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-rw-r--r--fg21sim/extragalactic/clusters/halo.py39
1 files changed, 24 insertions, 15 deletions
diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py
index 81a185c..6b1d4a8 100644
--- a/fg21sim/extragalactic/clusters/halo.py
+++ b/fg21sim/extragalactic/clusters/halo.py
@@ -679,7 +679,7 @@ class RadioHalo:
return helper.magnetic_field(mass=mass, z=z, configs=self.configs)
@lru_cache()
- def _gas_density_profile_f(self, t):
+ def _rho_gas_f(self, t):
"""
The gas density profile of the merged cluster.
@@ -697,8 +697,7 @@ class RadioHalo:
@lru_cache()
def _velocity_turb(self, t):
"""
- Calculate the turbulence velocity dispersion (i.e., turbulence Mach
- number).
+ Calculate the turbulence velocity dispersion.
NOTE
----
@@ -707,15 +706,19 @@ class RadioHalo:
Then estimate the turbulence velocity dispersion from its energy.
Merger energy:
- E_merger ≅ 0.5 * f_gas * M_sub * v_vir^2
- v_vir = sqrt(G*M_main / R_vir)
+ E_merger ≅ <ρ_gas> * v_i^2 * V_turb
+ V_turb = ᴨ * r_s^2 * R_vir
Turbulence energy:
- E_turb ≅ η_turb * E_merger
- ≅ 0.5 * M_turb * <v_turb^2>
+ E_turb ≅ η_turb * E_merger ≅ 0.5 * M_turb * <v_turb^2>
=> Velocity dispersion:
- <v_turb^2> ≅ v_vir^2 * η_turb*f_gas * (M_sub/M_turb)
+ <v_turb^2> ≅ 2*η_turb * <ρ_gas> * v_i^2 * V_turb / M_turb
+ M_turb = int_0^R_turb[ ρ_gas(r)*4ᴨ*r^2 ]dr
where:
- M_turb = int_0^R_turb ρ_gas(r)*4ᴨ*r^2 dr
+ <ρ_gas>: mean gas density of the main cluster
+ R_vir: virial radius of the main cluster
+ R_turb: radius of turbulence region
+ v_i: impact velocity
+ r_s: stripping radius of the in-falling sub-cluster
Returns
-------
@@ -724,17 +727,23 @@ class RadioHalo:
Unit: [km/s]
"""
z = COSMO.redshift(t)
- rho_gas_f = self._gas_density_profile_f(t)
+ rho_gas_f = self._rho_gas_f(t)
R_turb = self.radius_turbulence(t) # [kpc]
M_turb = 4*np.pi * integrate.quad(lambda r: rho_gas_f(r) * r**2,
a=0, b=R_turb)[0] # [Msun]
+
M_main = self.mass_main(t)
M_sub = self.mass_sub(t)
- R_vir = helper.radius_virial(M_main+M_sub, z) # [kpc]
- R_vir *= AUC.kpc2cm # [cm]
- v2_vir = (AC.G * M_main*AUC.Msun2g / R_vir) * AUC.cm2km**2
- v2_turb = v2_vir * self.eta_turb*COSMO.baryon_fraction * (M_sub/M_turb)
- return np.sqrt(v2_turb)
+ v_i = helper.velocity_impact(M_main, M_sub, z) # [km/s]
+ rho_main = helper.density_number_thermal(M_main, z) # [cm^-3]
+ rho_main *= AC.mu*AC.u * AUC.g2Msun * AUC.kpc2cm**3 # [Msun/kpc^3]
+ R_vir = helper.radius_virial(M_main, z) # [kpc]
+ r_s = self.radius_stripping(t) # [kpc]
+
+ V_turb = np.pi * r_s**2 * R_vir # [kpc^3]
+ E_turb = self.eta_turb * rho_main * v_i**2 * V_turb
+ v2_turb = 2 * E_turb / M_turb # [km^2/s^2]
+ return np.sqrt(v2_turb) # [km/s]
def _is_turb_active(self, t):
"""