#Set up logarithmic a bins
dloga = (np.log(a_max)-np.log(a_min))/N_a
a_bins = np.array([a_min*np.exp(dloga*i) for i in range(N_a)])
#Set up logarithmic M_p bins
dlogM = (np.log(M_p_max)-np.log(M_p_min))/N_M
M_p_bins = np.array([M_p_min*np.exp(dlogM*i) for i in range(N_M)])
#Average fractional difference in a
a_frac_avg = np.zeros((N_a, N_M), dtype=float)
#b=parsec
for j in range(N_M):
n_p = rho/M_p_bins[j]
for i in range(N_a):
b = calc_b_max(M_p_bins[j], v_rms, a_bins[i], m1, m2)
for k in range(N_enc):
(notBound, a_new, e_new) = impulseEncounter(m1, m2, v_rms, b, a_bins[i], e, M_p_bins[j])
a_frac_avg[i,j] += (a_new-a_bins[i])/a_bins[i]
#Normalise a_frac_avg
a_frac_avg /= N_enc
#Plot
plt.title(r'Absolute average fractional change in semi-major axis due to single encounter at $b=b_{\mathrm{max}}$')
ax = plt.gca()
cs = ax.contourf(a_bins/au, M_p_bins/(2.0*10.0**30.0), np.transpose(np.absolute(a_frac_avg)), locator=ticker.LogLocator())
plt.colorbar(cs)
plt.ylabel(r'Perturber mass, $M_\odot$')
plt.xlabel('Initial semi-major axis, au')
plt.xscale('log')
plt.yscale('log')
plt.show()
N_a = 100
#Set up logarithmic a bins
dloga = (np.log(a_max)-np.log(a_min))/N_a
a_bins = np.array([a_min*np.exp(dloga*i) for i in range(N_a)])
#Fraction of encounters that break binary
F_enc = np.zeros((N_M, N_a))
#Number density of perturbers
n_p = rho/M_bins
#Minimum impact parameter
b_min = (np.pi*n_p*v_rms*(10.0*giga*year))**(-0.5)
for k in range(N_a):
for j in range(N_M):
for i in range(N_enc):
(notBound, a_new, e_new) = impulseEncounter(m1, m2, v_rms, b_min[j], a_bins[k], e, M_bins[j])
if notBound:
F_enc[j,k] += 1
#Normalise F_enc
F_enc /= N_enc
#Contour plot
#plt.title(r'Fraction of binaries broken due to a single encounter at $b=b_\mathrm{min}$')
plt.contourf(M_bins/(2.0*10.0**30.0), a_bins/au, np.transpose(F_enc), levels=np.linspace(0.0, 1.0, 11))
plt.xlabel('Perturber mass, solar masses')
plt.ylabel('Semi-major axis, au')
plt.xscale('log')
plt.yscale('log')
plt.colorbar();
plt.show()
b_max = 100.0 * 1.5 * (G * M_p**2.0 * a_max**3.0 /
((m1 + m2) * v_rms**2.0))**0.25
#Number of masses to test
N_b = 100
#Set up logarithmic mass bins
dlogb = (np.log(b_max) - np.log(b_min)) / N_b
b_bins = np.array([b_min * np.exp(dlogb * i) for i in range(N_b)])
#Fraction of encounters that break binary
F_enc = np.zeros((N_b, N_a))
for k in range(N_a):
for j in range(N_b):
for i in range(N_enc):
(notBound, a_new,
e_new) = impulseEncounter(m1, m2, v_rms, b_bins[j], a_bins[k], e,
M_p)
if notBound:
F_enc[j, k] += 1
#Normalise F_enc
F_enc /= N_enc
#Contour plot
plt.title(
r'Fraction of binaries broken due to a single encounter with $M_p=1000M_\odot$'
)
plt.contourf(b_bins / parsec,
a_bins / parsec,
np.transpose(F_enc),
levels=np.linspace(0.0, 1.0, 11))
plt.plot(1.5 * (G * M_p**2.0 * a_bins**3.0 / ((m1 + m2) * v_rms**2.0))**0.25 /
#WSW b_max
b_max_wsw = v_rms * P / (2.0 * np.pi)
b = 0.05 * b_max_wsw
print('b = ', b)
#Number of encounters
N_enc = 10**4
#Average energy change from impulse
dE_imp_mean = 0.0
dE_imp_meansq = 0.0
#Number of negative energy changes
#N_neg = 0
for i in range(N_enc):
notBound_new, a_new, e_new = impulseEncounter(m1, m2, v_rms, b, a, e, M_p)
#print('a_new =', a_new)
#if notBound_new:
#print('BINARY BROKEN!')
E_new = -G * (m1 + m2) / (2.0 * a_new)
#print('E_new =', E_new)
#print('E_new-E_old =', E_new-E_old)
#if (E_new-E_old) < 0.0:
#N_neg += 1
dE_imp_mean += (E_new - E_old)
dE_imp_meansq += (E_new - E_old)**2.0
#Normalise
dE_imp_mean /= N_enc
dE_imp_meansq /= N_enc
#Calculate variance
#Set up logarithmic mass bins
dlogM = (np.log(M_max) - np.log(M_min)) / N_M
M_bins = np.array([M_min * np.exp(dlogM * i) for i in range(N_M)])
v = v_rms
#Fraction of encounters that break binary
F_enc = np.zeros(N_M)
for j in range(N_M):
#Number density of perturbers
n_p = rho / M_bins[j]
#Minimum impact parameter
b_min = (np.pi * n_p * v_rms * (10.0 * giga * year))**(-0.5)
b = b_min
#Implement encounters
for i in range(N_enc):
(notBound, a_new, e_new) = impulseEncounter(m1, m2, v, b, a, e,
M_bins[j])
if notBound:
F_enc[j] += 1
#Normalise F_enc
F_enc /= N_enc
#Plot
plt.semilogx(M_bins / (2.0 * 10.0**30.0), F_enc)
plt.xlabel('Perturber mass, solar masses')
plt.ylabel('Fraction of binaries broken')
plt.title(
r'Fraction of binaries broken due to single encounter at $b=b_\mathrm{min}$, $a = 0.1$pc'
)
plt.show()