def compare_evolutions():
'''
Compare precession averaged and orbit averaged integrations. Plot the
evolution of xi, J, S and their relative differences between the two
approaches. Since precession-averaged estimates of S require a random
sampling, this plot will look different every time this routine is executed.
Output is saved in ./spin_angles.pdf.
**Run using**
import precession.test
precession.test.compare_evolutions()
'''
fig = pylab.figure(figsize=(6, 6)) # Create figure object and axes
L, Ws, Wm, G = 0.85, 0.15, 0.3, 0.03 # Sizes
ax_Sd = fig.add_axes([0, 0, L, Ws]) # bottom-small
ax_S = fig.add_axes([0, Ws, L, Wm]) # bottom-main
ax_Jd = fig.add_axes([0, Ws + Wm + G, L, Ws]) # middle-small
ax_J = fig.add_axes([0, Ws + Ws + Wm + G, L, Wm]) # middle-main
ax_xid = fig.add_axes([0, 2 * (Ws + Wm + G), L, Ws]) # top-small
ax_xi = fig.add_axes([0, Ws + 2 * (Ws + Wm + G), L, Wm]) # top-main
q = 0.8 # Mass ratio. Must be q<=1.
chi1 = 0.6 # Primary spin. Must be chi1<=1
chi2 = 1. # Secondary spin. Must be chi2<=1
M, m1, m2, S1, S2 = precession.get_fixed(q, chi1,
chi2) # Total-mass units M=1
ri = 100. * M # Initial separation.
rf = 10. * M # Final separation.
r_vals = numpy.linspace(ri, rf, 1001) # Output requested
Ji = 2.24 # Magnitude of J: Jmin<J<Jmax as given by J_lim
xi = -0.5 # Effective spin: xi_low<xi<xi_up as given by xi_allowed
Jf_P = precession.evolve_J(xi, Ji, r_vals, q, S1, S2) # Pr.av. integration
Sf_P = [
precession.samplingS(xi, J, q, S1, S2, r)
for J, r in zip(Jf_P[0::10], r_vals[0::10])
] # Resample S (reduce output for clarity)
Sb_min, Sb_max = zip(*[
precession.Sb_limits(xi, J, q, S1, S2, r)
for J, r in zip(Jf_P, r_vals)
]) # Envelopes
S = numpy.average([precession.Sb_limits(xi, Ji, q, S1, S2,
ri)]) # Initialize S
Jf_O, xif_O, Sf_O = precession.orbit_averaged(Ji, xi, S, r_vals, q, S1,
S2) # Orb.av. integration
Pcol, Ocol, Dcol = 'blue', 'red', 'green'
Pst, Ost = 'solid', 'dashed'
ax_xi.axhline(xi, c=Pcol, ls=Pst, lw=2) # Plot xi, pr.av. (constant)
ax_xi.plot(r_vals, xif_O, c=Ocol, ls=Ost, lw=2) # Plot xi, orbit averaged
ax_xid.plot(r_vals, (xi - xif_O) / xi * 1e11, c=Dcol,
lw=2) # Plot xi deviations (rescaled)
ax_J.plot(r_vals, Jf_P, c=Pcol, ls=Pst, lw=2) # Plot J, pr.av.
ax_J.plot(r_vals, Jf_O, c=Ocol, ls=Ost, lw=2) # Plot J, orb.av
ax_Jd.plot(r_vals, (Jf_P - Jf_O) / Jf_O * 1e3, c=Dcol,
lw=2) # Plot J deviations (rescaled)
ax_S.scatter(r_vals[0::10], Sf_P, facecolor='none',
edgecolor=Pcol) # Plot S, pr.av. (resampled)
ax_S.plot(r_vals, Sb_min, c=Pcol, ls=Pst,
lw=2) # Plot S, pr.av. (envelopes)
ax_S.plot(r_vals, Sb_max, c=Pcol, ls=Pst,
lw=2) # Plot S, pr.av. (envelopes)
ax_S.plot(r_vals, Sf_O, c=Ocol, ls=Ost, lw=2) # Plot S, orb.av (evolved)
ax_Sd.plot(r_vals[0::10], (Sf_P - Sf_O[0::10]) / Sf_O[0::10], c=Dcol,
lw=2) # Plot S deviations
# Options for nice plotting
for ax in [ax_xi, ax_xid, ax_J, ax_Jd, ax_S, ax_Sd]:
ax.set_xlim(ri, rf)
ax.yaxis.set_label_coords(-0.16, 0.5)
ax.spines['left'].set_lw(1.5)
ax.spines['right'].set_lw(1.5)
for ax in [ax_xi, ax_J, ax_S]:
ax.spines['top'].set_lw(1.5)
for ax in [ax_xid, ax_Jd, ax_Sd]:
ax.axhline(0, c='black', ls='dotted')
ax.spines['bottom'].set_lw(1.5)
for ax in [ax_xid, ax_J, ax_Jd, ax_S]:
ax.set_xticklabels([])
ax_xi.set_ylim(-0.55, -0.45)
ax_J.set_ylim(0.4, 2.3)
ax_S.set_ylim(0.24, 0.41)
ax_xid.set_ylim(-0.2, 1.2)
ax_Jd.set_ylim(-3, 5.5)
ax_Sd.set_ylim(-0.7, 0.7)
ax_xid.yaxis.set_major_locator(matplotlib.ticker.MultipleLocator(0.5))
ax_Jd.yaxis.set_major_locator(matplotlib.ticker.MultipleLocator(2))
ax_S.yaxis.set_major_locator(matplotlib.ticker.MultipleLocator(0.05))
ax_Sd.yaxis.set_major_locator(matplotlib.ticker.MultipleLocator(0.5))
ax_xi.xaxis.set_ticks_position('top')
ax_xi.xaxis.set_label_position('top')
ax_Sd.set_xlabel("$r/M$")
ax_xi.set_xlabel("$r/M$")
ax_xi.set_ylabel("$\\xi$")
ax_J.set_ylabel("$J/M^2$")
ax_S.set_ylabel("$S/M^2$")
ax_xid.set_ylabel("$\\Delta\\xi/\\xi \;[10^{-11}]$")
ax_Jd.set_ylabel("$\\Delta J/J \;[10^{-3}]$")
ax_Sd.set_ylabel("$\\Delta S / S$")
fig.savefig("compare_evolutions.pdf", bbox_inches='tight') # Save pdf file
def PNwrappers():
'''
Wrappers of the PN integrators. Here we show how to perform orbit-averaged,
precession-averaged and hybrid PN inspirals using the various wrappers
implemented in the code. We also show how to estimate the final mass, spin
and recoil of the BH remnant following a merger.
**Run using**
import precession.test
precession.test.PNwrappers()
'''
q = 0.9 # Mass ratio. Must be q<=1.
chi1 = 0.5 # Primary spin. Must be chi1<=1
chi2 = 0.5 # Secondary spin. Must be chi2<=1
print "We study a binary with\n\tq=%.3f, chi1=%.3f, chi2=%.3f" % (q, chi1,
chi2)
M, m1, m2, S1, S2 = precession.get_fixed(q, chi1,
chi2) # Total-mass units M=1
ri = 1000 * M # Initial separation.
rf = 10. * M # Final separation.
rt = 100. * M # Intermediate separation for hybrid evolution.
r_vals = numpy.logspace(numpy.log10(ri), numpy.log10(rf),
10) # Output requested
t1i = numpy.pi / 4.
t2i = numpy.pi / 4.
dpi = numpy.pi / 4. # Initial configuration
xii, Ji, Si = precession.from_the_angles(t1i, t2i, dpi, q, S1, S2, ri)
print "Configuration at ri=%.0f\n\t(xi,J,S)=(%.3f,%.3f,%.3f)\n\t(theta1,theta2,deltaphi)=(%.3f,%.3f,%.3f)" % (
ri, xii, Ji, Si, t1i, t2i, dpi)
print " *Orbit-averaged evolution*"
print "Evolution ri=%.0f --> rf=%.0f" % (ri, rf)
Jf, xif, Sf = precession.orbit_averaged(Ji, xii, Si, r_vals, q, S1, S2)
print "\t(xi,J,S)=(%.3f,%.3f,%.3f)" % (xif[-1], Jf[-1], Sf[-1])
t1f, t2f, dpf = precession.orbit_angles(t1i, t2i, dpi, r_vals, q, S1, S2)
print "\t(theta1,theta2,deltaphi)=(%.3f,%.3f,%.3f)" % (t1f[-1], t2f[-1],
dpf[-1])
Jvec, Lvec, S1vec, S2vec, Svec = precession.Jframe_projection(
xii, Si, Ji, q, S1, S2, ri)
Lxi, Lyi, Lzi = Lvec
S1xi, S1yi, S1zi = S1vec
S2xi, S2yi, S2zi = S2vec
Lx, Ly, Lz, S1x, S1y, S1z, S2x, S2y, S2z = precession.orbit_vectors(
Lxi, Lyi, Lzi, S1xi, S1yi, S1zi, S2xi, S2yi, S2zi, r_vals, q)
print "\t(Lx,Ly,Lz)=(%.3f,%.3f,%.3f)\n\t(S1x,S1y,S1z)=(%.3f,%.3f,%.3f)\n\t(S2x,S2y,S2z)=(%.3f,%.3f,%.3f)" % (
Lx[-1], Ly[-1], Lz[-1], S1x[-1], S1y[-1], S1z[-1], S2x[-1], S2y[-1],
S2z[-1])
print " *Precession-averaged evolution*"
print "Evolution ri=%.0f --> rf=%.0f" % (ri, rf)
Jf = precession.evolve_J(xii, Ji, r_vals, q, S1, S2)
print "\t(xi,J,S)=(%.3f,%.3f,-)" % (xii, Jf[-1])
t1f, t2f, dpf = precession.evolve_angles(t1i, t2i, dpi, r_vals, q, S1, S2)
print "\t(theta1,theta2,deltaphi)=(%.3f,%.3f,%.3f)" % (t1f[-1], t2f[-1],
dpf[-1])
print "Evolution ri=%.0f --> infinity" % ri
kappainf = precession.evolve_J_backwards(xii, Jf[-1], rf, q, S1, S2)
print "\tkappainf=%.3f" % kappainf
Jf = precession.evolve_J_infinity(xii, kappainf, r_vals, q, S1, S2)
print "Evolution infinity --> rf=%.0f" % rf
print "\tJ=%.3f" % Jf[-1]
print " *Hybrid evolution*"
print "Prec.Av. infinity --> rt=%.0f & Orb.Av. rt=%.0f --> rf=%.0f" % (
rt, rt, rf)
t1f, t2f, dpf = precession.hybrid(xii, kappainf, r_vals, q, S1, S2, rt)
print "\t(theta1,theta2,deltaphi)=(%.3f,%.3f,%.3f)" % (t1f[-1], t2f[-1],
dpf[-1])
print " *Properties of the BH remnant*"
Mfin = precession.finalmass(t1f[-1], t2f[-1], dpf[-1], q, S1, S2)
print "\tM_f=%.3f" % Mfin
chifin = precession.finalspin(t1f[-1], t2f[-1], dpf[-1], q, S1, S2)
print "\tchi_f=%.3f, S_f=%.3f" % (chifin, chifin * Mfin**2)
vkick = precession.finalkick(t1f[-1], t2f[-1], dpf[-1], q, S1, S2)
print "\tvkick=%.5f" % (vkick) # Geometrical units c=1
