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-rw-r--r--fg21sim/configs/20-extragalactic.conf.spec1
-rw-r--r--fg21sim/extragalactic/clusters/halo.py167
2 files changed, 98 insertions, 70 deletions
diff --git a/fg21sim/configs/20-extragalactic.conf.spec b/fg21sim/configs/20-extragalactic.conf.spec
index 320c3c1..b35507e 100644
--- a/fg21sim/configs/20-extragalactic.conf.spec
+++ b/fg21sim/configs/20-extragalactic.conf.spec
@@ -45,6 +45,7 @@
# Reference: Cassano et al. 2012, A&A, 548, A100, Eq.(1)
#
# The mean magnetic field assumed
+ # Unit: [uG]
b_mean = float(default=1.9, min=0.1, max=10)
# The index of the scaling relation
b_index = float(default=1.5, min=0.0, max=3.0)
diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py
index 958dd6c..b2f935e 100644
--- a/fg21sim/extragalactic/clusters/halo.py
+++ b/fg21sim/extragalactic/clusters/halo.py
@@ -2,25 +2,47 @@
# MIT license
"""
-Simulate (giant) radio halos following the "statistical
-magneto-turbulent model" proposed by Cassano & Brunetti (2005).
+Simulate (giant) radio halo originating from the last/ most recent
+cluster-cluster major merger event, following the "statistical
+magneto-turbulent model" proposed by [cassano2005]_, but with many
+modifications and simplifications.
References
----------
-[1] Cassano & Brunetti 2005, MNRAS, 357, 1313
- http://adsabs.harvard.edu/abs/2005MNRAS.357.1313C
-[2] Cassano, Brunetti & Setti, 2006, MNRAS, 369, 1577
- http://adsabs.harvard.edu/abs/2006MNRAS.369.1577C
-[3] Cassano et al. 2012, A&A, 548, A100
- http://adsabs.harvard.edu/abs/2012A%26A...548A.100C
-[4] Donnert 2013, AN, 334, 615
- http://adsabs.harvard.edu/abs/2013AN....334..515D
+.. [brunetti2011]
+ Brunetti & Lazarian 2011, MNRAS, 410, 127
+ http://adsabs.harvard.edu/abs/2011MNRAS.410..127B
+
+.. [cassano2005]
+ Cassano & Brunetti 2005, MNRAS, 357, 1313
+ http://adsabs.harvard.edu/abs/2005MNRAS.357.1313C
+
+.. [cassano2006]
+ Cassano, Brunetti & Setti, 2006, MNRAS, 369, 1577
+ http://adsabs.harvard.edu/abs/2006MNRAS.369.1577C
+
+.. [cassano2012]
+ Cassano et al. 2012, A&A, 548, A100
+ http://adsabs.harvard.edu/abs/2012A%26A...548A.100C
+
+.. [donnert2013]
+ Donnert 2013, AN, 334, 615
+ http://adsabs.harvard.edu/abs/2013AN....334..515D
+
+.. [donnert2014]
+ Donnert & Brunetti 2014, MNRAS, 443, 3564
+ http://adsabs.harvard.edu/abs/2014MNRAS.443.3564D
+
+.. [sarazin1999]
+ Sarazin 1999, ApJ, 520, 529
+ http://adsabs.harvard.edu/abs/1999ApJ...520..529S
"""
import logging
import numpy as np
+from . import helper
from .solver import FokkerPlanckSolver
from ...utils import cosmo
from ...utils.units import (Units as AU,
@@ -33,13 +55,22 @@ logger = logging.getLogger(__name__)
class RadioHalo:
"""
- Simulate a single (giant) radio halos following the "statistical
- magneto-turbulent model" proposed by Cassano & Brunetti (2005).
-
- First, simulate the cluster merging history from the extended
- Press-Schecter formalism using the Monte Carlo method; then derive
- the merger energy and turbulence energy as well as its spectrum;
- after that, calculate the electron acceleration and time evolution
+ Simulate the extended radio halo emission from galaxy cluster
+ experiencing on-going/recent merger.
+
+ Description
+ -----------
+ 1. Calculate the merger crossing time (t_cross; ~1 Gyr);
+ 2. Calculate the diffusion coefficient (Dpp) from the systematic
+ acceleration timescale (tau_acc; ~0.1 Gyr). The acceleration
+ diffusion is assumed to have an action time ~ t_cross (i.e.,
+ only during merger crossing), and then been disabled (i.e.,
+ only radiation and ionization losses later);
+ 3. Assume the electrons are constantly injected and has a power-law
+ energy spectrum;
+ 4. Determine the initial electron density
+
+ after that, calculate the electron acceleration and time evolution
by solving the Fokker-Planck equation; and finally derive the radio
emission from the electron spectra.
@@ -70,18 +101,16 @@ class RadioHalo:
Default: ``self.z0``.
n0_e : 1D `~numpy.ndarray`, optional
The initial electron number distribution.
- Should have the same shape as ``self.pgrid`` and has unit
- [cm^-3 mec^-1].
+ Unit: [cm^-3].
Default: accumulated constant-injected electrons until zbegin.
Returns
-------
- p : `~numpy.ndarray`
- The momentum grid adopted for solving the equation.
- Unit: [mec]
+ gamma : `~numpy.ndarray`
+ The Lorentz factor grid adopted for solving the equation.
n_e : `~numpy.ndarray`
The solved electron spectrum at ``zend``.
- Unit: [cm^-3 mec^-1]
+ Unit: [cm^-3]
"""
if zbegin is None:
tstart = cosmo.age(self.zmax)
@@ -93,21 +122,21 @@ class RadioHalo:
tstop = cosmo.age(zend)
fpsolver = FokkerPlanckSolver(
- xmin=self.pmin, xmax=self.pmax,
- grid_num=self.pgrid_num,
- buffer_np=self.buffer_np,
+ xmin=self.gamma_min, xmax=self.gamma_max,
+ x_np=self.gamma_np,
tstep=self.time_step,
f_advection=self.fp_advection,
f_diffusion=self.fp_diffusion,
f_injection=self.fp_injection,
+ buffer_np=self.buffer_np,
)
- p = fpsolver.x
+ gamma = fpsolver.x
if n0_e is None:
# Accumulated constant-injected electrons until ``tstart``.
- n_inj = np.array([self.fp_injection(p_) for p_ in p])
+ n_inj = np.array([self.fp_injection(gm) for gm in gamma])
n0_e = n_inj * tstart
n_e = fpsolver.solve(u0=n0_e, tstart=tstart, tstop=tstop)
- return (p, n_e)
+ return (gamma, n_e)
def _z_end(self, z_begin, time):
"""
@@ -205,69 +234,67 @@ class RadioHalo:
Dpp = chi * p**2 / 4 # [mec^2/Gyr]
return Dpp
- def fp_advection(self, p, t):
+ def fp_advection(self, gamma, t):
"""
Advection term/coefficient for the Fokker-Planck equation,
which describes a systematic tendency for upward or downard
drift of particles.
- This term is also called the "generalized cooling function" by
- Donnert & Brunetti (2014), which includes all relevant energy
- loss functions and the energy gain function due to turbulence.
+ This term is also called the "generalized cooling function"
+ by [donnert2014], which includes all relevant energy loss
+ functions and the energy gain function due to turbulence.
Returns
-------
- Hp : float
- Advection coefficient
- Unit: [mec/Gyr]
-
- References
- ----------
- [1] Donnert & Brunetti 2014, MNRAS, 443, 3564
- http://adsabs.harvard.edu/abs/2014MNRAS.443.3564D
- Eq.(15)
- [2] Cassano & Brunetti 2005, MNRAS, 357, 1313
- http://adsabs.harvard.edu/abs/2005MNRAS.357.1313C
- Eqs.(30,36,38,39)
+ advection : float
+ Advection coefficient, describing the energy loss/gain rate.
+ Unit: [Gyr^-1]
"""
- Hp = (abs(self._dpdt_ion(p, t)) +
- abs(self._dpdt_rad(p, t)) -
- (self.fp_diffusion(p, t) * 2 / p))
- return Hp
+ advection = (abs(self._loss_ion(gamma, t)) +
+ abs(self._loss_rad(gamma, t)) -
+ (self.fp_diffusion(gamma, t) * 2 / gamma))
+ return advection
- def _dpdt_ion(self, p, t):
+ def _loss_ion(self, gamma, t):
"""
Energy loss through ionization and Coulomb collisions.
- References
+ Parameters
----------
- [1] Cassano & Brunetti 2005, MNRAS, 357, 1313
- http://adsabs.harvard.edu/abs/2005MNRAS.357.1313C
- Eq.(38)
- """
- z = cosmo.redshift(t)
- n_th = self._n_thermal(self.M0, z)
- coef = -3.3e-29 * AUC.Gyr2s / self.mec # [mec/Gyr]
- dpdt = coef * n_th * (1 + np.log(p/n_th) / 75)
- return dpdt
+ gamma : float
+ The Lorentz factor of electrons
+ t : float
+ The cosmic time/age
+ Unit: [Gyr]
- def _dpdt_rad(self, p, t):
- """
- Energy loss via synchrotron emission and IC scattering off the CMB.
+ Returns
+ -------
+ loss : float
+ The energy loss rate
+ Unit: [Gyr^-1]
References
----------
- [1] Cassano & Brunetti 2005, MNRAS, 357, 1313
- http://adsabs.harvard.edu/abs/2005MNRAS.357.1313C
- Eq.(39)
+ Ref.[sarazin1999],Eq.(9)
"""
z = cosmo.redshift(t)
- coef = -4.8e-4 * AUC.Gyr2s / self.mec # [mec/Gyr]
- dpdt = (coef * (p*self.mec)**2 *
- ((self.magnetic_field/3.2)**2 + (1+z)**4))
- return dpdt
+ mass = self._mass(t)
+ n_th = helper.density_number_thermal(mass, z)
+ coef = -1.20e-12 * AUC.Gyr2s # [Gyr^-1]
+ loss = coef * n_th * (1 + np.log(gamma/n_th) / 75)
+ return loss
+ def _loss_rad(self, gamma, t):
"""
+ Energy loss via synchrotron emission and inverse Compton
+ scattering off the CMB photons.
+ References
----------
+ Ref.[sarazin1999],Eq.(6,7)
"""
+ z = cosmo.redshift(t)
+ coef = -1.37e-20 * AUC.Gyr2s # [Gyr^-1]
+ loss = (coef * gamma**2 *
+ ((self.magnetic_field/3.25)**2 + (1+z)**4))
+ return loss
Copyright © 2017-2018 Aaron LI. All Rights Reserved.