External Compton#

The external Compton implementation gives you the possibility to use a double approach

transformation of the external fields to the blob rest frame Dermer and Schlickeiser (2002) [Dermer2002], Dermer and Menon (2009) [DermerMenon2009]
transformation of the electron emitting distribution from the blob restframe to disk/BH restframe Dermer(1995) [Dermer95] and Georganopoulos, Kirk, and Mastichiadis (2001) [GKM01], Dermer and Menon (2009) [DermerMenon2009]

The implemented external radiative fields are

Broad Line Region radiative field using the approach of Donea & Protheroe (2003) [Donea2003]
Dusty torus implemented as a uniform BB field within R_DT
accretion disk (mono-energetic, single-temperature BB or a multi-temperature BB)
Cosmic Microwave Background (CMB)

Please read jet_physical_guide_SSC if you skipped it.

Broad Line Region#

import jetset
print('tested on jetset',jetset.__version__)

tested on jetset 1.3.0rc8

import matplotlib.pyplot as plt
import numpy as np

from jetset.jet_model import Jet
my_jet=Jet(name='EC_example',electron_distribution='bkn',beaming_expr='bulk_theta')
my_jet.add_EC_component(['EC_BLR','EC_Disk'],disk_type='BB')

===> setting C threads to 12

The show_model method provides, among other information, information concerning the accretion disk, in this case we use a mono temperature black body BB

my_jet.show_model()

--------------------------------------------------------------------------------
model description:
--------------------------------------------------------------------------------
type: Jet
name: EC_example
geometry: spherical

electrons distribution:
 type: bkn
 gamma energy grid size:  201
 gmin grid : 2.000000e+00
 gmax grid : 1.000000e+06
 normalization:  True
 log-values:  False
 ratio of cold protons to relativistic electrons: 1.000000e+00

accretion disk:
 disk Type: BB
 L disk: 1.000000e+45 (erg/s)
 T disk: 1.000000e+05 (K)
 nu peak disk: 8.171810e+15 (Hz)
radiative fields:
 seed photons grid size:  100
 IC emission grid size:  100
 source emissivity lower bound :  1.000000e-120
 spectral components:
   name:Sum, state: on
   name:Sum, hidden: False
   name:Sync, state: self-abs
   name:Sync, hidden: False
   name:SSC, state: on
   name:SSC, hidden: False
   name:EC_BLR, state: on
   name:EC_BLR, hidden: False
   name:Disk, state: on
   name:Disk, hidden: False
   name:EC_Disk, state: on
   name:EC_Disk, hidden: False
external fields transformation method: blob

SED info:
 nu grid size jetkernel: 1000
 nu size: 500
 nu mix (Hz): 1.000000e+06
 nu max (Hz): 1.000000e+30

flux plot lower bound   :  1.000000e-30

--------------------------------------------------------------------------------

Table length=18

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
EC_example	R	region_size	cm	5.000000e+15	1.000000e+03	1.000000e+30	False	False
EC_example	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
EC_example	B	magnetic_field	gauss	1.000000e-01	0.000000e+00	--	False	False
EC_example	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
EC_example	theta	jet-viewing-angle	deg	1.000000e-01	0.000000e+00	9.000000e+01	False	False
EC_example	BulkFactor	jet-bulk-factor	lorentz-factor*	1.000000e+01	1.000000e+00	1.000000e+05	False	False
EC_example	z_cosm	redshift		1.000000e-01	0.000000e+00	--	False	False
EC_example	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
EC_example	gmax	high-energy-cut-off	lorentz-factor*	1.000000e+06	1.000000e+00	1.000000e+15	False	False
EC_example	N	emitters_density	1 / cm3	1.000000e+02	0.000000e+00	--	False	False
EC_example	gamma_break	turn-over-energy	lorentz-factor*	1.000000e+04	1.000000e+00	1.000000e+09	False	False
EC_example	p	LE_spectral_slope		2.500000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	p_1	HE_spectral_slope		3.500000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	tau_BLR	BLR		1.000000e-01	0.000000e+00	1.000000e+00	False	False
EC_example	R_BLR_in	BLR	cm	1.000000e+18	0.000000e+00	--	False	True
EC_example	R_BLR_out	BLR	cm	2.000000e+18	0.000000e+00	--	False	True
EC_example	L_Disk	Disk	erg / s	1.000000e+45	0.000000e+00	--	False	False
EC_example	T_Disk	Disk	K	1.000000e+05	0.000000e+00	--	False	False

--------------------------------------------------------------------------------

change Disk type#

the disk type can be set as a more realistic multi temperature black body (MultiBB). In this case the show_model method provides physical parameters regarding the multi temperature black body accretion disk:

the Schwarzschild (Sw radius)
the Eddington luminosity (L Edd.)
the accretion rate (accr_rate)
the Eddington accretion rate (accr_rate Edd.)

my_jet.add_EC_component(['EC_BLR','EC_Disk'],disk_type='MultiBB')
my_jet.set_par('L_Disk',val=1E46)
my_jet.set_par('gmax',val=5E4)
my_jet.set_par('gmin',val=2.)
my_jet.set_par('R_H',val=1E17)

my_jet.set_par('p',val=1.5)
my_jet.set_par('p_1',val=3.2)
my_jet.set_par('R',val=1E16)
my_jet.set_par('B',val=1.5)
my_jet.set_par('z_cosm',val=0.6)
my_jet.set_par('BulkFactor',val=20)
my_jet.set_par('theta',val=1)
my_jet.set_par('gamma_break',val=5E2)
my_jet.set_N_from_nuLnu(nu_src=3E13,nuLnu_src=5E45)
my_jet.set_IC_nu_size(100)
my_jet.show_model()

--------------------------------------------------------------------------------
model description:
--------------------------------------------------------------------------------
type: Jet
name: EC_example
geometry: spherical

electrons distribution:
 type: bkn
 gamma energy grid size:  201
 gmin grid : 2.000000e+00
 gmax grid : 5.000000e+04
 normalization:  True
 log-values:  False
 ratio of cold protons to relativistic electrons: 1.000000e+00

accretion disk:
 disk Type: MultiBB
 L disk: 1.000000e+46 (erg/s)
 T disk: 5.015768e+04 (K)
 nu peak disk: 4.098790e+15 (Hz)
 Sw radius 2.953539e+14 (cm)
 L Edd. 1.300000e+47 (erg/s)
 accr_rate: 2.205171e+00 (M_sun/yr)
 accr_rate Edd.: 2.866722e+01 (M_sun/yr)
radiative fields:
 seed photons grid size:  100
 IC emission grid size:  100
 source emissivity lower bound :  1.000000e-120
 spectral components:
   name:Sum, state: on
   name:Sum, hidden: False
   name:Sync, state: self-abs
   name:Sync, hidden: False
   name:SSC, state: on
   name:SSC, hidden: False
   name:EC_BLR, state: on
   name:EC_BLR, hidden: False
   name:Disk, state: on
   name:Disk, hidden: False
   name:EC_Disk, state: on
   name:EC_Disk, hidden: False
external fields transformation method: blob

SED info:
 nu grid size jetkernel: 1000
 nu size: 500
 nu mix (Hz): 1.000000e+06
 nu max (Hz): 1.000000e+30

flux plot lower bound   :  1.000000e-30

--------------------------------------------------------------------------------

Table length=21

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
EC_example	R	region_size	cm	1.000000e+16	1.000000e+03	1.000000e+30	False	False
EC_example	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
EC_example	B	magnetic_field	gauss	1.500000e+00	0.000000e+00	--	False	False
EC_example	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
EC_example	theta	jet-viewing-angle	deg	1.000000e+00	0.000000e+00	9.000000e+01	False	False
EC_example	BulkFactor	jet-bulk-factor	lorentz-factor*	2.000000e+01	1.000000e+00	1.000000e+05	False	False
EC_example	z_cosm	redshift		6.000000e-01	0.000000e+00	--	False	False
EC_example	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
EC_example	gmax	high-energy-cut-off	lorentz-factor*	5.000000e+04	1.000000e+00	1.000000e+15	False	False
EC_example	N	emitters_density	1 / cm3	1.126221e+02	0.000000e+00	--	False	False
EC_example	gamma_break	turn-over-energy	lorentz-factor*	5.000000e+02	1.000000e+00	1.000000e+09	False	False
EC_example	p	LE_spectral_slope		1.500000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	p_1	HE_spectral_slope		3.200000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	tau_BLR	BLR		1.000000e-01	0.000000e+00	1.000000e+00	False	False
EC_example	R_BLR_in	BLR	cm	1.000000e+18	0.000000e+00	--	False	True
EC_example	R_BLR_out	BLR	cm	2.000000e+18	0.000000e+00	--	False	True
EC_example	R_inner_Sw	Disk	Sw. radii*	3.000000e+00	0.000000e+00	--	False	False
EC_example	R_ext_Sw	Disk	Sw. radii*	5.000000e+02	0.000000e+00	--	False	False
EC_example	accr_eff	Disk		8.000000e-02	6.000000e-02	1.000000e-01	False	False
EC_example	M_BH	Disk	M_sun*	1.000000e+09	0.000000e+00	--	False	False
EC_example	L_Disk	Disk	erg / s	1.000000e+46	0.000000e+00	--	False	False

--------------------------------------------------------------------------------

now we set some parameter for the model

my_jet.eval()

p=my_jet.plot_model(frame='obs')
p.setlim(y_min=1E-13,y_max=5E-11,x_min=1E9,x_max=1E27)

../../../../_images/Jet_example_phys_EC_16_0.png

Dusty Torus#

my_jet.add_EC_component('DT')
my_jet.show_model()

--------------------------------------------------------------------------------
model description:
--------------------------------------------------------------------------------
type: Jet
name: EC_example
geometry: spherical

electrons distribution:
 type: bkn
 gamma energy grid size:  201
 gmin grid : 2.000000e+00
 gmax grid : 5.000000e+04
 normalization:  True
 log-values:  False
 ratio of cold protons to relativistic electrons: 1.000000e+00

accretion disk:
 disk Type: MultiBB
 L disk: 1.000000e+46 (erg/s)
 T disk: 5.015768e+04 (K)
 nu peak disk: 4.098790e+15 (Hz)
 Sw radius 2.953539e+14 (cm)
 L Edd. 1.300000e+47 (erg/s)
 accr_rate: 2.205171e+00 (M_sun/yr)
 accr_rate Edd.: 2.866722e+01 (M_sun/yr)
radiative fields:
 seed photons grid size:  100
 IC emission grid size:  100
 source emissivity lower bound :  1.000000e-120
 spectral components:
   name:Sum, state: on
   name:Sum, hidden: False
   name:Sync, state: self-abs
   name:Sync, hidden: False
   name:SSC, state: on
   name:SSC, hidden: False
   name:EC_BLR, state: on
   name:EC_BLR, hidden: False
   name:Disk, state: on
   name:Disk, hidden: False
   name:EC_Disk, state: on
   name:EC_Disk, hidden: False
   name:DT, state: on
   name:DT, hidden: False
external fields transformation method: blob

SED info:
 nu grid size jetkernel: 1000
 nu size: 500
 nu mix (Hz): 1.000000e+06
 nu max (Hz): 1.000000e+30

flux plot lower bound   :  1.000000e-30

--------------------------------------------------------------------------------

Table length=24

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
EC_example	R	region_size	cm	1.000000e+16	1.000000e+03	1.000000e+30	False	False
EC_example	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
EC_example	B	magnetic_field	gauss	1.500000e+00	0.000000e+00	--	False	False
EC_example	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
EC_example	theta	jet-viewing-angle	deg	1.000000e+00	0.000000e+00	9.000000e+01	False	False
EC_example	BulkFactor	jet-bulk-factor	lorentz-factor*	2.000000e+01	1.000000e+00	1.000000e+05	False	False
EC_example	z_cosm	redshift		6.000000e-01	0.000000e+00	--	False	False
EC_example	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
EC_example	gmax	high-energy-cut-off	lorentz-factor*	5.000000e+04	1.000000e+00	1.000000e+15	False	False
EC_example	N	emitters_density	1 / cm3	1.126221e+02	0.000000e+00	--	False	False
EC_example	gamma_break	turn-over-energy	lorentz-factor*	5.000000e+02	1.000000e+00	1.000000e+09	False	False
EC_example	p	LE_spectral_slope		1.500000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	p_1	HE_spectral_slope		3.200000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	tau_BLR	BLR		1.000000e-01	0.000000e+00	1.000000e+00	False	False
EC_example	R_BLR_in	BLR	cm	1.000000e+18	0.000000e+00	--	False	True
EC_example	R_BLR_out	BLR	cm	2.000000e+18	0.000000e+00	--	False	True
EC_example	T_DT	DT	K	1.000000e+02	0.000000e+00	--	False	False
EC_example	R_DT	DT	cm	5.000000e+18	0.000000e+00	--	False	False
EC_example	tau_DT	DT		1.000000e-01	0.000000e+00	1.000000e+00	False	False
EC_example	L_Disk	Disk	erg / s	1.000000e+46	0.000000e+00	--	False	False
EC_example	R_inner_Sw	Disk	Sw. radii*	3.000000e+00	0.000000e+00	--	False	False
EC_example	R_ext_Sw	Disk	Sw. radii*	5.000000e+02	0.000000e+00	--	False	False
EC_example	accr_eff	Disk		8.000000e-02	6.000000e-02	1.000000e-01	False	False
EC_example	M_BH	Disk	M_sun*	1.000000e+09	0.000000e+00	--	False	False

--------------------------------------------------------------------------------

my_jet.eval()

p=my_jet.plot_model()
p.setlim(y_min=1E-13,y_max=5E-11,x_min=1E9,x_max=1E27)

../../../../_images/Jet_example_phys_EC_20_0.png

my_jet.save_model('test_EC_model.pkl')

my_jet=Jet.load_model('test_EC_model.pkl')

===> setting C threads to 12

my_jet.eval()

p=my_jet.plot_model(frame='obs')
p.setlim(y_min=1E-13,y_max=5E-11,x_min=1E9,x_max=1E27)

../../../../_images/Jet_example_phys_EC_24_0.png

setting the BLR and DT radius as a function of the disk luminosity#

Using the depending parameters (see Depending parameters, for more details) we can set the BLR and DT radius, as a function of the disk luminosity

#kaspi+ 2007:https://iopscience.iop.org/article/10.1086/512094/pdf
my_jet.make_dependent_par(par='R_BLR_in', depends_on=['L_Disk'], par_expr='1E17*(L_Disk/1E46)**0.5')

my_jet.make_dependent_par(par='R_BLR_out', depends_on=['R_BLR_in'], par_expr='R_BLR_in*1.1')

#Cleary+ 2007:https://iopscience.iop.org/article/10.1086/511969/pdf
my_jet.make_dependent_par(par='R_DT', depends_on=['L_Disk'], par_expr='2E19*(L_Disk/1E46)**0.5')

adding par: L_Disk to  R_BLR_in
==> par R_BLR_in is depending on ['L_Disk'] according to expr:   R_BLR_in =
1E17*(L_Disk/1E46)**0.5
adding par: R_BLR_in to  R_BLR_out
==> par R_BLR_out is depending on ['R_BLR_in'] according to expr:   R_BLR_out =
R_BLR_in*1.1
adding par: L_Disk to  R_DT
==> par R_DT is depending on ['L_Disk'] according to expr:   R_DT =
2E19*(L_Disk/1E46)**0.5

my_jet.parameters.L_Disk.val=5E45

my_jet.parameters

Table length=24

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
EC_example	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
EC_example	gmax	high-energy-cut-off	lorentz-factor*	5.000000e+04	1.000000e+00	1.000000e+15	False	False
EC_example	N	emitters_density	1 / cm3	1.126221e+02	0.000000e+00	--	False	False
EC_example	gamma_break	turn-over-energy	lorentz-factor*	5.000000e+02	1.000000e+00	1.000000e+09	False	False
EC_example	p	LE_spectral_slope		1.500000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	p_1	HE_spectral_slope		3.200000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	tau_BLR	BLR		1.000000e-01	0.000000e+00	1.000000e+00	False	False
EC_example	*R_BLR_in(D,L_Disk)	BLR	cm	7.071068e+16	0.000000e+00	--	False	True
EC_example	*R_BLR_out(D,R_BLR_in)	BLR	cm	7.778175e+16	0.000000e+00	--	False	True
EC_example	R_inner_Sw	Disk	Sw. radii*	3.000000e+00	0.000000e+00	--	False	False
EC_example	R_ext_Sw	Disk	Sw. radii*	5.000000e+02	0.000000e+00	--	False	False
EC_example	accr_eff	Disk		8.000000e-02	6.000000e-02	1.000000e-01	False	False
EC_example	M_BH	Disk	M_sun*	1.000000e+09	0.000000e+00	--	False	False
EC_example	T_DT	DT	K	1.000000e+02	0.000000e+00	--	False	False
EC_example	*R_DT(D,L_Disk)	DT	cm	1.414214e+19	0.000000e+00	--	False	True
EC_example	tau_DT	DT		1.000000e-01	0.000000e+00	1.000000e+00	False	False
EC_example	L_Disk(M)	Disk	erg / s	5.000000e+45	0.000000e+00	--	False	False
EC_example	R	region_size	cm	1.000000e+16	1.000000e+03	1.000000e+30	False	False
EC_example	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
EC_example	B	magnetic_field	gauss	1.500000e+00	0.000000e+00	--	False	False
EC_example	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
EC_example	theta	jet-viewing-angle	deg	1.000000e+00	0.000000e+00	9.000000e+01	False	False
EC_example	BulkFactor	jet-bulk-factor	lorentz-factor*	2.000000e+01	1.000000e+00	1.000000e+05	False	False
EC_example	z_cosm	redshift		6.000000e-01	0.000000e+00	--	False	False

None

my_jet.eval()
p=my_jet.plot_model()
p.setlim(y_min=1E-13,y_max=1E-10,x_min=1E9,x_max=1E27)

../../../../_images/Jet_example_phys_EC_30_0.png

Important

Starting from version 1.3.0 there are two convenience methods to set the EC dependencies and setting the jet with a conical profile

method JetBase.make_conical_jet() class will set parameters dependencies to have conical jet constraining the blob radius
method JetBase.set_EC_dependencies() class will set parameters dependencies to have scaling relations between BLR and DT radius and disk luminosity

Important

if you use a jet model with R depending (i.e. you used JetBase.make_conical_jet()) to perform a temporal evolution (in the JetTimeEvol class), the dependencies on R will be removed, and to have R dependent on the position across the jet axis, use the parameter beta_exp_R in the JetTimeEvol instead. In the next release a more flexible and direct approach will be provided.

my_jet.make_conical_jet(theta_open=5,R=1E16)

adding par: R_H to  R
adding par: theta_open to  R
==> par R is depending on ['R_H', 'theta_open'] according to expr:   R =
np.tan(np.radians(theta_open))*R_H
setting R_H to 1.1430052302761344e+17

my_jet.parameters

Table length=25

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
EC_example	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
EC_example	gmax	high-energy-cut-off	lorentz-factor*	5.000000e+04	1.000000e+00	1.000000e+15	False	False
EC_example	N	emitters_density	1 / cm3	1.126221e+02	0.000000e+00	--	False	False
EC_example	gamma_break	turn-over-energy	lorentz-factor*	5.000000e+02	1.000000e+00	1.000000e+09	False	False
EC_example	p	LE_spectral_slope		1.500000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	p_1	HE_spectral_slope		3.200000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	tau_BLR	BLR		1.000000e-01	0.000000e+00	1.000000e+00	False	False
EC_example	*R_BLR_in(D,L_Disk)	BLR	cm	7.071068e+16	0.000000e+00	--	False	True
EC_example	*R_BLR_out(D,R_BLR_in)	BLR	cm	7.778175e+16	0.000000e+00	--	False	True
EC_example	R_inner_Sw	Disk	Sw. radii*	3.000000e+00	0.000000e+00	--	False	False
EC_example	R_ext_Sw	Disk	Sw. radii*	5.000000e+02	0.000000e+00	--	False	False
EC_example	accr_eff	Disk		8.000000e-02	6.000000e-02	1.000000e-01	False	False
EC_example	M_BH	Disk	M_sun*	1.000000e+09	0.000000e+00	--	False	False
EC_example	T_DT	DT	K	1.000000e+02	0.000000e+00	--	False	False
EC_example	*R_DT(D,L_Disk)	DT	cm	1.414214e+19	0.000000e+00	--	False	True
EC_example	tau_DT	DT		1.000000e-01	0.000000e+00	1.000000e+00	False	False
EC_example	L_Disk(M)	Disk	erg / s	5.000000e+45	0.000000e+00	--	False	False
EC_example	R	region_size	cm	1.000000e+16	1.000000e+03	1.000000e+30	False	True
EC_example	R_H(M)	region_position	cm	1.143005e+17	0.000000e+00	--	False	False
EC_example	B	magnetic_field	gauss	1.500000e+00	0.000000e+00	--	False	False
EC_example	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
EC_example	theta	jet-viewing-angle	deg	1.000000e+00	0.000000e+00	9.000000e+01	False	False
EC_example	BulkFactor	jet-bulk-factor	lorentz-factor*	2.000000e+01	1.000000e+00	1.000000e+05	False	False
EC_example	z_cosm	redshift		6.000000e-01	0.000000e+00	--	False	False
EC_example	theta_open(M)	user_defined	deg	5.000000e+00	1.000000e+00	1.000000e+01	False	False

None

my_jet.set_EC_dependencies()

==> par R_BLR_in is depending on ['L_Disk'] according to expr:   R_BLR_in =
3E17*(L_Disk/1E46)**0.5
==> par R_BLR_out is depending on ['R_BLR_in'] according to expr:   R_BLR_out =
R_BLR_in*1.1
==> par R_DT is depending on ['L_Disk'] according to expr:   R_DT =
2E19*(L_Disk/1E46)**0.5

my_jet.parameters

Table length=25

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
EC_example	gmin	low-energy-cut-off	lorentz-factor*	2.000000e+00	1.000000e+00	1.000000e+09	False	False
EC_example	gmax	high-energy-cut-off	lorentz-factor*	5.000000e+04	1.000000e+00	1.000000e+15	False	False
EC_example	N	emitters_density	1 / cm3	1.126221e+02	0.000000e+00	--	False	False
EC_example	gamma_break	turn-over-energy	lorentz-factor*	5.000000e+02	1.000000e+00	1.000000e+09	False	False
EC_example	p	LE_spectral_slope		1.500000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	p_1	HE_spectral_slope		3.200000e+00	-1.000000e+01	1.000000e+01	False	False
EC_example	tau_BLR	BLR		1.000000e-01	0.000000e+00	1.000000e+00	False	False
EC_example	*R_BLR_in(D,L_Disk)	BLR	cm	7.071068e+16	0.000000e+00	--	False	True
EC_example	*R_BLR_out(D,R_BLR_in)	BLR	cm	7.778175e+16	0.000000e+00	--	False	True
EC_example	R_inner_Sw	Disk	Sw. radii*	3.000000e+00	0.000000e+00	--	False	False
EC_example	R_ext_Sw	Disk	Sw. radii*	5.000000e+02	0.000000e+00	--	False	False
EC_example	accr_eff	Disk		8.000000e-02	6.000000e-02	1.000000e-01	False	False
EC_example	M_BH	Disk	M_sun*	1.000000e+09	0.000000e+00	--	False	False
EC_example	T_DT	DT	K	1.000000e+02	0.000000e+00	--	False	False
EC_example	*R_DT(D,L_Disk)	DT	cm	1.414214e+19	0.000000e+00	--	False	True
EC_example	tau_DT	DT		1.000000e-01	0.000000e+00	1.000000e+00	False	False
EC_example	L_Disk(M)	Disk	erg / s	5.000000e+45	0.000000e+00	--	False	False
EC_example	*R(D,theta_open)	region_size	cm	1.000000e+16	1.000000e+03	1.000000e+30	False	True
EC_example	R_H(M)	region_position	cm	1.143005e+17	0.000000e+00	--	False	False
EC_example	B	magnetic_field	gauss	1.500000e+00	0.000000e+00	--	False	False
EC_example	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
EC_example	theta	jet-viewing-angle	deg	1.000000e+00	0.000000e+00	9.000000e+01	False	False
EC_example	BulkFactor	jet-bulk-factor	lorentz-factor*	2.000000e+01	1.000000e+00	1.000000e+05	False	False
EC_example	z_cosm	redshift		6.000000e-01	0.000000e+00	--	False	False
EC_example	theta_open(M)	user_defined	deg	5.000000e+00	1.000000e+00	1.000000e+01	False	False

None

my_jet.eval()
p=my_jet.plot_model()
p.setlim(y_min=1E-13,y_max=5E-11,x_min=1E9,x_max=1E27)

../../../../_images/Jet_example_phys_EC_37_0.png

Changing the external field transformation#

Default method, is the transformation of the external photon field from the disk/BH frame to the relativistic blob

my_jet.set_external_field_transf('blob')

Alternatively, in the case of istropric fields as the CMB or the BLR and DT within the BLR radius, and DT radius, respectively, it is possible to transform the the electron distribution, moving the blob to the disk/BH frame.

my_jet.set_external_field_transf('disk')

Note

Anyhow, the disk transformation is riogorously valid only for isotropic external fields, such as the CMB, or the BLR and Dusty torus seed photons within the DT radius and BLR radius, respectively. Beyond the isotropic region, the code will reproduce the expected beaming pattern as in Fig 13 of Finke (2106) [Finke2016], but the spectral shape might be slightly different.

External photon field energy density along the jet#

def iso_field_transf(L,R,BulckFactor):
    beta=1.0 - 1/(BulckFactor*BulckFactor)
    return L/(4*np.pi*R*R*3E10)*BulckFactor*BulckFactor*(1+((beta**2)/3))

def external_iso_behind_transf(L,R,BulckFactor):
    beta=1.0 - 1/(BulckFactor*BulckFactor)
    return L/((4*np.pi*R*R*3E10)*(BulckFactor*BulckFactor*(1+beta)**2))

EC seed photon fields, in the Disk rest frame

%matplotlib inline
my_jet.add_EC_component(disk_type='BB')
fig = plt.figure(figsize=(8,6))
ax=fig.subplots(1)
N=50
G=1
R_range=np.logspace(13,25,N)
y=np.zeros((8,N))
my_jet.set_verbosity(0)

for ID,R in enumerate(R_range):
    my_jet.set_par('R_H',val=R)
    my_jet.set_external_fields()
    my_jet.energetic_report(verbose=False)

    y[1,ID]=my_jet.energetic_dict['U_BLR_DRF']
    y[0,ID]=my_jet.energetic_dict['U_Disk_DRF']
    y[2,ID]=my_jet.energetic_dict['U_DT_DRF']

y[4,:]=iso_field_transf(my_jet._blob.L_Disk_radiative*my_jet.parameters.tau_DT.val,my_jet.parameters.R_DT.val,G)
y[3,:]=iso_field_transf(my_jet._blob.L_Disk_radiative*my_jet.parameters.tau_BLR.val,my_jet.parameters.R_BLR_in.val,G)
y[5,:]=external_iso_behind_transf(my_jet._blob.L_Disk_radiative*my_jet.parameters.tau_BLR.val,R_range,G)
y[6,:]=external_iso_behind_transf(my_jet._blob.L_Disk_radiative*my_jet.parameters.tau_DT.val,R_range,G)
y[7,:]=external_iso_behind_transf(my_jet._blob.L_Disk_radiative,R_range,G)

ax.plot(np.log10(R_range),np.log10(y[0,:]),label=r'Disk')
ax.plot(np.log10(R_range),np.log10(y[1,:]),'-',label=r'BLR')
ax.plot(np.log10(R_range),np.log10(y[2,:]),label=r'DT')
ax.plot(np.log10(R_range),np.log10(y[3,:]),'--',label=r'BLR uniform')
ax.plot(np.log10(R_range),np.log10(y[4,:]),'--',label=r'DT uniform')
ax.plot(np.log10(R_range),np.log10(y[5,:]),'--',label=r'BLR 1/$R^2$')
ax.plot(np.log10(R_range),np.log10(y[6,:]),'--',label=r'DT 1/$R2^2$')
ax.plot(np.log10(R_range),np.log10(y[7,:]),'--',label=r'Disk 1/$R^2$')
ax.set_xlabel('log(R_H) cm')
ax.set_ylabel('log(Uph) erg cm-3 s-1')

ax.legend()

<matplotlib.legend.Legend at 0x157ba2530>

../../../../_images/Jet_example_phys_EC_47_1.png

%matplotlib inline

fig = plt.figure(figsize=(8,6))
ax=fig.subplots(1)

L_Disk=1E45
N=50
G=my_jet.parameters.BulkFactor.val
R_range=np.logspace(15,22,N)
y=np.zeros((8,N))
my_jet.set_par('L_Disk',val=L_Disk)
my_jet._blob.theta_n_int=100
my_jet._blob.l_n_int=100
my_jet._blob.theta_n_int=100
my_jet._blob.l_n_int=100
for ID,R in enumerate(R_range):
    my_jet.set_par('R_H',val=R)

    my_jet.eval()
    my_jet.energetic_report(verbose=False)

    y[1,ID]=my_jet.energetic_dict['U_BLR']
    y[0,ID]=my_jet.energetic_dict['U_Disk']
    y[2,ID]=my_jet.energetic_dict['U_DT']



y[4,:]=iso_field_transf(my_jet._blob.L_Disk_radiative*my_jet.parameters.tau_DT.val,my_jet.parameters.R_DT.val,G)
y[3,:]=iso_field_transf(my_jet._blob.L_Disk_radiative*my_jet.parameters.tau_BLR.val,my_jet.parameters.R_BLR_in.val,G)
y[5,:]=external_iso_behind_transf(my_jet._blob.L_Disk_radiative*my_jet.parameters.tau_BLR.val,R_range,G)
y[6,:]=external_iso_behind_transf(my_jet._blob.L_Disk_radiative*my_jet.parameters.tau_DT.val,R_range,G)
y[7,:]=external_iso_behind_transf(my_jet._blob.L_Disk_radiative,R_range,G)

ax.plot(np.log10(R_range),np.log10(y[0,:]),label=r'Disk')
ax.plot(np.log10(R_range),np.log10(y[1,:]),'-',label=r'BLR')
ax.plot(np.log10(R_range),np.log10(y[2,:]),'-',label=r'DT')
ax.plot(np.log10(R_range),np.log10(y[3,:]),'--',label=r'BLR uniform')
ax.plot(np.log10(R_range),np.log10(y[4,:]),'--',label=r'DT uniform')
ax.plot(np.log10(R_range),np.log10(y[5,:]),'--',label=r'BLR 1/$R^2$')
ax.plot(np.log10(R_range),np.log10(y[6,:]),'--',label=r'DT 1/$R^2$')
ax.plot(np.log10(R_range),np.log10(y[7,:]),'--',label=r'Disk 1/$R^2$')
ax.axvline(np.log10( my_jet.parameters.R_DT.val ))
ax.axvline(np.log10( my_jet.parameters.R_BLR_out.val))

ax.set_xlabel('log(R_H) cm')
ax.set_ylabel('log(Uph`) erg cm-3 s-1')

ax.legend()

<matplotlib.legend.Legend at 0x15812f3a0>

../../../../_images/Jet_example_phys_EC_48_1.png

IC against the CMB#

my_jet=Jet(name='test_equipartition',electron_distribution='lppl',beaming_expr='bulk_theta')
my_jet.set_par('R',val=1E21)
my_jet.set_par('z_cosm',val= 0.651)
my_jet.set_par('B',val=2E-5)
my_jet.set_par('gmin',val=50)
my_jet.set_par('gamma0_log_parab',val=35.0E3)
my_jet.set_par('gmax',val=30E5)
my_jet.set_par('theta',val=12.0)
my_jet.set_par('BulkFactor',val=3.5)
my_jet.set_par('s',val=2.58)
my_jet.set_par('r',val=0.42)
my_jet.set_N_from_nuFnu(5E-15,1E12)
my_jet.add_EC_component('EC_CMB')

===> setting C threads to 12

We can now compare the different beaming pattern for the EC emission if the CMB, and realize that the beaming pattern is different. This is very important in the case of radio galaxies. The src transformation is the one to use in the case of radio galaxies or misaligned AGNs in general, and gives a more accurate results for the beaming patter of an isotropic external field.

from jetset.plot_sedfit import PlotSED
p=PlotSED()

my_jet.set_external_field_transf('blob')
c= ['k', 'g', 'r', 'c']
for ID,theta in enumerate(np.linspace(2,20,4)):
    my_jet.parameters.theta.val=theta
    my_jet.eval()
    my_jet.plot_model(plot_obj=p,comp='Sum',label='blob, theta=%2.2f'%theta,line_style='--',color=c[ID])

my_jet.set_external_field_transf('disk')
for ID,theta in enumerate(np.linspace(2,20,4)):
    my_jet.parameters.theta.val=theta
    my_jet.eval()
    my_jet.plot_model(plot_obj=p,comp='Sum',label='disk, theta=%2.2f'%theta,line_style='',color=c[ID])

p.setlim(y_min=5E-18,y_max=5E-13,x_max=1E28)

../../../../_images/Jet_example_phys_EC_52_0.png

Equipartition#

It is also possible to set our jet at the equipartition, that is achieved not using analytical approximation, but by numerically finding the equipartition value over a grid. We have to provide the value of the observed flux (nuFnu_obs) at a given observed frequency (nu_obs), the minimum value of B (B_min), and the number of grid points (N_pts)

my_jet.parameters.theta.val=12
B_min,b_grid,U_B,U_e=my_jet.set_B_eq(nuFnu_obs=5E-15,nu_obs=1E12,B_min=1E-9,N_pts=50,plot=True)
my_jet.show_pars()

my_jet.eval()

B grid min  1e-09
B grid max  1.0
grid points 50

../../../../_images/Jet_example_phys_EC_55_1.png

setting B to  0.0001389495494373139
setting N to  9.160733610838076e-06

Table length=13

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
test_equipartition	R	region_size	cm	1.000000e+21	1.000000e+03	1.000000e+30	False	False
test_equipartition	R_H	region_position	cm	1.000000e+17	0.000000e+00	--	False	True
test_equipartition	B	magnetic_field	gauss	1.389495e-04	0.000000e+00	--	False	False
test_equipartition	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
test_equipartition	theta	jet-viewing-angle	deg	1.200000e+01	0.000000e+00	9.000000e+01	False	False
test_equipartition	BulkFactor	jet-bulk-factor	lorentz-factor*	3.500000e+00	1.000000e+00	1.000000e+05	False	False
test_equipartition	z_cosm	redshift		6.510000e-01	0.000000e+00	--	False	False
test_equipartition	gmin	low-energy-cut-off	lorentz-factor*	5.000000e+01	1.000000e+00	1.000000e+09	False	False
test_equipartition	gmax	high-energy-cut-off	lorentz-factor*	3.000000e+06	1.000000e+00	1.000000e+15	False	False
test_equipartition	N	emitters_density	1 / cm3	9.160734e-06	0.000000e+00	--	False	False
test_equipartition	gamma0_log_parab	turn-over-energy	lorentz-factor*	3.500000e+04	1.000000e+00	1.000000e+09	False	False
test_equipartition	s	LE_spectral_slope		2.580000e+00	-1.000000e+01	1.000000e+01	False	False
test_equipartition	r	spectral_curvature		4.200000e-01	-1.500000e+01	1.500000e+01	False	False

p=my_jet.plot_model()
p.setlim(y_min=5E-18,y_max=2E-14,x_max=1E28)

../../../../_images/Jet_example_phys_EC_56_0.png