Implements synchrotron emission from cooling electrons. This is the model used in Burgess et al (2019). Please cite if you find this code useful for your research.

• This code gets rid of the need for GSL which was originally relied on for a quick computation of the of the synchrotron kernel which is an integral over a Bessel function.
• This code has been ported from GSL and written directly in python as well as accelerated with numba
• An astromodels function is also supplied for direct use in 3ML.

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
%matplotlib inline 

import pynchrotron

/Users/jburgess/.environs/pynchro/lib/python3.7/site-packages/astromodels/core/parameter.py:555: UserWarning: We have set the min_value of K to 1e-99 because there was a postive transform
  warnings.warn('We have set the min_value of %s to 1e-99 because there was a postive transform' % self.path)
/Users/jburgess/.environs/pynchro/lib/python3.7/site-packages/astromodels/core/parameter.py:555: UserWarning: We have set the min_value of xc to 1e-99 because there was a postive transform
  warnings.warn('We have set the min_value of %s to 1e-99 because there was a postive transform' % self.path)

model = pynchrotron.SynchrotronNumerical()

model

• description: Synchrotron emission from cooling electrions
• formula: $ $
• parameters:
  • K:
    • value: 1.0
    • desc: normalization
    • min_value: 0.0
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: True
  • B:
    • value: 100.0
    • desc: energy scaling
    • min_value: 0.01
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 10.0
    • free: True
  • index:
    • value: 3.5
    • desc: spectral index of electrons
    • min_value: 2.0
    • max_value: 6.0
    • unit:
    • is_normalization: False
    • delta: 0.35000000000000003
    • free: True
  • gamma_min:
    • value: 500000.0
    • desc: minimum electron lorentz factor
    • min_value: 1.0
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 50000.0
    • free: False
  • gamma_cool:
    • value: 90000000.0
    • desc: cooling time of electrons
    • min_value: None
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 9000000.0
    • free: True
  • gamma_max:
    • value: 100000000.0
    • desc: minimum electron lorentz factor
    • min_value: 1000000.0
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 10000000.0
    • free: False
  • bulk_gamma:
    • value: 1.0
    • desc: bulk Lorentz factor
    • min_value: 1.0
    • max_value: None
    • unit:
    • is_normalization: False
    • delta: 0.1
    • free: False

fig, ax = plt.subplots()


ene = np.logspace(1,6,400)

ax.loglog(ene, ene**2 * model(ene))
ax.set_xlabel('energy')
ax.set_ylabel(r'$\nu F_{\nu}$')

Text(0, 0.5, '$\\nu F_{\\nu}$')

fig, ax = plt.subplots()

gamma_min = 500000.

gamma_cool = np.linspace(.1 * gamma_min, 5* gamma_min, 10)



ene = np.logspace(-1,6,400)

for gc in gamma_cool:
    model.gamma_cool = gc
    model.gamma_min = gamma_min
    
    ax.loglog(ene, ene**2 * model(ene))
ax.set_xlabel('energy')
ax.set_ylabel(r'$\nu F_{\nu}$')

Text(0, 0.5, '$\\nu F_{\\nu}$')