clusters/halo: calc turbulence velocity dispersion based on merger

Also update the description of option "extragalactic/halos/eta_turb"
and change its default value to 0.1

2 files changed, 41 insertions, 9 deletions

diff --git a/fg21sim/configs/20-extragalactic.conf.spec b/fg21sim/configs/20-extragalactic.conf.spec
index 44fb1ca..52f66da 100644
--- a/fg21sim/configs/20-extragalactic.conf.spec
+++ b/fg21sim/configs/20-extragalactic.conf.spec
@@ -167,17 +167,11 @@
   # used to determine the radio halo size.
   f_lturb = float(default=0.33, min=0.1, max=1.0)
 
-  # The fraction of cluster thermal energy originating from turbulent
-  # dissipation, which describes the turbulence intensity in the ICM,
-  # and determines its Mach number.
-  # NOTE: Currently, this parameter only determines the turbulence Mach
-  #       number, which affects only the turbulent acceleration efficiency,
-  #       which is also controlled by the above ``f_acc`` parameter.
-  #       So we can just *fix* this parameter to its default value.
-  eta_turb = float(default=0.2, min=0.1, max=1.0)
-
   # Ratio of the total energy injected into cosmic-ray electrons during
   # the cluster life to its total thermal energy.
+  # The fraction of merger energy transferred into the turbulence.
+  eta_turb = float(default=0.1, min=0.1, max=0.5)
+
   eta_e = float(default=0.001, min=0.001, max=0.1)
 
   # Electron injection, which is assumed to have a constant injection
diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py
index 03e891c..47f8078 100644
--- a/fg21sim/extragalactic/clusters/halo.py
+++ b/fg21sim/extragalactic/clusters/halo.py
@@ -813,6 +813,44 @@ class RadioHalo:
         mass = rate * (t - t_merger) + self.M_main
         return mass
 
+    def _velocity_turb(self, t):
+        """
+        Calculate the turbulence velocity dispersion (i.e., turbulence
+        Mach number).
+
+        NOTE
+        ----
+        During the merger, a fraction of the merger kinetic energy is
+        transferred into the turbulence within the assumed regions
+        (radius <= L, the injection scale).  Then estimate the turbulence
+        velocity dispersion from its energy.
+
+        Merger energy:
+            E_m ≅ 0.5 * f_gas * M_sub * v^2
+                ≅ 0.5 * f_gas * M_sub * (G*M_main / R_vir)
+        Turbulence energy:
+            E_turb ≅ η_turb * E_m
+                   ≅ 0.5 * M_turb * <v_turb^2>
+                   = 0.5 * f_gas * M_main(<L) * <v_turb^2>
+                   = 0.5 * f_gas * f_mass(L/R_vir) * M_main * <v_turb^2>
+        => Velocity dispersion:
+            <v_turb^2> ≅ (η_turb/f_mass) * (G*M_sub/R_vir)
+
+        Returns
+        -------
+        v_turb : float
+            The turbulence velocity dispersion
+            Unit: [km/s]
+        """
+        mass = self.M_main + self.M_sub
+        z = COSMO.redshift(t)
+        R_vir = helper.radius_virial(mass=mass, z=z) * AUC.kpc2cm  # [cm]
+        v2 = np.sqrt(AC.G * self.M_sub*AUC.Msun2g / R_vir)  # [cm/s]
+        v2 *= AUC.cm2km  # [km/s]
+        fmass = helper.fmass_nfw(self.f_lturb)
+        v_turb = v2 * np.sqrt(self.eta_turb / fmass)
+        return v_turb
+
     def _magnetic_field(self, t):
         """
         Calculate the mean magnetic field strength of the main cluster mass