From 0ad0d16dd5b12b4f172a873673399106fa99b1fa Mon Sep 17 00:00:00 2001
From: Aaron LI <aly@aaronly.me>
Date: Sat, 26 Jan 2019 15:47:16 +0800
Subject: clusters/halo: Simplify tau_acceleration() method
Move the turbulence activity check into the fp_diffusion() method.
---
fg21sim/extragalactic/clusters/halo.py | 59 ++++++++--------------------------
1 file changed, 14 insertions(+), 45 deletions(-)
diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py
index ed05edf..b480b9c 100644
--- a/fg21sim/extragalactic/clusters/halo.py
+++ b/fg21sim/extragalactic/clusters/halo.py
@@ -256,7 +256,8 @@ class RadioHalo1M:
return helper.radius_stripping(M_main, M_sub, z,
f_rc=self.f_rc, beta=self.beta)
- def tau_acceleration(self, t):
+ @lru_cache()
+ def tau_acceleration(self, t_merger):
"""
Calculate the electron acceleration timescale due to turbulent
waves, which describes the turbulent acceleration efficiency.
@@ -289,42 +290,13 @@ class RadioHalo1M:
= X_cr * c_s^3 * (M_main/1e15)^(-m) / (8*f_acc * k_L * v_t^4)
with: f_acc = f_m * ΞΆ
- WARNING
- -------
- Tests show 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
- ----------
- t : float, optional
- The cosmic time when to determine the acceleration timescale.
- Unit: [Gyr]
-
- Returns
- -------
- tau : float
- The acceleration timescale at the requested time.
- Unit: [Gyr]
-
References
----------
* 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
+ self._validate_t_merger(t_merger)
- t_merger = self._merger_time(t)
L = 2 * self.radius_turbulence(t_merger) # [kpc]
k_L = 2 * np.pi / L_turb
cs = helper.speed_sound(self.kT(t_merger)) # [km/s]
@@ -338,10 +310,7 @@ class RadioHalo1M:
tau *= f_mass
tau /= self.f_acc # tune factor (folded with "zeta_ins")
- # Impose the maximum acceleration timescale
- if tau > tau_max:
- tau = tau_max
- return tau
+ return tau # [Gyr]
@property
@lru_cache()
@@ -530,13 +499,14 @@ class RadioHalo1M:
Diffusion term/coefficient for the Fokker-Planck equation.
The diffusion is directly related to the electron acceleration
- which is described by the ``tau_acc`` acceleration timescale
- parameter.
+ and calculated from the acceleration timescale ``tau_acc``.
WARNING
-------
A zero diffusion coefficient may lead to unstable/wrong results,
since it is not properly taken care of by the solver.
+ By carrying out some tests, the maximum acceleration timescale
+ ``tau_acc`` is assumed to be 10 [Gyr].
Parameters
----------
@@ -551,15 +521,14 @@ class RadioHalo1M:
diffusion : float, or float 1D `~numpy.ndarray`
Diffusion coefficients
Unit: [Gyr^-1]
-
- References
- ----------
- Ref.[donnert2013],Eq.(15)
"""
- tau_acc = self.tau_acceleration(t)
- gamma = np.asarray(gamma)
- diffusion = gamma**2 / 4 / tau_acc
- return diffusion
+ tau_acc = tau_max = 10.0 # [Gyr]
+ if self._is_turb_active(t):
+ t_merger = self._merger_time(t)
+ tau_acc = self.tau_acceleration(t_merger)
+ if tau_acc > tau_max:
+ tau_acc = tau_max
+ return np.square(gamma) / (4 * tau_acc) # [Gyr^-1]
def fp_advection(self, gamma, t):
"""
--
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