From 929076afedf121aee0778ccd7efe013b8fb68db1 Mon Sep 17 00:00:00 2001
From: Aaron LI <aly@aaronly.me>
Date: Fri, 25 Jan 2019 15:08:35 +0800
Subject: clusters: Assume equipartition between B field and CR

Equipartition between the magnetic fields and cosmic rays is assumed,
i.e., eta_b == x_cr.  Therefore remove "extragalactic/clusters/eta_b"
configuration option.
---
 fg21sim/configs/config.spec              | 16 +++-------------
 fg21sim/extragalactic/clusters/halo.py   |  2 +-
 fg21sim/extragalactic/clusters/helper.py | 16 ++++++++++++++--
 3 files changed, 18 insertions(+), 16 deletions(-)

diff --git a/fg21sim/configs/config.spec b/fg21sim/configs/config.spec
index d580d3f..1ba8dd3 100644
--- a/fg21sim/configs/config.spec
+++ b/fg21sim/configs/config.spec
@@ -354,13 +354,6 @@ stream = option("stderr", "stdout", "", default="stderr")
   # Unit: [Gyr]
   time_traceback = float(default=3.0, min=1.0, max=5.0)
 
-  # The fraction of the magnetic field energy density w.r.t. the ICM
-  # thermal energy density, which is used to determine the mean magnetic
-  # field strength within the ICM and is also assumed to be uniform.
-  # * ~< 0.4% (Ref: Pfrommer & Ensslin 2004, MNRAS)
-  # * ~0.3%-1% (Ref: Bohringer et al. 2016, A&A)
-  eta_b = float(default=0.001, min=1e-5, max=0.1)
-
   # The temperature of the outer gas surrounding the cluster.  Accretion
   # shocks form near the cluster virial radius during the cluster formation,
   # which can heat the cluster ICM to have a higher temperature than the
@@ -401,12 +394,9 @@ stream = option("stderr", "stdout", "", default="stderr")
   # electrons during the cluster life time.
   eta_e = float(default=0.003, min=0.001, max=0.1)
 
-  # The ratio of cosmic ray (including protons and electrons) energy
-  # density (i.e., pressure) to the thermal energy density.
-  # NOTE: Fermi-LAT has placed an upper limit of ~1.25%-1.4%
-  #       (Ackermann et al. 2014, ApJ, 787, 18)
-  # NOTE: The energy ratio of cosmic-ray electrons to protons K_ep ~0.01
-  #       for our Galaxy (Pinzke et al. 2017, MNRAS, 465, 4800)
+  # The energy density ratio of cosmic ray to the thermal ICM.
+  # NOTE: Equipartition between the magnetic field and cosmic ray is
+  #       assumed, i.e., eta_b == x_cr.
   x_cr = float(default=0.015, 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 50d7c6d..68abfad 100644
--- a/fg21sim/extragalactic/clusters/halo.py
+++ b/fg21sim/extragalactic/clusters/halo.py
@@ -632,7 +632,7 @@ class RadioHalo1M:
 
         Unit: [uG]
         """
-        eta_b = self.configs.getn("extragalactic/clusters/eta_b")
+        eta_b = self.x_cr  # Equipartition between magnetic field and CR
         kT_out = self.configs.getn("extragalactic/clusters/kT_out")
         z = COSMO.redshift(t)
         mass = self.mass_main(t)  # [Msun]
diff --git a/fg21sim/extragalactic/clusters/helper.py b/fg21sim/extragalactic/clusters/helper.py
index 18e7133..c4fdecc 100644
--- a/fg21sim/extragalactic/clusters/helper.py
+++ b/fg21sim/extragalactic/clusters/helper.py
@@ -10,6 +10,10 @@ References
    Arnaud, Pointecouteau & Pratt 2005, A&A, 441, 893;
    http://adsabs.harvard.edu/abs/2005A%26A...441..893
 
+.. [beck2005]
+   Beck & Krause 2005, AN, 326, 414
+   http://adsabs.harvard.edu/abs/2005AN....326..414B
+
 .. [cassano2005]
    Cassano & Brunetti 2005, MNRAS, 357, 1313
    http://adsabs.harvard.edu/abs/2005MNRAS.357.1313C
@@ -353,7 +357,7 @@ def density_energy_electron(n_e, gamma):
 def magnetic_field(
         mass,
         z=0.0,
-        eta_b=CONFIGS.getn("extragalactic/clusters/eta_b"),
+        eta_b=CONFIGS.getn("extragalactic/halos/x_cr"),
         kT_out=CONFIGS.getn("extragalactic/clusters/kT_out"),
     ):
     """
@@ -366,6 +370,14 @@ def magnetic_field(
     Magnetic field energy density: u_B = B^2 / (8π),
     where "B" in units of [G], then "u_B" has unit of [erg/cm^3].
 
+    NOTE
+    ----
+    Magnetic fields and cosmic rays are strongly coupled and exchange
+    energy.  Therefore equipartition between them is assumed, i.e.,
+    X_cr (= ε_cr / ε_th) = η_b (= ε_b / ε_th)
+
+    Reference: [beck2005],App.A
+
     Returns
     -------
     B : float
@@ -380,7 +392,7 @@ def magnetic_field(
 def plasma_beta(
         mass,
         z=0.0,
-        eta_b=CONFIGS.getn("extragalactic/clusters/eta_b"),
+        eta_b=CONFIGS.getn("extragalactic/halos/x_cr"),
         kT_out=CONFIGS.getn("extragalactic/clusters/kT_out"),
     ):
     """
-- 
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