Tutorial 2 for JetSeT v.1.1.2¶
In [25]:
from IPython.core.display import display, HTML
display(HTML("<style>.container { width:95% !important; }</style>"))
import matplotlib
from matplotlib import pyplot as plt
import matplotlib.colors as mcolors
font = {'family' : 'sans-serif',
'weight' : 'normal',
'size' : 18}
matplotlib.rc('font', **font)
matplotlib.pyplot.rc('font', **font)
colors=list(mcolors.TABLEAU_COLORS)
import numpy as np
import warnings
warnings.filterwarnings('ignore')
In [26]:
from jetset.poly_fit import do_log_Parab_FIT,do_linear_fit
from jetset.loglog_poly_model import LogLinear
from jetset.model_manager import FitModel
from jetset.minimizer import fit_SED
from jetset.data_loader import Data,ObsData
In [27]:
def n_distr_plot(j,ax,c=None,gmin=None):
x=my_jet.electron_distribution.gamma_e
y=my_jet.electron_distribution.n_gamma_e
ax.plot(np.log10(x),np.log10(y*x*x*x),color=c)
if gmin is not None:
ymax=np.log10(y[0]*x[0]*x[0]*x[0])
ymin=np.log10(y[-1]*x[-1]*x[-1]*x[-1])
#print('ymax',ymax)
ax.vlines(np.log10(gmin),ymin=ymin,ymax=ymax,color=colors[ID])
In [28]:
def get_gamma_3p(j):
j.electron_distribution.update()
x=np.log10(j.electron_distribution.gamma_e)
y=np.log10(j.electron_distribution.n_gamma_e)+3*x
y_p=y.max()
x_p=x[np.argmax(y)]
p,err=do_log_Parab_FIT(x,y,x_p,y_p,-1,x_range=[x_p-0.5,x_p+0.5],dy=np.ones(x.size))
return p
def get_pl_slope_n(j,x_range):
x=np.log10(j.electron_distribution.gamma_e)
y=np.log10(j.electron_distribution.n_gamma_e)
p,err=do_linear_fit(x,y,x_range=x_range,dy=np.ones(x.size))
return p,err
def get_log_par_peak(x_p,y_p,j,comp,delta_p=[-1,1]):
c=j.get_spectral_component_by_name(comp)
x=np.log10(c.SED.nu.value)
y=np.log10(c.SED.nuFnu.value)
p,err=do_log_Parab_FIT(x,y,x_p,y_p,-0.1,x_range=[x_p + delta_p[0], x_p + delta_p[1] ],dy=np.ones(x.size))
p,err=do_log_Parab_FIT(x,y,p[0],p[1],p[2],x_range=[p[0] + delta_p[0], p[0] + delta_p[1] ],dy=np.ones(x.size))
return p,err
def get_pl_slope_SED_1(j,comp,x_range):
c=j.get_spectral_component_by_name(comp)
x=np.log10(c.SED.nu.value)
y=np.log10(c.SED.nuFnu.value)
p,err=do_linear_fit(x,y,x_range=x_range,dy=np.ones(x.size))
return p,err
def get_pl_slope_SED_2(j,comp,x_range):
c=j.get_spectral_component_by_name(comp)
x=c.SED.nu.value
y= c.SED.nuFnu.value
data=Data(n_rows=x.shape[0])
data.set_field('x',x)
data.set_field('y',y)
#data.set_field('dy',value=1E-15)
data.set_meta_data('z',j.parameters.z_cosm.val)
data.set_meta_data('restframe','obs')
data.set_meta_data('data_scale','lin-lin')
sed_data=ObsData(data_table=data)
loglog_poly=LogLinear()
loglog_pl=FitModel(name=None,loglog_poly=loglog_poly)
mm,best_fit=fit_SED(loglog_pl,
sed_data,
10**x_range[0],
10**x_range[1],
loglog=True,
silent=True,
fitname='spectral-indices-best-fit',
minimizer='lsb')
par=loglog_pl.get_par_by_name(loglog_poly,'alpha')
#print(par.best_fit_val,par.best_fit_err)
return par.best_fit_val,par.best_fit_err,loglog_pl
def nu_p_S_delta_approx(my_jet,gp):
B=my_jet.parameters.B.val
delta=my_jet.get_beaming()
z=my_jet.parameters.z_cosm.val
return np.log10(3.2E6*B*delta/(1+z))+2*gp
In [29]:
from jetset.plot_sedfit import PlotSED,PlotPdistr,PlotSpecComp
from jetset.jet_model import Jet
In [30]:
my_jet=Jet(electron_distribution='lppl')
my_jet.parameters.r.val=1.0
my_jet.show_model()
-------------------------------------------------------------------------------------------------------------------
jet model description
-------------------------------------------------------------------------------------------------------------------
name: jet_leptonic
electrons distribution:
type: lppl
gamma energy grid size: 1001
gmin grid : 2.000000e+00
gmax grid : 1.000000e+06
normalization True
log-values False
radiative fields:
seed photons grid size: 100
IC emission grid size: 50
source emissivity lower bound : 1.000000e-120
spectral components:
name:Sum, state: on
name:Sync, state: self-abs
name:SSC, state: on
external fields transformation method: blob
SED info:
nu grid size :200
nu mix (Hz): 1.000000e+06
nu max (Hz): 1.000000e+30
flux plot lower bound : 1.000000e-120
name par type units val phys. bound. min phys. bound. max log frozen
---------------- ------------------- --------------- ------------ ---------------- ---------------- ----- ------
gmin low-energy-cut-off lorentz-factor* 2.000000e+00 1.000000e+00 1.000000e+09 False False
gmax high-energy-cut-off lorentz-factor* 1.000000e+06 1.000000e+00 1.000000e+15 False False
N emitters_density 1 / cm3 1.000000e+02 0.000000e+00 -- False False
s LE_spectral_slope 2.000000e+00 -1.000000e+01 1.000000e+01 False False
r spectral_curvature 1.000000e+00 -1.500000e+01 1.500000e+01 False False
gamma0_log_parab turn-over-energy lorentz-factor* 1.000000e+04 1.000000e+00 1.000000e+09 False False
R region_size cm 5.000000e+15 1.000000e+03 1.000000e+30 False False
R_H region_position cm 1.000000e+17 0.000000e+00 -- False True
B magnetic_field G 1.000000e-01 0.000000e+00 -- False False
beam_obj beaming Lorentz-factor* 1.000000e+01 1.000000e-04 -- False False
z_cosm redshift 1.000000e-01 0.000000e+00 -- False False
-------------------------------------------------------------------------------------------------------------------
In [31]:
my_jet.set_par('B',val=0.2)
my_jet.set_par('gamma0_log_parab',val=5E3)
my_jet.set_par('gmin',val=1E2)
my_jet.set_par('gmax',val=1E8)
my_jet.set_par('R',val=1E15)
my_jet.set_par('N',val=1E3)
my_jet.set_par('r',val=0.4)
In [32]:
my_jet.eval()
p=my_jet.electron_distribution.plot()
p.ax.axvline(4.0,ls='--',c='black',label=r'$\gamma_0$')
p.ax.legend()
Out[32]:
<matplotlib.legend.Legend at 0x1231f0ad0>
In [33]:
p=my_jet.electron_distribution.plot3p()
p.ax.axvline(4.0,ls='--',c='black',label=r'$\gamma_0$')
p.ax.legend()
Out[33]:
<matplotlib.legend.Legend at 0x123964510>
In [34]:
my_plot=my_jet.plot_model()
my_plot.rescale(y_max=-11,y_min=-17.5,x_min=9)
In [35]:
my_plot=my_jet.plot_model(frame='src')
my_plot.rescale(y_max=44,y_min=38,x_min=9)
Synchrotron trends: full computation and $\delta$-approx comparison¶
Synchrotron trend for $\gamma_{min}$¶
In [36]:
matplotlib.rc('font', **font)
p=PlotSED(figsize=(18,12))
ax=p.fig.add_subplot(222)
my_jet.parameters.gmax.val=1E7
my_jet.parameters.r.val=1.0
my_jet.parameters.s.val=2.0
my_jet.parameters.N.val=500
my_jet.parameters.z_cosm.val=0.05
my_jet.set_nu_grid_size(500)
my_jet.set_gamma_grid_size(100)
my_jet.set_IC_nu_size(100)
size=10
#Synch
nu_p_S=np.zeros(size)
nuFnu_p_S=np.zeros(size)
S_index=np.zeros(size)
S_index_err=np.zeros(size)
my_jet.set_IC_mode('off')
#Switch off sych self-abs
my_jet.spectral_components.Sync.state='on'
gmin_values=np.logspace(0.1,4.5,size)
for ID,gmin in enumerate(gmin_values):
my_jet.parameters.gmin.val=gmin
my_jet.set_N_from_nuFnu(nu_obs=8E16,nuFnu_obs=1E-11)
my_jet.eval()
x_p,y_p=my_jet.get_component_peak('Sync',log_log=True)
S_index[ID],S_index_err[ID],loglog_pl=get_pl_slope_SED_2(my_jet,'Sync',[10,13])
my_jet.plot_model(p,label=r'$\gamma_{min}$=%2.2e'%gmin,color=colors[ID],auto_label=False,comp='Sync',line_style='--')
p.add_model_plot(loglog_pl,label=r'pl fit for $\gamma_{min}$=%2.2e'%gmin,color=colors[ID],line_style='-')
n_distr_plot(my_jet,ax,c=colors[ID],gmin=gmin)
ax.set_xlabel(r'log($\gamma$)')
ax.set_ylabel(r'log(n($\gamma$) $\gamma^3$)')
p.sedplot.axvline([10],ls='--',c='black')
p.sedplot.axvline([13],ls='--',c='black')
p.sedplot.scatter(nu_p_S,nuFnu_p_S)
p.rescale(y_min=-18,y_max=-9,x_min=7,x_max=32)
In [37]:
S_spectral_index=S_index-1
matplotlib.rc('font', **font)
fig = plt.figure(figsize=(12,8))
ax=fig.add_subplot(111)
ax.plot(np.log10(gmin_values),S_spectral_index,'-o',label=r'Synch index from fit')
ax.fill_between(np.log10(gmin_values), S_spectral_index - S_index_err, S_spectral_index + S_index_err,
color='gray', alpha=0.2)
ax.set_ylabel('Synch index')
ax.set_xlabel(r'log($\gamma_{min}$)')
ax.axhline(-(my_jet.parameters.s.val-1)/2,ls='--',c='green',label='-(s-1)/2 Synch. theory')
ax.axhline(1/3,ls='--',c='red',label='1/3 Synch. theory asymp.')
ax.legend()
Out[37]:
<matplotlib.legend.Legend at 0x125bd5f10>
Synchrotron trend for the low-energy spectral slope¶
In [38]:
matplotlib.rc('font', **font)
p=PlotSED(figsize=(18,12))
ax=p.fig.add_subplot(222)
my_jet.parameters.gmax.val=1E7
my_jet.parameters.gmin.val=2
my_jet.parameters.r.val=1.0
my_jet.parameters.s.val=2.0
my_jet.parameters.N.val=500
my_jet.parameters.z_cosm.val=0.05
my_jet.set_nu_grid_size(500)
my_jet.set_gamma_grid_size(100)
my_jet.set_IC_nu_size(100)
size=10
#Synch
nu_p_S=np.zeros(size)
nuFnu_p_S=np.zeros(size)
S_index=np.zeros(size)
S_index_err=np.zeros(size)
my_jet.set_IC_mode('off')
#Switch off sych self-abs
my_jet.spectral_components.Sync.state='on'
s_values=np.linspace(1.5,2.5,size)
for ID,s in enumerate(s_values):
my_jet.parameters.s.val=s
my_jet.set_N_from_nuFnu(nu_obs=5E13,nuFnu_obs=1E-11)
my_jet.eval()
x_p,y_p=my_jet.get_component_peak('Sync',log_log=True)
S_index[ID],S_index_err[ID],loglog_pl=get_pl_slope_SED_2(my_jet,'Sync',[10,13])
my_jet.plot_model(p,label=r'$\gamma_{min}$=%2.2e'%gmin,color=colors[ID],auto_label=False,comp='Sync',line_style='--')
p.add_model_plot(loglog_pl,label=r'pl fit for $\gamma_{min}$=%2.2e'%gmin,color=colors[ID],line_style='-')
n_distr_plot(my_jet,ax,c=colors[ID])
ax.set_xlabel(r'log($\gamma$)')
ax.set_ylabel(r'log(n($\gamma$) $\gamma^3$)')
p.sedplot.axvline([10],ls='--',c='black')
p.sedplot.axvline([13],ls='--',c='black')
p.sedplot.scatter(nu_p_S,nuFnu_p_S)
p.rescale(y_min=-18,y_max=-9,x_min=7,x_max=34)
In [39]:
S_spectral_index=S_index-1
matplotlib.rc('font', **font)
fig = plt.figure(figsize=(12,8))
ax=fig.add_subplot(111)
ax.plot(s_values,S_spectral_index,'-o',label=r'Synch index from fit')
ax.fill_between(s_values, S_spectral_index - S_index_err, S_spectral_index + S_index_err,
color='gray', alpha=0.2)
ax.set_ylabel('Synch index')
ax.set_xlabel(r's')
ax.plot(s_values,-(s_values-1)/2,ls='--',c='green',label='-(s-1)/2 Synch. theory')
ax.legend()
Out[39]:
<matplotlib.legend.Legend at 0x126332b50>
Change in the peak frequency of the SED¶
In [40]:
matplotlib.rc('font', **font)
p=PlotSED(figsize=(18,12))
ax=p.fig.add_subplot(222)
my_jet.parameters.gmax.val=1E8
my_jet.parameters.r.val=1.0
my_jet.parameters.s.val=2.0
my_jet.parameters.N.val=500
my_jet.parameters.z_cosm.val=0.05
size=10
#Synch
nu_p_S=np.zeros(size)
nuFnu_p_S=np.zeros(size)
nu_p_S_delta=np.zeros(size)
#e- distr
g_p_e=np.zeros(size)
n3g_p_e=np.zeros(size)
my_jet.set_IC_mode('off')
for ID,gamma0_log_parab in enumerate(np.logspace(2.5,4,size)):
my_jet.set_nu_grid_size(100)
my_jet.set_gamma_grid_size(200)
my_jet.parameters.gamma0_log_parab.val=gamma0_log_parab
my_jet.eval()
x_p,y_p=my_jet.get_component_peak('Sync',log_log=True)
(nu_p_S[ID],nuFnu_p_S[ID],_),err=get_log_par_peak(x_p,y_p,my_jet,'Sync')
my_jet.electron_distribution.update()
g_p_e[ID],n3g_p_e[ID],_=get_gamma_3p(my_jet)
nu_p_S_delta[ID]=nu_p_S_delta_approx(my_jet,g_p_e[ID])
my_jet.plot_model(p,label=r'$\gamma 0$=%2.2e'%gamma0_log_parab,color=colors[ID],auto_label=False,comp='Sync')
n_distr_plot(my_jet,ax,c=colors[ID])
ax.set_xlabel(r'log($\gamma$)')
ax.set_ylabel(r'log(n($\gamma$) $\gamma^3$)')
p.sedplot.scatter(nu_p_S,nuFnu_p_S)
ax.scatter(g_p_e,n3g_p_e)
p.rescale(y_min=-18,y_max=-11,x_min=8.9,x_max=30)
ax.set_ylim(2,9)
Out[40]:
(2, 9)
In [41]:
#plt.plot(nu_p_S, 10**(nu_p_S - nu_p_S_delta))
#plt.ylim(0,1.5)
matplotlib.rc('font', **font)
fig = plt.figure(figsize=(12,8))
ax=fig.add_subplot(111)
ax.plot(nu_p_S,10**(nu_p_S - nu_p_S_delta),'-o',label=r'$\nu_p$ S from $\delta$-approx / $\nu_p$ S peak from SED fit')
ax.set_ylabel('ratio')
ax.set_xlabel(r'log($\gamma_{3p}$ e-)')
#ax.axvline(4.0,ls='--',c='black')
ax.axhline(1.0,ls='--',c='red')
ax.legend(fontsize='large',loc='best')
ax.set_ylim(0,1.5)
Out[41]:
(0, 1.5)
Trends for the inverse Compton and synchrotron emission¶
Changing $\gamma_{min}$¶
In [42]:
matplotlib.rc('font', **font)
p=PlotSED(figsize=(12,9))
my_jet=Jet(electron_distribution='lppl')
my_jet.parameters.gmax.val=1E8
my_jet.parameters.r.val=1.0
for ID,gmin in enumerate([10,5000,10000]):
my_jet.set_gamma_grid_size(200)
my_jet.set_IC_nu_size(100)
my_jet.parameters.gmin.val=gmin
my_jet.set_N_from_nuFnu(nu_obs=1E17,nuFnu_obs=1E-13)
my_jet.eval()
my_jet.plot_model(p,label='gmin=%2.2e'%gmin,color=colors[ID])
In [ ]:
Changing the turn-over energy¶
In [43]:
my_jet=Jet(electron_distribution='lppl')
matplotlib.rc('font', **font)
p=PlotSED(figsize=(12,9))
my_jet.parameters.gmax.val=1E8
my_jet.parameters.r.val=1.0
my_jet.parameters.s.val=2.0
my_jet.parameters.N.val=500
my_jet.parameters.z_cosm.val=0.05
for ID,gamma0_log_parab in enumerate(np.logspace(3,5,5)):
my_jet.set_nu_grid_size(1000)
my_jet.set_gamma_grid_size(200)
my_jet.set_IC_nu_size(100)
my_jet.parameters.gamma0_log_parab.val=gamma0_log_parab
my_jet.eval()
my_jet.plot_model(p,label='gammma_0=%2.2e'%gamma0_log_parab,color=colors[ID])
p.rescale(y_min=-20,y_max=-11,x_min=9)
Transition from TH to KN regime for the IC emission: changing the curvature in the high-enegy branch of the emitters¶
In [44]:
my_jet=Jet(electron_distribution='lppl')
matplotlib.rc('font', **font)
p=PlotSED(figsize=(12,9))
pe=PlotPdistr()
pe.fig.set_size_inches(8,6)
my_jet.parameters.gmax.val=1E8
my_jet.parameters.gamma0_log_parab.val=5E3
my_jet.parameters.B.val=.5
my_jet.nu_max=1E30
my_jet.set_gamma_grid_size(100)
my_jet.set_IC_nu_size(100)
size=10
nu_p_S=np.zeros(size)
nu_p_IC=np.zeros(size)
nuFnu_p_S=np.zeros(size)
nuFnu_p_IC=np.zeros(size)
r_S=np.zeros(size)
r_S_err=np.zeros(size)
r_IC=np.zeros(size)
r_IC_err=np.zeros(size)
r_values=np.linspace(2.0,0.5,size)
for ID,r in enumerate(r_values):
my_jet.parameters.r.val=r
my_jet.set_N_from_nuFnu(nu_obs=1E10,nuFnu_obs=1E-14)
my_jet.eval()
my_jet.plot_model(p,label='r=%2.2e'%r,color=colors[ID])
x_p,y_p=my_jet.get_component_peak('Sync',log_log=True)
(nu_p_S[ID],nuFnu_p_S[ID],r_S[ID]),err=get_log_par_peak(x_p,y_p,my_jet,'Sync',delta_p=[0,1])
r_S_err[ID]=err[2]
x_p,y_p=my_jet.get_component_peak('SSC',log_log=True)
(nu_p_IC[ID],nuFnu_p_IC[ID],r_IC[ID]),err=get_log_par_peak(x_p,y_p,my_jet,'SSC',delta_p=[0,1])
r_IC_err[ID]=err[2]
my_jet.electron_distribution.plot3p(pe)
p.rescale(y_min=-14,y_max=-10.5,x_min=10,x_max=29)
pe.rescale(y_min=0)
the following plot shows the trend for the S curvature (b) and the IC curvature (both measured over one decade starting from the peak) versus the curvature of the electron distribution (r)
In [45]:
fig = plt.figure(figsize=(12,8))
ax=fig.add_subplot(111)
ax.errorbar(r_values,r_S,yerr=r_S_err,fmt='-o',label='S curvature')
ax.fill_between(r_values, r_S - r_S_err, r_S + r_S_err,
color='gray', alpha=0.2)
ax.errorbar(r_values,r_IC,yerr=r_IC_err,fmt='-o',label='IC curvature')
ax.fill_between(r_values, r_IC - r_IC_err, r_IC + r_IC_err,
color='gray', alpha=0.2)
ax.plot(r_values,-r_values/5, label='b = r/5')
ax.set_ylabel('spectral curvature')
ax.set_xlabel(r'e- curvature r')
#ax.axvline(,ls='--',c='black')
#ax.axhline(-0.2,ls='--',c='red',label='sync theor. b~r/5')
ax.legend(fontsize='large')
Out[45]:
<matplotlib.legend.Legend at 0x123e3f790>
Transition from TH to KN regime for the IC emission: changing the turnover energy¶
In [46]:
my_jet=Jet(electron_distribution='lppl')
matplotlib.rc('font', **font)
p=PlotSED(figsize=(12,9))
size=10
my_jet.parameters.gmax.val=1E8
my_jet.parameters.r.val=1.0
my_jet.parameters.s.val=2.0
my_jet.parameters.N.val=500
my_jet.parameters.z_cosm.val=0.05
my_jet.set_nu_grid_size(200)
my_jet.set_gamma_grid_size(200)
my_jet.set_IC_nu_size(200)
nu_p_S=np.zeros(size)
nu_p_IC=np.zeros(size)
nuFnu_p_S=np.zeros(size)
nuFnu_p_IC=np.zeros(size)
r_S=np.zeros(size)
r_S_err=np.zeros(size)
r_IC=np.zeros(size)
r_IC_err=np.zeros(size)
g_p_e=np.zeros(size)
n3g_p_e=np.zeros(size)
#colors=list(mcolors.CSS4_COLORS)
for ID,gamma0_log_parab in enumerate(np.logspace(2.5,5,size)):
my_jet.parameters.gamma0_log_parab.val=gamma0_log_parab
my_jet.eval()
my_jet.plot_model(p,comp='Sum',label='$\gamma0$_log_parab = %2.2e'%gamma0_log_parab)
#with log_log=True, the values are already logarthmic
x_p,y_p=my_jet.get_component_peak('Sync',log_log=True)
(nu_p_S[ID],nuFnu_p_S[ID],r_S[ID]),err=get_log_par_peak(x_p,y_p,my_jet,'Sync', delta_p=[0,1])
r_S_err[ID]=err[2]
x_p,y_p=my_jet.get_component_peak('SSC',log_log=True)
(nu_p_IC[ID],nuFnu_p_IC[ID],r_IC[ID]),err=get_log_par_peak(x_p,y_p,my_jet,'SSC', delta_p=[0,1])
r_IC_err[ID]=err[2]
g_p_e[ID],n3g_p_e[ID],_=get_gamma_3p(my_jet)
p.rescale(y_min=-18,y_max=-11.5,x_min=9)
p.sedplot.scatter(nu_p_S,nuFnu_p_S)
p.sedplot.scatter(nu_p_IC,nuFnu_p_IC)
Out[46]:
<matplotlib.collections.PathCollection at 0x1223ba390>
In [47]:
matplotlib.rc('font', **font)
fig = plt.figure(figsize=(12,8))
ax=fig.add_subplot(111)
ax.plot(g_p_e,(nu_p_IC-nu_p_S)-2*g_p_e,'-o')
ax.set_ylabel(r'log($ \frac{(\nu_p^{IC} / \nu_p^{S})}{\gamma_{3p}^2} $)''')
ax.set_xlabel(r'log($\gamma_{3p}$ e-)')
ax.axvline(4.0,ls='--',c='black')
ax.axhline(np.log10(4/3),ls='--',c='red',label=r"$ \frac{(\nu_p^{IC} / \nu_p^{S})}{\gamma_{3p}^2} =4/3 $")
ax.legend(fontsize='large',loc='lower left')
Out[47]:
<matplotlib.legend.Legend at 0x11fae4e10>
In [48]:
fig = plt.figure(figsize=(12,8))
ax=fig.add_subplot(111)
ax.errorbar(g_p_e,r_S,yerr=r_S_err,fmt='-o',label='S')
ax.fill_between(g_p_e, r_S - r_S_err, r_S + r_S_err,
color='gray', alpha=0.2)
ax.errorbar(g_p_e,r_IC,yerr=r_IC_err,fmt='-o',label='IC')
ax.fill_between(g_p_e, r_IC - r_IC_err, r_IC + r_IC_err,
color='gray', alpha=0.2)
ax.set_ylabel('spectral curvature')
ax.set_xlabel(r'log($\gamma_{3p}$ e-)')
ax.axvline(4.0,ls='--',c='black')
ax.axhline(-0.2,ls='--',c='red',label='sync theor. b~r/5')
ax.legend(fontsize='large')
Out[48]:
<matplotlib.legend.Legend at 0x124a3e090>
Exercise¶
derive the trend for the Compton dominance (CD) as a function of N a gamma0_log_parab
hint: use the get_component_peak to extract the peak of the SED for each component
In [ ]: