From f38ae76e6b2cef5a36e9e290f6679da36e100e34 Mon Sep 17 00:00:00 2001 From: Aaron LI Date: Fri, 5 Jan 2018 17:55:54 +0800 Subject: clusters/halo: move tau_max and time dependence to tau_acceleration() --- fg21sim/extragalactic/clusters/halo.py | 54 +++++++++++++++++----------------- 1 file changed, 27 insertions(+), 27 deletions(-) (limited to 'fg21sim/extragalactic/clusters/halo.py') diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py index 3812df6..c0d6df1 100644 --- a/fg21sim/extragalactic/clusters/halo.py +++ b/fg21sim/extragalactic/clusters/halo.py @@ -298,17 +298,28 @@ class RadioHalo: mirror) rather than Coulomb scattering. Therefore, the fast modes damp by TTD (transit time damping) on relativistic rather than thermal particles, and the diffusion coefficient is given by: - D_pp = (2*p^2 * ζ / η_e) * k_L * ^2 / c_s^3 + D_pp = (2*p^2 * ζ / x_cr) * k_L * ^2 / c_s^3 where: ζ: efficiency factor for the effectiveness of plasma instabilities - η_e: relative energy density of cosmic rays (injected relativistic - electrons??) + x_cr: relative energy density of cosmic rays k_L = 2π/L: turbulence injection scale v_turb: turbulence velocity dispersion c_s: sound speed Thus the acceleration timescale is: τ_acc = p^2 / (4*D_pp) - = (η_e * c_s^3 * L) / (16π * ζ * ^2) + = (x_cr * c_s^3 * L) / (16π * ζ * ^2) + + WARNING + ------- + Current test shows that a very large acceleration timescale (e.g., + 1000 or even larger) will cause problems (maybe due to some + limitations within the current calculation scheme), for example, + the energy losses don't seem to have effect in such cases, so the + derived initial electron spectrum is almost the same as the raw + input one, and the emissivity at medium/high frequencies even + decreases when the turbulence acceleration begins! + By carrying out some tests, the value of 10 [Gyr] is adopted for + the maximum acceleration timescale. Parameters ---------- @@ -328,6 +339,12 @@ class RadioHalo: * Ref.[pinzke2017],Eq.(37) * Ref.[miniati2015],Eq.(29) """ + # Maximum acceleration timescale when no turbulence acceleration + # NOTE: see the above WARNING! + tau_max = 10.0 # [Gyr] + if not self._is_turb_active(t): + return tau_max + t_merger = self._merger_time(t) z_merger = COSMO.redshift(t_merger) mass_main = self.mass_main(t_merger) @@ -339,6 +356,10 @@ class RadioHalo: (16*np.pi * self.zeta_ins * v_turb**4)) # [s kpc/km] tau *= AUC.s2Gyr * AUC.kpc2km # [Gyr] tau *= self.f_acc # custom tune parameter + + # Impose the maximum acceleration timescale + if tau > tau_max: + tau = tau_max return tau @property @@ -517,18 +538,7 @@ class RadioHalo: WARNING ------- A zero diffusion coefficient may lead to unstable/wrong results, - since it is not properly taken care of by the solver. Therefore - give the acceleration timescale a large enough but finite value - after turbulent acceleration. - Also note that a very large acceleration timescale (e.g., 1000 or - even 10000) will also cause problems (maybe due to some limitations - within the current calculation scheme), for example, the energy - losses don't seem to have effect in such cases, so the derived - initial electron spectrum is almost the same as the raw input one, - and the emissivity at medium/high frequencies even decreases when - the turbulence acceleration begins! - By carrying out some tests, the value of 10 [Gyr] is adopted for - the maximum acceleration timescale. + since it is not properly taken care of by the solver. Parameters ---------- @@ -548,17 +558,7 @@ class RadioHalo: ---------- Ref.[donnert2013],Eq.(15) """ - # Maximum acceleration timescale when no turbulence acceleration - # NOTE: see the above WARNING! - tau_max = 10.0 # [Gyr] - if self._is_turb_active(t): - tau_acc = self.tau_acceleration(t=t) - else: - tau_acc = tau_max - # Impose the maximum acceleration timescale - if tau_acc > tau_max: - tau_acc = tau_max - + tau_acc = self.tau_acceleration(t=t) gamma = np.asarray(gamma) diffusion = gamma**2 / 4 / tau_acc return diffusion -- cgit v1.2.2