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 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):
self.v_shock_approx = self.r_c / self.tau_cc # Good when conduction is not dynamically important
T_ps = max(self.tau_s, 1.0)
T_ps = T_ps * self.T_a
n_ps = self.n_a * 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
self.rho_c = self.rho_c * p_ps / p_therm_a
# ----------------------------------------------------------------
# note 1: How do we define R_c after cloud shock?
self.r_c = (0.75 * self.M_c / self.rho_c / pi)**(1. / 3.
) # # SPHERICAL cloud
if (ADJUST_RCLOUD_FOR_VAPORPRESSURE):
p_evap = 3.59 * conduction.sigma_cond(self.r_c, n_ps, T_ps)**0.28
self.rho_c *= p_evap
rc_prev = self.r_c
self.r_c *= (p_evap)**(-1. / 3.)
print "p_evap = %5.3f, r_c(before) = %5.3f pc, r_c(now) = %5.3f pc" % (
p_evap, rc_prev / ac.pc, self.r_c / ac.pc)
# L_c changes according the internal structure we assume
# ----------------------------------------------------------------
self.n_c = self.rho_c / (pc.mh * self.mu) # Assuming neutral
p_evap = 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.a_ram = p_ps * pi * (
self.r_c)**2 / self.M_c / self.pressure_factor
self.debug_flag = 1
def cloud_shock(self):
self.v_shock_approx = self.r_c / self.tau_cc # Good when conduction is not dynamically important
T_ps = max(self.tau_s, 1.0)
T_ps = T_ps * self.T_a
n_ps = self.n_a * 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
if (USE_MINIMUM_EXPANSION_SPEED):
self.v_max = self.v_shock_approx / self.cs_c - 3.0 # upper limit
# self.v_max = self.v_shock_approx # upper limit
self.v_max = min(self.v_max, log(self.rho_c / self.rho_c0))
else:
self.v_max = log(self.rho_c / self.rho_c0)
print "v_shock_approx = %5.3f; v_shock = %5.3f; c*log(rho_c/rho_c0) = %5.3f" % (
self.v_shock_approx / 1.e5, self.v_shock / 1.e5,
log(self.rho_c / self.rho_c0) * self.cs_c / 1.e5)
# self.v_max = log(self.rho_c/self.rho_c0)
self.v_max0 = self.v_max
# ----------------------------------------------------------------
# note 1: How do we define R_c after cloud shock?
self.r_c = (self.M_c / self.rho_c / pi / 2.)**(
1. / 3.) # cylindrical geometry
p_evap_ratio = conduction.evap_pressure_fac(self.r_c, n_ps, T_ps)
print " ---> P_evap initial: ", p_evap_ratio
if (ADJUST_RHOC_WITH_PEVAP):
if (p_evap_ratio > 1):
self.rho_c *= p_evap_ratio
self.r_c *= (p_evap_ratio)**(-1. / 3.)
# L_c changes according the internal structure we assume
# 180712: We no longer accept the case with constant density!
self.L = 2. * self.r_c
self.tau_sc = 2.0 * self.r_c / self.cs_c
if (self.n_poly == 1.0):
# self.L = self.r_c * self.v_max # isothermal, 5.0 by default, constrained from x300v1700
self.L = self.r_c * 4.0
self.v_max = self.v_max
else:
self.L = self.r_c * (self.n_poly + 1.0) / (self.n_poly - 1.0)
# ----------------------------------------------------------------
self.n_c = self.rho_c / (pc.mh * self.mu) # Assuming neutral
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.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 * pi * (
self.r_c)**2 / self.M_c / self.pressure_factor
self.debug_flag = 1
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, self.n_a,
self.T_a) * self.L / (2.0 * self.r_c)
self.tau_evap = self.M_c / mlr
print 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_ps = fac_ram * self.rho_a * self.vrel**2
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
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
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
if (compression_flag == False):
L_eq = self.M_c / (rho_eq * self.r_c * self.r_c * pi)
self.L = self.L + self.cs_c * dt * 3.0
# Here using free expansion approximation: v = 2.0 * c / (gamma - 1)
self.r_c = sqrt(self.M_c / (self.N_c * pc.mh * 1.30) / 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 * 1.30)
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)