def test_u_dt_vs_point_source(self):
"""test that in the stationary reference frame, for large enough
distances, the energy density of the DT tends to the one of a point like
source approximating it"""
# point source with the same luminosity as the DT
ps_dt = PointSourceBehindJet(dt_test.xi_dt * dt_test.L_disk, dt_test.epsilon_dt)
# r >> R_dt
r = np.logspace(21, 24, 10) * u.cm
assert u.allclose(
dt_test.u(r), ps_dt.u(r), atol=0 * u.Unit("erg cm-3"), rtol=1e-2
)
def test_u_blr_vs_point_source(self):
"""test that for large enough distances the energy density of the
BLR tends to the one of a point like source approximating it"""
# point source with the same luminosity as the BLR
ps_blr = PointSourceBehindJet(BLR.xi_line * BLR.L_disk,
BLR.epsilon_line)
# r >> R_line
r = np.logspace(19, 23, 10) * u.cm
assert u.allclose(BLR.u(r),
ps_blr.u(r),
atol=0 * u.Unit("erg cm-3"),
rtol=1e-2)
def test_u_dt_vs_point_source_comoving(self):
"""test that in the reference frame comoving with the Blob, for large
enough distances, the energy density of the DT tends to the one of
a point like source approximating it"""
# point source with the same luminosity as the DT
ps_dt = PointSourceBehindJet(DT.xi_dt * DT.L_disk, DT.epsilon_dt)
# r >> R_line
r = np.logspace(21, 24, 10) * u.cm
assert u.allclose(
DT.u(r, PWL_BLOB),
ps_dt.u(r, PWL_BLOB),
atol=0 * u.Unit("erg cm-3"),
rtol=1e-1,
)
def test_ec_dt_vs_point_source(self):
"""check if in the limit of large distances the EC on the DT tends to
the one of a point-like source approximating it"""
r = 1e22 * u.cm
# point like source approximating the dt
ps_dt = PointSourceBehindJet(dt_test.xi_dt * dt_test.L_disk,
dt_test.epsilon_dt)
# external Compton
ec_dt = ExternalCompton(bpwl_blob_test, dt_test, r)
ec_ps_dt = ExternalCompton(bpwl_blob_test, ps_dt, r)
# seds
nu = np.logspace(15, 28) * u.Hz
sed_ec_dt = ec_dt.sed_flux(nu)
sed_ec_ps_dt = ec_ps_dt.sed_flux(nu)
make_comparison_plot(
nu,
sed_ec_ps_dt,
sed_ec_dt,
"point source approximating the DT",
"ring Dust Torus",
"External Compton on Ring Dust Torus, " +
r"$r = 10^{22}\,{\rm cm} \gg R_{\rm dt}$",
f"{figures_dir}/ec/dt/comparison_point_source.png",
"sed",
)
# requires a 20% deviation from the two SED points
assert check_deviation(nu, sed_ec_dt, sed_ec_ps_dt, 0.2)
def test_ec_blr_vs_point_source(self):
"""check if in the limit of large distances the EC on the BLR tends to
the one of a point-like source approximating it"""
r = 1e22 * u.cm
# point like source approximating the blr
ps_blr = PointSourceBehindJet(blr_test.xi_line * blr_test.L_disk,
blr_test.epsilon_line)
# external Compton
ec_blr = ExternalCompton(bpwl_blob_test, blr_test, r)
ec_ps_blr = ExternalCompton(bpwl_blob_test, ps_blr, r)
# seds
nu = np.logspace(15, 30) * u.Hz
sed_ec_blr = ec_blr.sed_flux(nu)
sed_ec_ps_blr = ec_ps_blr.sed_flux(nu)
# sed comparison plot
make_comparison_plot(
nu,
sed_ec_ps_blr,
sed_ec_blr,
"point source approximating the BLR",
"spherical shell BLR",
"External Compton on Spherical Shell BLR, " +
r"$r = 10^{22}\,{\rm cm} \gg R_{\rm line}$",
f"{figures_dir}/ec/blr/comparison_point_source.png",
"sed",
)
# requires a 20% deviation from the two SED points
assert check_deviation(nu, sed_ec_ps_blr, sed_ec_blr, 0.2)
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_ec_dt_vs_point_source(self):
"""check if in the limit of large distances the EC on the DT tends to
the one of a point-like source approximating it"""
# dust torus
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)
# point like source approximating the dt
ps_dt = PointSourceBehindJet(dt.xi_dt * L_disk, dt.epsilon_dt)
# external Compton
ec_dt = ExternalCompton(BPL_BLOB, dt, r=1e22 * u.cm)
ec_ps_dt = ExternalCompton(BPL_BLOB, ps_dt, r=1e22 * u.cm)
# seds
nu = np.logspace(15, 28) * u.Hz
ec_dt_sed = ec_dt.sed_flux(nu)
ec_ps_dt_sed = ec_ps_dt.sed_flux(nu)
# requires a 20% deviation from the two SED points
assert u.allclose(
ec_dt_sed, ec_ps_dt_sed, atol=0 * u.Unit("erg cm-2 s-1"), rtol=0.2
)
def test_ec_blr_vs_point_source(self):
"""check if in the limit of large distances the EC on the BLR tends to
the one of a point-like source approximating it"""
# broad line region
L_disk = 2 * 1e46 * u.Unit("erg s-1")
xi_line = 0.024
R_line = 1e17 * u.cm
blr = SphericalShellBLR(L_disk, xi_line, "Lyalpha", R_line)
# point like source approximating the blr
ps_blr = PointSourceBehindJet(blr.xi_line * L_disk, blr.epsilon_line)
# external Compton
ec_blr = ExternalCompton(BPL_BLOB, blr, r=1e22 * u.cm)
ec_ps_blr = ExternalCompton(BPL_BLOB, ps_blr, r=1e22 * u.cm)
# seds
nu = np.logspace(15, 28) * u.Hz
ec_blr_sed = ec_blr.sed_flux(nu)
ec_ps_blr_sed = ec_ps_blr.sed_flux(nu)
# requires a 20% deviation from the two SED points
assert u.allclose(
ec_blr_sed, ec_ps_blr_sed, atol=0 * u.Unit("erg cm-2 s-1"), rtol=0.2
)
_integrand = np.power(_gamma, -2) * _N_e * _kernel
integral_gamma = integrate(_integrand, gamma, axis=0)
prefactor_num = (3 * sigma_T * target.L_0 * np.power(epsilon_s, 2) *
np.power(blob.delta_D, 3))
prefactor_denom = (np.power(2, 7) * np.power(np.pi, 2) *
np.power(blob.d_L, 2) * np.power(r, 2) *
np.power(target.epsilon_0, 2))
sed = prefactor_num / prefactor_denom * integral_gamma
return sed.to("erg cm-2 s-1")
# target and distance
r = 1e16 * u.cm
L_0 = 2e46 * u.Unit("erg s-1")
epsilon_0 = 1e-3
ps = PointSourceBehindJet(L_0, epsilon_0)
nu = np.logspace(20, 30) * u.Hz
# increase the size of the gamma grid
blob.set_gamma_size(500)
sed_trapz = sed_flux_point_source(nu, blob, ps, r, np.trapz)
sed_trapz_loglog = sed_flux_point_source(nu, blob, ps, r, trapz_loglog)
plt.loglog(nu, sed_trapz, marker="o", label="np.trapz")
plt.loglog(nu,
sed_trapz_loglog,
ls="--",
marker=".",
label="naima trapz_loglog")
plt.legend()
plt.show()
"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 CMB at z = 1
CMB_Z_1 = CMB(z=1)
# global PointSourceBehindJet
PS = PointSourceBehindJet(1e46 * u.Unit("erg s-1"), 1e-5)
# global disk
M_BH = 1.2 * 1e9 * M_sun
L_DISK = 1.512 * 1e46 * u.Unit("erg s-1")
ETA = 1 / 12
R_G = 1.77 * 1e14 * u.cm
R_IN_G_UNITS = 6
R_OUT_G_UNITS = 200
R_IN = R_IN_G_UNITS * R_G
R_OUT = R_OUT_G_UNITS * R_G
DISK = SSDisk(M_BH, L_DISK, ETA, R_IN, R_OUT)
# useful for checks
L_EDD = 15.12 * 1e46 * u.Unit("erg s-1")
M_DOT = 2.019 * 1e26 * u.Unit("g s-1")
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
ps_blr = PointSourceBehindJet(blr.xi_line * L_disk, blr.epsilon_line)
ec_dt = ExternalCompton(blob, dt, r=1e22 * u.cm)
ec_blr = ExternalCompton(blob, blr, r=1e22 * u.cm)
ec_ps_dt = ExternalCompton(blob, ps_dt, r=1e22 * u.cm)
ec_ps_blr = ExternalCompton(blob, ps_blr, r=1e22 * u.cm)
# seds
nu = np.logspace(15, 30) * u.Hz
sed_blr = ec_blr.sed_flux(nu)
sed_ps_blr = ec_ps_blr.sed_flux(nu)
sed_dt = ec_dt.sed_flux(nu)
sed_ps_dt = ec_ps_dt.sed_flux(nu)
