def plot_S_model():
# Debug plotting
B = 5e-10
print('huhu')
nu_range = np.logspace(np.log10(30e6), 9, 6)
age_range = np.linspace(0, 200, 5)
from agnpy.emission_regions import Blob
from agnpy.synchrotron import Synchrotron
blob = Blob(z=0.001,
B=10**4 * B * u.gauss,
spectrum_dict={
"type": "PowerLaw",
"parameters": {
"p": 2.3,
"gamma_min": 2,
"gamma_max": 1e7
}
})
synch = Synchrotron(blob)
sed = synch.sed_flux(nu_range * u.Hz)
sed = sed.value / nu_range
results = np.zeros((len(age_range), len(nu_range)))
for i, age in enumerate(age_range):
with mp.Pool() as p:
results[i] = p.starmap(S_model, [[nu, B, 0.65, 1000, age]
for nu in nu_range])
print(results[i], nu_range)
PL = (nu_range**-0.65)
PL /= (PL[0] / sed[0])
print((results[0, 0] / sed[0]))
results /= (results[0, 0] / sed[0])
import matplotlib.pyplot as plt
plt.close()
print(nu_range, sed)
plt.plot(nu_range, sed, c='k', label=f'AGNPY for 0 Myr; B = {B}T')
plt.plot(nu_range, PL, label=f'PL alpha = 0.65', c='k', ls='dotted')
for age, res in zip(age_range, results):
plt.plot(nu_range, res, label=f'{age}Myr; B = {B}T')
plt.xscale('log')
plt.yscale('log')
plt.xlabel('frequency [Hz]')
plt.ylabel('S')
# plt.xlim([np.min(nu_range), np.max(nu_range)])
# plt.ylim([np.min(res), 1.05*np.max(res)])
plt.legend()
plt.savefig(
__file__.replace('lib_aging.py', '') +
'lib_aging_data/synch_vs_nu.png')
def test_ssa_reference_sed(
self,
file_ref,
spectrum_type,
spectrum_parameters,
figure_title,
figure_path,
):
"""test SSA SED generated by a given electron distribution against the
ones generated with jetset version 1.1.2, via jetset_ssa_sed.py script"""
# reference SED
nu_ref, sed_ref = extract_columns_sample_file(file_ref, "Hz",
"erg cm-2 s-1")
# same parameters used to produce the jetset SED
spectrum_norm = 1e2 * u.Unit("cm-3")
spectrum_dict = {
"type": spectrum_type,
"parameters": spectrum_parameters
}
blob = Blob(
R_b=5e15 * u.cm,
z=0.1,
delta_D=10,
Gamma=10,
B=0.1 * u.G,
spectrum_norm=spectrum_norm,
spectrum_dict=spectrum_dict,
)
# recompute the SED at the same ordinates where the figure was sampled
ssa = Synchrotron(blob, ssa=True)
sed_agnpy = ssa.sed_flux(nu_ref)
# sed comparison plot, we will check between 10^(11) and 10^(19) Hz
nu_range = [1e11, 1e19] * u.Hz
make_comparison_plot(
nu_ref,
sed_agnpy,
sed_ref,
"agnpy",
"jetset 1.1.2",
figure_title,
figure_path,
"sed",
comparison_range=nu_range.to_value("Hz"),
)
# requires that the SED points deviate less than 5% from the figure
assert check_deviation(nu_ref, sed_agnpy, sed_ref, 0.05, nu_range)
def test_absorption_pointlike_and_homogeneous(self):
"""Simple test for checking the attenuation factors in both considered cases."""
blob = Blob()
absorb = Absorption(blob)
nu_tau = np.logspace(22, 34, 100) * u.Hz # for absorption calculations
tau = absorb.tau(nu_tau)
abs_pointlike = absorb.absorption(nu_tau)
abs_homogeneous = absorb.absorption_homogeneous(nu_tau)
# select good points (to avoid division by zero)
idxs = tau > 1.0e-3
# if this fails something is wrong with the test itself (e.g. default parameters of the blob)
assert sum(idxs) > 10
# the formulas reproduce what should be in the function, so the agreement should be down to numerical accuracy
assert np.allclose(np.exp(-tau), abs_pointlike, atol=1.0e-5)
assert np.allclose((1 - np.exp(-tau)) / tau,
abs_homogeneous,
atol=1.0e-5)
},
}
R_b = 1e16 * u.cm
B = 1 * u.G
z = Distance(1e27, unit=u.cm).z
delta_D = 10
Gamma = 10
for spectrum_dict in (spectrum_dict_pwl, spectrum_dict_bpl, spectrum_dict_bpl_2):
for norm_type in ("integral", "differential", "gamma=1"):
blob = Blob(
R_b,
z,
delta_D,
Gamma,
B,
spectrum_norm,
spectrum_dict,
spectrum_norm_type=norm_type,
)
blob.plot_n_e()
# let us trigger the error
blob = Blob(
R_b,
z,
delta_D,
Gamma,
B,
1e48 * u.Unit("erg"),
spectrum_dict_bpl_2,
r0 = 1.0e14 * u.m
dist = 3.0e16 * u.cm
xi = 1.0e-4
nu = np.logspace(8, 26, 200) * u.Hz
norm = 15000.0 * u.Unit("cm-3")
parameters = {
"p1": 2.0,
"p2": 3.0,
"gamma_b": gbreak,
"gamma_min": gmin0,
"gamma_max": gmax0,
}
spectrum_dict = {"type": "BrokenPowerLaw", "parameters": parameters}
blob = Blob(r0, z, delta_D, Gamma, B0, norm, spectrum_dict, xi=xi)
# plt.loglog(blob.gamma, blob.n_e (blob.gamma))
#############################################
# limits from confinement of particles inside the blob:
gmaxconf = blob.gamma_max_larmor
# computing larmor radius of this electron, should be of the size of the blob
# R_L = 33.36 km * (p/(GeV/c)) * (G/B) * Z^-1
# https://w3.iihe.ac.be/~aguilar/PHYS-467/PA3.pdf
rlarmor = (33.36 * u.km * gmaxconf * 511.0e3 / 1.0e9 / (blob.B / u.G)).to("cm")
# both values are similar
print("R_L (gmaxconf)=", rlarmor, "R_b=", blob.R_b)
#############################################
"p1": 1.5,
"p2": 2.5,
"gamma_b": 1.0e3,
"gamma_min": 1,
"gamma_max": 1.0e6,
}
spectrum_dict = {"type": "BrokenPowerLaw", "parameters": parameters}
delta_D = 1.01
Gamma = 1.01
B = 1.0 * u.G
r_b = 1.0e15 * u.cm
# no beaming
blob0 = Blob(r_b,
0.01,
delta_D,
Gamma,
B,
spectrum_norm,
spectrum_dict,
xi=0.01)
synch0 = Synchrotron(blob0, ssa=True)
synch0_sed = synch0.sed_flux(nu)
# beaming
delta_D = 20
Gamma = 15
blob1 = Blob(r_b,
0.01,
delta_D,
Gamma,
B,
from astropy.coordinates import Distance
from agnpy.emission_regions import Blob
import matplotlib.pyplot as plt
from agnpy.utils.plot import load_mpl_rc
# matplotlib adjustments
load_mpl_rc()
# set the spectrum normalisation (total energy in electrons in this case)
spectrum_norm = 1e48 * u.Unit("erg")
# define the spectral function parametrisation through a dictionary
spectrum_dict = {
"type": "PowerLaw",
"parameters": {
"p": 2.8,
"gamma_min": 1e2,
"gamma_max": 1e7
},
}
# set the remaining quantities defining the blob
R_b = 1e16 * u.cm
B = 1 * u.G
z = Distance(1e27, unit=u.cm).z
delta_D = 10
Gamma = 10
blob = Blob(R_b, z, delta_D, Gamma, B, spectrum_norm, spectrum_dict)
# plot the electron distribution
blob.plot_n_e(gamma_power=2)
plt.show()
bpwl_dict_test = {
"type": "BrokenPowerLaw",
"parameters": {
"p1": 2.0,
"p2": 3.5,
"gamma_b": 1e4,
"gamma_min": 20,
"gamma_max": 5e7,
},
}
# blob reproducing Figure 7.4 of Dermer Menon 2009
pwl_blob_test = Blob(
1e16 * u.cm,
Distance(1e27, unit=u.cm).z,
10,
10,
1 * u.G,
pwl_spectrum_norm_test,
pwl_dict_test,
)
# blob reproducing the EC scenarios in Finke 2016
bpwl_blob_test = Blob(
1e16 * u.cm,
1,
40,
40,
0.56 * u.G,
bpwl_spectrum_norm_test,
bpwl_dict_test,
)
bpwl_blob_test.set_gamma_size(400)
def test_tau_on_synchrotron_compare_with_delta_approximation(self):
"""Compare the output of the calculation of absorption of gamma rays
in synchrotron radiation and compare it with simplified delta approximation.
"""
# create a test blob
r_b = 1.0e16 * u.cm
z = 2.01
delta_D = 10.1
Gamma = 10.05
B0 = 1.1 * u.G
gmin = 10
gbreak = 1.0e3
gmax = 1.0e5
spectrum_norm = 0.1 * u.Unit("erg cm-3")
parameters = {
"p1": 1.5,
"p2": 2.5,
"gamma_b": gbreak,
"gamma_min": gmin,
"gamma_max": gmax,
}
spectrum_dict = {"type": "BrokenPowerLaw", "parameters": parameters}
blob = Blob(r_b, z, delta_D, Gamma, B0, spectrum_norm, spectrum_dict)
nu_tau = np.logspace(22, 34, 100) * u.Hz # for absorption calculations
e_tau = nu_tau.to("eV", equivalencies=u.spectral())
# full calculations
absorb = Absorption(blob)
tau = absorb.tau(nu_tau)
# now simplified calculations using Eq. 37 of Finke 2008
mec2 = (m_e * c**2).to("eV")
eps1 = e_tau / mec2
eps1p = eps1 * (1 + z) / blob.delta_D
eps_bar = 2 * blob.delta_D**2 / (1 + z)**2 / eps1
nu_bar = (eps_bar * mec2).to("Hz", equivalencies=u.spectral())
synch = Synchrotron(blob, ssa=True)
synch_sed_ebar = synch.sed_flux(nu_bar)
tau_delta = (synch_sed_ebar * sigma_T * Distance(z=z)**2 * eps1p /
(2 * m_e * c**3 * blob.R_b * blob.delta_D**4))
tau_delta = tau_delta.to("")
# the delta approximation does not work well with sharp cut-offs of synchrotron SED.
# We first find the peak of the synchr SED
maxidx = np.where(synch_sed_ebar == np.amax(synch_sed_ebar))[0][0]
# and only take energies below the peak, (note that energies are ordered
# in reversed order), and take only those that are at least 1% of the peak
idxs = synch_sed_ebar[maxidx:] > 1.0e-2 * synch_sed_ebar[maxidx]
# if there are not many points something went wrong with the test
assert sum(idxs) > 10
# the agreement in the middle range is pretty good, but at the edges
# of energy range it spoils very fast, so only rough agreement is checked
# (0.6 in the log space)
assert np.allclose(np.log(tau)[maxidx:][idxs],
np.log(tau_delta)[maxidx:][idxs],
atol=0.6)
import numpy as np import astropy.units as u from agnpy.emission_regions import Blob from agnpy.compton import SynchrotronSelfCompton from agnpy.utils.plot import plot_sed import matplotlib.pyplot as plt from agnpy.utils.plot import load_mpl_rc # matplotlib adjustments load_mpl_rc() # define the emission region and the radiative process blob = Blob() ssc = SynchrotronSelfCompton(blob) # compute the SED over an array of frequencies nu = np.logspace(15, 28) * u.Hz sed = ssc.sed_flux(nu) # plot it plot_sed(nu, sed, label="Synchrotron Self Compton") plt.show()
import numpy as np
import astropy.units as u
from astropy.coordinates import Distance
from astropy.constants import e, c, m_e, M_sun, G, sigma_sb
from agnpy.emission_regions import Blob
from agnpy.targets import (
CMB,
PointSourceBehindJet,
SSDisk,
SphericalShellBLR,
RingDustTorus,
)
import pytest
# variables with _test are global and meant to be used in all tests
blob_test = Blob()
# CMB at z = 1
cmb_test = CMB(z=1)
# PointSourceBehindJet
ps_test = PointSourceBehindJet(1e46 * u.Unit("erg s-1"), 1e-5)
# disk
M_BH_test = 1.2 * 1e9 * M_sun
L_disk_test = 1.512 * 1e46 * u.Unit("erg s-1")
eta_test = 1 / 12
R_g_test = 1.77 * 1e14 * u.cm
R_in_tilde_test = 6
R_out_tilde_test = 200
R_in_test = R_in_tilde_test * R_g_test
spectrum_norm = 6e42 * u.erg
parameters = {
"p1": 2.0,
"p2": 3.5,
"gamma_b": 1e4,
"gamma_min": 20,
"gamma_max": 5e7,
}
spectrum_dict = {"type": "BrokenPowerLaw", "parameters": parameters}
R_b = 1e16 * u.cm
B = 0.56 * u.G
z = 1
delta_D = 40
Gamma = 40
blob = Blob(R_b, z, delta_D, Gamma, B, spectrum_norm, spectrum_dict)
blob.set_gamma_size(500)
L_disk = 2 * 1e46 * u.Unit("erg s-1")
# dust torus
T_dt = 1e3 * u.K
csi_dt = 0.1
dt = RingDustTorus(L_disk, csi_dt, T_dt)
# blr
xi_line = 0.024
R_line = 1e17 * u.cm
blr = SphericalShellBLR(L_disk, xi_line, "Lyalpha", R_line)
# point source behind the jet approximating the DT
ps_dt = PointSourceBehindJet(dt.xi_dt * L_disk, dt.epsilon_dt)
# point source behind the jet approximating the BLR
# global PWL blob, same parameters of Figure 7.4 in Dermer Menon 2009
SPECTRUM_NORM = 1e48 * u.Unit("erg")
PWL_DICT = {
"type": "PowerLaw",
"parameters": {
"p": 2.8,
"gamma_min": 1e2,
"gamma_max": 1e5
},
}
R_B = 1e16 * u.cm
B = 1 * u.G
Z = Distance(1e27, unit=u.cm).z
DELTA_D = 10
GAMMA = 10
PWL_BLOB = Blob(R_B, Z, DELTA_D, GAMMA, B, SPECTRUM_NORM, PWL_DICT)
# global blob with BPL law of electrons, to test the parametrisation of the
# delta function approximation
BPL_DICT = {
"type": "BrokenPowerLaw",
"parameters": {
"p1": 2.5,
"p2": 3.5,
"gamma_b": 1e4,
"gamma_min": 1e2,
"gamma_max": 1e7,
},
}
BPL_BLOB = Blob(R_B, Z, DELTA_D, GAMMA, B, SPECTRUM_NORM, BPL_DICT)
"gamma_0": 1e3,
"gamma_min": gamma_min_test,
"gamma_max": gamma_max_test,
},
}
# blob parameters
R_b_test = 1e16 * u.cm
z_test = 0.1
delta_D_test = 10
Gamma_test = 10
B_test = 0.1 * u.G
pwl_blob_test = Blob(
R_b_test,
z_test,
delta_D_test,
Gamma_test,
B_test,
spectrum_norm_test,
pwl_dict_test,
)
bpwl_blob_test = Blob(
R_b_test,
z_test,
delta_D_test,
Gamma_test,
B_test,
spectrum_norm_test,
bpwl_dict_test,
)
lp_blob_test = Blob(
R_b_test,
#####################
# test one with emission region in the center of the DT
L_disk = 0.91e45 * u.Unit("erg s-1")
xi_dt = 0.6
T_dt = 100 * u.K
R_dt = 1.0e18 * u.cm
h = 0.01 * R_dt
## test with lower numbers, gives virtually the same
# B0/=10
# T_dt/=10
# L_disk/=100
blob1 = Blob(r0, z, delta_D, Gamma, B0, norm, spectrum_dict, xi=xi)
dt1 = RingDustTorus(L_disk, xi_dt, T_dt, R_dt=R_dt)
# energy density of DT radiation field in the blob
u_dt1 = dt1.u_ph(h, blob1)
u_synch1 = blob1.u_ph_synch
print(
"energy density in the blob, DT radiation: ",
u_dt1,
"synchrotron photons: ",
u_synch1,
)
dt1_sed = dt1.sed_flux(nu, z)
# energy density was set to be the same
synch1 = Synchrotron(blob1, ssa=False)
mec2 = m_e.to("erg", equivalencies=u.mass_energy())
# a global test blob with spectral index 2
SPECTRUM_NORM = 1e-13 * u.Unit("cm-3")
GAMMA_MIN = 1
GAMMA_MAX = 1e6
PWL_IDX_2_DICT = {
"type": "PowerLaw",
"parameters": {"p": 2.0, "gamma_min": GAMMA_MIN, "gamma_max": GAMMA_MAX},
}
# blob parameters
R_B = 1e16 * u.cm
Z = 0.1
DELTA_D = 10
GAMMA = 10
B = 0.1 * u.G
PWL_BLOB = Blob(R_B, Z, DELTA_D, GAMMA, B, SPECTRUM_NORM, PWL_IDX_2_DICT)
# useful for checks
BETA = 1 - 1 / np.power(GAMMA, 2)
V_B = 4 / 3 * np.pi * np.power(R_B, 3)
class TestBlob:
"""class grouping all tests related to the Blob emission region"""
def test_default_norm_type(self):
"""the default norm type should be 'integral'"""
assert PWL_BLOB.spectrum_norm_type == "integral"
def test_integral_norm_cm3(self):
"""test if the integral norm in cm-3 is correctly set"""
PWL_BLOB.set_n_e(SPECTRUM_NORM, PWL_IDX_2_DICT, "integral")
n = -2.0
x = np.logspace(2, 5)
y = line_loglog(x, m, n)
analytical_integral = integral_line_loglog(x[0], x[-1], m, n)
trapz_loglog_integral = trapz_loglog(y, x)
np_trapz_integral = np.trapz(y, x)
print(f"analyitcal integral: {analytical_integral:e}")
print(f"trapz_loglog integral: {analytical_integral:e}")
print(f"np.trapz integral: {analytical_integral:e}")
# a test with sycnhrotron radiation
print("-> test with synchrotron radiation")
blob = Blob()
nu = np.logspace(9, 20, 20) * u.Hz
# check the blob
print(blob)
def sed_synch(nu, blob, integration):
"""compute the synchrotron SED"""
epsilon = nu_to_epsilon_prime(nu, blob.z, blob.delta_D)
# electrond distribution lorentz factor
gamma = blob.gamma
N_e = blob.N_e(gamma)
prefactor = np.sqrt(3) * epsilon * np.power(e, 3) * blob.B_cgs / h
# for multidimensional integration
# axis 0: electrons gamma
# define the blob
spectrum_norm = 6e42 * u.erg
parameters = {
"p1": 2.0001,
"p2": 3.5,
"gamma_b": 1e4,
"gamma_min": 20,
"gamma_max": 5e7,
}
spectrum_dict = {"type": "BrokenPowerLaw", "parameters": parameters}
R_b = 1e16 * u.cm
B = 0.56 * u.G
z = 1
delta_D = 40
Gamma = 40
blob = Blob(R_b, z, delta_D, Gamma, B, spectrum_norm, spectrum_dict)
print("\nblob definition:")
print(blob)
# disk parameters
M_sun = const.M_sun.cgs
M_BH = 1.2 * 1e9 * M_sun
R_g = ((const.G * M_BH) / (const.c * const.c)).cgs
L_disk = 2 * 1e46 * u.Unit("erg s-1")
eta = 1 / 12
R_in = 6 * R_g
R_out = 200 * R_g
disk = SSDisk(M_BH, L_disk, eta, R_in, R_out)
print("\ndisk definition:")
print(disk)
fig.savefig(f"{tests_dir}/crosscheck_figures/{fig_name}.png")
# global PWL blob, same parameters of Figure 7.4 in Dermer Menon 2009
PWL_SPECTRUM_NORM = 1e48 * u.Unit("erg")
PWL_DICT = {
"type": "PowerLaw",
"parameters": {"p": 2.8, "gamma_min": 1e2, "gamma_max": 1e5},
}
R_B_PWL = 1e16 * u.cm
B_PWL = 1 * u.G
Z_PWL = Distance(1e27, unit=u.cm).z
DELTA_D_PWL = 10
GAMMA_PWL = 10
PWL_BLOB = Blob(
R_B_PWL, Z_PWL, DELTA_D_PWL, GAMMA_PWL, B_PWL, PWL_SPECTRUM_NORM, PWL_DICT
)
# global BPL blob, same parameters of the examples in Finke 2016
BPL_SPECTRUM_NORM = 6e42 * u.Unit("erg")
BPL_DICT = {
"type": "BrokenPowerLaw",
"parameters": {
"p1": 2.0,
"p2": 3.5,
"gamma_b": 1e4,
"gamma_min": 20,
"gamma_max": 5e7,
},
}
R_B_BPL = 1e16 * u.cm