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authorAaron LI <aly@aaronly.me>2017-12-31 16:36:56 +0800
committerAaron LI <aly@aaronly.me>2017-12-31 16:36:56 +0800
commit695cb0272a2d6ea22e2d8988fdf723c1b944072f (patch)
tree987d7c58a875d5341c14f968970133584eafaf30 /fg21sim/extragalactic/clusters
parent46c36b299dbe29d2872ae1ae6d98f1bde320bad0 (diff)
downloadfg21sim-695cb0272a2d6ea22e2d8988fdf723c1b944072f.tar.bz2
clusters/halo: Rework the turbulence acceleration timescale calculation
The new method adopted to determine the turbulence acceleration timescale follows [miniati2015] and [pinzke2017], in which the merger-induced turbulence cascades into small scales (and thus accelerate electrons) through the TTD (transit-time damping) mechanism by scattering mainly with the relativistic particles (cosmic-ray protons and electrons).
Diffstat (limited to 'fg21sim/extragalactic/clusters')
-rw-r--r--fg21sim/extragalactic/clusters/halo.py86
1 files changed, 39 insertions, 47 deletions
diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py
index 47f8078..6605763 100644
--- a/fg21sim/extragalactic/clusters/halo.py
+++ b/fg21sim/extragalactic/clusters/halo.py
@@ -42,8 +42,12 @@ References
http://adsabs.harvard.edu/abs/1999astro.ph..5116H
.. [miniati2015]
- Miniati & Beresnyak 2015, Nature, 523, 59
- http://adsabs.harvard.edu/abs/2015Natur.523...59M
+ Miniati 2015, ApJ, 800, 60
+ http://adsabs.harvard.edu/abs/2015ApJ...800...60M
+
+.. [pinzke2017]
+ Pinzke, Oh & Pfrommer 2017, MNRAS, 465, 4800
+ http://adsabs.harvard.edu/abs/2017MNRAS.465.4800P
.. [sarazin1999]
Sarazin 1999, ApJ, 520, 529
@@ -141,10 +145,12 @@ class RadioHalo:
def _set_configs(self):
comp = "extragalactic/halos"
- self.f_lturb = self.configs.getn(comp+"/f_lturb")
self.f_acc = self.configs.getn(comp+"/f_acc")
+ self.f_lturb = self.configs.getn(comp+"/f_lturb")
+ self.zeta_ins = self.configs.getn(comp+"/zeta_ins")
self.eta_turb = self.configs.getn(comp+"/eta_turb")
self.eta_e = self.configs.getn(comp+"/eta_e")
+ self.x_cr = self.configs.getn(comp+"/x_cr")
self.gamma_min = self.configs.getn(comp+"/gamma_min")
self.gamma_max = self.configs.getn(comp+"/gamma_max")
self.gamma_np = self.configs.getn(comp+"/gamma_np")
@@ -303,58 +309,44 @@ class RadioHalo:
@property
@lru_cache()
- def Mach_turbulence(self):
- """
- The Mach number of the merger-induced turbulence.
-
- The turbulence Mach number:
- Mach_turb = sqrt(<δv>^2) / c_s
- ≅ sqrt(sqrt(3)/α) * sqrt(η_turb/0.37)
- where:
- c_s is the sound speed,
- α is a parameter ranges about 1.5-3, and we take it as:
- α = 3^(3/2) / 2 ≅ 2.6
- η_turb describes the fraction of thermal energy originating from
- turbulent dissipation, ~0.2-0.4.
-
- Reference: Ref.[miniati2015],Eq.(1)
- """
- alpha = 3**1.5 / 2
- mach = np.sqrt(3**0.5 * self.eta_turb / alpha / 0.37)
- return mach
-
- @property
- @lru_cache()
def tau_acceleration(self):
"""
Calculate the electron acceleration timescale due to turbulent
- waves at the given (cosmic) time, which describes the turbulent
- acceleration efficiency.
+ waves, which describes the turbulent acceleration efficiency.
+ The turbulent acceleration timescale has order of ~0.1 Gyr.
+
+ Here we consider the turbulence cascade mode through scattering
+ in the high-β ICM mediated by plasma instabilities (firehose,
+ 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
+ where:
+ ζ: efficiency factor for the effectiveness of plasma instabilities
+ η_e: relative energy density of cosmic rays (injected relativistic
+ electrons??)
+ 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)
Unit: [Gyr]
- NOTE
- ----
- Generally, the turbulent acceleration timescale is about 0.1 Gyr.
- It is shown that this acceleration timescale depends weakly on
- cluster mass and redshift, therefore, its value is derived at the
- beginning of the merger and assumed to be constant during the
- merging period.
-
- Reference: Ref.[brunetti2016],Eq.(8,9)
+ Reference
+ ---------
+ * Ref.[pinzke2017],Eq.(37)
+ * Ref.[miniati2015],Eq.(29)
"""
- # Turbulence injection scale: assumed to be correlated with the
- # radius of the in-falling sub cluster.
- Rvir_sub = helper.radius_virial(mass=self.M_sub, z=self.z_merger)
- L0 = self.f_lturb * Rvir_sub # [kpc]
-
+ R_vir = helper.radius_virial(mass=self.M_main, z=self.z_merger)
+ L = self.f_lturb * R_vir # [kpc]
cs = helper.speed_sound(self.kT_main) # [km/s]
- x = cs*AUC.km2cm / AC.c
- fx = x * (x**4/4 + x*x - (1+2*x*x) * np.log(x) - 5/4)
-
- term1 = self.f_acc * 2.5 / fx / (self.Mach_turbulence/0.5)**4
- term2 = (L0/300) / (cs/1500)
- tau = term1 * term2 / 1000 # [Gyr]
+ v_turb = self._velocity_turb(t=self.age_merger) # [km/s]
+ tau = (self.x_cr * cs**3 * L /
+ (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
return tau
@property