def cloud_shock(self):
v_shock_approx = self.r_c / self.tau_cc
T_ps = bowshock.rh_temperature_ratio(self.mach) * self.tau_s
if (T_ps < 1): T_ps = 1
T_ps = T_ps * self.T_a
n_ps = self.n_a * bowshock.rh_density_ratio(self.mach) * self.eta_s
p_ps = n_ps * T_ps * pc.k
p_therm_c = self.n_c * self.T_c * pc.k
p_therm_a = self.n_a * self.T_a * pc.k
self.v_shock = sqrt(p_ps / self.p_c) * self.cs_c
# WARNING: Ignore the pressure difference between stagnation point and the shock front
# if(self.mach < 1.2):
# p_ps *= bowshock.postshock_pressure_fac(self.mach)
self.rho_c = self.rho_c * p_ps / p_therm_a # Isothermal shock condition
self.r_c = (self.M_c / self.rho_c / pi)**(1. / 3.
) # cylindrical geometry
self.n_c = self.rho_c / (pc.mh * self.mu) # Assuming neutral
self.r_c = (self.M_c / self.rho_c / pi)**(1. / 3.
) # cylindrical geometry
p_cond = conduction.evap_pressure_fac(self.r_c, n_ps, T_ps) * p_therm_a
self.tau_evap = conduction.tau_evap(self.M_c, self.r_c, n_ps,
T_ps) * self.f_cond
self.tau_khi = bowshock.fac_khi(self.mach) * self.tau_cc
self.N_c = self.M_c / (self.mu * pc.mh * pi * self.r_c * self.r_c)
self.L = self.r_c
# self.vrel = self.vrel - v_shock
# fac_ram = bowshock.ram_pressure_fac(self.mach) * params.ram
# p_ps = fac_ram * self.rho_a * self.vrel ** 2
self.a_ram = (p_ps - p_therm_a) * pi * (self.r_c)**2 / self.M_c
def cloud_shock(self, conduction_flag=False, verbose=False):
v_shock_approx = self.r_c / self.tau_cc
fac_ram = bowshock.ram_pressure_fac(self.mach) * params.ram
p_ps = fac_ram * self.rho_a * self.vrel**2
v_shock = sqrt(p_ps / self.p_c) * self.cs_c
self.rho_c = self.rho_a * (self.vrel / self.cs_c)**2
# self.rho_c = self.rho_c * (v_shock / self.cs_c) ** 2
self.r_c = (self.M_c / self.rho_c / pi)**(1. / 3.
) # cylindrical geometry
if (conduction_flag == True):
T_ps = bowshock.rh_temperature_ratio(self.mach) * params.T_ps
if (T_ps < 1): T_ps = 1
T_ps = T_ps * self.T_a
n_ps = self.n_a * bowshock.rh_density_ratio(
self.mach) * params.n_ps
# self.rho_c *= conduction.evap_pressure_fac(self.r_c, self.n_a, self.T_a)
else:
n_ps, T_ps = self.n_a, self.T_a
self.rho_c *= conduction.evap_pressure_fac(self.r_c, n_ps, T_ps)
print "fac =", conduction.evap_pressure_fac(self.r_c, n_ps, T_ps)
self.n_c = self.rho_c / (pc.mh * 1.30)
p_therm_c = self.n_c * self.T_c * pc.k
p_therm_a = n_ps * T_ps * pc.k
print "c_evap = ", conduction.evap_pressure_fac(self.r_c, n_ps, T_ps) * p_therm_a * \
4. * pi * self.r_c ** 2 / conduction.mass_loss_rate(self.r_c, n_ps, T_ps) / (1.e5)
self.r_c = (self.M_c / self.rho_c / pi)**(1. / 3.
) # cylindrical geometry
v_ps = v_shock - self.cs_c**2 / v_shock # post-shock velocity in rest-frame
p_cond = conduction.evap_pressure_fac(self.r_c, n_ps, T_ps) * p_therm_a
self.tau_evap = conduction.tau_evap(self.M_c, self.r_c, n_ps, T_ps)
self.tau_khi = bowshock.fac_khi(self.mach) * self.tau_cc
self.N_c = self.M_c / (1.30 * pc.mh * pi * self.r_c * self.r_c)
self.L = self.r_c
# self.vrel = self.vrel - v_shock
fac_ram = bowshock.ram_pressure_fac(self.mach) * params.ram
p_ps = fac_ram * self.rho_a * self.vrel**2
# self.a_ram = (p_ps - p_therm_a) * pi * self.r_c ** 2 / self.M_c
self.a_ram = (p_ps - self.T_a * self.n_a * pc.k) * pi * (
0.1 * ac.kpc)**2 / self.M_c
self.vrel = self.vrel - self.a_ram * self.tau_cc
if (verbose == True):
print ""
print "Post Cloud Shock"
print "--------------------------------"
print "n_c = ", self.n_c, "[cm^-3]"
print "R_c = ", self.r_c / ac.kpc * 1.e3, "[pc]"
print "v_shock = ", v_shock / 1.e5, "[km/s]"
print "v_shock_approx = ", v_shock_approx / 1.e5, "[km/s]"
print "Pc/k = ", p_therm_c / pc.k, "[K]"
print "Pa/k = ", p_therm_a / pc.k, "[K]"
print "Pps/k = ", p_ps / pc.k, "[K]"
print "Pcond/k = ", p_cond / pc.k, "[K]"
print "sigma0 = ", conduction.sigma_cond(self.r_c, n_ps, T_ps)
print "t_cc = ", self.tau_cc / 1.e6 / ac.yr, "[Myr]"
print "t_khi = ", self.tau_khi / 1.e6 / ac.yr, "[Myr]"
print "t_evap = ", self.tau_evap / 1.e6 / ac.yr, "[Myr]"
print "N_c = ", self.N_c, "[cm^-2]"
def dynamical_update(self, dt):
self.eta_s = conduction.fac_conduction_density(self.q_s, self.mach)
self.tau_s = conduction.fac_conduction_temperature(self.q_s, self.mach)
T_ps = bowshock.rh_temperature_ratio(self.mach) * self.tau_s
if (T_ps < 1): T_ps = 1
T_ps = T_ps * self.T_a
n_ps = self.n_a * bowshock.rh_density_ratio(self.mach) * self.eta_s
self.tau_evap = conduction.tau_evap(self.M_c, self.r_c, n_ps,
T_ps) * self.f_cond
self.tau_evap = self.tau_evap / (self.L / (2.0 * self.r_c))
mlr = conduction.mass_loss_rate(self.r_c, n_ps, T_ps) * 0.5 # Head
mlr += conduction.mass_loss_rate(self.r_c, FACDENS * self.n_a,
FACTEMP * self.T_a) * self.L / (
2.0 * self.r_c) # Tail
self.tau_evap = self.M_c / mlr * self.f_cond
# Calculate Acceleration
p_therm_c = self.n_c * self.T_c * pc.k
p_therm_a = self.n_a * self.T_a * pc.k
p_ps = n_ps * T_ps * pc.k
self.a_ram = (p_ps - p_therm_a) * pi * self.r_c**2 / self.M_c
self.tau_khi = bowshock.fac_khi(self.mach) * self.tau_cc
# Update Cloud Properties
self.time = self.time + dt
self.r = self.r + self.vrel * dt
self.vrel = self.vrel - self.a_ram * dt
if (self.gravity == True):
a_grav = self.V_c**2 / self.r
self.vrel = self.vrel - a_grav * dt
self.mach = self.vrel / self.cs_a
P_evap = 3.59 * conduction.sigma_cond(self.r_c, n_ps, T_ps)**0.28
if (self.tau_evap > 0):
if (P_evap > 1.0): tau_disrupt = self.tau_evap
else: tau_disrupt = 1. / (1. / self.tau_evap + 1. / self.tau_khi)
else: tau_disrupt = self.tau_khi
self.M_c = self.M_c * exp(-dt / tau_disrupt)
print "Mc=%4.2f t(KHI,evap,cc)=%5.2f, %5.2f, %5.2f mach=%4.2f Pevap/Pth=%4.2f" % (
self.M_c / params.M_c, self.tau_khi / ac.myr,
self.tau_evap / ac.myr, self.tau_cc / ac.myr, self.mach, P_evap)
# ---------------- The Expansion ----------------
rho_eq = self.rho_a * self.T_a / self.T_c
L_eq = self.M_c / (rho_eq * self.r_c * self.r_c * pi)
v_exp = self.v_shock - (self.v_h - self.vrel)
if (v_exp < 0): v_exp = 0
self.L = self.L + v_exp * dt
# Here using free expansion approximation: v = 2.0 * c / (gamma - 1)
self.r_c = sqrt(self.M_c / (self.N_c * pc.mh * self.mu) / pi)
if (self.L > L_eq): self.L = L_eq
self.rho_c = self.M_c / (self.L * self.r_c * self.r_c * pi)
self.n_c = self.rho_c / (pc.mh * self.mu)
def show_heat_flux(mach, M_c, v, n_a, T_a, qguess):
import bowshock
# conduction.show_heat_flux(3.8, 6.7e4*ac.msolar, 1.e8, 1./300., 3.e6, 0.95)
n_e = fac_conduction_density(qguess,
mach) * n_a * bowshock.rh_density_ratio(mach)
T_e = fac_conduction_temperature(
qguess, mach) * T_a * bowshock.rh_temperature_ratio(mach)
n_c = n_e * T_e / 1.e4
r_c = (M_c / (pi * n_c * 0.62 * pc.mh))**(1. / 3.)
qclass = (5.6e-7 * T_e**2.5) * (T_e - T_a) / r_c
qsat = 0.34 * n_e * pc.k * T_e * sqrt(pc.k * T_e / pc.me)
qflow = 0.5 * n_a * v**3 * pc.mh * 0.60
qratio = min(qsat, qclass) / qflow
print("Density, Temperature Ratios: %5.3f, %5.3f" % (n_e / n_a, T_e / T_a))
print("Cloud Radius: %5.3f [pc]" % (r_c * 1.e3 / ac.kpc))
print("Classical Flux: %5.3e" % (qclass))
print("Saturated Flux: %5.3e" % (qsat))
print("Flow Heat Flux: %5.3e" % (qflow))
print("Min(qcond/qflow) = %5.3f" % (qratio))
print("Density Enhancement = %5.3f" %
(fac_conduction_density(qratio, mach)))
print("Temperature Enhancement = %5.3f" %
(fac_conduction_temperature(qratio, mach)))
def dynamical_update(self,
dt,
verbose=False,
conduction_flag=True,
compression_flag=False,
geometry="spherical"):
if (conduction_flag == True):
# TRICK
# self.a_ram *= conduction.evap_pressure_fac(self.r_c, self.n_a, self.T_a)
T_ps = bowshock.rh_temperature_ratio(self.mach) * params.T_ps
if (T_ps < 1): T_ps = 1
T_ps = T_ps * self.T_a
n_ps = self.n_a * bowshock.rh_density_ratio(
self.mach) * params.n_ps
else:
T_ps, n_ps = self.T_a, self.n_a
self.tau_evap = conduction.tau_evap(self.M_c, self.r_c, n_ps, T_ps)
# print self.tau_evap / ac.yr / 1.e6, n_ps, T_ps, self.r_c, self.L
if (geometry == "cylindrical"):
self.tau_evap = self.tau_evap / (self.L / (2.0 * self.r_c))
# self.tau_evap = self.tau_evap
mlr = conduction.mass_loss_rate(self.r_c, n_ps, T_ps) * 0.5
# mlr += conduction.mass_loss_rate(self.r_c, FACDENS*self.n_a, FACTEMP*self.T_a) * self.L / (2.0 * self.r_c)
mlr += conduction.mass_loss_rate(self.r_c, n_ps,
T_ps) * self.L / (2.0 * self.r_c)
# mlr += conduction.mass_loss_rate(self.r_c, self.n_a, self.T_a) * self.L / (2.0 * self.r_c)
self.tau_evap = self.M_c / mlr
# print "MLR[Total] / MLR[Head] = ", mlr / (conduction.mass_loss_rate(self.r_c, n_ps, T_ps) * 0.5)
# Calculate Acceleration
fac_ram = bowshock.ram_pressure_fac(self.mach) * params.ram
p_therm_c = self.n_c * self.T_c * pc.k
# p_therm_a = n_ps * T_ps * pc.k
p_therm_a = self.n_a * self.T_a * pc.k
# print "c_evap = ", conduction.evap_pressure_fac(self.r_c, self.n_a, self.T_a) * p_therm_a * \
# 4. * pi * self.r_c ** 2 / conduction.mass_loss_rate(self.r_c, self.n_a, self.T_a) / (1.e5)
# p_ps = fac_ram * self.rho_a * self.vrel ** 2
p_ps = n_ps * T_ps * pc.k
self.a_ram = (p_ps - p_therm_a) * pi * self.r_c**2 / self.M_c
print "Log(P_ram) = ", log10(p_ps)
self.tau_khi = bowshock.fac_khi(self.mach) * self.tau_cc
# Update Cloud Properties
self.time = self.time + dt
self.r = self.r + self.vrel * dt
self.vrel = self.vrel - self.a_ram * dt
self.mach = self.vrel / self.cs_a
self.M_c = self.M_c * exp(-dt / self.tau_evap)
# self.M_c = self.M_c * exp(-dt / self.tau_khi)
# TRICK
# rho_eq = conduction.evap_pressure_fac(self.r_c, n_ps, T_ps) * (n_ps / self.n_a) * self.rho_a * T_ps / self.T_c
# print rho_eq, self.rho_c, n_ps, T_ps, conduction.evap_pressure_fac(self.r_c, self.n_a, T_ps)
# rho_eq = self.rho_a * self.T_a / self.T_c
# print rho_eq, self.n_a, self.T_a, conduction.evap_pressure_fac(self.r_c, self.n_a, self.T_a)
# rho_eq = conduction.evap_pressure_fac(self.r_c, self.n_a, self.T_a) * self.rho_a * self.T_a / self.T_c
rho_eq = self.rho_a * self.T_a / self.T_c
if (compression_flag == False):
L_eq = self.M_c / (rho_eq * self.r_c * self.r_c * pi)
# v_exp = self.cs_c * 3.0
# v_exp = VEXP * 1.e5
v_exp = self.cs_c * sqrt(1.0 + self.mach * self.mach) - (self.v_h -
self.vrel)
if (v_exp < 0): v_exp = 0
self.L = self.L + v_exp * dt
# Here using free expansion approximation: v = 2.0 * c / (gamma - 1)
self.r_c = sqrt(self.M_c / (self.N_c * pc.mh * 0.62) / pi)
if (self.L > L_eq): self.L = L_eq
else:
L_eq = self.M_c / (
(self.T_a * self.rho_a / self.T_c) * self.r_c * self.r_c * pi)
# Lower pressure (no vapor pressure), therefore longer L_eq
self.L = self.L + self.cs_c * dt * 3.0
if (self.L > L_eq): self.L = L_eq
self.rho_c = self.M_c / (self.L * self.r_c * self.r_c * pi)
# Allow cloud size to shrink
# However, problem is it induces a positive feedback:
# Smaller Rc leads to higher vapor pressure and higher rho_eq, the cloud will collapse!
if (self.rho_c < rho_eq):
self.r_c = sqrt(self.M_c / (rho_eq * self.L * pi))
self.rho_c = self.M_c / (self.L * self.r_c * self.r_c * pi)
self.n_c = self.rho_c / (pc.mh * 0.62)
if (verbose == True):
print "%5.3f(%5.3f) %6.2f %6.1f %5.3f %6.2f(%5.3f) %6.2f %5.3f %7.2f" % \
(self.time/ac.yr/1.e6, self.time/self.tau_cc, self.r / ac.kpc, self.vrel / 1.e5, self.M_c / M_0, \
self.L * 1.e3 / ac.kpc, self.L / L_eq, self.r_c * 1.e3 / ac.kpc, \
self.n_c, self.tau_evap / ac.yr / 1.e6)