added synchrotron documentation

docs/emission_regions.rst

@@ -20,11 +20,7 @@ Follows an example of how to initialise a `Blob` using `astropy` quantities:
 	# define the spectral function through a dictionary
 	spectrum_dict = {
 		"type": "PowerLaw", 
-		"parameters": {
-	    	"p": 2.8, 
-	    	"gamma_min": 1e2, 
-	    	"gamma_max": 1e7
-		}
+		"parameters": {"p": 2.8, "gamma_min": 1e2, "gamma_max": 1e7}
 	}
 	R_b = 1e16 * u.cm
 	B = 1 * u.G

docs/synchrotron.rst

@@ -1,7 +1,81 @@
+.. _synchrotron:
+
+
 Synchrotron Radiation
 =====================
 
-At the moment we compute synchrotron radiation following the approach in
+At the moment we compute synchrotron radiation following the approach of [DermerMenon2009]_ and [Finke2008]_.
+
+Expanding the example in :ref:`emission_regions`, it is here illustrated how to produce a synchrotron spectral energy distribution (SED) staring from a `~agnpy.emission_regions.Blob`. The Synchrotron Self Absorption (SSA) mechanism is considered. 
+
+.. code-block:: python
+
+	import numpy as np
+	import astropy.units as u
+	from astropy.coordinates import Distance
+	from agnpy.emission_regions import Blob
+	from agnpy.synchrotron import Synchrotron
+	import matplotlib.pyplot as plt
+
+	# set the spectrum normalisation (total energy in electrons in this case)
+	spectrum_norm = 1e48 * u.Unit("erg") 
+	# define the spectral function through a dictionary
+	spectrum_dict = {
+		"type": "PowerLaw", 
+		"parameters": {"p": 2.8, "gamma_min": 1e2, "gamma_max": 1e7}
+	}
+	R_b = 1e16 * u.cm
+	B = 1 * u.G
+	z = Distance(1e27, unit=u.cm).z
+	delta_D = 10
+	Gamma = 10
+	blob = Blob(R_b, z, delta_D, Gamma, B, spectrum_norm, spectrum_dict)
+
+to initialise the synchrotron radiation just pass the blob to the Synchrotron object
+
+.. code-block:: python
+
+	synch = Synchrotron(blob)
+	# define a grid of frequency with astropy units and compute the synchrotron SED
+	nu = np.logspace(8, 23) * u.Hz
+	synch_sed = synch.sed_flux(nu)
+	print(synch_sed)
+
+this produces an array of `~astropy.units.Quantity`
+
+.. code-block:: python
+
+	[9.07847459e-16 2.32031260e-15 5.92493131e-15 1.51066918e-14
+ 	3.84225947e-14 9.73302915e-14 2.44919517e-13 6.09602446e-13
+ 	1.49002539e-12 3.53274287e-12 7.95174302e-12 1.63760084e-11
+ 	2.91395183e-11 4.20896994e-11 4.96023122e-11 5.36546912e-11
+ 	5.75762828e-11 6.17811330e-11 6.62930673e-11 7.11345123e-11
+ 	7.63295326e-11 8.19039501e-11 8.78854724e-11 9.43038305e-11
+ 	1.01190926e-10 1.08580991e-10 1.16510753e-10 1.25019617e-10
+ 	1.34149851e-10 1.43946773e-10 1.54458910e-10 1.65738088e-10
+ 	1.77839278e-10 1.90819844e-10 2.04737198e-10 2.19642423e-10
+ 	2.35563710e-10 2.52464433e-10 2.70139425e-10 2.87965635e-10
+ 	3.04330867e-10 3.15437411e-10 3.13250483e-10 2.83748080e-10
+ 	2.11999976e-10 1.06769353e-10 2.42794688e-11 1.12784155e-12
+ 	2.22960447e-15 8.03665999e-21] erg / (cm2 s)
+	
+we can also plot the SED, accounting, for example, for the SSA
+
+.. code-block:: python
+
+	synch_sed_SSA = synch.sed_flux(nu, SSA=True)
+	plt.loglog(nu, synch_sed, color="k", lw=2, label="synchr.")
+	plt.loglog(nu, synch_sed_SSA, lw=2, ls="--", color="gray", label="self absorbed synchr.")
+	plt.xlabel(r"$\nu\,/\,\mathrm{Hz}$")
+	plt.ylabel(r"$\nu F_{\nu}\,/\,(\mathrm{erg}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1})$")
+	plt.legend()
+	plt.show()
+
+.. image:: _static/synch.png
+    :width: 500px
+    :align: center
+
+
 
 
 API