def __init__(self, beta, xi=None, xmin=None,
method='match head to tail'):
"""`xmin` is minimum x value of natural matching point. If `x_m` <
`xmin`, then the matching point will be forced to be `xmin`"""
#
# Set head parameters
#
self.A_h = A(beta, xi)
self.theta_h = theta_c(beta, xi)
self.sig_h = np.sign(self.theta_h)
self.tau_h = np.tan(np.abs(self.theta_h))
self.a_h = self.A_h/self.tau_h**2
self.x0_h = 1.0 - self.sig_h*self.a_h
self.head_conic = Conic(A=self.A_h, th_conic=np.degrees(self.theta_h))
self.t_h = self.head_conic.make_t_array()
#
# Set tail parameters
#
# Distance to other star in units of R0
self.D = (1 + np.sqrt(beta)) / np.sqrt(beta)
if xi == None:
# Opening angle of tail
self.theta_t = theta_tail(beta, xi, f=finf_CRW)
# This was formerly known as phi1_over_phi
self.J = phi_ratio_CRW(beta, self.theta_t)
self.K = K_func_CRW(beta, self.theta_t, self.J)
# Empirically determined correction factor
self.K *= 0.5*self.J*(1.0 + beta)
else:
self.theta_t = theta_tail(beta, xi, f=finf)
self.J = phi_ratio_anisotropic(beta, xi, self.theta_t)
self.K = K_func_anisotropic(beta, xi, self.theta_t, self.J)
self.tau_t = np.tan(self.theta_t)
self.T = (self.tau_h/self.tau_t)**2
self.R90 = B(beta, xi)
self.m90 = m90_func(beta, xi)
if method == 'match R90 and gradient':
# New 30 Sep 2016 - fit tail to y, dy/dx @ 90 deg, instead
# of to head conic
self.x0_t = self.R90*self.m90 / self.tau_t**2
self.a_t = np.sqrt(self.x0_t**2 - (self.R90/self.tau_t)**2)
self.x_m = 0.0 # for completeness, but we don't use it
elif method == 'match head to tail':
# Original method, that I am not satisfied with (30 Sep 2016)
# Center of tail hyperbola in units of R_0
self.x0_t = self.D / (1.0 + self.J)
# New 30 Aug 2016
# Scale of hyperbola now determined from the K coefficient
# self.a_t = self.x0_t*a_over_x(self.tau_t, self.J, self.K)
# Find the x value where two conics match in dy/dx
self.x_m = (self.x0_t + self.sig_h*self.T*self.x0_h) / (1 + self.sig_h*self.T)
if xmin is not None: # and self.x_m < xmin:
# 30 Aug 2016: Match at x = xmin if gradients would naturally
# match at a more negative value of x
self.x_m = xmin
# And throw away the previous value of x0_t so that we can
# force y and dy/dx to match at x=xmin
self.x0_t = (1 + self.sig_h*self.T)*xmin - self.sig_h*self.T*self.x0_h
# Major and minor axes of tail hyperbola
self.a_t = np.sqrt(
(self.x_m - self.x0_t)**2
- self.T*np.abs(self.a_h**2 - (self.x_m - self.x0_h)**2)
)
elif method == 'match R90 and asymptote':
# Hyperbola center depends on asymptote only
self.x0_t = self.D / (1.0 + self.J)
self.a_t = np.sqrt(self.x0_t**2 - (self.R90/self.tau_t)**2)
self.x_m = 0.0
else:
raise NotImplementedError('Unknown match method: "{}"'.format(method))
self.t_t = np.linspace(0.0, max(2.0, 10.0/self.a_t), 500)
figfilename = sys.argv[0].replace('.py', '.pdf')
fig, axes = plt.subplots(nxi, nbeta, sharex=True, sharey=True)
for j, xi in enumerate(xigrid):
for i, beta in enumerate(betagrid):
ax = axes[j, i]
# Geberalized CRW solution
R_crw = R_from_theta(theta, beta, xi)
x_crw = R_crw*np.cos(theta)
y_crw = R_crw*np.sin(theta)
# Matched conic parameters
A = conic_parameters.A(beta, xi)
th_conic = np.degrees(conic_parameters.theta_c(beta, xi))
c = Conic(A=A, th_conic=th_conic)
t = c.make_t_array()
x_con = c.x(t)
y_con = c.y(t)
# Hyperbola fit to tail
th_tail = np.degrees(conic_parameters.theta_tail(beta, xi))
# First draw the asymptote
D = (1 + np.sqrt(beta))/np.sqrt(beta)
b_a = np.tan(np.radians(th_tail))
x_cone = np.linspace(-10*D, 10*D, 3)
y_cone = -b_a*(x_cone - 0.5*(1 + np.sqrt(beta))*D)
print(th_tail, b_a, x_cone, y_cone)
# Step 2: Initialize arrays
print(CRW)
beta = [5e-4, 0.001, 0.002, 0.005, 0.01, 0.02, 0.05, 0.1]
sns.set_style("ticks")
colors = sns.color_palette("Blues", len(beta))
inc = np.linspace(0, 75, 100)
# print(inc)
# step 3: Beta loop for plotting
for b, c in zip(beta, colors):
th_inf = theta_infty(b, Xi, CRW)
imax = np.degrees(np.arctan(-1.0 / np.tan(th_inf)))
imask = inc <= imax
conic = Conic(A=A(b, Xi), th_conic=np.degrees(theta_c(b, Xi)))
print(r"$\beta={}$".format(b), imax)
q_prime = q(b) * conic.g(inc[imask])
A_prime = conic.Aprime(inc[imask])
plt.plot(
q_prime,
A_prime,
linestyle="-",
linewidth=2.0,
color=c,
label=r"$\beta={}${}$\theta_c={:.0f}^\circ$".format(b, "\n", np.degrees(theta_c(b, Xi))),
)
every15 = np.zeros(q_prime.shape, dtype=bool)
for thisinc in 0.0, 15.0, 30.0, 45.0, 60.0, 75.0:
iclosest = np.argmin(np.abs(inc[imask] - thisinc))
every15[iclosest] = True
