agnpy package

Modules

agnpy.spectra module

class agnpy.spectra.BrokenPowerLaw(k=<Quantity 1.e-13 1 / cm3>, p1=2.0, p2=3.0, gamma_b=1000.0, gamma_min=10, gamma_max=10000000.0, mass=<<class 'astropy.constants.codata2018.CODATA2018'> name='Electron mass' value=9.1093837015e-31 uncertainty=2.8e-40 unit='kg' reference='CODATA 2018'>, integrator=<function trapz>)[source]

Bases: ParticleDistribution

Class describing a broken power-law particle distribution. When called, the particle density \(n(\gamma)\) in \(\mathrm{cm}^{-3}\) is returned.

\[n(\gamma') = k \left[ \left(\frac{\gamma'}{\gamma'_b}\right)^{-p_1} \, H(\gamma'; \gamma'_{\rm min}, \gamma'_b) + \left(\frac{\gamma'}{\gamma'_b}\right)^{-p_2} \, H(\gamma'; \gamma'_{b}, \gamma'_{\rm max}) \right]\]

Parameters:

k (Quantity) – spectral normalisation
p1 (float) – spectral index before the break (positive by definition)
p2 (float) – spectral index after the break (positive by definition)
gamma_b (float) – Lorentz factor at which the change in spectral index is occurring
gamma_min (float) – minimum Lorentz factor of the particle distribution
gamma_max (float) – maximum Lorentz factor of the particle distribution
mass (Quantity) – particle mass, default is the electron mass
integrator (func) – function to be used for integration, default is trapz

SSA_integrand(gamma)[source]

static evaluate(gamma, k, p1, p2, gamma_b, gamma_min, gamma_max)[source]

static evaluate_SSA_integrand(gamma, k, p1, p2, gamma_b, gamma_min, gamma_max)[source]: Analytical integrand for the synchrotron self-absorption: \(\gamma'^2 \frac{d}{d \gamma'} \left(\frac{n_e(\gamma)}{\gamma'^2}\right)\).

property parameters

class agnpy.spectra.ExpCutoffPowerLaw(k=<Quantity 1.e-13 1 / cm3>, p=2.1, gamma_c=1000.0, gamma_min=10, gamma_max=100000.0, mass=<<class 'astropy.constants.codata2018.CODATA2018'> name='Electron mass' value=9.1093837015e-31 uncertainty=2.8e-40 unit='kg' reference='CODATA 2018'>, integrator=<function trapz>)[source]

Bases: ParticleDistribution

Class describing a power-law with an exponetial cutoff particle distribution. When called, the particle density \(n_e(\gamma)\) in \(\mathrm{cm}^{-3}\) is returned.

\[n(\gamma'_c) = k \, \gamma'^{-p} exp(-\gamma'/\gamma_c) \, H(\gamma'; \gamma'{\rm min}, \gamma'{\rm max})\]

Parameters:

k (Quantity) – spectral normalisation
p (float) – spectral index, note it is positive by definition, will change sign in the function
gamma_c (float) – cutoff Lorentz factor of the particle distribution
gamma_min (float) – minimum Lorentz factor of the particle distribution
gamma_max (float) – maximum Lorentz factor of the particle distribution
mass (Quantity) – particle mass, default is the electron mass
integrator (func) – function to be used for integration, default is trapz

SSA_integrand(gamma)[source]

static evaluate(gamma, k, p, gamma_c, gamma_min, gamma_max)[source]

static evaluate_SSA_integrand(gamma, k, p, gamma_c, gamma_min, gamma_max)[source]: (analytical) integrand for the synchrotron self-absorption: \(\gamma'^2 \frac{d}{d \gamma'} \left(\frac{n(\gamma)}{\gamma'^2}\right)\)

property parameters

class agnpy.spectra.InterpolatedDistribution(gamma, n, norm=1, mass=<<class 'astropy.constants.codata2018.CODATA2018'> name='Electron mass' value=9.1093837015e-31 uncertainty=2.8e-40 unit='kg' reference='CODATA 2018'>, integrator=<function trapz>)[source]

Bases: ParticleDistribution

Class describing a particle distribution with an arbitrary shape. The spectrum is interpolated from an array of Lorentz factor and densities.

Parameters:

gamma (ndarray) – array of Lorentz factors where the density has been computed
n (Quantity) – array of densities to be interpolated
norm (float) – parameter to scale the density
mass (Quantity) – particle mass, default is the electron mass
integrator (func) – function to be used for integration, default is trapz

SSA_integrand(gamma)[source]

Integrand for the synchrotron self-absorption. It is

\[\gamma^2 \frac{d}{d \gamma} (\frac{n_e(\gamma)}{\gamma^2}) = ( \frac{dn_e(\gamma)}{d\gamma}+\frac{2n_e(\gamma)}{\gamma})\]

The derivative is:

\[\frac{dn_e(\gamma)}{d\gamma} = \frac{d 10^{f(u(\gamma))}}{d\gamma} = \frac{d10^{f(u)}}{du} \cdot \frac{du(\gamma)}{d\gamma}\]

where we have \(\frac{d 10^{f(u(\gamma))}}{d\gamma} = \frac{d10^{f(u)}}{du} \cdot \frac{du(\gamma)}{d\gamma}\), where \(u\) is the \(log_{10}(\gamma)\). This is equal to \(\frac{d 10^{f(u(\gamma))}}{d\gamma} = 10^{f(u)} \cdot \frac{df(u)}{du} \cdot \frac{1}{\gamma}\)

evaluate(gamma, norm, gamma_min, gamma_max)[source]

log10_interpolation()[source]: Returns the function interpolating in log10 the particle spectrum. TODO: make possible to pass arguments to CubicSpline.

class agnpy.spectra.LogParabola(k=<Quantity 1.e-13 1 / cm3>, p=2.0, q=0.1, gamma_0=1000.0, gamma_min=10, gamma_max=10000000.0, mass=<<class 'astropy.constants.codata2018.CODATA2018'> name='Electron mass' value=9.1093837015e-31 uncertainty=2.8e-40 unit='kg' reference='CODATA 2018'>, integrator=<function trapz>)[source]

Bases: ParticleDistribution

Class describing a log-parabolic particle distribution. When called, the particle density \(n(\gamma)\) in \(\mathrm{cm}^{-3}\) is returned.

\[n(\gamma') = k \, \left(\frac{\gamma'}{\gamma'_0}\right)^{-(p + q \log_{10}(\gamma' / \gamma'_0))}\]

Parameters:

k (Quantity) – spectral normalisation
p (float) – spectral index, note it is positive by definition, will change sign in the function
q (float) – spectral curvature, note it is positive by definition, will change sign in the function
gamma_0 (float) – reference Lorentz factor
gamma_min (float) – minimum Lorentz factor of the particle distribution
gamma_max (float) – maximum Lorentz factor of the particle distribution
mass (Quantity) – particle mass, default is the electron mass
integrator (func) – function to be used for integration, default is trapz

SSA_integrand(gamma)[source]

static evaluate(gamma, k, p, q, gamma_0, gamma_min, gamma_max)[source]

static evaluate_SSA_integrand(gamma, k, p, q, gamma_0, gamma_min, gamma_max)[source]: Analytical integrand for the synchrotron self-absorption: \(\gamma'^2 \frac{d}{d \gamma'} \left(\frac{n_e(\gamma)}{\gamma'^2}\right)\).

property parameters

class agnpy.spectra.ParticleDistribution(mass=<<class 'astropy.constants.codata2018.CODATA2018'> name='Electron mass' value=9.1093837015e-31 uncertainty=2.8e-40 unit='kg' reference='CODATA 2018'>, integrator=<function trapz>)[source]

Bases: object

Base class grouping common functionalities to be used by all particles distributions.

Parameters:

mass (~astropy.units.Quantity) – particle mass, default is the electron mass
integrator (function) – function to be used to integrate the particle distribution

classmethod from_density_at_gamma_1(n_gamma_1, mass, **kwargs)[source]

Set the normalisation of the particle distribution, \(k [{\rm cm}^{-3}]\), such that norm = \(n(\gamma=1)\).

Parameters:

n_gamma_1 (Quantity) – value \(n(\gamma)\) should have at \(\gamma=1\), in cm-3
mass (Quantity) – particle mass

classmethod from_total_density(n_tot, mass, **kwargs)[source]

Set the normalisation of the particle distribution, \(k [{\rm cm}^{-3}]\), from the total particle density \(n_{\rm tot} [{\rm cm}^{-3}]\).

Parameters:

n_tot (Quantity) – total particle density (integral of \(n(\gamma)\)), in cm-3
mass (Quantity) – particle mass

classmethod from_total_energy(W, V, mass, **kwargs)[source]

Set the normalisation of the particle distribution, \(k [{\rm cm}^{-3}]\), based on the total energy in particles \(W = m c^2 \, \int {\rm d}\gamma \, \gamma \, n(\gamma)\).

Parameters:

W (Quantity) – total energy in particles, in erg
V (Quantity) – volume of the emission region, in cm^3
mass (~astropy.units.Quantity) – particle mass

classmethod from_total_energy_density(u_tot, mass, **kwargs)[source]

Set the normalisation of the particle distribution, \(k [{\rm cm}^{-3}]\), from the total energy density \(u_{\rm tot} [{\rm erg}{\rm cm}^{-3}]\), Eq. 6.64 in [DermerMenon2009].

Parameters:

u_tot (Quantity) – total energy density (integral of \(\gamma\,n(\gamma)\)), in erg cm-3
mass (Quantity) – particle mass

static integral(self, gamma_low, gamma_up, gamma_power=0, integrator=<function trapz>, **kwargs)[source]

Integral of the particle distribution over the range gamma_low, gamma_up for a general set of parameters.

Parameters:

gamma_low (float) – lower integration limit
gamma_up (float) – higher integration limit
gamma_power (int) – power of gamma to raise the particle distribution before integration
integrator (func) – function to be used for integration, default is trapz
kwargs (dict) – parameters of the particle distribution

integrate(gamma_low, gamma_up, gamma_power=0)[source]

Integral of this particular particle distribution over the range gamma_low, gamma_up.

Parameters:

gamma_low (float) – lower integration limit
gamma_up (float) – higher integration limit

plot(gamma=None, gamma_power=0, ax=None, **kwargs)[source]

Plot the particle energy distribution.

Parameters:

gamma (ndarray) – array of Lorentz factors over which to plot the SED
gamma_power (float) – power of gamma to raise the electron distribution
ax (Axes, optional) – Axis

class agnpy.spectra.PowerLaw(k=<Quantity 1.e-13 1 / cm3>, p=2.1, gamma_min=10, gamma_max=100000.0, mass=<<class 'astropy.constants.codata2018.CODATA2018'> name='Electron mass' value=9.1093837015e-31 uncertainty=2.8e-40 unit='kg' reference='CODATA 2018'>, integrator=<function trapz>)[source]

Bases: ParticleDistribution

Class describing a power-law particle distribution. When called, the particle density \(n(\gamma)\) in \(\mathrm{cm}^{-3}\) is returned.

\[n(\gamma') = k \, \gamma'^{-p} \, H(\gamma'; \gamma'_{\rm min}, \gamma'_{\rm max})\]

Parameters:

k (Quantity) – spectral normalisation
p (float) – spectral index, note it is positive by definition, will change sign in the function
gamma_min (float) – minimum Lorentz factor of the particle distribution
gamma_max (float) – maximum Lorentz factor of the particle distribution
mass (Quantity) – particle mass, default is the electron mass
integrator (func) – function to be used for integration, default is trapz

SSA_integrand(gamma)[source]

static evaluate(gamma, k, p, gamma_min, gamma_max)[source]

static evaluate_SSA_integrand(gamma, k, p, gamma_min, gamma_max)[source]: Analytical integrand for the synchrotron self-absorption: \(\gamma'^2 \frac{d}{d \gamma'} \left(\frac{n(\gamma)}{\gamma'^2}\right)\).

property parameters

agnpy.emission_regions module

class agnpy.emission_regions.Blob(R_b=<Quantity 1.e+16 cm>, z=0.069, delta_D=10, Gamma=10, B=<Quantity 1. G>, n_e=<agnpy.spectra.spectra.PowerLaw object>, n_p=None, xi=1.0, gamma_e_size=200, gamma_p_size=200)[source]

Bases: object

Simple spherical emission region.

Note: all these quantities are defined in the comoving frame so they are actually primed quantities, when referring the notation in [DermerMenon2009].

All the quantities returned from the base attributes (e.g. volume of the emission region and variability time scale are derived from the blob radius) will be returned as properties, such that their value will be updated if the parameter from which they are derived is updated.

Parameters:

R_b (Quantity) – radius of the blob
z (float) – redshift of the source
delta_D (float) – Doppler factor of the relativistic outflow
Gamma (float) – Lorentz factor of the relativistic outflow
B (Quantity) – magnetic field in the blob (Gauss)
n_e (ParticleDistribution) – electron distribution contained in the blob
n_p (ParticleDistribution) – proton distribution contained in the blob
xi (float) – acceleration coefficient \(\xi\) for first-order Fermi acceleration \((\mathrm{d}E/\mathrm{d}t \propto v \approx c)\) used to compute limits on the maximum Lorentz factor via \((\mathrm{d}E/\mathrm{d}t)_{\mathrm{acc}} = \xi c E / R_L\)
gamma_e_size (int) – size of the array of electrons Lorentz factors
gamma_p_size (int) – size of the array of protons Lorentz factors

property B_cgs: Magnetic field decomposed in Gaussian-cgs units.

property Beta: Bulk Lorentz factor of the Blob.

N_e(gamma)[source]

Number of electrons as a function of the Lorentz factor, \(N_{\rm e}(\gamma') = V_{\rm b}\,n_{\rm e}(\gamma')\).

Parameters:: gamma (ndarray) – array of Lorentz factor over which to evaluate the number of electrons

property N_e_tot: Total number of electrons

\[N_{\rm e,\,tot} = \int^{\gamma'_{\rm max}}_{\gamma'_{\rm min}} {\rm d}\gamma' N_{\rm e}(\gamma').\]

N_p(gamma)[source]

Number of protons as a function of the Lorentz factor, \(N_{\rm p}(\gamma') = V_{\rm b}\,n_{\rm p}(\gamma')\).

Parameters:: gamma (ndarray) – array of Lorentz factor over which to evaluate the number of electrons

property N_p_tot: total number of electrons

\[N_{\rm p,\,tot} = \int^{\gamma'_{\rm max}}_{\gamma'_{\rm min}} {\rm d}\gamma' N_{\rm p}(\gamma').\]

property P_jet_B: Jet power in magnetic field

\[P_{\mathrm{jet},\,B} = 2 \pi R_{\rm b}^2 \beta \Gamma^2 c \frac{B^2}{8\pi}.\]

property P_jet_ke: Total jet power in kinetic energy of the particles

\[P_{{\rm jet},\,{\rm ke}} = 2 \pi R_{\rm b}^2 \beta \Gamma^2 c (u_{\rm e} + u_{\rm p}).\]

property U_B: Energy density of magnetic field

\[U_B = B^2 / (8 \pi)\]

property V_b: Volume of the blob.

property W_e: Total energy in electrons

\[W_{\rm e} = m_{\rm e} c^2\,\int^{\gamma'_{\rm max}}_{\gamma'_{\rm min}} {\rm d}\gamma' \gamma' N_{\rm e}(\gamma').\]

property W_p: Total energy in protons

\[W_{\rm p} = m_{\rm p} c^2\,\int^{\gamma'_{\rm max}}_{\gamma'_{\rm min}} {\rm d}\gamma' \gamma' N_{\rm p}(\gamma').\]

property d_L: Luminosity distance.

property gamma_e: Array of electrons Lorentz factors, to be used for integration in the reference frame comoving with the emission region.

property gamma_e_external_frame: Array of electrons Lorentz factors, to be used for integration in the reference frame external to the emission region.

property gamma_p: Array of protons Lorentz factors, to be used for integration in the reference frame comoving with the emission region.

property k_eq

ratio between totoal particle energy density and magnetic field energy density, Eq. 7.75 of [DermerMenon2009]

Type:: Equipartition parameter

property mu_s: Cosine of the viewing angle from the jet axis to the observer.

property n_e: Electron distribution.

property n_e_tot: Total density of electrons

\[n_{\rm e,\,tot} = \int^{\gamma'_{\rm max}}_{\gamma'_{\rm min}} {\rm d}\gamma' n_{\rm e}(\gamma').\]

property n_p: Proton distribution.

property n_p_tot: Total density of protons

\[n_{\rm p,\,tot} = \int^{\gamma'_{\rm max}}_{\gamma'_{\rm min}} {\rm d}\gamma' n_{\rm p}(\gamma').\]

set_delta_D(Gamma, theta_s)[source]

Set the Doppler factor by specifying the bulk Lorentz factor of the outflow and the viewing angle.

Parameters:

Gamma (float) – Lorentz factor of the relativistic outflow
theta_s (Quantity) – viewing angle of the jet

set_gamma_e(gamma_size, gamma_min=1, gamma_max=100000000.0)[source]: Set the array of Lorentz factors for the electrons.

set_gamma_p(gamma_size, gamma_min=1, gamma_max=100000000.0)[source]: Set the array of Lorentz factors for the protons.

property t_var: Variability time scale, defined as \(t_{\rm var} = \frac{(1 + z) R_{\rm b}}{c \delta_{\rm D}}\).

property theta_s: Viewing angle from the jet axis to the observer.

property u_e: Total energy density of electrons

\[u_{\rm e} = m_{\rm e} c^2\,\int^{\gamma'_{\rm max}}_{\gamma'_{\rm min}} {\rm d}\gamma' \gamma' n_{\rm e}(\gamma').\]

property u_p: Total energy density of protons

\[u_{\rm p} = m_{\rm p} c^2\,\int^{\gamma'_{\rm max}}_{\gamma'_{\rm min}} {\rm d}\gamma' \gamma' n_{\rm p}(\gamma').\]

property u_ph_synch

Energy density of the synchrotron photons energy losses are:

\[(\mathrm{d}E/\mathrm{d}t)_{\mathrm{synch}} = 4 / 3 \sigma_T c U_B \gamma^2\]

the radiation stays an average time of \((3/4) (R_b/c)\) (the factor of 3/4 cames from averaging over a sphere), so an e- with Lorentz factor \(\gamma\) produces:

\[0.75\,(\mathrm{d}E/\mathrm{d}t)_{\mathrm{synch}}\,(R_b/c)\,/\,V_b\]

of radiation. We need to integrate over the electron spectrum (and multiply back by V_b)

\[0.75\,\int n_e(\gamma) (\mathrm{d}E/\mathrm{d}t)_{\mathrm{synch}} R_b \mathrm{d}\gamma\]

so

\[u_{\mathrm{synch}} = \sigma_T U_B R_b \int n_e(\gamma) \, \gamma^2 \mathrm{d}\gamma\]

WARNING: this does not take into account SSA!

agnpy.targets module

class agnpy.targets.CMB(z)[source]

Bases: object

Cosmic Microwave Background radiation, approximated as an isotropic monochromatic target.

Parameters:: z (float) – redshift at which the CMB is considered

u(blob=None)[source]

integral energy density of the CMB

Parameters:: blob (Blob) – if provided, the energy density is computed in a reference frame comvoing with the blob

class agnpy.targets.PointSourceBehindJet(L_0, epsilon_0)[source]

Bases: object

Monochromatic point source behind the jet.

Parameters:

L_0 (Quantity) – luminosity of the source
epsilon_0 (float) – dimensionless monochromatic energy of the source

u(r, blob=None)[source]

integral energy density of the point source at distance r along the jet axis

Parameters:

r (Quantity) – array of distances along the jet axis
blob (Blob) – if provided, the energy density is computed in a reference frame comvoing with the blob

class agnpy.targets.RingDustTorus(L_disk, xi_dt, T_dt, R_dt=None)[source]

Bases: object

Dust Torus as infinitesimally thin annulus, from [Finke2016]. For the Compton scattering monochromatic emission at the peak energy of the Black Body spectrum is considered.

Parameters:

L_disk (Quantity) – Luminosity of the disk whose radiation is being reprocessed by the Torus
xi_dt (float) – fraction of the disk radiation reprocessed
T_dt (Quantity) – peak temperature of the black body emission of the Torus
R_dt (Quantity) – radius of the Torus, if not specified the saturation radius of Eq. 96 in [Finke2016] will be used

static evaluate_bb_norm_sed(nu, z, L_dt, T_dt, R_dt, d_L)[source]: evaluate the torus black-body SED such that its integral luminosity is equal to the torus luminosity (xi_dt * L_disk)

static evaluate_bb_sed(nu, z, T_dt, R_dt, d_L)[source]: evaluate the black body SED corresponding to the torus temperature

sed_flux(nu, z)[source]: evaluate the black-body SED for the Dust Torus

u(r, blob=None)[source]

Density of radiation produced by the Torus at the distance r along the jet axis. Integral over the solid angle of Eq. 85 in [Finke2016]

Parameters:

r (Quantity) – array of distances along the jet axis
blob (Blob) – if provided, the energy density is computed in a reference frame comvoing with the blob

class agnpy.targets.SSDisk(M_BH, L_disk, eta, R_in, R_out, R_g_units=False)[source]

Bases: object

[Shakura1973] accretion disk as modeled by [Dermer2002]

Parameters:

M_BH (Quantity) – Black Hole mass
L_disk (Quantity) – luminosity of the disk
eta (float) – accretion efficiency
R_in (Quantity / float) – inner disk radius
R_out (Quantity / float) – outer disk radius
R_g_units (bool) – whether or not input radiuses are specified in units of the gravitational radius

T(R)[source]: temperature of the disk at radius \(R\). Eq. 64 in [Dermer2009].

epsilon(R_tilde)[source]: dimensionless energy emitted at the disk radius \(\tilde{R}\)

epsilon_mu(mu, r_tilde)[source]

static evaluate_T(R, M_BH, m_dot, R_in)[source]: black body temperature (K) at the radial coordinate R

static evaluate_epsilon(L_disk, M_BH, eta, R_tilde)[source]: evaluate the dimensionless energy emitted at the radius R_tilde Eq. 65 [Dermer2009]

static evaluate_epsilon_mu(L_disk, M_BH, eta, mu, r_tilde)[source]: same as evaluate_epsilon() but considering the cosine of the subtended zenith mu and the height above the disk r instead of the radius R_tilde

static evaluate_mu_from_r_tilde(R_in_tilde, R_out_tilde, r_tilde, size=100)[source]: array of cosine angles, spanning from \(R_{\mathrm{in}}\) to \(R_{\mathrm{out}}\), viewed from a given height \(\tilde{r}\) above the disk, Eq. 72 and 73 in [Finke2016].

static evaluate_multi_T_bb_norm_sed(nu, z, L_disk, M_BH, m_dot, R_in, R_out, d_L, mu_s=1)[source]: Evaluate a normalised, multi-temperature black body SED as in evaluate_multi_T_bb_sed(), but the integral luminosity is set to be equal to L_disk.

static evaluate_multi_T_bb_sed(nu, z, M_BH, m_dot, R_in, R_out, d_L, mu_s=1)[source]

Evaluate a multi-temperature black body SED in the case of the SS Disk. The SED is calculated for an observer far away from the disk (\(d_L \gg R\)) with the following:

\[\nu F_{\nu} \approx \mu_s \, \nu \frac{2 \pi}{d_L^2} \int_{R_{\rm in}}^{R_{\rm out}}{\rm d}R \, R \, I_{\nu}(T(R)),\]

where \(I_{\nu}\) is Planck’s law, \(R\) the radial coordinate along the disk, and \(d_L\) the luminosity distance. \(\mu_s\) is the cosine of the angle between the disk axis and the observer’s line of sight.

Parameters:

nu (Quantity) – array of frequencies, in Hz, to compute the sed note these are observed frequencies (observer frame)
z (float) – redshift of the source
M_BH (Quantity) – Black Hole mass
m_dot (float) – mass accretion rate
R_in (Quantity) – inner disk radius
R_out (Quantity) – outer disk radius
d_L (Quantity) – luminosity of the source
mu_s (float) – cosine of the angle between the observer line of sight and the disk axis

static evaluate_phi_disk_mu(mu, R_in_tilde, r_tilde)[source]: dependency of the radiant surface-energy flux from the disk radius, here obtained from the cosine of the zenith mu and the height above the disk r_tilde (in graviational radius units), Eq. 63 [Dermer2009]

phi_disk(R_tilde)[source]

phi_disk_mu(mu, r_tilde)[source]

sed_flux(nu, z, mu_s=1)[source]: evaluate the multi-temperature black body SED for this SS Disk, refer to evaluate_multi_T_bb_sed() and to evaluate_multi_T_bb_norm_sed()

u(r, blob=None)[source]

integral energy density of radiation produced by the Disk at the distance r along the jet axis. Integral over the solid angle of Eq. 69 in [Dermer2009].

Parameters:

r (Quantity) – array of distances along the jet axis
blob (Blob) – if provided, the energy density is computed in a reference frame comvoing with the blob

class agnpy.targets.SphericalShellBLR(L_disk, xi_line, line, R_line)[source]

Bases: object

Spherical Shell Broad Line Region, from [Finke2016]. Each line is emitted from an infinitesimally thin spherical shell.

Parameters:

L_disk (Quantity) – Luminosity of the disk whose radiation is being reprocessed by the BLR
xi_line (float) – fraction of the disk radiation reprocessed by the BLR
line (string) – type of line emitted
R_line (Quantity) – radius of the BLR spherical shell

print_lines_list()[source]: Print the list of the available spectral lines. The dictionary with the possible emission lines is taken from Table 5 in [Finke2016] and contains the value of the line wavelength and the ratio of its radius to the radius of the \(H_{\beta}\) shell, not used at the moment.

u(r, blob=None)[source]

Density of radiation produced by the BLR at the distance r along the jet axis. Integral over the solid angle of Eq. 80 in [Finke2016].

Parameters:

r (Quantity) – array of distances along the jet axis
blob (Blob) – if provided, the energy density is computed in a reference frame comvoing with the blob

agnpy.synchrotron module

class agnpy.synchrotron.ProtonSynchrotron(blob, integrator=<function trapz>)[source]

Bases: object

Class for synchrotron radiation computation

Parameters:

blob (Blob) – emitting region and proton distribution
ssa (bool) – whether or not to consider synchrotron self absorption (SSA). The absorption factor will be taken into account in com_sed_emissivity(), in order to be propagated to sed_luminosity() and sed_flux().
integrator (func) – function to be used for integration (default = np.trapz)

static evaluate_sed_flux(nu, z, d_L, delta_D, B, R_b, n_p, *args, integrator=<function trapz>, gamma=array([1.00000000e+01, 1.09698580e+01, 1.20337784e+01, 1.32008840e+01, 1.44811823e+01, 1.58856513e+01, 1.74263339e+01, 1.91164408e+01, 2.09704640e+01, 2.30043012e+01, 2.52353917e+01, 2.76828663e+01, 3.03677112e+01, 3.33129479e+01, 3.65438307e+01, 4.00880633e+01, 4.39760361e+01, 4.82410870e+01, 5.29197874e+01, 5.80522552e+01, 6.36824994e+01, 6.98587975e+01, 7.66341087e+01, 8.40665289e+01, 9.22197882e+01, 1.01163798e+02, 1.10975250e+02, 1.21738273e+02, 1.33545156e+02, 1.46497140e+02, 1.60705282e+02, 1.76291412e+02, 1.93389175e+02, 2.12145178e+02, 2.32720248e+02, 2.55290807e+02, 2.80050389e+02, 3.07211300e+02, 3.37006433e+02, 3.69691271e+02, 4.05546074e+02, 4.44878283e+02, 4.88025158e+02, 5.35356668e+02, 5.87278661e+02, 6.44236351e+02, 7.06718127e+02, 7.75259749e+02, 8.50448934e+02, 9.32930403e+02, 1.02341140e+03, 1.12266777e+03, 1.23155060e+03, 1.35099352e+03, 1.48202071e+03, 1.62575567e+03, 1.78343088e+03, 1.95639834e+03, 2.14614120e+03, 2.35428641e+03, 2.58261876e+03, 2.83309610e+03, 3.10786619e+03, 3.40928507e+03, 3.73993730e+03, 4.10265811e+03, 4.50055768e+03, 4.93704785e+03, 5.41587138e+03, 5.94113398e+03, 6.51733960e+03, 7.14942899e+03, 7.84282206e+03, 8.60346442e+03, 9.43787828e+03, 1.03532184e+04, 1.13573336e+04, 1.24588336e+04, 1.36671636e+04, 1.49926843e+04, 1.64467618e+04, 1.80418641e+04, 1.97916687e+04, 2.17111795e+04, 2.38168555e+04, 2.61267523e+04, 2.86606762e+04, 3.14403547e+04, 3.44896226e+04, 3.78346262e+04, 4.15040476e+04, 4.55293507e+04, 4.99450512e+04, 5.47890118e+04, 6.01027678e+04, 6.59318827e+04, 7.23263390e+04, 7.93409667e+04, 8.70359136e+04, 9.54771611e+04, 1.04737090e+05, 1.14895100e+05, 1.26038293e+05, 1.38262217e+05, 1.51671689e+05, 1.66381689e+05, 1.82518349e+05, 2.00220037e+05, 2.19638537e+05, 2.40940356e+05, 2.64308149e+05, 2.89942285e+05, 3.18062569e+05, 3.48910121e+05, 3.82749448e+05, 4.19870708e+05, 4.60592204e+05, 5.05263107e+05, 5.54266452e+05, 6.08022426e+05, 6.66991966e+05, 7.31680714e+05, 8.02643352e+05, 8.80488358e+05, 9.65883224e+05, 1.05956018e+06, 1.16232247e+06, 1.27505124e+06, 1.39871310e+06, 1.53436841e+06, 1.68318035e+06, 1.84642494e+06, 2.02550194e+06, 2.22194686e+06, 2.43744415e+06, 2.67384162e+06, 2.93316628e+06, 3.21764175e+06, 3.52970730e+06, 3.87203878e+06, 4.24757155e+06, 4.65952567e+06, 5.11143348e+06, 5.60716994e+06, 6.15098579e+06, 6.74754405e+06, 7.40196000e+06, 8.11984499e+06, 8.90735464e+06, 9.77124154e+06, 1.07189132e+07, 1.17584955e+07, 1.28989026e+07, 1.41499130e+07, 1.55222536e+07, 1.70276917e+07, 1.86791360e+07, 2.04907469e+07, 2.24780583e+07, 2.46581108e+07, 2.70495973e+07, 2.96730241e+07, 3.25508860e+07, 3.57078596e+07, 3.91710149e+07, 4.29700470e+07, 4.71375313e+07, 5.17092024e+07, 5.67242607e+07, 6.22257084e+07, 6.82607183e+07, 7.48810386e+07, 8.21434358e+07, 9.01101825e+07, 9.88495905e+07, 1.08436597e+08, 1.18953407e+08, 1.30490198e+08, 1.43145894e+08, 1.57029012e+08, 1.72258597e+08, 1.88965234e+08, 2.07292178e+08, 2.27396575e+08, 2.49450814e+08, 2.73644000e+08, 3.00183581e+08, 3.29297126e+08, 3.61234270e+08, 3.96268864e+08, 4.34701316e+08, 4.76861170e+08, 5.23109931e+08, 5.73844165e+08, 6.29498899e+08, 6.90551352e+08, 7.57525026e+08, 8.30994195e+08, 9.11588830e+08, 1.00000000e+09]))[source]

Evaluates the flux SED (\(\nu F_{\nu}\)) due to synchrotron radiation, for a general set of model parameters. As for electrons, we implement Eq. 21 in [Finke2008] with just a change in the mass value (we are using the proton mass now). For a reference on proton synchrotron and other hadronic processes see [Cerruti2015].

Note parameters after *args need to be passed with a keyword

Parameters:

nu (Quantity) – array of frequencies, in Hz, to compute the sed note these are observed frequencies (observer frame)
z (float) – redshift of the source
d_L (Quantity) – luminosity distance of the source
delta_D (float) – Doppler factor of the relativistic outflow
B (Quantity) – magnetic field in the blob
R_b (Quantity) – size of the emitting region (spherical blob assumed)
n_p (ProtonDistribution) – proton energy distribution
*args – parameters of the proton energy distribution (k_e, p, …)
ssa (#) –
self-absorption (# whether to consider or not the) –
false (default) –
integrator (func) – which function to use for integration, default numpy.trapz
gamma (ndarray) – array of Lorentz factor over which to integrate the proton distribution

Returns:

array of the SED values corresponding to each frequency

Return type:

agnpy package

Modules

agnpy.spectra module

agnpy.emission_regions module

agnpy.targets module

agnpy.synchrotron module

agnpy.compton module

agnpy.absorption module

agnpy.constraints module

agnpy.fit module