def generate(x, tstart=1, tend=5.3, npts=100, ning=100, neg=100):
"""Generate a synthetic light curve."""
# Instantiate the star (params known exactly)
star = Primary()
star[1] = 0.4
star[2] = 0.26
# Instantiate the planet
planet = Secondary(lmax=1)
planet.lambda0 = 270
planet.r = 0.0916
planet.L = 5e-3
planet.inc = 87
planet.a = 11.12799
planet.prot = 4.3
planet.porb = 4.3
planet.tref = 2.0
# Instantiate the system
system = System(star, planet)
# Set the map coeffs
set_coeffs(x, planet)
# Time array w/ extra resolution at ingress/egress
ingress = (1.94, 1.96)
egress = (2.04, 2.06)
time = np.linspace(tstart, tend, npts)
if ingress is not None:
t = np.linspace(ingress[0], ingress[1], ning)
time = np.append(time, t)
if egress is not None:
t = np.linspace(egress[0], egress[1], neg)
time = np.append(time, t)
time = time[np.argsort(time)]
# Compute and plot the starry flux
system.compute(time)
flux = np.array(system.lightcurve)
# Noise it
yerr = 1e-4 * np.nanmedian(flux)
y = flux + yerr * np.random.randn(len(flux))
# Compute the flux at hi res for plotting
time_hires = np.linspace(tstart, tend, npts * 100)
system.compute(time_hires)
flux_hires = np.array(system.lightcurve)
return time, y, yerr, star, planet, system, time_hires, flux_hires
def test_transits():
"""Test transit light curve generation."""
# Input params
u1 = 0.4
u2 = 0.26
mstar = 1 # solar masses
rstar = 1 # solar radii
rplanet = 0.1 # fraction of stellar radius
b0 = 0.5 # impact parameter
P = 50 # orbital period in days
npts = 25
time = np.linspace(-0.25, 0.25, npts)
# Compute the semi-major axis from Kepler's third law in units of rstar
a = ((P * 86400) ** 2 * (1.32712440018e20 * mstar) /
(4 * np.pi ** 2)) ** (1. / 3.) / (6.957e8 * rstar)
# Get the inclination in degrees
inc = np.arccos(b0 / a) * 180 / np.pi
# Compute the flux from numerical integration
f = 2 * np.pi / P * time
b = a * np.sqrt(1 - np.sin(np.pi / 2. + f) ** 2
* np.sin(inc * np.pi / 180) ** 2)
nF = np.zeros_like(time)
for i in range(npts):
nF[i] = NumericalFlux(b[i], rplanet, u1, u2)
nF /= np.nanmax(nF)
den = (1 - nF)
den[den == 0] = 1e-10
# Compute the starry flux
# Instantiate a second-order map and a third-order map with u(3) = 0
# The second-order map is optimized for speed and uses different
# equations, but they should yield identical results.
for lmax in [2, 3]:
star = Primary(lmax)
star[1] = u1
star[2] = u2
planet = Secondary()
planet.r = rplanet
planet.a = a
planet.inc = inc
planet.porb = P
planet.lambda0 = 90
system = System(star, planet)
system.compute(time)
sF = np.array(star.lightcurve)
sF /= sF[0]
# Compute the error, check that it's better than 1 ppb
error = np.max((np.abs(nF - sF) / den)[np.where(nF < 1)])
assert error < 1e-9
def get_system(n_sec=1):
primary = Primary()
secondaries = []
for i in range(n_sec):
secondaries.append(Secondary())
return System(primary, *secondaries)
ax[0].set_xlim(0, 20) ax[1].set_xlim(0, 20) time = np.linspace(0, 20, 10000) # System #1: A one-planet system with a hotspot offset # ---------------------------------------------------- # Instantiate the star star = Primary() # Give the star a quadratic limb darkening profile star[1] = 0.4 star[2] = 0.26 # Instantiate planet b b = Secondary() b.r = 0.091679 b.L = 5e-3 b.inc = 90 b.porb = 4.3 b.prot = 4.3 b.a = 11.127991 b.lambda0 = 90 b.tref = 2 b.axis = [0, 1, 0] # Give the planet a simple dipole map b[1, 0] = 0.5 # Rotate the planet map to produce a hotspot offset of 15 degrees b.rotate(theta=15)
"""Return the LaTeX form of the partial deriv of x with respect to F."""
return r'$\frac{\partial F}{\partial %s}$' % x
# Time arrays
time_transit = np.linspace(-0.3, 0.2, 2500)
time_secondary = np.linspace(24.75, 25.5, 2500)
# Limb-darkened star
star = Primary()
star[1] = 0.4
star[2] = 0.26
star.r_m = 0
# Dipole-map hot jupiter
planet = Secondary()
planet.r = 0.1
planet.a = 60
planet.inc = 89.5
planet.porb = 50
planet.prot = 2.49
planet.lambda0 = 89.9
planet.ecc = 0.3
planet.w = 89
planet.L = 1e-3
planet[1, 0] = 0.5
# Instantiate the system
system = System(star, planet)
system.exposure_time = 0
def test_gradients(plot=False):
"""Test the gradients in the `System` class."""
# Limb-darkened star
A = Primary(lmax=3)
A[1] = 0.4
A[2] = 0.26
A[3] = -0.25
A.r_m = 1e11
# Dipole-map hot jupiter
b = Secondary(lmax=2)
b.r = 0.09
b.a = 60
b.inc = 89.943
b.porb = 50
b.prot = 2.49
b.lambda0 = 89.9
b.ecc = 0.3
b.w = 89
b.L = 1.75e-3
b[1, 0] = 0.5
b[2, 1] = 0.1
b[2, 2] = -0.05
# Dipole-map hot jupiter
c = Secondary(lmax=1)
c.r = 0.12
c.a = 80
c.inc = 89.95
c.porb = 100
c.prot = 7.83
c.lambda0 = 85
c.ecc = 0.29
c.w = 87.4
c.L = 1.5e-3
c[1, 0] = 0.4
# Instantiate the system
# We're adding a ton of light travel delay
# and a finite exposure time: this is a
# comprehensive test of the main `starry` features
system = System(A, b, c)
system.exposure_time = 0.02
# Light curves and gradients of this object
object = system
# Let's plot transit, eclipse, and a PPO
for t1, t2, figname in zip([-0.425, 25.1, -2.6], [0.0, 25.75, -2.0], [
"gradients_transit.png", "gradients_eclipse.png",
"gradients_ppo.png"
]):
# Time arrays
time = np.linspace(t1, t2, 500)
time_num = np.linspace(t1, t2, 50)
# Set up the plot
if plot:
fig = pl.figure(figsize=(6, 10))
fig.subplots_adjust(hspace=0, bottom=0.05, top=0.95)
# Run!
system.compute(time, gradient=True)
flux = np.array(object.lightcurve)
grad = dict(object.gradient)
# Numerical flux
system.compute(time_num, gradient=True)
flux_num = np.array(object.lightcurve)
# Plot it
if plot:
ax = pl.subplot2grid((18, 3), (0, 0), rowspan=5, colspan=3)
ax.plot(time, flux, color='C0')
ax.plot(time_num, flux_num, 'o', ms=3, color='C1')
ax.set_yticks([])
ax.set_xticks([])
[i.set_linewidth(0.) for i in ax.spines.values()]
col = 0
row = 0
eps = 1e-8
error_rel = []
for key in grad.keys():
if key.endswith('.y') or key.endswith('.u'):
for i, gradient in enumerate(grad[key]):
if plot:
axg = pl.subplot2grid((18, 3), (5 + row, col),
colspan=1)
axg.plot(time, gradient, lw=1, color='C0')
if key.endswith('.y'):
y0 = eval(key)
y = np.array(y0)
y[i + 1] += eps
exec(key[0] + "[:, :] = y")
system.compute(time)
exec(key[0] + "[:, :] = y0")
else:
u0 = eval(key)
u = np.array(u0)
u[i] += eps
exec(key[0] + "[:] = u")
system.compute(time)
exec(key[0] + "[:] = u0")
numgrad = (object.lightcurve - flux) / eps
error_rel.append(np.max(abs(numgrad - gradient)))
if plot:
axg.plot(time, numgrad, lw=1, alpha=0.5, color='C1')
axg.set_ylabel(r"$%s_%d$" % (key, i), fontsize=5)
axg.margins(None, 0.5)
axg.set_xticks([])
axg.set_yticks([])
[i.set_linewidth(0.) for i in axg.spines.values()]
if row < 12:
row += 1
else:
row = 0
col += 1
else:
if plot:
axg = pl.subplot2grid((18, 3), (5 + row, col), colspan=1)
axg.plot(time, grad[key], lw=1, color='C0')
exec(key + " += eps")
system.compute(time)
exec(key + " -= eps")
numgrad = (object.lightcurve - flux) / eps
error_rel.append(np.max(abs(numgrad - grad[key])))
if plot:
axg.plot(time, numgrad, lw=1, alpha=0.5, color='C1')
axg.margins(None, 0.5)
axg.set_xticks([])
axg.set_yticks([])
axg.set_ylabel(r"$%s$" % key, fontsize=5)
[i.set_linewidth(0.) for i in axg.spines.values()]
if row < 12:
row += 1
else:
row = 0
col += 1
# Generous error tolerance
assert np.all(np.array(error_rel) < 1e-5)
# Save the figure
if plot:
fig.savefig(figname, bbox_inches='tight', dpi=300)
pl.close()
def test_light_travel():
"""Run the test."""
# No delay
star = Primary()
star[1] = 0.40
star[2] = 0.26
star.r_m = 0
planet = Secondary()
planet.L = 1e-3
planet.r = 0.1
planet.porb = 10
planet.prot = 10
planet.a = 22
planet[1, 0] = 0.5
system = System(star, planet)
time = np.concatenate(
(np.linspace(0, 0.5, 10000,
endpoint=False), np.linspace(0.5,
4.5,
100,
endpoint=False),
np.linspace(4.5, 5.5, 10000,
endpoint=False), np.linspace(5.5,
9.5,
100,
endpoint=False),
np.linspace(9.5, 10, 10000)))
phase = time / 10.
system.compute(time)
transit = phase[np.argmax(planet.Z)]
eclipse = phase[np.argmin(planet.Z)]
assert transit == 0
assert eclipse == 0.5
# Let's give the system a real length scale now
star.r_m = 6.95700e8
eps = 1e-3
time = np.concatenate(
(np.linspace(0, 0.5, 100000, endpoint=False),
np.linspace(0.5, 5 - eps, 100, endpoint=False),
np.linspace(5 - eps, 5 + eps, 1000000, endpoint=False),
np.linspace(5 + eps, 9.5, 100,
endpoint=False), np.linspace(9.5, 10, 100000)))
phase = time / planet.porb
system.compute(time)
transit = phase[np.argmin(np.abs(planet.X) + (planet.Z < 0))]
eclipse = phase[np.argmin(np.abs(planet.X) + (planet.Z > 0))]
assert transit == 0.999940999409994
assert eclipse == 0.5000590894
# Run some extra tests
c = 299792458.
RSUN = 6.957e8
time = np.concatenate(
(np.linspace(0, 0.5, 100000,
endpoint=False), np.linspace(0.5,
4.5,
100,
endpoint=False),
np.linspace(4.5, 5.5, 100000,
endpoint=False), np.linspace(5.5,
9.5,
100,
endpoint=False),
np.linspace(9.5, 10, 100000)))
phase = time / planet.porb
# Test this on an inclined orbit
planet.inc = 30
system.compute(time)
transit = phase[np.argmax(planet.Z)]
eclipse = phase[np.argmin(planet.Z)]
delay_starry = (0.5 - (transit - eclipse)) * planet.porb * 86400
a = planet.a * star.r_m
delay_analytic = 2 * a / c * np.sin(planet.inc * np.pi / 180)
assert np.abs(1 - delay_starry / delay_analytic) < 0.01
# Test this on an orbit with nonzero Omega
planet.inc = 90
planet.Omega = 90
system.compute(time)
transit = phase[np.argmax(planet.Z)]
eclipse = phase[np.argmin(planet.Z)]
delay_starry = (0.5 - (transit - eclipse)) * planet.porb * 86400
a = planet.a * star.r_m
delay_analytic = 2 * a / c
assert np.abs(1 - delay_starry / delay_analytic) < 0.01
# Compute the light travel time from the secondary
# eclipse to the barycenter for an eccentric orbit.
# First, compute the phase of secondary eclipse
# with no light travel time delay:
planet.inc = 90
planet.Omega = 0
planet.w = 30
planet.ecc = 0.25
star.r_m = 0
system.compute(time)
eclipse0 = phase[np.argmin(planet.Z)]
z0 = planet.Z[np.argmin(planet.Z)]
# Now, compute the phase w/ the delay
star.r_m = 6.95700e8
system.compute(time)
eclipse = phase[np.argmin(planet.Z)]
# Compute the light travel time to the barycenter in days:
travel_time_starry = (eclipse - eclipse0) * planet.porb * 86400
# Compute the analytic light travel time to the barycenter in days:
travel_time_analytic = (0 - z0) * star.r_m / c
assert np.abs(1 - travel_time_starry / travel_time_analytic) < 0.01
npts = 500
time = np.linspace(-0.25, 0.25, npts)
# Compute the semi-major axis from Kepler's third law in units of rstar
a = ((P * 86400)**2 * (1.32712440018e20 * mstar) /
(4 * np.pi**2))**(1. / 3.) / (6.957e8 * rstar)
# Get the inclination in degrees
inc = np.arccos(b0 / a) * 180 / np.pi
# Compute and plot the starry flux
star = Primary()
star[1] = u1
star[2] = u2
planet = Secondary()
planet.r = rplanet
planet.inc = inc
planet.porb = P
planet.a = a
planet.lambda0 = 90
system = System(star, planet)
system.compute(time)
sF = np.array(star.lightcurve)
sF /= sF[0]
ax[0].plot(time, sF, '-', color='C0', label='starry')
# Compute and plot the flux from numerical integration
print("Computing numerical flux...")
f = 2 * np.pi / P * time
b = a * np.sqrt(1 - np.sin(np.pi / 2. + f)**2 * np.sin(inc * np.pi / 180)**2)