diff options
Diffstat (limited to 'fg21sim/extragalactic/clusters')
| -rw-r--r-- | fg21sim/extragalactic/clusters/halo.py | 167 |
1 files changed, 97 insertions, 70 deletions
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 |