From 1e1f573e2f4910471a9f7b92e9ff12de48d4c0db Mon Sep 17 00:00:00 2001
From: Aaron LI <aly@aaronly.me>
Date: Thu, 21 Feb 2019 21:43:36 +0800
Subject: clusters/halo: Add velocity_turb_base() method

This method calculates the velocity dispersion of the base turbulence,
i.e., the turbulence existing in a relaxed system without the merger
injection.

Add new configuration option 'extragalactic/halos/x_turb' to
parameterize the energy fraction of the base turbulence w.r.t. the ICM
thernal energy.
---
 fg21sim/configs/config.spec            |  5 +++++
 fg21sim/extragalactic/clusters/halo.py | 41 ++++++++++++++++++++++++++++++++++
 2 files changed, 46 insertions(+)

diff --git a/fg21sim/configs/config.spec b/fg21sim/configs/config.spec
index 0ab5843..9a466d1 100644
--- a/fg21sim/configs/config.spec
+++ b/fg21sim/configs/config.spec
@@ -384,6 +384,11 @@ stream = option("stderr", "stdout", "", default="stderr")
   # to derive the radio halo radius.
   f_radius = float(default=1, min=0.1, max=10)
 
+  # The base energy fraction of the turbulence to the ICM thermal energy
+  # (for a relaxed system).
+  # x_turb ~< 5% [Vazza et al. 2011, A&A, 529, A17]
+  x_turb = float(default=0, min=0, max=0.5)
+
   # The fraction of merger energy transferred into the turbulence.
   eta_turb = float(default=0.1, min=0, max=1)
 
diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py
index 5eda8da..214aefe 100644
--- a/fg21sim/extragalactic/clusters/halo.py
+++ b/fg21sim/extragalactic/clusters/halo.py
@@ -57,6 +57,10 @@ References
 .. [sarazin1999]
    Sarazin 1999, ApJ, 520, 529
    http://adsabs.harvard.edu/abs/1999ApJ...520..529S
+
+.. [vazza2011]
+   Vazza et al. 2011, A&A, 529, A17
+   http://adsabs.harvard.edu/abs/2011A%26A...529A..17V
 """
 
 import logging
@@ -155,6 +159,7 @@ class RadioHalo1M:
         self.configs = configs
         self.f_acc = configs.getn(sec+"/f_acc")
         self.f_radius = configs.getn(sec+"/f_radius")
+        self.x_turb = configs.getn(sec+"/x_turb")
         self.eta_turb = configs.getn(sec+"/eta_turb")
         self.eta_e = configs.getn(sec+"/eta_e")
         self.x_cr = configs.getn(sec+"/x_cr")
@@ -282,6 +287,42 @@ class RadioHalo1M:
         uconv = AUC.kpc2km * AUC.s2Gyr  # [kpc]/[km/s] => [Gyr]
         return uconv * d / v_i  # [Gyr]
 
+    @lru_cache()
+    def velocity_turb_base(self, t):
+        """
+        Calculate the velocity dispersion of the base turbulence.
+
+        Without injection by mergers, the ICM can has some turbulence,
+        which can amount ~< 5% of the thermal energy in relaxed systems
+        (Ref.[vazza2011]).
+
+        ε_turb = (1/2) * ρ_gas * <v_turb^2> = x_turb * ε_th
+        ε_th = (3/2) * n_th * kT
+        ρ_gas = μ * m_u * n_th
+        c_s^2 = γ_gas * kT / (μ * m_u)
+        =>
+        v_turb = c_s * sqrt(3 * x_turb / γ_gas)
+
+        Parameters
+        ----------
+        t_merger : float
+            The beginning or ending time of the merger.
+            Unit: [Gyr]
+
+        Returns
+        -------
+        v_turb : float
+            The velocity dispersion of the base turbulence.
+            Unit: [km/s]
+        """
+        self._validate_time(t)
+
+        if np.isclose(self.x_turb, 0):
+            return 0
+
+        c_s = helper.speed_sound(self.kT(t))  # [km/s]
+        return c_s * np.sqrt(3*self.x_turb / AC.gamma)
+
     @lru_cache()
     def velocity_turb(self, t_merger):
         """
-- 
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