pynchrotron

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.

Usage

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)

Create an astromodels model

model = pynchrotron.SynchrotronNumerical()

model

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

Plot the model

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, '$\\nu F_{\\nu}$')