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authorAaron LI <aly@aaronly.me>2018-01-05 17:55:54 +0800
committerAaron LI <aly@aaronly.me>2018-01-05 17:55:54 +0800
commitf38ae76e6b2cef5a36e9e290f6679da36e100e34 (patch)
treeabe6a6058dcb8ba66ff1f6e141130b82af4ca0b1 /fg21sim/extragalactic/clusters
parent713c5144c8f0b0cad8e0287a895b24861888cc9f (diff)
downloadfg21sim-f38ae76e6b2cef5a36e9e290f6679da36e100e34.tar.bz2
clusters/halo: move tau_max and time dependence to tau_acceleration()
Diffstat (limited to 'fg21sim/extragalactic/clusters')
-rw-r--r--fg21sim/extragalactic/clusters/halo.py54
1 files changed, 27 insertions, 27 deletions
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 * <v_turb^2>^2 / c_s^3
+ D_pp = (2*p^2 * ζ / x_cr) * k_L * <v_turb^2>^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 * <v_turb^2>^2)
+ = (x_cr * c_s^3 * L) / (16π * ζ * <v_turb^2>^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