import warnings
warnings.filterwarnings('ignore')

Model fitting 3: External Compton#

Loading data#

see the Data format and SED data user guide for further information about loading data and External Compton for the information regarding the implementation of the external Conpton model

from jetset.jet_model import Jet
from jetset.data_loader import Data,ObsData
from jetset.test_data_helper import  test_SEDs
test_SEDs

['/Users/orion/miniforge3/envs/jetset/lib/python3.10/site-packages/jetset/test_data/SEDs_data/SED_3C345.ecsv',
 '/Users/orion/miniforge3/envs/jetset/lib/python3.10/site-packages/jetset/test_data/SEDs_data/SED_MW_Mrk421_EBL_DEABS.ecsv',
 '/Users/orion/miniforge3/envs/jetset/lib/python3.10/site-packages/jetset/test_data/SEDs_data/SED_MW_Mrk501_EBL_ABS.ecsv',
 '/Users/orion/miniforge3/envs/jetset/lib/python3.10/site-packages/jetset/test_data/SEDs_data/SED_MW_Mrk501_EBL_DEABS.ecsv']

data=Data.from_file(test_SEDs[0])

sed_data=ObsData(data_table=data)

%matplotlib inline
p=sed_data.plot_sed(show_dataset=True)

../../../../_images/Jet_example_model_fit_EC_8_0.png

we filter out the data set -1

sed_data.show_data_sets()
sed_data.filter_data_set('-1',exclude=True)
sed_data.filter_data_set('2',exclude=True)
sed_data.show_data_sets()
p=sed_data.plot_sed()

current datasets
dataset -1
dataset 0
dataset 1
dataset 2
---> excluding  data_set/s ['-1']
filter -1 192
current datasets
dataset 0
dataset 1
dataset 2
---> data sets left after filtering None
---> data len after filtering=192
---> excluding  data_set/s ['2']
filter 2 191
current datasets
dataset 0
dataset 1
---> data sets left after filtering None
---> data len after filtering=191
current datasets
dataset 0
dataset 1

../../../../_images/Jet_example_model_fit_EC_10_1.png

sed_data.group_data(bin_width=.15)
sed_data.add_systematics(0.1,[10.**6,10.**29])
#sed_data.add_systematics(0.05,[10.**19,10.**30])

p=sed_data.plot_sed()

================================================================================

*  binning data  *
---> N bins= 100
---> bin_widht= 0.15
================================================================================

../../../../_images/Jet_example_model_fit_EC_11_1.png

sed_data.save('3C454_data.pkl')

Phenomenological model constraining#

see the Phenomenological model constraining: application user guide for further information about phenomenological model constraining

from jetset.sed_shaper import  SEDShape
my_shape=SEDShape(sed_data)
my_shape.eval_indices(silent=True)
p=my_shape.plot_indices()
p.setlim(y_min=1E-15,y_max=1E-9)

================================================================================

* evaluating spectral indices for data *
================================================================================

../../../../_images/Jet_example_model_fit_EC_15_1.png

for the synchrotron sed_shaping we include the check for Big Blue Bump (BBB) component. Moreover, we force the model to use a pure log-parabolic function and not a log-cubic one in order to get a better estimation of the BBB component. The fit values of the BBB component will be used in the ObsConstrain to guess the accretion disk luminosity and temperature

mm,best_fit=my_shape.sync_fit(check_BBB_template=True,
                              check_host_gal_template=False,
                              use_log_par=True,
                              Ep_start=None,
                              minimizer='lsb',
                              silent=True,
                              fit_range=[9,16])

================================================================================

* Log-Polynomial fitting of the synchrotron component *
---> first blind fit run,  fit range: [9, 16]
--> class:  LSP

--> class:  LSP

Table length=5

model name	name	val	bestfit val	err +	err -	start val	fit range min	fit range max	frozen
LogParabolaEp	b	-3.083929e-01	-3.083929e-01	2.309292e-02	--	-1.560623e-01	-1.000000e+01	0.000000e+00	False
LogParabolaEp	Ep	1.168757e+01	1.168757e+01	9.352232e-02	--	1.281229e+01	0.000000e+00	3.000000e+01	False
LogParabolaEp	Sp	-1.122282e+01	-1.122282e+01	3.377790e-02	--	-1.089599e+01	-3.000000e+01	0.000000e+00	False
BBB	nuFnu_p_BBB	-1.155675e+01	-1.155675e+01	1.991849e-02	--	-1.089599e+01	-1.289599e+01	-8.895992e+00	False
BBB	nu_scale	9.430361e-03	9.430361e-03	4.189487e-04	--	0.000000e+00	-5.000000e-01	5.000000e-01	False

---> sync       nu_p=+1.168757e+01 (err=+9.352232e-02)  nuFnu_p=-1.122282e+01 (err=+3.377790e-02) curv.=-3.083929e-01 (err=+2.309292e-02)
================================================================================

my_shape.IC_fit(fit_range=[16,26],minimizer='minuit', silent=True)
p=my_shape.plot_shape_fit()
p.setlim(y_min=1E-15)

================================================================================

* Log-Polynomial fitting of the IC component *
---> fit range: [16, 26]
---> LogCubic fit
====> simplex
====> migrad
====> simplex
====> migrad
====> simplex
====> migrad

Table length=4

model name	name	val	bestfit val	err +	err -	start val	fit range min	fit range max	frozen
LogCubic	b	-1.239523e-01	-1.239523e-01	1.307983e-02	--	-1.000000e+00	-1.000000e+01	0.000000e+00	False
LogCubic	c	-1.215669e-02	-1.215669e-02	2.221392e-03	--	-1.000000e+00	-1.000000e+01	1.000000e+01	False
LogCubic	Ep	2.238469e+01	2.238469e+01	1.156381e-01	--	2.235747e+01	0.000000e+00	3.000000e+01	False
LogCubic	Sp	-1.038704e+01	-1.038704e+01	4.359969e-02	--	-1.000000e+01	-3.000000e+01	0.000000e+00	False

---> IC         nu_p=+2.238469e+01 (err=+1.156381e-01)  nuFnu_p=-1.038704e+01 (err=+4.359969e-02) curv.=-1.239523e-01 (err=+1.307983e-02)
================================================================================

../../../../_images/Jet_example_model_fit_EC_18_3.png

In this case we use the constrain_SSC_EC_model, and we ask to use a dusty torus and BLR component external component

read the section External Compton for more information regarding the EC model

from jetset.obs_constrain import ObsConstrain
from jetset.minimizer import fit_SED
sed_obspar=ObsConstrain(B_range=[0.1,0.2],
                        distr_e='bkn',
                        t_var_sec=15*86400,
                        nu_cut_IR=1E9,
                        theta=2,
                        bulk_factor=20,
                        SEDShape=my_shape)


prefit_jet=sed_obspar.constrain_SSC_EC_model(electron_distribution_log_values=False,EC_components_list=['EC_DT','EC_BLR'],R_H=2E18,silent=True,)

================================================================================

*  constrains parameters from observable *

===> setting C threads to 12
adding par: L_Disk to  R_BLR_in
==> par R_BLR_in is depending on ['L_Disk'] according to expr:   R_BLR_in =
3E17*(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

Table length=21

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	R	region_size	cm	7.607512e+16	1.000000e+03	1.000000e+30	False	False
jet_leptonic	R_H	region_position	cm	2.000000e+18	0.000000e+00	--	False	True
jet_leptonic	B	magnetic_field	gauss	1.500000e-01	0.000000e+00	--	False	False
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	theta	jet-viewing-angle	deg	2.000000e+00	0.000000e+00	9.000000e+01	False	False
jet_leptonic	BulkFactor	jet-bulk-factor	lorentz-factor*	2.000000e+01	1.000000e+00	1.000000e+05	False	False
jet_leptonic	z_cosm	redshift		5.930000e-01	0.000000e+00	--	False	False
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	1.033091e+01	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.311585e+04	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	8.405479e+02	0.000000e+00	--	False	False
jet_leptonic	gamma_break	turn-over-energy	lorentz-factor*	2.279937e+02	1.000000e+00	1.000000e+09	False	False
jet_leptonic	p	LE_spectral_slope		2.309926e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	p_1	HE_spectral_slope		3.500000e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	T_DT	DT	K	1.000000e+02	0.000000e+00	--	False	False
jet_leptonic	*R_DT(D,L_Disk)	DT	cm	1.305539e+19	0.000000e+00	--	False	True
jet_leptonic	tau_DT	DT		1.000000e-01	0.000000e+00	1.000000e+00	False	False
jet_leptonic	tau_BLR	BLR		1.000000e-01	0.000000e+00	1.000000e+00	False	False
jet_leptonic	*R_BLR_in(D,L_Disk)	BLR	cm	1.958309e+17	0.000000e+00	--	False	True
jet_leptonic	*R_BLR_out(D,R_BLR_in)	BLR	cm	2.154140e+17	0.000000e+00	--	False	True
jet_leptonic	L_Disk(M)	Disk	erg / s	4.261082e+45	0.000000e+00	--	False	False
jet_leptonic	T_Disk	Disk	K	3.018434e+04	0.000000e+00	--	False	False

================================================================================

prefit_jet.eval()
p=prefit_jet.plot_model(sed_data=sed_data)

../../../../_images/Jet_example_model_fit_EC_22_0.png

prefit_jet.make_conical_jet(theta_open=5)

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 8.695425919436543e+17

prefit_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

prefit_jet.set_external_field_transf('disk')

prefit_jet.eval()
p=prefit_jet.plot_model(sed_data=sed_data)
prefit_jet.save_model('prefit_jet_EC.pkl')

../../../../_images/Jet_example_model_fit_EC_26_0.png

The prefit model should works well for the synchrotron component, but the EC one is a bit problematic. We can set as starting values a slightly harder value of p, and a larger value of gamma_break and gmax. We freeze some parameters, and we also set some fit_range values. Setting fit_range can speed-up the fit convergence but should be judged by the user each time according to the physics of the particular source

EC model fit#

Note

Please, read the introduction and the caveat for the frequentist model fitting to understand the frequentist fitting workflow see the Composite Models and depending pars user guide for further information about the implementation of FitModel, in particular for parameter setting

from jetset.data_loader import ObsData
sed_data=ObsData.load('3C454_data.pkl')
from jetset.jet_model import Jet

from jetset.model_manager import  FitModel
jet=Jet.load_model('prefit_jet_EC.pkl')
jet.set_gamma_grid_size(100)
fit_model=FitModel( jet=jet, name='EC-best-fit-lsb')
fit_model.show_model_components()

===> setting C threads to 12
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
adding par: L_Disk to  R_BLR_in
==> par R_BLR_in is depending on ['L_Disk'] according to expr:   R_BLR_in =
3E17*(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: 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

--------------------------------------------------------------------------------
Composite model description
--------------------------------------------------------------------------------
name: EC-best-fit-lsb
type: composite_model
components models:
 -model name: jet_leptonic model type: jet

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

fit_model.freeze('jet_leptonic','z_cosm')
fit_model.freeze('jet_leptonic','theta')

fit_model.free('jet_leptonic','R_H')
fit_model.freeze('jet_leptonic','L_Disk')
fit_model.freeze('jet_leptonic','tau_DT')
fit_model.freeze('jet_leptonic','tau_BLR')

fit_model.jet_leptonic.parameters.R_H.fit_range=[8E17,5E19]
fit_model.jet_leptonic.parameters.T_Disk.fit_range=[1E4,1E5]
fit_model.jet_leptonic.parameters.T_DT.fit_range=[100,1000]
fit_model.jet_leptonic.parameters.gamma_break.fit_range=[100,500]
fit_model.jet_leptonic.parameters.gmin.fit_range=[2,100]
fit_model.jet_leptonic.parameters.gmax.fit_range=[1E4,1E5]
fit_model.jet_leptonic.parameters.B.fit_range=[1E-2,1]
fit_model.jet_leptonic.parameters.p.fit_range=[1,2.5]
fit_model.jet_leptonic.parameters.p_1.fit_range=[3,4]
fit_model.jet_leptonic.parameters.theta_open.fit_range=[4,6]
fit_model.jet_leptonic.parameters.BulkFactor.fit_range=[10,30]

from jetset.minimizer import ModelMinimizer
model_minimizer_lsb=ModelMinimizer('lsb')
best_fit_lsb=model_minimizer_lsb.fit(fit_model,sed_data,3E10,1E29,fitname='EC-best-fit-lsb',repeat=1)

filtering data in fit range = [3.000000e+10,1.000000e+29]
data length 24
================================================================================

* start fit process *
-----

0it [00:00, ?it/s]

- best chisq=1.71336e+02

-------------------------------------------------------------------------
Fit report

Model: EC-best-fit-lsb

Table length=22

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	6.675472e+00	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	1.581028e+04	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	5.485583e+02	0.000000e+00	--	False	False
jet_leptonic	gamma_break	turn-over-energy	lorentz-factor*	1.894755e+02	1.000000e+00	1.000000e+09	False	False
jet_leptonic	p	LE_spectral_slope		1.588509e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	p_1	HE_spectral_slope		3.466529e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	T_DT	DT	K	4.502140e+02	0.000000e+00	--	False	False
jet_leptonic	*R_DT(D,L_Disk)	DT	cm	1.305539e+19	0.000000e+00	--	False	True
jet_leptonic	tau_DT	DT		1.000000e-01	0.000000e+00	1.000000e+00	False	True
jet_leptonic	tau_BLR	BLR		1.000000e-01	0.000000e+00	1.000000e+00	False	True
jet_leptonic	*R_BLR_in(D,L_Disk)	BLR	cm	1.958309e+17	0.000000e+00	--	False	True
jet_leptonic	*R_BLR_out(D,R_BLR_in)	BLR	cm	2.154140e+17	0.000000e+00	--	False	True
jet_leptonic	L_Disk(M)	Disk	erg / s	4.261082e+45	0.000000e+00	--	False	True
jet_leptonic	T_Disk	Disk	K	2.991580e+04	0.000000e+00	--	False	False
jet_leptonic	*R(D,theta_open)	region_size	cm	9.134742e+16	1.000000e+03	1.000000e+30	False	True
jet_leptonic	R_H(M)	region_position	cm	8.694991e+17	0.000000e+00	--	False	False
jet_leptonic	B	magnetic_field	gauss	9.141046e-02	0.000000e+00	--	False	False
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	theta	jet-viewing-angle	deg	2.000000e+00	0.000000e+00	9.000000e+01	False	True
jet_leptonic	BulkFactor	jet-bulk-factor	lorentz-factor*	1.842049e+01	1.000000e+00	1.000000e+05	False	False
jet_leptonic	z_cosm	redshift		5.930000e-01	0.000000e+00	--	False	True
jet_leptonic	theta_open(M)	user_defined	deg	5.997353e+00	1.000000e+00	1.000000e+01	False	False

converged=True
calls=633
mesg=

'ftol termination condition is satisfied.'

dof=12
chisq=171.335707, chisq/red=14.277976 null hypothesis sig=0.000000

best fit pars

Table length=22

model name	name	val	bestfit val	err +	err -	start val	fit range min	fit range max	frozen
jet_leptonic	gmin	6.675472e+00	6.675472e+00	2.084490e+01	--	1.033091e+01	2.000000e+00	1.000000e+02	False
jet_leptonic	gmax	1.581028e+04	1.581028e+04	1.907208e+04	--	1.311585e+04	1.000000e+04	1.000000e+05	False
jet_leptonic	N	5.485583e+02	5.485583e+02	4.158130e+03	--	8.405479e+02	0.000000e+00	--	False
jet_leptonic	gamma_break	1.894755e+02	1.894755e+02	3.075634e+02	--	2.279937e+02	1.000000e+02	5.000000e+02	False
jet_leptonic	p	1.588509e+00	1.588509e+00	2.908949e+00	--	2.309926e+00	1.000000e+00	2.500000e+00	False
jet_leptonic	p_1	3.466529e+00	3.466529e+00	3.550985e-01	--	3.500000e+00	3.000000e+00	4.000000e+00	False
jet_leptonic	T_DT	4.502140e+02	4.502140e+02	3.219246e+03	--	1.000000e+02	1.000000e+02	1.000000e+03	False
jet_leptonic	*R_DT(D,L_Disk)	1.305539e+19	--	--	--	1.305539e+19	0.000000e+00	--	True
jet_leptonic	tau_DT	1.000000e-01	--	--	--	1.000000e-01	0.000000e+00	1.000000e+00	True
jet_leptonic	tau_BLR	1.000000e-01	--	--	--	1.000000e-01	0.000000e+00	1.000000e+00	True
jet_leptonic	*R_BLR_in(D,L_Disk)	1.958309e+17	--	--	--	1.958309e+17	0.000000e+00	--	True
jet_leptonic	*R_BLR_out(D,R_BLR_in)	2.154140e+17	--	--	--	2.154140e+17	0.000000e+00	--	True
jet_leptonic	L_Disk(M)	4.261082e+45	--	--	--	4.261082e+45	0.000000e+00	--	True
jet_leptonic	T_Disk	2.991580e+04	2.991580e+04	1.307071e+04	--	3.018434e+04	1.000000e+04	1.000000e+05	False
jet_leptonic	*R(D,theta_open)	9.134742e+16	--	--	--	7.607512e+16	1.000000e+03	1.000000e+30	True
jet_leptonic	R_H(M)	8.694991e+17	8.694991e+17	6.630953e+16	--	8.695426e+17	8.000000e+17	5.000000e+19	False
jet_leptonic	B	9.141046e-02	9.141046e-02	2.996898e-02	--	1.500000e-01	1.000000e-02	1.000000e+00	False
jet_leptonic	NH_cold_to_rel_e	1.000000e+00	--	--	--	1.000000e+00	0.000000e+00	--	True
jet_leptonic	theta	2.000000e+00	--	--	--	2.000000e+00	0.000000e+00	9.000000e+01	True
jet_leptonic	BulkFactor	1.842049e+01	1.842049e+01	3.696853e+01	--	2.000000e+01	1.000000e+01	3.000000e+01	False
jet_leptonic	z_cosm	5.930000e-01	--	--	--	5.930000e-01	0.000000e+00	--	True
jet_leptonic	theta_open(M)	5.997353e+00	5.997353e+00	5.466490e+00	--	5.000000e+00	4.000000e+00	6.000000e+00	False

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

================================================================================

p=model_minimizer_lsb.plot_corr_matrix()

../../../../_images/Jet_example_model_fit_EC_34_0.png

%matplotlib inline
fit_model.set_nu_grid(1E6,1E30,200)
fit_model.eval()
p2=fit_model.plot_model(sed_data=sed_data)
p2.setlim(y_min=1E-14,y_max=1E-9,x_min=1E6,x_max=2E28)

../../../../_images/Jet_example_model_fit_EC_35_0.png

from jetset.minimizer import ModelMinimizer
model_minimizer_minuit=ModelMinimizer('minuit')
#fit_model.freeze('jet_leptonic','theta_open')
best_fit_minuit=model_minimizer_minuit.fit(fit_model,sed_data,3E10,1E29,fitname='EC-best-fit-minuit',repeat=2)

filtering data in fit range = [3.000000e+10,1.000000e+29]
data length 24
================================================================================

* start fit process *
-----
fit run: 0

0it [00:00, ?it/s]

====> simplex
====> migrad
- best chisq=3.21399e+01

fit run: 1
- old chisq=3.21399e+01

0it [00:00, ?it/s]

====> simplex
====> migrad
- best chisq=3.16610e+01

-------------------------------------------------------------------------
Fit report

Model: EC-best-fit-minuit

Table length=22

model name	name	par type	units	val	phys. bound. min	phys. bound. max	log	frozen
jet_leptonic	gmin	low-energy-cut-off	lorentz-factor*	3.893234e+00	1.000000e+00	1.000000e+09	False	False
jet_leptonic	gmax	high-energy-cut-off	lorentz-factor*	8.993352e+04	1.000000e+00	1.000000e+15	False	False
jet_leptonic	N	emitters_density	1 / cm3	9.909851e+01	0.000000e+00	--	False	False
jet_leptonic	gamma_break	turn-over-energy	lorentz-factor*	1.734853e+02	1.000000e+00	1.000000e+09	False	False
jet_leptonic	p	LE_spectral_slope		1.274681e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	p_1	HE_spectral_slope		3.503112e+00	-1.000000e+01	1.000000e+01	False	False
jet_leptonic	T_DT	DT	K	5.893807e+02	0.000000e+00	--	False	False
jet_leptonic	*R_DT(D,L_Disk)	DT	cm	1.305539e+19	0.000000e+00	--	False	True
jet_leptonic	tau_DT	DT		1.000000e-01	0.000000e+00	1.000000e+00	False	True
jet_leptonic	tau_BLR	BLR		1.000000e-01	0.000000e+00	1.000000e+00	False	True
jet_leptonic	*R_BLR_in(D,L_Disk)	BLR	cm	1.958309e+17	0.000000e+00	--	False	True
jet_leptonic	*R_BLR_out(D,R_BLR_in)	BLR	cm	2.154140e+17	0.000000e+00	--	False	True
jet_leptonic	L_Disk(M)	Disk	erg / s	4.261082e+45	0.000000e+00	--	False	True
jet_leptonic	T_Disk	Disk	K	2.778004e+04	0.000000e+00	--	False	False
jet_leptonic	*R(D,theta_open)	region_size	cm	3.603492e+17	1.000000e+03	1.000000e+30	False	True
jet_leptonic	R_H(M)	region_position	cm	3.509696e+18	0.000000e+00	--	False	False
jet_leptonic	B	magnetic_field	gauss	5.312839e-02	0.000000e+00	--	False	False
jet_leptonic	NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00	0.000000e+00	--	False	True
jet_leptonic	theta	jet-viewing-angle	deg	2.000000e+00	0.000000e+00	9.000000e+01	False	True
jet_leptonic	BulkFactor	jet-bulk-factor	lorentz-factor*	1.000000e+01	1.000000e+00	1.000000e+05	False	False
jet_leptonic	z_cosm	redshift		5.930000e-01	0.000000e+00	--	False	True
jet_leptonic	theta_open(M)	user_defined	deg	5.862158e+00	1.000000e+00	1.000000e+01	False	False

converged=True
calls=1021
mesg=

Migrad
FCN = 31.66		Nfcn = 1021
EDM = 0.00019 (Goal: 0.0002)		time = 31.5 sec
Valid Minimum		SOME Parameters at limit
Below EDM threshold (goal x 10)		Below call limit
Covariance	Hesse ok	Accurate	Pos. def.	Not forced

	Name	Value	Hesse Error	Minos Error-	Minos Error+	Limit-	Limit+	Fixed
0	par_0	3.89323	0.00023			2	100
1	par_1	89.93352e3	0.00028e3			1E+04	1E+05
2	par_2	99.0985	0.0014			0
3	par_3	173.4853	0.0017			100	500
4	par_4	1.274681	0.000007			1	2.5
5	par_5	3.50311218	0.00000004			3	4
6	par_6	589	14			100	1E+03
7	par_7	27.8e3	2.4e3			1E+04	1E+05
8	par_8	3.50970e18	0.00014e18			8E+17	5E+19
9	par_9	53.1284e-3	0.0027e-3			0.01	1
10	par_10	10.0	0.4			10	30
11	par_11	5.862158	0.000008			4	6

dof=12
chisq=31.661039, chisq/red=2.638420 null hypothesis sig=0.001561

best fit pars

Table length=22

model name	name	val	bestfit val	err +	err -	start val	fit range min	fit range max	frozen
jet_leptonic	gmin	3.893234e+00	3.893234e+00	2.336607e-04	--	6.675472e+00	2.000000e+00	1.000000e+02	False
jet_leptonic	gmax	8.993352e+04	8.993352e+04	2.756248e-01	--	1.581028e+04	1.000000e+04	1.000000e+05	False
jet_leptonic	N	9.909851e+01	9.909851e+01	1.397515e-03	--	5.485583e+02	0.000000e+00	--	False
jet_leptonic	gamma_break	1.734853e+02	1.734853e+02	1.658699e-03	--	1.894755e+02	1.000000e+02	5.000000e+02	False
jet_leptonic	p	1.274681e+00	1.274681e+00	6.788564e-06	--	1.588509e+00	1.000000e+00	2.500000e+00	False
jet_leptonic	p_1	3.503112e+00	3.503112e+00	3.994333e-08	--	3.466529e+00	3.000000e+00	4.000000e+00	False
jet_leptonic	T_DT	5.893807e+02	5.893807e+02	1.422676e+01	--	4.502140e+02	1.000000e+02	1.000000e+03	False
jet_leptonic	*R_DT(D,L_Disk)	1.305539e+19	--	--	--	1.305539e+19	0.000000e+00	--	True
jet_leptonic	tau_DT	1.000000e-01	--	--	--	1.000000e-01	0.000000e+00	1.000000e+00	True
jet_leptonic	tau_BLR	1.000000e-01	--	--	--	1.000000e-01	0.000000e+00	1.000000e+00	True
jet_leptonic	*R_BLR_in(D,L_Disk)	1.958309e+17	--	--	--	1.958309e+17	0.000000e+00	--	True
jet_leptonic	*R_BLR_out(D,R_BLR_in)	2.154140e+17	--	--	--	2.154140e+17	0.000000e+00	--	True
jet_leptonic	L_Disk(M)	4.261082e+45	--	--	--	4.261082e+45	0.000000e+00	--	True
jet_leptonic	T_Disk	2.778004e+04	2.778004e+04	2.427427e+03	--	2.991580e+04	1.000000e+04	1.000000e+05	False
jet_leptonic	*R(D,theta_open)	3.603492e+17	--	--	--	9.134742e+16	1.000000e+03	1.000000e+30	True
jet_leptonic	R_H(M)	3.509696e+18	3.509696e+18	1.379374e+14	--	8.694991e+17	8.000000e+17	5.000000e+19	False
jet_leptonic	B	5.312839e-02	5.312839e-02	2.726890e-06	--	9.141046e-02	1.000000e-02	1.000000e+00	False
jet_leptonic	NH_cold_to_rel_e	1.000000e+00	--	--	--	1.000000e+00	0.000000e+00	--	True
jet_leptonic	theta	2.000000e+00	--	--	--	2.000000e+00	0.000000e+00	9.000000e+01	True
jet_leptonic	BulkFactor	1.000000e+01	1.000000e+01	3.890289e-01	--	1.842049e+01	1.000000e+01	3.000000e+01	False
jet_leptonic	z_cosm	5.930000e-01	--	--	--	5.930000e-01	0.000000e+00	--	True
jet_leptonic	theta_open(M)	5.862158e+00	5.862158e+00	8.085871e-06	--	5.997353e+00	4.000000e+00	6.000000e+00	False

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

================================================================================

p=model_minimizer_minuit.plot_corr_matrix()

../../../../_images/Jet_example_model_fit_EC_37_0.png

%matplotlib inline
fit_model.set_nu_grid(1E6,1E30,500)
fit_model.eval()
p2=fit_model.plot_model(sed_data=sed_data)
p2.setlim(y_min=1E-14,y_max=1E-9,x_min=1E6,x_max=2E28)

../../../../_images/Jet_example_model_fit_EC_38_0.png

jet.energetic_report()

Table length=39

name	type	units	val
BulkLorentzFactor	jet-bulk-factor		1.000000e+01
U_e	Energy dens. blob rest. frame	erg / cm3	3.869527e-03
U_p_cold	Energy dens. blob rest. frame	erg / cm3	1.489725e-01
U_B	Energy dens. blob rest. frame	erg / cm3	1.123087e-04
U_Synch	Energy dens. blob rest. frame	erg / cm3	9.582487e-06
U_Synch_DRF	Energy dens. disk rest. frame	erg / cm3	9.614802e-01
U_Disk	Energy dens. blob rest. frame	erg / cm3	2.827817e-06
U_BLR	Energy dens. blob rest. frame	erg / cm3	2.188308e-07
U_DT	Energy dens. blob rest. frame	erg / cm3	1.331679e-03
U_CMB	Energy dens. blob rest. frame	erg / cm3	0.000000e+00
U_Star	Energy dens. blob rest. frame	erg / cm3	0.000000e+00
U_Disk_DRF	Energy dens. disk rest. frame	erg / cm3	9.199862e-04
U_BLR_DRF	Energy dens. disk rest. frame	erg / cm3	5.115778e-05
U_DT_DRF	Energy dens. disk rest. frame	erg / cm3	6.675126e-06
U_CMB_DRF	Energy dens. disk rest. frame	erg / cm3	0.000000e+00
U_Star_DRF	Energy dens. disk rest. frame	erg / cm3	0.000000e+00
U_seed_tot	Energy dens. blob rest. frame	erg / cm3	1.344308e-03
L_Sync_rf	Lum. blob rest. frame.	erg / s	4.687658e+41
L_SSC_rf	Lum. blob rest. frame.	erg / s	1.279464e+41
L_EC_Disk_rf	Lum. blob rest. frame.	erg / s	0.000000e+00
L_EC_BLR_rf	Lum. blob rest. frame.	erg / s	1.203063e+39
L_EC_DT_rf	Lum. blob rest. frame.	erg / s	6.871948e+42
L_EC_CMB_rf	Lum. blob rest. frame.	erg / s	0.000000e+00
L_EC_Star_rf	Lum. blob rest. frame.	erg / s	0.000000e+00
jet_L_Sync	jet Lum.	erg / s	1.166040e+43
jet_L_SSC	jet Lum.	erg / s	3.182626e+42
jet_L_EC_Disk	jet Lum.	erg / s	0.000000e+00
jet_L_EC_BLR	jet Lum.	erg / s	2.992582e+40
jet_L_EC_Star	jet Lum.	erg / s	0.000000e+00
jet_L_EC_DT	jet Lum.	erg / s	1.709376e+44
jet_L_EC_CMB	jet Lum.	erg / s	0.000000e+00
jet_L_pp_gamma	jet Lum.	erg / s	0.000000e+00
jet_L_rad	jet Lum.	erg / s	1.858105e+44
jet_L_kin	jet Lum.	erg / s	1.859850e+47
jet_L_tot	jet Lum.	erg / s	1.863075e+47
jet_L_e	jet Lum.	erg / s	4.708616e+45
jet_L_B	jet Lum.	erg / s	1.366623e+44
jet_L_p_cold	jet Lum.	erg / s	1.812764e+47
NH_cold_to_rel_e	cold_p_to_rel_e_ratio		1.000000e+00

best_fit_minuit.save_report('EC-best-fit-minuit.pkl')
model_minimizer_minuit.save_model('EC_model_minimizer_minuit.pkl')
fit_model.save_model('EC_fit_model_minuit.pkl')

MCMC#

Note

Please, read the introduction and the caveat for the Bayesian model fitting to understand the MCMC sampler workflow.

creating and setting the sampler#

from jetset.mcmc import McmcSampler
from jetset.minimizer import ModelMinimizer
model_minimizer_minuit = ModelMinimizer.load_model('EC_model_minimizer_minuit.pkl')

===> setting C threads to 12
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
adding par: L_Disk to  R_BLR_in
==> par R_BLR_in is depending on ['L_Disk'] according to expr:   R_BLR_in =
3E17*(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: 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

mcmc=McmcSampler(model_minimizer_minuit)

labels=['N','B','BulkFactor','p_1','gamma_break']
model_name='jet_leptonic'
use_labels_dict={model_name:labels}
mcmc.set_labels(use_labels_dict=use_labels_dict)

mcmc.set_bounds(bound=5.0,bound_rel=True)

par: N  best fit value:  99.09851082377608  mcmc bounds: [0, 594.5910649426565]
par: B  best fit value:  0.05312839237542956  mcmc bounds: [0.01, 0.3187703542525773]
par: BulkFactor  best fit value:  10.000000042111171  mcmc bounds: [10, 30]
par: p_1  best fit value:  3.503112178392646  mcmc bounds: [3, 4]
par: gamma_break  best fit value:  173.4853486770854  mcmc bounds: [100, 500]

mcmc.run_sampler(nwalkers=20, burnin=50,steps=500,progress='notebook')

===> setting C threads to 12
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
adding par: L_Disk to  R_BLR_in
==> par R_BLR_in is depending on ['L_Disk'] according to expr:   R_BLR_in =
3E17*(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: 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
mcmc run starting

0%|          | 0/500 [00:00<?, ?it/s]

mcmc run done, with 1 threads took 484.08 seconds

print(mcmc.acceptance_fraction)

0.4997

plotting the model#

To plot the sampled model range against the input best-fit model

mcmc.model.set_nu_grid(1E6,1E30,200)

p=mcmc.plot_model(sed_data=sed_data,fit_range=[3E10, 1E29],size=100)
p.setlim(y_min=1E-13,x_min=1E6,x_max=2E28)

../../../../_images/Jet_example_model_fit_EC_52_0.png

To plot the sampled model range,providing quantiles, against the input best-fit model, providing quantiles

p=mcmc.plot_model(sed_data=sed_data,fit_range=[3E10, 1E29],size=100,quantiles=[0.05,0.95])
p.setlim(y_min=1E-13,x_min=1E6,x_max=2E28)

../../../../_images/Jet_example_model_fit_EC_54_0.png

To plot the sampled model range,providing quantiles, against the mcmc model at 0.5 quantile (plot_mcmc_best_fit_model==True provides the 0.5 quantile sampled model)

p=mcmc.plot_model(sed_data=sed_data,fit_range=[3E10, 1E29],size=100,quantiles=[0.05,0.95], plot_mcmc_best_fit_model=True)
p.setlim(y_min=1E-13,x_min=1E6,x_max=2E28)

../../../../_images/Jet_example_model_fit_EC_56_0.png

plotting the posterior corner plot#

To have a better rendering on the scatter plot, we redefine the plot labels

mcmc.labels

['N', 'B', 'BulkFactor', 'p_1', 'gamma_break']

mcmc.set_plot_label('N',r'$N$')
mcmc.set_plot_label('B',r'$B$')
mcmc.set_plot_label('BulkFactor',r'$\Gamma$')
mcmc.set_plot_label('p_1',r'$p_1$')
mcmc.set_plot_label('gamma_break',r'$\gamma_{\rm break}$')

the code below lets you tuning the output

mpl.rcParams[‘figure.dpi’] if you increase it you get a better definition
title_fmt=“.2E” this is the format for python, 2 significant digits, scientific notation
title_kwargs=dict(fontsize=12) you can change the fontsize

import matplotlib as mpl
mpl.rcParams['figure.dpi'] = 80
f=mcmc.corner_plot(quantiles=(0.16, 0.5, 0.84),title_kwargs=dict(fontsize=12),title_fmt=".2E",use_math_text=True)

../../../../_images/Jet_example_model_fit_EC_62_0.png

f=mcmc.plot_chain(log_plot=False)

../../../../_images/Jet_example_model_fit_EC_63_0.png

Save and reuse MCMC#

mcmc.save('mcmc_sampler.pkl')

from jetset.mcmc import McmcSampler
from jetset.data_loader import ObsData
from jetset.plot_sedfit import PlotSED
from jetset.test_data_helper import  test_SEDs

sed_data=ObsData.load('3C454_data.pkl')

ms=McmcSampler.load('mcmc_sampler.pkl')

===> setting C threads to 12
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
adding par: L_Disk to  R_BLR_in
==> par R_BLR_in is depending on ['L_Disk'] according to expr:   R_BLR_in =
3E17*(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: 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 C threads to 12
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
adding par: L_Disk to  R_BLR_in
==> par R_BLR_in is depending on ['L_Disk'] according to expr:   R_BLR_in =
3E17*(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: 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

ms.model.set_nu_grid(1E6,1E30,200)

p=ms.plot_model(sed_data=sed_data,fit_range=[3E10, 1E29],size=100)
p.setlim(y_min=1E-13,x_min=1E6,x_max=2E28)

../../../../_images/Jet_example_model_fit_EC_67_0.png

p=ms.plot_model(sed_data=sed_data,fit_range=[3E10, 1E29],size=100,quantiles=[0.05,0.95])
p.setlim(y_min=1E-13,x_min=1E6,x_max=2E28)

../../../../_images/Jet_example_model_fit_EC_68_0.png

f=ms.plot_par('p_1',log_plot=False)

../../../../_images/Jet_example_model_fit_EC_69_0.png

Model fitting 3: External Compton

Contents

Model fitting 3: External Compton#

Loading data#

Phenomenological model constraining#

EC model fit#

MCMC#

creating and setting the sampler#

plotting the model#

plotting the posterior corner plot#

Save and reuse MCMC#