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, 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 dynamical_update(self, dt):
self.eta_s = 1. / conduction.fac_conduction_x(self.q_s, self.mach)
self.tau_s = conduction.ratio_temperature(self.q_s, self.mach)
T_ps = max(self.tau_s, 1.0)
T_ps = T_ps * self.T_a
n_ps = self.n_a * self.eta_s
# The Cowie & McKee 1977 conduction rate
self.tau_evap = conduction.tau_evap(self.M_c, self.r_c, n_ps,
T_ps) * self.f_cond
# 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.rho_c = self.rho_c0 * p_ps / p_therm_a
self.a_ram = p_ps * pi * self.r_c**2 / self.M_c #/ self.pressure_factor
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)
if (VERBOSE == True):
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 ----------------
self.tclock -= dt
self.rho_c = self.rho_c0 * (p_ps / p_therm_a / self.pressure_factor)
if (ADJUST_RCLOUD_FOR_VAPORPRESSURE):
self.rho_c *= P_evap
self.r_c = (0.75 * self.M_c / self.rho_c / pi)**(1. / 3.
) # # SPHERICAL cloud
# self.r_c = sqrt(self.M_c / (self.N_c * pc.mh * self.mu) / pi)
self.n_c = self.rho_c / (pc.mh * self.mu)
def dynamical_update(self, dt):
self.eta_s = 1. / conduction.fac_conduction_x(self.q_s, self.mach)
self.tau_s = conduction.ratio_temperature(self.q_s, self.mach)
T_ps = max(self.tau_s, 1.0)
T_ps = T_ps * self.T_a
n_ps = self.n_a * 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_tail = conduction.mass_loss_rate(self.r_c, self.n_a, self.T_a)
# mlr += mlr_tail * self.L / (2.0 * self.r_c) # Tail
# mlr = conduction.mass_loss_rate(self.r_c, n_ps, T_ps) / self.v_max * self.L / (2.0 * self.r_c)
# mlr = conduction.mass_loss_rate(self.r_c, n_ps, T_ps) / 3.5 * self.L / (2.0 * self.r_c)
# mlr = 2.3e-34 * T_ps ** 2.5 * self.L / 3.5 * 2. * pi * ac.pc / 3.5
mlr_tail = 4.46e-15 * self.T_a**2.5 / (self.r_c)
self.v_max = -log(mlr_tail * self.time / self.rho_c / self.r_c)
# SH191104: Huge bug identified here... Used to be > 0
# SH191106: A more robust way of doing evaporation
if (conduction.evaluate_saturation_point(self.T_c, n_ps, T_ps,
self.r_c) < 0):
# The classical conduction all the way down. No turning point.
T_star = 1.e4
# mlr = 4.46e-15 * (T_ps ** 2.5 - T_star ** 2.5) * self.L / 3.5 # Equation (1)
else:
T_star = conduction.solve_for_saturation_point(n_ps,
T_ps,
self.r_c,
T_c=self.T_c,
verbose=False)
# mlr = 1.42e-25 * n_ps * T_ps * self.r_c * T_star ** 1.03 * self.L / 3.5 Equation (2)
# Should be equivalent to Equation (1)
mlr = 4.46e-15 * (T_ps**2.5 -
T_star**2.5) * self.L / 3.5 # Equation (1)
# print n_ps, T_ps/1.e6, T_star/1.e6
# mlr = 1.56e-15 * T_ps ** 2.5 * self.L
self.tau_evap = self.M_c / mlr / self.f_cond
# pdb.set_trace()
# 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
# Here we assume rho_c do not change with time???
# if(ADJUST_RHOC_WITH_PEVAP):
# p_evap_ratio = conduction.evap_pressure_fac(self.r_c, n_ps, T_ps)
# if(p_evap_ratio > 1):
# self.rho_c *= p_evap_ratio
# self.r_c *= (p_evap_ratio) ** (-1./3.)
# self.rho_c = self.rho_c0 * p_ps / p_therm_a
self.a_ram = p_ps * pi * self.r_c**2 / self.M_c #/ self.pressure_factor
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 (KHI_MODIFIED_TIMESCALE):
lkh = conduction.lambda_kh(1.0,
self.n_c / n_ps,
T_ps,
n_ps,
fcond=self.f_cond)
# print "LKH, Rc = ", lkh/ac.pc, self.r_c/ac.pc
tau_disrupt = 1. / (1. / self.tau_evap +
exp(-lkh / self.r_c) / self.tau_khi)
self.lkh = lkh
self.n_ps, self.T_ps = n_ps, T_ps
else:
tau_disrupt = self.tau_evap
self.M_c = self.M_c * exp(-dt / tau_disrupt)
if (VERBOSE == True):
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 ----------------
self.tclock -= dt
self.v_max = min(self.v_max, log(self.rho_c / self.rho_c0))
# print self.v_max, log(self.rho_c/self.rho_c0)
# self.v_max = log(self.rho_c/self.rho_c0)
if (self.n_poly == 1.0):
v_exp = self.cs_c * self.v_max
elif (self.n_poly > 1.0):
v_exp = 2.0 * self.cs_c / (self.n_poly - 1.0)
# flux_cond = mlr_tail
# flux_mass = self.rho_c * exp(-self.v_max) * self.v_max * self.cs_c
# if(flux_cond <= flux_mass and self.rho_c * exp(-self.v_max) > self.rho_c0 and self.L < 250.*ac.pc): # Only expand when evaporation is inefficient
if (self.v_max > 0.0): # Only expand when evaporation is inefficient
self.L_prev = self.L
self.L = self.L + v_exp * dt
# if(self.time / self.tau_cc >= 15. and self.debug_flag == 1):
# print flux_cond / flux_mass
# self.debug_flag = 0
else:
if (self.L_prev < self.L):
print "Lmax reached: t= %5.1f, L= %5.2f, v_max = %3.1f\n" % \
(self.time/self.tau_cc, self.L/ac.pc, self.v_max)
self.L_prev = self.L
# Set a timer when the new tail end reaches L
# self.L = self.L - (self.v_h - self.vrel) * dt
# ----------------------------------------------------------------
# note 3: How does the internal structure evolve with time?
# ----------------------------------------------------------------
# OPTION 1: Allow rho_c (head density) to change
# if(self.rho_c > self.rho_c0 * (p_ps / p_therm_a / self.pressure_factor)): # Density is still large
# self.rho_c = self.rho_c * self.L_prev / self.L
# self.r_c = sqrt(self.M_c / (self.rho_c * pi * self.L / 4.0))
# else: # Density reaches the 1/3 value
# OPTION 2: Make rho_c strictly as constrained by the post-shock gas. Let R_c change
self.rho_c = self.rho_c0 * (p_ps / p_therm_a / self.pressure_factor)
# self.r_c = sqrt(self.M_c / (self.rho_c * pi * self.L / self.v_max)) # If we let the Pc = Pa
self.r_c = sqrt(self.M_c / (self.N_c * pc.mh * self.mu) / pi)
self.n_c = self.rho_c / (pc.mh * self.mu)