clusters/halo: Estimate turbulence acceleration w.r.t. injection scale

The turbulence injection scale ~ halo size

3 files changed, 39 insertions, 16 deletions

diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py
index 1d9c9aa..5df47cd 100644
--- a/fg21sim/extragalactic/clusters/halo.py
+++ b/fg21sim/extragalactic/clusters/halo.py
@@ -75,11 +75,11 @@ class RadioHalo:
 
     Description
     -----------
-    1. Calculate the merger crossing time (t_cross; ~1 Gyr);
-    2. Calculate the diffusion coefficient (Dpp) from the systematic
+    1. Calculate the turbulence persistence time (tau_turb; ~<1 Gyr);
+    2. Calculate the diffusion coefficient (D_pp) from the systematic
        acceleration timescale (tau_acc; ~0.1 Gyr).  The acceleration
-       diffusion is assumed to have an action time ~ t_cross (i.e.,
-       only during merger crossing), and then been disabled (i.e.,
+       diffusion is assumed to have an action time ~ tau_turb (i.e.,
+       only during turbulence persistence), and then is disabled (i.e.,
        only radiation and ionization losses later);
     3. Assume the electrons are constantly injected and has a power-law
        energy spectrum, determine the injection rate by further assuming
@@ -192,16 +192,16 @@ class RadioHalo:
 
     @property
     @lru_cache()
-    def time_crossing(self):
+    def time_turbulence(self):
         """
-        The time duration of the sub-cluster crossing the main cluster,
-        which is also used to approximate the merging time, during which
-        the turbulence acceleration is regarded as effective.
+        The time duration the merger-induced turbulence persists, which
+        is used to approximate the effective turbulence acceleration
+        timescale.
 
         Unit: [Gyr]
         """
-        return helper.time_crossing(self.M_main, self.M_sub,
-                                    z=self.z_merger)
+        return helper.time_turbulence(self.M_main, self.M_sub,
+                                      z=self.z_merger, configs=self.configs)
 
     @property
     def radius_virial_obs(self):
@@ -706,10 +706,10 @@ class RadioHalo:
         NOTE
         ----
         Considering that the turbulence acceleration is a 2nd-order Fermi
-        process, it has only an effective acceleration time of several 1e8
-        years.  Therefore, the turbulence is assumed to only accelerate
-        the electrons during the merging period, i.e., the acceleration
-        timescale is set to be infinite after "t_merger + time_cross".
+        process, it has only an effective acceleration time ~<1 Gyr.
+        Therefore, only during the period that strong turbulence persists
+        in the ICM that the turbulence could effectively accelerate the
+        relativistic electrons.
 
         WARNING
         -------
@@ -745,7 +745,7 @@ class RadioHalo:
         ----------
         Ref.[donnert2013],Eq.(15)
         """
-        if (t < self.age_merger) or (t > self.age_merger+self.time_crossing):
+        if (t < self.age_merger) or (t > self.age_merger+self.time_turbulence):
             # NO acceleration (see also the above NOTE and WARNING!)
             tau_acc = 10  # [Gyr]
         else:
diff --git a/fg21sim/extragalactic/clusters/helper.py b/fg21sim/extragalactic/clusters/helper.py
index cac6401..10c4f12 100644
--- a/fg21sim/extragalactic/clusters/helper.py
+++ b/fg21sim/extragalactic/clusters/helper.py
@@ -360,6 +360,29 @@ def time_crossing(M_main, M_sub, z=0.0):
     return time
 
 
+def time_turbulence(M_main, M_sub, z=0.0, configs=CONFIGS):
+    """
+    The timescale that the compressive turbulence persists, which is
+    estimated as:
+        τ_turb ≅ 2*d / v_impact,
+    where d ≅ L ≅ R_vir / 3,
+    and L is also the turbulence injection scale.
+    During this timescale, the merger-induced turbulence is regarded
+    to accelerate the relativistic electrons effectively.
+
+    Unit: [Gyr]
+    """
+    # Turbulence injection scale factor
+    key = "extragalactic/halos/f_lturb"
+    f_lturb = configs.getn(key)
+    R_vir = radius_virial(M_main, z)  # [kpc]
+    distance = 2*R_vir * f_lturb
+    vi = velocity_impact(M_main, M_sub, z)  # [km/s]
+    uconv = AUC.kpc2km * AUC.s2Gyr  # [s kpc/km] => [Gyr]
+    time = uconv * distance / vi  # [Gyr]
+    return time
+
+
 def draw_halo(radius, nr=2.0, felong=None, rotation=None):
     """
     Draw the template image of one halo, which is used to simulate
diff --git a/fg21sim/extragalactic/clusters/main.py b/fg21sim/extragalactic/clusters/main.py
index 5bfbf30..a02cbb0 100644
--- a/fg21sim/extragalactic/clusters/main.py
+++ b/fg21sim/extragalactic/clusters/main.py
@@ -288,7 +288,7 @@ class GalaxyClusters:
                 ("Rvir_main", halo.radius_virial_main),  # [kpc] at z_merger
                 ("Rvir_sub", halo.radius_virial_sub),  # [kpc] at z_merger
                 ("tback_merger", halo.tback_merger),  # [Gyr]
-                ("time_crossing", halo.time_crossing),  # [Gyr]
+                ("time_turbulence", halo.time_turbulence),  # [Gyr]
                 ("Rhalo", halo.radius),  # [kpc]
                 ("Rhalo_angular", halo.angular_radius),  # [arcsec]
                 ("volume", halo.volume),  # [kpc^3]