clusters/halo: Determine magnetic field by fraction of its energy density

* Rewrite "magnetic_field()" function to calculate the mean magnetic field
  strength within ICM according its energy density fraction w.r.t. the ICM
  thermal energy density.

* Remove config options "b_mean" and "b_index", which are replaced with the
  option "eta_b", the assumed magnetic energy density fraction w.r.t. the
  ICM thermal energy density.

2 files changed, 26 insertions, 32 deletions

diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py
index e34d91c..e6fe152 100644
--- a/fg21sim/extragalactic/clusters/halo.py
+++ b/fg21sim/extragalactic/clusters/halo.py
@@ -229,7 +229,7 @@ class RadioHalo:
 
         Unit: [uG]
         """
-        return helper.magnetic_field(self.M_obs)
+        return helper.magnetic_field(mass=self.M_obs, z=self.z_obs)
 
     @property
     def kT_merger(self):
@@ -716,6 +716,6 @@ class RadioHalo:
         """
         z = COSMO.redshift(t)
         mass = self._mass(t)  # [Msun]
-        B = helper.magnetic_field(mass)  # [uG]
+        B = helper.magnetic_field(mass=mass, z=z)  # [uG]
         loss = -4.32e-4 * gamma**2 * ((B/3.25)**2 + (1+z)**4)
         return loss
diff --git a/fg21sim/extragalactic/clusters/helper.py b/fg21sim/extragalactic/clusters/helper.py
index 6fd99fb..1c6e48e 100644
--- a/fg21sim/extragalactic/clusters/helper.py
+++ b/fg21sim/extragalactic/clusters/helper.py
@@ -210,6 +210,30 @@ def density_energy_thermal(mass, z=0.0):
     return e_th
 
 
+def magnetic_field(mass, z=0.0):
+    """
+    Calculate the mean magnetic field strength within the ICM, which is
+    also assumed to be uniform, according to the assumed fraction of the
+    the magnetic field energy density w.r.t. the ICM thermal energy density.
+
+    NOTE
+    ----
+    Magnetic field energy density: u_B = B^2 / (8π),
+    where "B" in units of [G], then "u_B" has unit of [erg/cm^3].
+
+    Returns
+    -------
+    B : float
+        The mean magnetic field strength within the ICM.
+        Unit: [uG]
+    """
+    key = "extragalactic/clusters/eta_b"
+    eta_b = CONFIGS.getn(key)
+    e_th = density_energy_thermal(mass=mass, z=z)
+    B = np.sqrt(8*np.pi * eta_b * e_th) * 1e6  # [G] -> [uG]
+    return B
+
+
 def density_energy_electron(spectrum, gamma):
     """
     Calculate the energy density of relativistic electrons.
@@ -295,36 +319,6 @@ def time_crossing(M_main, M_sub, z=0.0):
     return time
 
 
-def magnetic_field(mass):
-    """
-    Calculate the mean magnetic field strength according to the
-    scaling relation between magnetic field and cluster mass.
-
-    Parameters
-    ----------
-    mass : float
-        Cluster mass
-        Unit: [Msun]
-
-    Returns
-    -------
-    B : float
-        The mean magnetic field strength
-        Unit: [uG]
-
-    References
-    ----------
-    Ref.[cassano2012],Eq.(1)
-    """
-    comp = "extragalactic/clusters"
-    b_mean = CONFIGS.getn(comp+"/b_mean")
-    b_index = CONFIGS.getn(comp+"/b_index")
-
-    M_mean = 1.6e15  # [Msun]
-    B = b_mean * (mass/M_mean) ** b_index
-    return B
-
-
 def halo_rprofile(re, num_re=5, I0=1.0):
     """
     Generate the radial profile of a halo.