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diff --git a/fg21sim/extragalactic/clusters/emission.py b/fg21sim/extragalactic/clusters/emission.py
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+# Copyright (c) 2017 Weitian LI <liweitianux@live.com>
+# MIT license
+
+"""
+Calculate the synchrotron emission for simulated radio halos.
+"""
+
+import logging
+
+import numpy as np
+import scipy.integrate
+import scipy.special
+
+from .units import (Units as AU, Constants as AC)
+
+
+logger = logging.getLogger(__name__)
+
+
+class SynchrotronEmission:
+    """
+    Calculate the synchrotron emission from a given population
+    of electrons.
+
+    References
+    ----------
+    [1] Cassano & Brunetti 2005, MNRAS, 357, 1313
+        http://adsabs.harvard.edu/abs/2005MNRAS.357.1313C
+        Appendix.C
+    """
+    def __init__(self, B):
+        # Uniform magnetic field strength
+        self.B = B  # [uG]
+
+    @property
+    def frequency_larmor(self):
+        """
+        Electron Larmor frequency:
+            ν_L = e * B / (2*π * m0 * c) = e * B / (2*π * mec)
+
+        Unit: MHz
+        """
+        coef = AC.e / (2*np.pi * AU.mec)  # [Hz/G]
+        coef *= 1e-12  # [MHz/uG]
+        nu = coef * self.B  # [MHz]
+        return nu
+
+    def frequency_crit(self, p, theta=np.pi/2):
+        """
+        Synchrotron critical frequency.
+
+        Critical frequency:
+            ν_c = (3/2) * γ^2 * sin(θ) * ν_L
+
+        Parameters
+        ----------
+        p : float
+            Electron momentum (unit: mec), i.e., Lorentz factor γ
+        theta : float, optional
+            The angle between the electron velocity and the magnetic field.
+            (unit: radian)
+
+        Returns
+        -------
+        nu : float
+            Critical frequency, unit: MHz
+        """
+        nu_L = self.frequency_larmor
+        nu = (3/2) * p**2 * np.sin(theta) * nu_L
+        return nu
+
+    def F(self, x):
+        """
+        Synchrotron kernel function.
+        """
+        val = x * scipy.integrate.quad(lambda t: scipy.special.kv(5/3, t),
+                                       a=x, b=np.inf)[0]
+        return val
+
+    def emissivity(self, nu, p, n_e):
+        """
+        Calculate the synchrotron emissivity (power emitted per volume
+        and per frequency) at the specified frequency from the given
+        electron number & energy distribution
+
+        Parameters
+        ----------
+        nu : float
+            Frequency (unit: MHz) where to calculate the emissivity.
+        p : `~numpy.ndarray`
+            The momentum grid adopted when solving the Fokker-Planck equation.
+            Unit: [mec]
+        n_e : `~numpy.ndarray`
+            Electron spectrum by solving the Fokker-Planck equation.
+            Unit: [cm^-3 mec^-1]
+
+        Returns
+        -------
+        j_nu : float
+            Synchrotron emissivity at frequency ``nu``.
+            Unit: [erg/s/cm^3/Hz]
+        """
+        def func(theta, _p, _n_e):
+            nu_c = self.frequency_crit(_p, theta)
+            x = nu / nu_c
+            return (np.sin(theta)**2 * _n_e * self.F(x))
+
+        coef = np.sqrt(3) * AC.e**3 * self.B / AC.c  # multiplied a [mec]
+        func_p = np.zeros(p.shape)
+        for i in range(len(p)):
+            # Integrate over ``theta``
+            func_p[i] = scipy.integrate.quad(
+                lambda t: func(t, p[i], n_e[i]),
+                a=0, b=np.pi/2)[0]
+        # Integrate over ``p``
+        j_nu = coef * scipy.integrate.trapz(func_p, p)
+        return j_nu