diff options
Diffstat (limited to 'fg21sim')
| -rw-r--r-- | fg21sim/extragalactic/clusters/halo.py | 114 |
1 files changed, 57 insertions, 57 deletions
diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py index 669f46e..14a9028 100644 --- a/fg21sim/extragalactic/clusters/halo.py +++ b/fg21sim/extragalactic/clusters/halo.py @@ -219,13 +219,68 @@ class RadioHalo1M: return uconv * 2*L_turb / vi # [Gyr] @lru_cache() + def velocity_turb(self, t_merger): + """ + Calculate the turbulence velocity dispersion. + + NOTE + ---- + During the merger, a fraction of the merger kinetic energy is + transferred into the turbulence within the region of radius R_turb. + Then estimate the turbulence velocity dispersion from its energy. + + Merger energy: + E_merger ≅ <ρ_gas> * v_i^2 * V_turb + V_turb = ᴨ * r_s^2 * (R_vir+r_s) + Turbulence energy: + E_turb ≅ η_turb * E_merger ≅ 0.5 * M_turb * <v_turb^2> + => Velocity dispersion: + <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: + <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 + ------- + v_turb : float + The turbulence velocity dispersion + Unit: [km/s] + """ + self._validate_t_merger(t_merger) + z = COSMO.redshift(t_merger) + M_main = self.mass_main(t_merger) + M_sub = self.mass_sub(t_merger) + r_s = self.radius_stripping(t_merger) # [kpc] + R_turb = self.radius_turbulence(t_merger) # [kpc] + + rho_gas_f = helper.calc_gas_density_profile( + M_main, z, f_rc=self.f_rc, beta=self.beta) + M_turb = 4*np.pi * integrate.quad( + lambda r: rho_gas_f(r) * r**2, + a=0, b=R_turb)[0] # [Msun] + + 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] + + 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] + + @lru_cache() def mach_turb(self, t_merger): """ The turbulence Mach number determined from its velocity dispersion. """ self._validate_t_merger(t_merger) cs = helper.speed_sound(self.kT(t_merger)) # [km/s] - v_turb = self._velocity_turb(t_merger) # [km/s] + v_turb = self.velocity_turb(t_merger) # [km/s] return v_turb / cs @lru_cache() @@ -302,7 +357,7 @@ class RadioHalo1M: L = 2 * self.radius_turbulence(t_merger) # [kpc] k_L = 2 * np.pi / L_turb cs = helper.speed_sound(self.kT(t_merger)) # [km/s] - v_t = self._velocity_turb(t_merger) # [km/s] + v_t = self.velocity_turb(t_merger) # [km/s] tau = self.x_cr * cs**3 / (8*k_L * v_t**4) tau *= AUC.s2Gyr * AUC.kpc2km # [s kpc/km] -> [Gyr] @@ -623,61 +678,6 @@ class RadioHalo1M: return helper.magnetic_field(mass=mass, z=z, eta_b=eta_b, kT_out=kT_out) - @lru_cache() - def _velocity_turb(self, t_merger): - """ - Calculate the turbulence velocity dispersion. - - NOTE - ---- - During the merger, a fraction of the merger kinetic energy is - transferred into the turbulence within the region of radius R_turb. - Then estimate the turbulence velocity dispersion from its energy. - - Merger energy: - E_merger ≅ <ρ_gas> * v_i^2 * V_turb - V_turb = ᴨ * r_s^2 * (R_vir+r_s) - Turbulence energy: - E_turb ≅ η_turb * E_merger ≅ 0.5 * M_turb * <v_turb^2> - => Velocity dispersion: - <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: - <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 - ------- - v_turb : float - The turbulence velocity dispersion - Unit: [km/s] - """ - self._validate_t_merger(t_merger) - z = COSMO.redshift(t_merger) - M_main = self.mass_main(t_merger) - M_sub = self.mass_sub(t_merger) - r_s = self.radius_stripping(t_merger) # [kpc] - R_turb = self.radius_turbulence(t_merger) # [kpc] - - rho_gas_f = helper.calc_gas_density_profile( - M_main, z, f_rc=self.f_rc, beta=self.beta) - M_turb = 4*np.pi * integrate.quad( - lambda r: rho_gas_f(r) * r**2, - a=0, b=R_turb)[0] # [Msun] - - 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] - - V_turb = np.pi * r_s**2 * (R_vir+r_s) # [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): """ Is the turbulence acceleration is active at the given time? |