diff options
Diffstat (limited to 'fg21sim/extragalactic')
| -rw-r--r-- | fg21sim/extragalactic/clusters/emission.py | 117 | ||||
| -rw-r--r-- | fg21sim/extragalactic/clusters/units.py | 6 |
2 files changed, 123 insertions, 0 deletions
diff --git a/fg21sim/extragalactic/clusters/emission.py b/fg21sim/extragalactic/clusters/emission.py new file mode 100644 index 0000000..e71632b --- /dev/null +++ b/fg21sim/extragalactic/clusters/emission.py @@ -0,0 +1,117 @@ +# 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 diff --git a/fg21sim/extragalactic/clusters/units.py b/fg21sim/extragalactic/clusters/units.py index 01891fa..a7e4ef5 100644 --- a/fg21sim/extragalactic/clusters/units.py +++ b/fg21sim/extragalactic/clusters/units.py @@ -30,10 +30,13 @@ class UnitConversions: Hold the conversion relations directly to avoid repeated/unnecessary calculations. """ + # Mass Msun2g = au.solMass.to(au.g) g2Msun = au.g.to(au.solMass) + # Time Gyr2s = au.Gyr.to(au.s) s2Gyr = au.s.to(au.Gyr) + # Length kpc2cm = au.kpc.to(au.cm) cm2kpc = au.cm.to(au.kpc) Mpc2cm = au.Mpc.to(au.cm) @@ -43,6 +46,7 @@ class UnitConversions: kpc2km = au.kpc.to(au.km) km2kpc = au.km.to(au.kpc) km2cm = au.km.to(au.cm) + # Energy keV2erg = au.keV.to(au.erg) @@ -60,6 +64,8 @@ class Constants: u = ac.u.cgs.value # [g] # Gravitational constant G = ac.G.cgs.value # [cm^3/g/s^2] + # Electron charge + e = ac.e.gauss.value # [Fr] = [esu] # Mean molecular weight # Ref.: Ettori et al, 2013, Space Science Review, 177, 119-154, Eq.(6) |