def q_p(**kwargs):
filename = os.path.join(plot_path, "q_p.pdf")
fig,axes = plt.subplots(2,4,figsize=(14,7.5),
sharex=True, sharey=True)
bins = np.linspace(0.,10,40)
nparticles = 5000
for kk,_m in enumerate(range(6,9+1)):
mass = "2.5e{}".format(_m)
m = float(mass)
print(mass)
sgr = SgrSimulation(sgr_path.format(_m), snapfile)
p = sgr.particles(n=nparticles, expr="(tub!=0)")#" & (tub<400)")
tub = p.tub
s = sgr.satellite()
potential = LawMajewski2010()
X = np.vstack((s._X[...,:3], p._X[...,:3].copy()))
V = np.vstack((s._X[...,3:], p._X[...,3:].copy()))
integrator = LeapfrogIntegrator(potential._acceleration_at,
np.array(X), np.array(V),
args=(X.shape[0], np.zeros_like(X)))
ts, rs, vs = integrator.run(t1=sgr.t1, t2=sgr.t2, dt=-1.)
s_orbit = np.vstack((rs[:,0][:,np.newaxis].T, vs[:,0][:,np.newaxis].T)).T
p_orbits = np.vstack((rs[:,1:].T, vs[:,1:].T)).T
t_idx = np.array([np.argmin(np.fabs(ts - t)) for t in p.tub])
p_x = np.array([p_orbits[jj,ii] for ii,jj in enumerate(t_idx)])
s_x = np.array([s_orbit[jj,0] for jj in t_idx])
#############################################
# determine tail_bit
diff = p_x-s_x
norm_r = s_x[:,:3] / np.sqrt(np.sum(s_x[:,:3]**2, axis=-1))[:,np.newaxis]
norm_diff_r = diff[:,:3] / np.sqrt(np.sum(diff[:,:3]**2, axis=-1))[:,np.newaxis]
dot_prod_r = np.sum(norm_diff_r*norm_r, axis=-1)
tail_bit = (dot_prod_r > 0.).astype(int)*2 - 1
#############################################
r_tide = potential._tidal_radius(m, s_orbit[...,:3])#*0.69336
s_R_orbit = np.sqrt(np.sum(s_orbit[...,:3]**2, axis=-1))
a_pm = (s_R_orbit + r_tide*tail_bit) / s_R_orbit
q = np.sqrt(np.sum((p_x[:,:3] - s_x[:,:3])**2,axis=-1))
f = r_tide / s_R_orbit
s_V = np.sqrt(np.sum(s_orbit[...,3:]**2, axis=-1))
vdisp = s_V * f / 1.4
p = np.sqrt(np.sum((p_x[:,3:] - s_x[...,3:])**2,axis=-1))
fig,axes = plt.subplots(2,1,figsize=(10,6),sharex=True)
axes[0].plot(tub, q, marker='.', alpha=0.5, color='#666666')
axes[0].plot(ts, r_tide*1.4, linewidth=2., alpha=0.8, color='k',
linestyle='-', marker=None)
axes[0].set_ylim(0., max(r_tide)*4)
axes[1].plot(tub, (p*u.kpc/u.Myr).to(u.km/u.s).value,
marker='.', alpha=0.5, color='#666666')
axes[1].plot(ts, (vdisp*u.kpc/u.Myr).to(u.km/u.s).value, color='k',
linewidth=2., alpha=0.75, linestyle='-', marker=None)
M_enc = potential._enclosed_mass(s_R_orbit)
#delta_E = 4/3.*G.decompose(usys).value**2*m*(M_enc / s_V)**2*r_tide**2/s_R_orbit**4
delta_v2 = 4/3.*G.decompose(usys).value**2*(M_enc / s_V)**2*\
np.mean(r_tide**2)/s_R_orbit**4
delta_v = (np.sqrt(2*delta_v2)*u.kpc/u.Myr).to(u.km/u.s).value
axes[1].plot(ts, delta_v, linewidth=2., color='#2166AC',
alpha=0.75, linestyle='--', marker=None)
axes[1].set_ylim(0., max((vdisp*u.kpc/u.Myr).to(u.km/u.s).value)*4)
axes[0].set_xlim(min(ts), max(ts))
fig.savefig(os.path.join(plot_path, "q_p_{}.png".format(mass)),
transparent=True)
def Lpts():
np.random.seed(42)
potential = LawMajewski2010()
filename = os.path.join(plot_path, "Lpts_r.{}".format(ext))
filename2 = os.path.join(plot_path, "Lpts_v.{}".format(ext))
fig,axes = plt.subplots(2,4,figsize=grid_figsize,
sharex=True, sharey=True)
fig2,axes2 = plt.subplots(2,4,figsize=grid_figsize,
sharex=True, sharey=True)
bins = np.linspace(-3,3,50)
nparticles = 2000
for k,_m in enumerate(range(6,9+1)):
mass = "2.5e{}".format(_m)
m = float(mass)
print(mass)
sgr = SgrSimulation(sgr_path.format(_m),snapfile)
p = sgr.particles(n=nparticles, expr=expr)
s = sgr.satellite()
dt = -1.
coord, r_tide, v_disp = particles_x1x2x3(p, s,
sgr.potential,
sgr.t1, sgr.t2, dt,
at_tub=False)
(x1,x2,x3,vx1,vx2,vx3) = coord
ts = np.arange(sgr.t1,sgr.t2+dt,dt)
t_idx = np.array([np.argmin(np.fabs(ts - t)) for t in p.tub])
_tcross = r_tide / np.sqrt(G.decompose(usys).value*m/r_tide)
for ii,jj in enumerate(t_idx):
#tcross = r_tide[jj,0] / _v[jj,ii]
tcross = _tcross[jj]
bnd = int(tcross / 2)
ix1,ix2 = jj-bnd, jj+bnd
if ix1 < 0: ix1 = 0
if ix2 > max(sgr.t1,sgr.t2): ix2 = -1
axes[0,k].set_rasterization_zorder(1)
axes[0,k].plot(x1[jj-bnd:jj+bnd,ii]/r_tide[jj-bnd:jj+bnd,0],
x2[jj-bnd:jj+bnd,ii]/r_tide[jj-bnd:jj+bnd,0],
linestyle='-', alpha=0.1, marker=None, color='#555555',
zorder=-1)
axes[1,k].set_rasterization_zorder(1)
axes[1,k].plot(x1[jj-bnd:jj+bnd,ii]/r_tide[jj-bnd:jj+bnd,0],
x3[jj-bnd:jj+bnd,ii]/r_tide[jj-bnd:jj+bnd,0],
linestyle='-', alpha=0.1, marker=None, color='#555555',
zorder=-1)
circ = Circle((0,0), radius=1., fill=False, alpha=0.75,
edgecolor='k', linestyle='solid')
axes[0,k].add_patch(circ)
circ = Circle((0,0), radius=1., fill=False, alpha=0.75,
edgecolor='k', linestyle='solid')
axes[1,k].add_patch(circ)
axes[0,k].axhline(0., color='k', alpha=0.75)
axes[1,k].axhline(0., color='k', alpha=0.75)
axes[0,k].set_xlim(-5,5)
axes[0,k].set_ylim(axes[0,k].get_xlim())
axes[1,k].set_xlabel(r"$x_1/r_{\rm tide}$")
if k == 0:
axes[0,k].set_ylabel(r"$x_2/r_{\rm tide}$")
axes[1,k].set_ylabel(r"$x_3/r_{\rm tide}$")
_tcross = r_tide / np.sqrt(G.decompose(usys).value*m/r_tide)
for ii,jj in enumerate(t_idx):
#tcross = r_tide[jj,0] / _v[jj,ii]
tcross = _tcross[jj]
bnd = int(tcross / 2)
ix1,ix2 = jj-bnd, jj+bnd
if ix1 < 0: ix1 = 0
if ix2 > max(sgr.t1,sgr.t2): ix2 = -1
axes2[0,k].set_rasterization_zorder(1)
axes2[0,k].plot(vx1[jj-bnd:jj+bnd,ii]/v_disp[jj-bnd:jj+bnd,0],
vx2[jj-bnd:jj+bnd,ii]/v_disp[jj-bnd:jj+bnd,0],
linestyle='-', alpha=0.1, marker=None, color='#555555',
zorder=-1)
axes2[1,k].set_rasterization_zorder(1)
axes2[1,k].plot(vx1[jj-bnd:jj+bnd,ii]/v_disp[jj-bnd:jj+bnd,0],
vx3[jj-bnd:jj+bnd,ii]/v_disp[jj-bnd:jj+bnd,0],
linestyle='-', alpha=0.1, marker=None, color='#555555',
zorder=-1)
circ = Circle((0,0), radius=1., fill=False, alpha=0.75,
edgecolor='k', linestyle='solid')
axes2[0,k].add_patch(circ)
circ = Circle((0,0), radius=1., fill=False, alpha=0.75,
edgecolor='k', linestyle='solid')
axes2[1,k].add_patch(circ)
axes2[0,k].axhline(0., color='k', alpha=0.75)
axes2[1,k].axhline(0., color='k', alpha=0.75)
axes2[1,k].set_xlim(-5,5)
axes2[1,k].set_ylim(axes2[1,k].get_xlim())
axes2[1,k].set_xlabel(r"$v_{x_1}/\sigma_v$")
if k == 0:
axes2[0,k].set_ylabel(r"$v_{x_2}/\sigma_v$")
axes2[1,k].set_ylabel(r"$v_{x_3}/\sigma_v$")
axes[0,k].text(0.5, 1.05, r"$2.5\times10^{}M_\odot$".format(_m),
horizontalalignment='center',
fontsize=24,
transform=axes[0,k].transAxes)
axes2[0,k].text(0.5, 1.05, r"$2.5\times10^{}M_\odot$".format(_m),
horizontalalignment='center',
fontsize=24,
transform=axes2[0,k].transAxes)
fig.tight_layout()
fig.subplots_adjust(top=0.92, hspace=0.025, wspace=0.1)
fig.savefig(filename)
fig2.tight_layout()
fig2.subplots_adjust(top=0.92, hspace=0.025, wspace=0.1)
fig2.savefig(filename2)
def total_rv():
filenamer = os.path.join(plot_path, "rel_r.png")
filenamev = os.path.join(plot_path, "rel_v.png")
figr,axesr = plt.subplots(4,1,figsize=(10,14),
sharex=True)
figv,axesv = plt.subplots(4,1,figsize=(10,14),
sharex=True)
nparticles = 2000
for k,_m in enumerate(range(6,9+1)):
mass = "2.5e{}".format(_m)
m = float(mass)
print(mass)
sgr = SgrSimulation(sgr_path.format(_m),snapfile)
p = sgr.particles(n=nparticles, expr=expr)
s = sgr.satellite()
X = np.vstack((s._X[...,:3], p._X[...,:3].copy()))
V = np.vstack((s._X[...,3:], p._X[...,3:].copy()))
integrator = LeapfrogIntegrator(sgr.potential._acceleration_at,
np.array(X), np.array(V),
args=(X.shape[0], np.zeros_like(X)))
ts, rs, vs = integrator.run(t1=sgr.t1, t2=sgr.t2, dt=-1.)
s_orbit = np.vstack((rs[:,0][:,np.newaxis].T, vs[:,0][:,np.newaxis].T)).T
p_orbits = np.vstack((rs[:,1:].T, vs[:,1:].T)).T
t_idx = np.array([np.argmin(np.fabs(ts - t)) for t in p.tub])
m_t = (-s.mdot*ts + s.m0)[:,np.newaxis]
s_R = np.sqrt(np.sum(s_orbit[...,:3]**2, axis=-1))
s_V = np.sqrt(np.sum(s_orbit[...,3:]**2, axis=-1))
r_tide = sgr.potential._tidal_radius(m_t, s_orbit[...,:3])
v_disp = s_V * r_tide / s_R
# cartesian basis to project into
x_hat = s_orbit[...,:3] / np.sqrt(np.sum(s_orbit[...,:3]**2, axis=-1))[...,np.newaxis]
_y_hat = s_orbit[...,3:] / np.sqrt(np.sum(s_orbit[...,3:]**2, axis=-1))[...,np.newaxis]
z_hat = np.cross(x_hat, _y_hat)
y_hat = -np.cross(x_hat, z_hat)
# translate to satellite position
rel_orbits = p_orbits - s_orbit
rel_pos = rel_orbits[...,:3]
rel_vel = rel_orbits[...,3:]
# project onto each
X = np.sum(rel_pos * x_hat, axis=-1)
Y = np.sum(rel_pos * y_hat, axis=-1)
Z = np.sum(rel_pos * z_hat, axis=-1)
RR = np.sqrt(X**2 + Y**2 + Z**2)
VX = np.sum(rel_vel * x_hat, axis=-1)
VY = np.sum(rel_vel * y_hat, axis=-1)
VZ = np.sum(rel_vel * z_hat, axis=-1)
VV = (np.sqrt(VX**2 + VY**2 + VZ**2)*u.kpc/u.Myr).to(u.km/u.s).value
v_disp = (v_disp*u.kpc/u.Myr).to(u.km/u.s).value
_tcross = r_tide / np.sqrt(G.decompose(usys).value*m/r_tide)
for ii,jj in enumerate(t_idx):
#tcross = r_tide[jj,0] / _v[jj,ii]
tcross = _tcross[jj]
bnd = int(tcross / 2)
ix1,ix2 = jj-bnd, jj+bnd
if ix1 < 0: ix1 = 0
if ix2 > max(sgr.t1,sgr.t2): ix2 = -1
axesr[k].plot(ts[ix1:ix2],
RR[ix1:ix2,ii],
linestyle='-', alpha=0.1, marker=None, color='#555555', zorder=-1)
axesv[k].plot(ts[ix1:ix2],
VV[ix1:ix2,ii],
linestyle='-', alpha=0.1, marker=None, color='#555555', zorder=-1)
axesr[k].plot(ts, r_tide*2., marker=None)
axesr[k].set_xlim(ts.min(), ts.max())
axesv[k].set_xlim(ts.min(), ts.max())
axesr[k].set_ylim(0,max(r_tide)*7)
axesv[k].set_ylim(0,max(v_disp)*7)
# axes[1,k].set_xlabel(r"$x_1$")
# if k == 0:
# axes[0,k].set_ylabel(r"$x_2$")
# axes[1,k].set_ylabel(r"$x_3$")
axesr[k].text(3000, max(r_tide)*5, r"$2.5\times10^{}M_\odot$".format(_m))
axesv[k].text(3000, max(v_disp)*5, r"$2.5\times10^{}M_\odot$".format(_m))
axesr[-1].set_xlabel("time [Myr]")
axesv[-1].set_xlabel("time [Myr]")
figr.suptitle("Relative distance", fontsize=26)
figr.tight_layout()
figr.subplots_adjust(top=0.92, hspace=0.025, wspace=0.1)
figr.savefig(filenamer)
figv.suptitle("Relative velocity", fontsize=26)
figv.tight_layout()
figv.subplots_adjust(top=0.92, hspace=0.025, wspace=0.1)
figv.savefig(filenamev)
def q_p(**kwargs):
filename = os.path.join(plot_path, "q_p.pdf")
fig, axes = plt.subplots(2, 4, figsize=(14, 7.5), sharex=True, sharey=True)
bins = np.linspace(0., 10, 40)
nparticles = 5000
for kk, _m in enumerate(range(6, 9 + 1)):
mass = "2.5e{}".format(_m)
m = float(mass)
print(mass)
sgr = SgrSimulation(sgr_path.format(_m), snapfile)
p = sgr.particles(n=nparticles, expr="(tub!=0)") #" & (tub<400)")
tub = p.tub
s = sgr.satellite()
potential = LawMajewski2010()
X = np.vstack((s._X[..., :3], p._X[..., :3].copy()))
V = np.vstack((s._X[..., 3:], p._X[..., 3:].copy()))
integrator = LeapfrogIntegrator(potential._acceleration_at,
np.array(X),
np.array(V),
args=(X.shape[0], np.zeros_like(X)))
ts, rs, vs = integrator.run(t1=sgr.t1, t2=sgr.t2, dt=-1.)
s_orbit = np.vstack(
(rs[:, 0][:, np.newaxis].T, vs[:, 0][:, np.newaxis].T)).T
p_orbits = np.vstack((rs[:, 1:].T, vs[:, 1:].T)).T
t_idx = np.array([np.argmin(np.fabs(ts - t)) for t in p.tub])
p_x = np.array([p_orbits[jj, ii] for ii, jj in enumerate(t_idx)])
s_x = np.array([s_orbit[jj, 0] for jj in t_idx])
#############################################
# determine tail_bit
diff = p_x - s_x
norm_r = s_x[:, :3] / np.sqrt(np.sum(s_x[:, :3]**2,
axis=-1))[:, np.newaxis]
norm_diff_r = diff[:, :3] / np.sqrt(np.sum(diff[:, :3]**2,
axis=-1))[:, np.newaxis]
dot_prod_r = np.sum(norm_diff_r * norm_r, axis=-1)
tail_bit = (dot_prod_r > 0.).astype(int) * 2 - 1
#############################################
r_tide = potential._tidal_radius(m, s_orbit[..., :3]) #*0.69336
s_R_orbit = np.sqrt(np.sum(s_orbit[..., :3]**2, axis=-1))
a_pm = (s_R_orbit + r_tide * tail_bit) / s_R_orbit
q = np.sqrt(np.sum((p_x[:, :3] - s_x[:, :3])**2, axis=-1))
f = r_tide / s_R_orbit
s_V = np.sqrt(np.sum(s_orbit[..., 3:]**2, axis=-1))
vdisp = s_V * f / 1.4
p = np.sqrt(np.sum((p_x[:, 3:] - s_x[..., 3:])**2, axis=-1))
fig, axes = plt.subplots(2, 1, figsize=(10, 6), sharex=True)
axes[0].plot(tub, q, marker='.', alpha=0.5, color='#666666')
axes[0].plot(ts,
r_tide * 1.4,
linewidth=2.,
alpha=0.8,
color='k',
linestyle='-',
marker=None)
axes[0].set_ylim(0., max(r_tide) * 4)
axes[1].plot(tub, (p * u.kpc / u.Myr).to(u.km / u.s).value,
marker='.',
alpha=0.5,
color='#666666')
axes[1].plot(ts, (vdisp * u.kpc / u.Myr).to(u.km / u.s).value,
color='k',
linewidth=2.,
alpha=0.75,
linestyle='-',
marker=None)
M_enc = potential._enclosed_mass(s_R_orbit)
#delta_E = 4/3.*G.decompose(usys).value**2*m*(M_enc / s_V)**2*r_tide**2/s_R_orbit**4
delta_v2 = 4/3.*G.decompose(usys).value**2*(M_enc / s_V)**2*\
np.mean(r_tide**2)/s_R_orbit**4
delta_v = (np.sqrt(2 * delta_v2) * u.kpc / u.Myr).to(u.km / u.s).value
axes[1].plot(ts,
delta_v,
linewidth=2.,
color='#2166AC',
alpha=0.75,
linestyle='--',
marker=None)
axes[1].set_ylim(0.,
max((vdisp * u.kpc / u.Myr).to(u.km / u.s).value) * 4)
axes[0].set_xlim(min(ts), max(ts))
fig.savefig(os.path.join(plot_path, "q_p_{}.png".format(mass)),
transparent=True)
