diff options
Diffstat (limited to 'fg21sim')
| -rw-r--r-- | fg21sim/configs/20-extragalactic.conf.spec | 14 | ||||
| -rw-r--r-- | fg21sim/extragalactic/clusters/halo.py | 147 | ||||
| -rw-r--r-- | fg21sim/extragalactic/clusters/main.py | 3 |
3 files changed, 104 insertions, 60 deletions
diff --git a/fg21sim/configs/20-extragalactic.conf.spec b/fg21sim/configs/20-extragalactic.conf.spec index 75ea0ec..32311a0 100644 --- a/fg21sim/configs/20-extragalactic.conf.spec +++ b/fg21sim/configs/20-extragalactic.conf.spec @@ -132,8 +132,18 @@ # Giant radio halos for clusters with recent major mergers [[halos]] - # Roughly the fraction of turbulence energy transformed to accelerate - # the electrons, describing the efficiency of turbulence acceleration. + # The turbulence is generally injected at the cluster center during + # a merger. This option parameterize the turbulence injection scale + # to be a fraction of the virial radius of the (main) cluster. + f_lturb = float(default=0.5, min=0.1, max=1.0) + + # The custom option to tune the turbulent acceleration timescale, which + # controls the relativistic particle acceleration efficiencies. + f_acc = float(default=1.5, min=0.1, max=10) + + # The fraction of cluster thermal energy originating from turbulent + # dissipation, which describes the turbulence intensity in the ICM, + # and determines its Mach number. eta_turb = float(default=0.2, min=0.1, max=1.0) # Ratio of the total energy injected into cosmic-ray electrons during diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py index 4bba5a9..d3b5dd1 100644 --- a/fg21sim/extragalactic/clusters/halo.py +++ b/fg21sim/extragalactic/clusters/halo.py @@ -13,6 +13,10 @@ References Brunetti & Lazarian 2011, MNRAS, 410, 127 http://adsabs.harvard.edu/abs/2011MNRAS.410..127B +.. [brunetti2016] + Brunetti 2016, PPCF, 58, 014011 + http://adsabs.harvard.edu/abs/2016PPCF...58a4011B + .. [cassano2005] Cassano & Brunetti 2005, MNRAS, 357, 1313 http://adsabs.harvard.edu/abs/2005MNRAS.357.1313C @@ -33,13 +37,17 @@ References Donnert & Brunetti 2014, MNRAS, 443, 3564 http://adsabs.harvard.edu/abs/2014MNRAS.443.3564D -.. [sarazin1999] - Sarazin 1999, ApJ, 520, 529 - http://adsabs.harvard.edu/abs/1999ApJ...520..529S - .. [hogg1999] Hogg 1999, arXiv:astro-ph/9905116 http://adsabs.harvard.edu/abs/1999astro.ph..5116H + +.. [miniati2015] + Miniati & Beresnyak 2015, Nature, 523, 59 + http://adsabs.harvard.edu/abs/2015Natur.523...59M + +.. [sarazin1999] + Sarazin 1999, ApJ, 520, 529 + http://adsabs.harvard.edu/abs/1999ApJ...520..529S """ import logging @@ -51,7 +59,8 @@ from .solver import FokkerPlanckSolver from .emission import SynchrotronEmission from ...share import CONFIGS, COSMO from ...utils.units import (Units as AU, - UnitConversions as AUC) + UnitConversions as AUC, + Constants as AC) from ...utils.convert import Fnu_to_Tb @@ -129,6 +138,8 @@ class RadioHalo: def _set_configs(self): comp = "extragalactic/halos" + self.f_lturb = self.configs.getn(comp+"/f_lturb") + self.f_acc = self.configs.getn(comp+"/f_acc") self.eta_turb = self.configs.getn(comp+"/eta_turb") self.eta_e = self.configs.getn(comp+"/eta_e") self.gamma_min = self.configs.getn(comp+"/gamma_min") @@ -274,6 +285,61 @@ class RadioHalo: return helper.kT_cluster(self.M_obs, z=self.z_obs) # [keV] @property + def Mach_turbulence(self): + """ + The Mach number of the merger-induced turbulence. + + The turbulence Mach number: + Mach_turb = sqrt(<δv>^2) / c_s + ≅ sqrt(sqrt(3)/α) * sqrt(η_turb/0.37) + where: + c_s is the sound speed, + α is a parameter ranges about 1.5-3, and we take it as: + α = 3^(3/2) / 2 ≅ 2.6 + η_turb describes the fraction of thermal energy originating from + turbulent dissipation, ~0.3. + + Reference: Ref.[miniati2015],Eq.(1) + """ + alpha = 3**1.5 / 2 + mach = np.sqrt(3**0.5 * self.eta_turb / alpha / 0.37) + return mach + + @property + def tau_acceleration(self): + """ + Calculate the electron acceleration timescale due to turbulent + waves at the given (cosmic) time, which describes the turbulent + acceleration efficiency. + + Unit: [Gyr] + + NOTE + ---- + Generally, the turbulent acceleration timescale is about 0.1 Gyr. + It is shown that this acceleration timescale depends weakly on + cluster mass and redshift, therefore, its value is derived at the + beginning of the merger and assumed to be constant throughout the + merging period. + + Reference: Ref.[brunetti2016],Eq.(8,9) + """ + if not hasattr(self, "_tau_acceleration"): + Mach = self.Mach_turbulence + Rvir = helper.radius_virial(mass=self.M_main, z=self.z_merger) + kT = helper.kT_cluster(mass=self.M_main, z=self.z_merger, + radius=Rvir) # [keV] + cs = helper.speed_sound(kT) # [km/s] + # Turbulence injection scale + L0 = self.f_lturb * Rvir # [kpc] + x = cs*AUC.km2cm / AC.c + fx = x * (x**4/4 + x*x - (1+2*x*x) * np.log(x) - 5/4) + term1 = self.f_acc * 2.5 / fx / (Mach/0.5)**4 + term2 = (L0/300) / (cs/1500) + self._tau_acceleration = term1 * term2 / 1000 # [Gyr] + return self._tau_acceleration + + @property def injection_rate(self): """ The constant electron injection rate assumed. @@ -578,11 +644,21 @@ class RadioHalo: """ Diffusion term/coefficient for the Fokker-Planck equation. + The diffusion is directly related to the electron acceleration + which is described by the ``tau_acc`` acceleration timescale + parameter. + NOTE ---- - The diffusion coefficients cannot be zero or negative, which - may cause unstable or wrong results. So constrain ``chi_acc`` - be a small positive number (e.g., 0.01 [Gyr^-1]). + 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". + + However, a zero diffusion coefficient may lead to unstable/wrong + results, so constrain the acceleration timescale to be a large + enough but finite number (e.g., 10 Gyr). Parameters ---------- @@ -602,8 +678,12 @@ class RadioHalo: ---------- Ref.[donnert2013],Eq.(15) """ - chi_acc = self._chi_acceleration(t) # [Gyr^-1] - diffusion = gamma**2 * chi_acc / 4 + if t < (self.age_merger + self.time_crossing): + tau_acc = self.tau_acceleration # [Gyr] + else: + # The large enough timescale to avoid unstable results + tau_acc = 10.0 # [Gyr] + diffusion = gamma**2 / 4 / tau_acc return diffusion def fp_advection(self, gamma, t): @@ -653,53 +733,6 @@ class RadioHalo: mass = rate * (t - t_merger) + self.M_main return mass - def _chi_acceleration(self, t=None): - """ - Calculate the electron acceleration coefficient due to turbulent - waves at the given (cosmic) time. - - Considering that the turbulence acceleration lies a 2nd-order - Fermi process, it has only a effective acceleration time of - several 1e8 years. Therefore, the turbulence is assumed to - only accelerate the electrons during the merging period, i.e., - this coefficient "chi" is zero after "t_merger + time_cross". - - NOTE - ---- - A zero diffusion coefficient may lead to unstable/wrong results, - so constrain this acceleration coefficient to be a small positive - but non-zero number. - - Parameters - ---------- - t : float, optional - The (cosmic) time/age. - If not given, then assumed to be within the merging process. - Unit: [Gyr] - - Returns - ------- - chi : float - The electron acceleration coefficient. - Unit: [Gyr^-1] - - References - ---------- - Ref.[cassano2005],Eq.(40,B12) - """ - # The minimum acceleration coefficient to avoid unstable results - chi_min = 0.01 # [Gyr^-1] - - if (t is None) or (t < self.age_merger + self.time_crossing): - mass = self.M_main + self.M_sub - term1 = (mass / 2e15) ** 1.5 - term2 = (self.kT_merger / 7) ** (-0.5) - term3 = 500 / self.radius - chi = 6.3 * self.eta_turb * term1 * term2 * term3 - else: - chi = chi_min - return chi - def _loss_ion(self, gamma, t): """ Energy loss through ionization and Coulomb collisions. diff --git a/fg21sim/extragalactic/clusters/main.py b/fg21sim/extragalactic/clusters/main.py index 506e77c..dfc8e6e 100644 --- a/fg21sim/extragalactic/clusters/main.py +++ b/fg21sim/extragalactic/clusters/main.py @@ -281,8 +281,9 @@ class GalaxyClusters: ("Rhalo", halo.radius), # [kpc] ("Rhalo_angular", halo.angular_radius), # [arcsec] ("volume", halo.volume), # [kpc^3] + ("Mach_turb", halo.Mach_turbulence), # turbulence Mach number + ("tau_acc", halo.tau_acceleration), # [Gyr] ("Ke", halo.injection_rate), # [cm^-3 Gyr^-1] - ("chi", halo._chi_acceleration()), # [Gyr^-1] ("gamma", halo.gamma), # Lorentz factors ("n_e", n_e), # [cm^-3] ]) |