=dist_star)
EnergyToPlot = np.logspace(-0.5, 9.6, n_en * 300) * u.keV
ECPL = ExponentialCutoffPowerLaw(
amplitude=norm_sed / u.eV,
e_0=Eref,
alpha=Alpha,
e_cutoff=Ecut
)
SYN = Synchrotron(
particle_distribution=ECPL,
B=b_sed * u.G,
Eemax=Emax,
Eemin=Emin
)
IC = InverseCompton(
particle_distribution=ECPL,
seed_photon_fields=[[
'STAR',
Tstar * u.K,
density_sed * u.erg / u.cm**3,
theta_ic * u.deg
]],
Eemax=Emax,
Eemin=Emin
)
tau = list()
for e in EnergyToPlot:
if e.value * u.keV.to(u.TeV) < 1e-4:
tau.append(0)
else:
tau.append(Abs.TauGG(
en=e.value * u.keV.to(u.TeV),
obs=Obs,
pos=pos * dist_star / norm(pos)
))
model = (
SYN.sed(photon_energy=EnergyToPlot, distance=SourceDist)
+ IC.sed(photon_energy=EnergyToPlot, distance=SourceDist)
)
model_abs = [math.exp(-t) * m.value for (m, t) in zip(model, tau)]
EnergyToPlot, model_abs = util.fix_naima_bug(EnergyToPlot, model_abs)
model_abs = util.smooth_break(EnergyToPlot, model_abs)
ax = plt.gca()
ax.plot(EnergyToPlot, model_abs, ls=ls, lw=lw, c=self.color, label=label)
def tophat(E0, g0, energy, time, theta_obs, D_L):
mu_obs = np.cos(theta_obs)
z = z_at_value(Planck15.luminosity_distance, D_L)
if isinstance(energy.to_value(u.eV), float):
energy = np.array([energy.to_value(u.eV)]) * u.eV
# calc: R_b, t_b, Gamma_sh
u0, b0 = np.sqrt(g0**2 - 1), np.sqrt(1 - 1 / g0**2)
if g0 == 1.0:
return 0 * u.erg / u.cm**2 / u.s
R_dec = ((3. * E0 / (4. * np.pi * n_amb * m_p * c**2 *
(g0**2 - 1)))**(1 / 3)).to(u.pc)
xi_z = (c * time / (1 + z) / R_dec).cgs
if np.isposinf(alpha_stf):
u_xi = lambda xi: u0 if xi < 1e-1 else (u0 * xi**(
-3 / 2) if xi > 1e1 else np.sqrt(
((g0 + 1) / 2 * xi**(-3) *
(np.sqrt(1 + 4 * g0 / (g0 + 1) * xi**3 + 4 /
(g0 + 1)**2 * xi**6) - 1))**2 - 1))
else:
ui = np.inf
eiso_u = lambda u: (max(u0, min(ui, u))**(-alpha_stf) - ui**(
-alpha_stf)) / (u0**(-alpha_stf) - ui**(-alpha_stf))
I = lambda u: alpha_stf / (alpha_stf + 2) * u**(-alpha_stf - 2) * (
1 + hyp2f1(-1 / 2, -1 - alpha_stf / 2, -alpha_stf / 2, -u**2))
miso_u = lambda u: (I(max(u0, min(ui, u))) - I(ui)) / (u0**(
-alpha_stf) - ui**(-alpha_stf))
u_xi = lambda xi: fsolve(
lambda _u: xi**3 *
(_u[0] / u0)**2 - eiso_u(_u[0]) + miso_u(_u[0]) *
(np.sqrt(_u[0]**2 + 1) - 1), u0)[0]
eats = lambda xi: -mu_obs * xi + quad(
lambda _xi: np.sqrt(u_xi(_xi)**2 + 1) / u_xi(_xi), 0, xi)[0]
xi = fsolve(lambda _xi: eats(_xi[0]) - xi_z,
b0 * xi_z / (1 - b0 * mu_obs))[0]
R_b = xi * R_dec
t_b = (R_dec / c).cgs * quad(
lambda _xi: np.sqrt(u_xi(_xi)**2 + 1) / u_xi(_xi), 0, xi)[0]
Gamma_sh = np.sqrt(u_xi(xi)**2 + 1)
if Gamma_sh == 1.0:
return 0 * u.erg / u.cm**2 / u.s
# calc: electron distribution
specific_heat_ratio = 4 / 3 + 1 / Gamma_sh
compression_ratio = (specific_heat_ratio * Gamma_sh +
1) / (specific_heat_ratio - 1)
B = (np.sqrt(8 * np.pi * eps_B * compression_ratio * n_amb * m_p * c**2 *
(Gamma_sh - 1))).to((u.erg * pcm)**(1 / 2))
Ne = zeta_e * 4 / 3 * np.pi * R_b**3 * n_amb
gm = (eps_e / zeta_e * (p_e - 2) / (p_e - 1) * m_p / m_e *
(Gamma_sh - 1)).cgs
_gc = 6 * np.pi * mec * Gamma_sh / (sigma_T * B**2 * t_b)
Y = (-1 +
np.sqrt(1 + 4 * min(1, (gm / _gc)**(p_e - 2)) * eps_e / eps_B)) / 2
gc = _gc.cgs / (1 + Y) # rough estimate from Sari & Esin (2001)
e_syn_max = (min(np.sqrt(3 * e / (sigma_T * B * (1 + Y))), (e * B * R_b) /
(12 * 2 * np.pi * Gamma_sh * mec2)) * mec2).to(u.TeV)
electrons = ExponentialCutoffBrokenPowerLaw(
amplitude=(Ne * (p_e - 1) / (max(2., gm) * mec2) *
min(1., (gm / 2.)**(p_e - 1)) if gm < gc else Ne /
(max(2., gc) * mec2) * min(1., gc / 2.)).to(1 / u.eV),
e_0=(max(2., min(gm, gc)) * mec2).to(u.TeV),
e_break=(max(2., max(gm, gc)) * mec2).to(u.TeV),
alpha_1=p_e if gm < gc else 2.,
alpha_2=p_e + 1,
e_cutoff=max(((max(2., min(gm, gc)) + 1) * mec2).to(u.TeV), e_syn_max),
beta=2.0,
)
# calc: syn+ic flux
SYN = Synchrotron(
electrons,
B=B.to_value((u.erg * pcm)**(1 / 2)) * u.G,
Eemax=electrons.e_cutoff,
Eemin=electrons.e_0,
nEed=50,
)
'''E_ph = np.logspace(-7, 14, 22) * u.eV
L_syn = self.SYN.flux(E_ph, distance=0 * u.cm)
phn_syn = L_syn / (4 * np.pi * self.R ** 2 * c) * 2.24
IC = InverseCompton(
self.electrons,
seed_photon_fields=[
#"CMB",
#["FIR", 70 * u.K, 0.5 * u.eV / u.cm ** 3],
#["NIR", 5000 * u.K, 1 * u.eV / u.cm ** 3],
["SSC", E_ph, phn_syn],
],
Eemax=self.electrons.e_cutoff,
Eemin=self.electrons.e_0,
nEed=50,
)'''
Doppler = 1 / (Gamma_sh * (1 - np.sqrt(1 - 1 / Gamma_sh**2) * mu_obs))
flx = Doppler**4 * SYN.sed((1 + z) * energy / Doppler, D_L)[0]
tran = EblAbsorptionModel(redshift=z).transmission(e=energy)[0]
return (flx * tran).to(u.erg / u.cm**2 / u.s)