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-rw-r--r--fg21sim/extragalactic/clusters/halo.py62
1 files changed, 51 insertions, 11 deletions
diff --git a/fg21sim/extragalactic/clusters/halo.py b/fg21sim/extragalactic/clusters/halo.py
index 9c6c70e..02d8891 100644
--- a/fg21sim/extragalactic/clusters/halo.py
+++ b/fg21sim/extragalactic/clusters/halo.py
@@ -85,8 +85,10 @@ class RadioHalo:
energy spectrum, determine the injection rate by further assuming
that the total injected electrons has energy of a fraction (eta_e)
of the ICM total thermal energy;
- 4. Set the initial electron density/spectrum be the total injected
- electrons during t_merger time;
+ 4. Set the electron density/spectrum be the accumulated electrons
+ injected during t_merger time, then evolve it for time_init period
+ considering only losses and constant injection, in order to derive
+ an approximately steady electron spectrum for following use;
5. Calculate the magnetic field from the cluster total mass (which
is assumed to be growth linearly from M_main+M_sub to M_obs);
6. Calculate the energy losses for the coefficients of Fokker-Planck
@@ -148,6 +150,7 @@ class RadioHalo:
self.gamma_np = self.configs.getn(comp+"/gamma_np")
self.buffer_np = self.configs.getn(comp+"/buffer_np")
self.time_step = self.configs.getn(comp+"/time_step")
+ self.time_init = self.configs.getn(comp+"/time_init")
self.injection_index = self.configs.getn(comp+"/injection_index")
def _set_solver(self):
@@ -383,6 +386,36 @@ class RadioHalo:
Ke = term1 * term2 / term3 # [cm^-3 Gyr^-1]
return Ke
+ @property
+ def electron_spec_init(self):
+ """
+ The (default) initial electron spectrum at ``age_merger`` from
+ which to solve the final electron spectrum at the observation
+ time by solving the Fokker-Planck equation.
+
+ This initial electron spectrum is derived from the accumulated
+ electron spectrum injected throughout the ``age_merger`` period,
+ by solving the same Fokker-Planck equation, but only considering
+ energy losses and constant injection, evolving for a period of
+ ``time_init`` in order to obtain an approximately steady electron
+ spectrum.
+
+ Units: [cm^-3]
+ """
+ # Accumulated electrons constantly injected until ``age_merger``
+ n_inj = self.fp_injection(self.gamma)
+ n0_e = n_inj * self.age_merger
+
+ logger.debug("Derive the initial electron spectrum ...")
+ tstart = self.age_merger - self.time_init
+ tstop = self.age_merger
+ # Use a bigger time step to save time
+ self.fpsolver.tstep *= 2
+ n_e = self.fpsolver.solve(u0=n0_e, tstart=tstart, tstop=tstop)
+ # Restore the original time step
+ self.fpsolver.tstep = self.time_step
+ return n_e
+
def calc_electron_spectrum(self, tstart=None, tstop=None, n0_e=None):
"""
Calculate the relativistic electron spectrum by solving the
@@ -402,8 +435,7 @@ class RadioHalo:
Unit: [Gyr]
n0_e : 1D `~numpy.ndarray`, optional
The initial electron spectrum (number distribution).
- Default: accumulated constantly injected electrons until
- ``tstart``.
+ Default: ``self.electron_spec_init``
Unit: [cm^-3]
Returns
@@ -417,9 +449,7 @@ class RadioHalo:
if tstop is None:
tstop = self.age_obs
if n0_e is None:
- # Accumulated constantly injected electrons until ``tstart``.
- n_inj = self.fp_injection(self.gamma)
- n0_e = n_inj * tstart
+ n0_e = self.electron_spec_init
# When the evolution time is too short, decrease the time step
# to improve the results.
@@ -697,11 +727,15 @@ class RadioHalo:
----------
Ref.[donnert2013],Eq.(15)
"""
- if t < (self.age_merger + self.time_crossing):
- tau_acc = self.tau_acceleration # [Gyr]
- else:
- # The large enough timescale to avoid unstable results
+ if (t < self.age_merger) or (t > self.age_merger+self.time_crossing):
+ # NO acceleration; use a large enough timescale to avoid
+ # unstable results.
tau_acc = 10.0 # [Gyr]
+ else:
+ # Turbulence acceleration
+ tau_acc = self.tau_acceleration # [Gyr]
+
+ gamma = np.asarray(gamma)
diffusion = gamma**2 / 4 / tau_acc
return diffusion
@@ -721,6 +755,12 @@ class RadioHalo:
Advection coefficients, describing the energy loss/gain rates.
Unit: [Gyr^-1]
"""
+ # Always use the properties at ``age_merger`` to derive the
+ # initial electron spectrum.
+ if t < self.age_merger:
+ t = self.age_merger
+
+ gamma = np.asarray(gamma)
advection = (abs(self._loss_ion(gamma, t)) +
abs(self._loss_rad(gamma, t)) -
(self.fp_diffusion(gamma, t) * 2 / gamma))