def test_abs_dt_vs_point_source(self):
"""check if in the limit of large distances the gamma-gamma optical depth
on the DT tends to the one of a point-like source approximating it"""
# dust torus
L_disk = 2e46 * u.Unit("erg s-1")
T_dt = 1e3 * u.K
csi_dt = 0.1
dt = RingDustTorus(L_disk, csi_dt, T_dt)
r = 1e22 * u.cm
# point like source approximating the dt
ps_dt = PointSourceBehindJet(dt.xi_dt * L_disk, dt.epsilon_dt)
# absorption
z = 0.859
theta_s = np.deg2rad(10)
abs_dt = Absorption(dt, r, z, mu_s=np.cos(theta_s))
abs_ps_dt = Absorption(ps_dt, r, z, mu_s=np.cos(theta_s))
# taus
E = np.logspace(2, 6) * u.GeV
nu = E.to("Hz", equivalencies=u.spectral())
tau_dt = abs_dt.tau(nu)
tau_ps_dt = abs_ps_dt.tau(nu)
make_comparison_plot(
nu,
tau_ps_dt,
tau_dt,
"point source approximating the DT",
"ring dust torus",
"Absorption on Ring Dust Torus, " +
r"$r = 10^{22}\,{\rm cm} \gg R_{\rm dt},\,\theta_s=10^{\circ}$",
f"{figures_dir}/dt/tau_dt_point_source_comparison.png",
"tau",
)
# requires a 10% deviation from the two SED points
assert check_deviation(nu, tau_dt, tau_ps_dt, 0.1)
def test_abs_blr_vs_point_source(self):
"""check if in the limit of large distances the gamma-gamma optical depth
on the BLR tends to the one of a point-like source approximating it"""
# broad line region
L_disk = 2e46 * u.Unit("erg s-1")
xi_line = 0.024
R_line = 1e17 * u.cm
blr = SphericalShellBLR(L_disk, xi_line, "Lyalpha", R_line)
r = 1e20 * u.cm
# point like source approximating the blr
ps_blr = PointSourceBehindJet(blr.xi_line * L_disk, blr.epsilon_line)
# absorption, consider a small viewing angle for this case
z = 0.859
theta_s = np.deg2rad(10)
abs_blr = Absorption(blr, r, z, mu_s=np.cos(theta_s))
abs_ps_blr = Absorption(ps_blr, r, z, mu_s=np.cos(theta_s))
# taus
E = np.logspace(2, 6) * u.GeV
nu = E.to("Hz", equivalencies=u.spectral())
tau_blr = abs_blr.tau(nu)
tau_ps_blr = abs_ps_blr.tau(nu)
# sed comparison plot
make_comparison_plot(
nu,
tau_ps_blr,
tau_blr,
"point source approximating the BLR",
"spherical shell BLR",
"Absorption on Spherical Shell BLR, " +
r"$r = 10^{20}\,{\rm cm} \gg R({\rm Ly\alpha}),\,\theta_s=10^{\circ}$",
f"{figures_dir}/blr/tau_blr_point_source_comparison.png",
"tau",
)
# requires a 10% deviation from the two SED points
assert check_deviation(nu, tau_blr, tau_ps_blr, 0.1)
def test_absorption_disk_reference_tau(self, r):
"""test agnpy gamma-gamma optical depth for Disk against the one in
Figure 14 of Finke 2016"""
# reference tau
E_ref, tau_ref = extract_columns_sample_file(
f"{data_dir}/reference_taus/finke_2016/figure_14_left/tau_SSdisk_r_{r}_R_Ly_alpha.txt",
"GeV",
)
nu_ref = E_ref.to("Hz", equivalencies=u.spectral())
# target
M_BH = 1.2 * 1e9 * M_sun.cgs
L_disk = 2e46 * u.Unit("erg s-1")
eta = 1 / 12
R_in = 6
R_out = 200
disk = SSDisk(M_BH, L_disk, eta, R_in, R_out, R_g_units=True)
R_Ly_alpha = 1.1e17 * u.cm
_r = float(r) * R_Ly_alpha
# recompute the tau, use the full energy range of figure 14
z = 0.859
abs_disk = Absorption(disk, _r, z)
tau_agnpy = abs_disk.tau(nu_ref)
# comparison plot
make_comparison_plot(
nu_ref,
tau_agnpy,
tau_ref,
"agnpy",
"Figure 14, Finke (2016)",
f"Absorption Shakura Sunyaev Disk, r = {r} R(Ly alpha)",
f"{figures_dir}/disk/tau_disk_comparison_r_{r}_R_Ly_alpha_figure_14_finke_2016.png",
"tau",
y_range=[1e-10, 1e5],
)
assert True
def test_absorption_blr_reference_tau(self, r):
"""test agnpy gamma-gamma optical depth for a Lyman alpha BLR against
the one in Figure 14 of Finke 2016"""
# reference tau
E_ref, tau_ref = extract_columns_sample_file(
f"{data_dir}/reference_taus/finke_2016/figure_14_left/tau_BLR_Ly_alpha_r_{r}_R_Ly_alpha.txt",
"GeV",
)
nu_ref = E_ref.to("Hz", equivalencies=u.spectral())
# target
L_disk = 2e46 * u.Unit("erg s-1")
xi_line = 0.024
R_line = 1e17 * u.cm
blr = SphericalShellBLR(L_disk, xi_line, "Lyalpha", R_line)
R_Ly_alpha = 1.1e17 * u.cm
_r = float(r) * R_Ly_alpha
# recompute the tau, use the full energy range of figure 14
z = 0.859
ec_blr = Absorption(blr, _r, z)
tau_agnpy = ec_blr.tau(nu_ref)
# comparison plot
make_comparison_plot(
nu_ref,
tau_agnpy,
tau_ref,
"agnpy",
"Figure 14, Finke (2016)",
f"Absorption on Spherical Shell BLR, r = {r} R(Ly alpha)",
f"{figures_dir}/blr/tau_blr_Ly_alpha_comprison_r_{r}_R_Ly_alpha_figure_14_finke_2016.png",
"tau",
y_range=[1e-5, 1e5],
)
assert True
def test_absorption_dt_reference_tau(self, r):
"""test agnpy gamma-gamma optical depth for DT against the one in
Figure 14 of Finke 2016"""
# reference tau
E_ref, tau_ref = extract_columns_sample_file(
f"{data_dir}/reference_taus/finke_2016/figure_14_left/tau_DT_r_{r}_R_Ly_alpha.txt",
"GeV",
)
nu_ref = E_ref.to("Hz", equivalencies=u.spectral())
# target
L_disk = 2e46 * u.Unit("erg s-1")
T_dt = 1e3 * u.K
csi_dt = 0.1
dt = RingDustTorus(L_disk, csi_dt, T_dt)
R_Ly_alpha = 1.1e17 * u.cm
_r = float(r) * R_Ly_alpha
# recompute the tau, use the full energy range of figure 14
z = 0.859
ec_dt = Absorption(dt, _r, z)
tau_agnpy = ec_dt.tau(nu_ref)
# comparison plot
make_comparison_plot(
nu_ref,
tau_agnpy,
2 * tau_ref,
"agnpy",
"Figure 14, Finke (2016)",
f"Absorption on Dust Torus, r = {r} R(Ly alpha)",
f"{figures_dir}/dt/tau_dt_comprison_r_{r}_R_Ly_alpha_figure_14_finke_2016.png",
"tau",
y_range=[1e-5, 1e5],
)
assert True
def test_abs_blr_mu_s_vs_on_axis(self, r_to_R):
"""check if the codes computing absorption on BLR for mu_s = 1 and !=1 cases are consistent """
# broad line region
L_disk = 2e46 * u.Unit("erg s-1")
xi_line = 0.024
R_line = 1e17 * u.cm
blr = SphericalShellBLR(L_disk, xi_line, "Lyalpha", R_line)
r = r_to_R * R_line
z = 0.859
abs_blr = Absorption(blr, r, z, mu_s=0.9999)
abs_blr_on_axis = Absorption(blr, r, z)
abs_blr.set_l(50)
abs_blr_on_axis.set_l(50)
# taus
E = np.logspace(0, 6) * u.GeV
nu = E.to("Hz", equivalencies=u.spectral())
tau_blr = abs_blr.tau(nu)
tau_blr_on_axis = abs_blr_on_axis.tau(nu)
# sed comparison plot
make_comparison_plot(
nu,
tau_blr_on_axis,
tau_blr,
"on-axis calculations",
"general",
"Absorption on Spherical Shell BLR, " + r"$r/R_{\rm line}=$" +
f"{r_to_R}",
f"{figures_dir}/blr/tau_blr_on_axis_vs_general_r_{r_to_R}_R_line_comparison.png",
"tau",
)
# only check in there range with measurable absorption
xmin = min(nu[tau_blr_on_axis > 1.0e-4])
xmax = max(nu[tau_blr_on_axis > 1.0e-4])
xrange = (xmin, xmax)
print(xrange)
# close to the threshold there are some differences up to ~25%
# which are probably due to numerical uncertainties in the integrals
assert check_deviation(nu,
tau_blr,
tau_blr_on_axis,
0.25,
x_range=xrange)
def test_tau_blr_mus_Rline(self, r_R_line):
"""
Checks if absorption on BLR works also fine
if one of the integration points falls on R_line
"""
L_disk = 2 * 1e46 * u.Unit("erg s-1")
xi_line = 0.024
R_line = 1.1 * 1e17 * u.cm
blr = SphericalShellBLR(L_disk, xi_line, "Lyalpha", R_line)
abs_blr = Absorption(blr, r=r_R_line * R_line, mu_s=0.99)
# reference (without problem)
abs_blr0 = Absorption(blr, r=r_R_line * R_line * 1.001, mu_s=0.99)
nu = np.logspace(22, 28) * u.Hz
tau_blr = abs_blr.tau(nu)
tau_blr0 = abs_blr0.tau(nu)
# the current integrals are not very precise, and this includes
# tricky part to integrate, so allowing for rather large error margin
assert np.allclose(tau_blr, tau_blr0, atol=0.01, rtol=1.04)
def test_tau_dt_mu_s_far(self, mu_s):
"""
comparing the DT absorption for mu_s !=1 with point source simplification
"""
L_disk = 2e46 * u.Unit("erg s-1")
xi_DT = 0.1
temp = 1000 * u.K
R_DT = 1.0e17 * u.cm # radius of DT
dt = RingDustTorus(L_disk, xi_DT, temp, R_dt=R_DT)
r = 10 * R_DT # distance at which the photon starts
nu_ref = np.logspace(26, 32, 60) * u.Hz
# absorption at mu_s
abs_dt_mu_s = Absorption(dt, r, z=0, mu_s=mu_s)
tau_dt_mu_s = abs_dt_mu_s.tau(nu_ref)
uu = np.logspace(-5, 5, 100) * r
_u, _nu_ref = axes_reshaper(uu, nu_ref)
eps = (2.7 * temp * k_B).to("eV") # energy of soft photons
# distance from the DT
_x = np.sqrt(r * r + _u * _u + 2 * mu_s * _u * r)
# soft photon density
_nph = (L_disk * xi_DT / (4 * np.pi * _x**2) / c / eps).to("cm-3")
_E = _nu_ref.to("eV", equivalencies=u.spectral())
_cospsi = (_u**2 + _x**2 - r**2) / (2 * _u * _x)
_beta2 = 1 - 2 * mec2**2 / (_E * eps * (1 - _cospsi))
_beta2[_beta2 < 0] = 0
integrand = sigma_pp(np.sqrt(_beta2)) * _nph * (1 - _cospsi)
tau_my = (np.trapz(integrand, uu, axis=0)).to("")
print(tau_my / tau_dt_mu_s)
max_agnpy = max(tau_dt_mu_s)
max_my = max(tau_my)
max_pos_agnpy = nu_ref[np.argmax(tau_dt_mu_s)]
max_pos_my = nu_ref[np.argmax(tau_my)]
# if r>>R_re this should be pretty precise, allowing for 10% accuracy
assert np.isclose(max_agnpy, max_my, atol=0, rtol=0.1)
assert np.isclose(max_pos_agnpy, max_pos_my, atol=0, rtol=0.1)
def test_tau_dt_mu_s_simple(self):
"""
order of magnitude test comparing with simplified calculations
the case of a perpendicularly moving photon starting at r~0.5 * R_re
"""
r = 1.0e17 * u.cm # distance at which the photon starts
mu_s = 0.0 # angle of propagation
L_disk = 2e46 * u.Unit("erg s-1")
xi_DT = 0.1
temp = 1000 * u.K
R_DT = 2 * r # radius of DT: assume the same as the distance r
dt = RingDustTorus(L_disk, xi_DT, temp, R_dt=R_DT)
nu_ref = np.logspace(26, 32, 120) * u.Hz
# absorption at mu_s
abs_dt_mu_s = Absorption(dt, r, z=0, mu_s=mu_s)
tau_dt_mu_s = abs_dt_mu_s.tau(nu_ref)
eps = (2.7 * temp * k_B).to("eV") # energy of soft photons
# soft photon density
nph = (L_disk * xi_DT / (4 * np.pi * (r**2 + R_DT**2)) / c /
eps).to("cm-3")
E = nu_ref.to("eV", equivalencies=u.spectral())
cospsi = 0 # assume perpendicular scattering
beta2 = 1 - 2 * mec2**2 / (E * eps * (1 - cospsi))
beta2[beta2 < 0] = 0 # below the threshold
# for tau calculations we assume that gamma ray moves
# roughtly the characteristic distance of ~R_DT
tau_my = (sigma_pp(np.sqrt(beta2)) * nph * R_DT * (1 - cospsi)).to("")
max_agnpy = max(tau_dt_mu_s)
max_my = max(tau_my)
max_pos_agnpy = nu_ref[np.argmax(tau_dt_mu_s)]
max_pos_my = nu_ref[np.argmax(tau_my)]
# very rough calculations so allowing for
# 15% accuracy in peak maximum and 30% in peak position
assert np.isclose(max_agnpy, max_my, atol=0, rtol=0.15)
assert np.isclose(max_pos_agnpy, max_pos_my, atol=0, rtol=0.3)
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)
def test_absorption_blr_reference_tau(self, r, nu_min):
"""test agnpy gamma-gamma optical depth for a Lyman alpha BLR against
the one in Figure 14 of Finke 2016"""
# reference tau
E_ref, tau_ref = extract_columns_sample_file(
f"{data_dir}/reference_taus/finke_2016/figure_14_left/tau_BLR_Ly_alpha_r_{r}_R_Ly_alpha.txt",
"GeV",
)
# Finke's frequencies are not corrected for the redshift
z = 0.859
nu_ref = E_ref.to("Hz", equivalencies=u.spectral()) / (1 + z)
# target
L_disk = 2 * 1e46 * u.Unit("erg s-1")
xi_line = 0.024
R_Ly_alpha = 1.1 * 1e17 * u.cm
blr = SphericalShellBLR(L_disk, xi_line, "Lyalpha", R_Ly_alpha)
# parse the string providing the distance in units of R_Ly_alpha
# numbers as 1e1.5 cannot be directly converted to float
num = r.split("e")
Ly_alpha_units = (float(num[0]) * 10)**(float(num[-1]))
_r = Ly_alpha_units * R_Ly_alpha
# recompute the tau, use the full energy range of figure 14
abs_blr = Absorption(blr, _r, z)
tau_agnpy = abs_blr.tau(nu_ref)
# check in a restricted energy range
nu_range = [nu_min, 3e28] * u.Hz
make_comparison_plot(
nu_ref,
tau_agnpy,
tau_ref,
"agnpy",
"Figure 14, Finke (2016)",
f"Absorption on Spherical Shell BLR, r = {Ly_alpha_units:.2e} R(Ly alpha)",
f"{figures_dir}/blr/tau_blr_Ly_alpha_comprison_r_{r}_R_Ly_alpha_figure_14_finke_2016.png",
"tau",
comparison_range=nu_range.to_value("Hz"),
y_range=[1e-6, 1e3],
)
# requires that the SED points deviate less than 35 % from those of the reference figure
assert check_deviation(nu_ref, tau_agnpy, tau_ref, 0.35, nu_range)
def test_absorption_dt_reference_tau(self, r, nu_min):
"""test agnpy gamma-gamma optical depth for DT against the one in
Figure 14 of Finke 2016"""
# reference tau
E_ref, tau_ref = extract_columns_sample_file(
f"{data_dir}/reference_taus/finke_2016/figure_14_left/tau_DT_r_{r}_R_Ly_alpha.txt",
"GeV",
)
nu_ref = E_ref.to("Hz", equivalencies=u.spectral())
# target
L_disk = 2 * 1e46 * u.Unit("erg s-1")
T_dt = 1e3 * u.K
csi_dt = 0.1
dt = RingDustTorus(L_disk, csi_dt, T_dt)
R_Ly_alpha = 1.1 * 1e17 * u.cm
# parse the string providing the distance in units of R_Ly_alpha
# numbers as 1e1.5 cannot be directly converted to float
num = r.split("e")
Ly_alpha_units = (float(num[0]) * 10)**(float(num[-1]))
_r = Ly_alpha_units * R_Ly_alpha
# recompute the tau, use the full energy range of figure 14
z = 0.859
abs_dt = Absorption(dt, _r, z)
tau_agnpy = abs_dt.tau(nu_ref)
# check in a restricted energy range
nu_range = [nu_min, 3e28] * u.Hz
make_comparison_plot(
nu_ref,
tau_agnpy,
2 * tau_ref,
"agnpy",
"Figure 14, Finke (2016)",
f"Absorption on Dust Torus, r = {Ly_alpha_units:.2e} R(Ly alpha)",
f"{figures_dir}/dt/tau_dt_comprison_r_{r}_R_Ly_alpha_figure_14_finke_2016.png",
"tau",
comparison_range=nu_range.to_value("Hz"),
y_range=[1e-6, 1e3],
)
# requires that the SED points deviate less than 20 % from those of the reference figure
assert check_deviation(nu_ref, tau_agnpy, 2 * tau_ref, 0.20, nu_range)
csi_dt = 0.1
dt = RingDustTorus(L_disk, csi_dt, T_dt)
# consider a fixed distance of the blob from the target fields
r = 1.1e16 * u.cm
# let us consider 3C 454.3 as source
z = 0.859
absorption_disk = Absorption(disk, r=r, z=z)
absorption_blr = Absorption(blr, r=r, z=z)
absorption_dt = Absorption(dt, r=r, z=z)
# plot using the same energy range as in Finke 2016
E = np.logspace(0, 5) * u.GeV
nu = E.to("Hz", equivalencies=u.spectral())
tau_disk = absorption_disk.tau(nu)
tau_blr = absorption_blr.tau(nu)
tau_dt = absorption_dt.tau(nu)
# plot it
plt.loglog(E, tau_disk, lw=2, ls="-", label="SS disk")
plt.loglog(E, tau_blr, lw=2, ls="--", label="spherical shell BLR")
plt.loglog(E, tau_dt, lw=2, ls="-.", label="ring dust torus")
plt.legend()
plt.xlabel(r"$E\,/\,GeV$")
plt.ylabel(r"$\tau_{\gamma \gamma}$")
plt.xlim([1, 1e5])
plt.ylim([1e-3, 1e5])
plt.show()
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)