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VBMicrolensing correspondence: BinarySources.md.
For a binary source, choose how the two source trajectories are specified.
Every form uses rho1, rho2, flux_ratio, and source_mass_ratio; the
last parameter determines the orbital state of source 2 from source 1.
| Form | Circular | Kepler |
|---|---|---|
| Elements | xallarap="circular_elements" with xi_1, xi_2, period_xa, inc_xa |
xallarap="orbital_elements" with ecc_xa, peri_xa added |
| Direct xallarap coordinates | xallarap="circular_velocity", source_orbit_coordinates="xallarap"; CoM t0, u0 and source-1 state xi_1, xi_2, w1, w2, w3 |
xallarap="kepler_velocity" with xa_szs, xa_ar added |
| Trajectory-offset coordinates | xallarap="circular_velocity", source_orbit_coordinates="trajectory_offset"; tracks t0, u0, t0_2, u0_2 and w1, w2, w3 |
xallarap="kepler_velocity" with xa_szs, xa_ar added |
The elements-mode source 1 is the same state used in the standalone circular-elements example.
import numpy as np
import matplotlib.pyplot as plt
import lcbinint
times = np.linspace(7470.0, 7530.0, 1200)
parameters = {
"s": 0.9, "q": 0.1, "alpha": 0.7, "tE": 30.0,
"t0": 7500.0, "u0": 0.20,
"rho1": 0.004, "rho2": 0.002, "flux_ratio": 0.4,
"source_mass_ratio": 0.7,
"xi_1": 0.006, "xi_2": -0.003,
"period_xa": 12.0, "inc_xa": 0.6,
}
binary_curve = lcbinint.LightCurve(
source="binary", xallarap="circular_elements", t_ref=7500.0,
)
components = binary_curve.binary_source_components(times, parameters)plt.figure(figsize=(4.2, 2.7))
plt.plot(times, components.source1.magnification, color="#0173B2", alpha=0.45, lw=1.0, label="source 1")
plt.plot(times, components.source2.magnification, color="#029E73", alpha=0.45, lw=1.0, label="source 2")
plt.plot(times, components.total, color="black", lw=1.5, label="total")
plt.xlabel("Time")
plt.ylabel("Magnification")
plt.legend(loc="upper left", fontsize=8)
plt.show()
caustics = binary_curve.caustics(parameters)
plt.figure(figsize=(3.4, 3.2))
for x, y in zip(caustics.x, caustics.y):
plt.plot(x, y, color="#6C6C6C", lw=1.1)
plt.plot(components.source1.trajectory.x, components.source1.trajectory.y, color="#0173B2", label="source 1")
plt.plot(components.source2.trajectory.x, components.source2.trajectory.y, color="#029E73", label="source 2")
plt.xlabel("Trajectory coordinate 1")
plt.ylabel("Trajectory coordinate 2")
plt.axis("equal")
plt.legend(fontsize=7)
plt.show()
orbital_elements extends the circular-elements state with eccentricity and
periapsis. The call returns the total binary-source magnification.
kepler_parameters = dict(parameters, ecc_xa=0.2, peri_xa=0.4)
kepler_curve = lcbinint.LightCurve(
source="binary", xallarap="orbital_elements", t_ref=7500.0,
)
kepler_magnification = kepler_curve(times, kepler_parameters)With source_orbit_coordinates="xallarap", t0 and u0 specify the CoM
track and xi_1, xi_2 specify source 1 relative to that track.
import numpy as np
import matplotlib.pyplot as plt
import lcbinint
times = np.linspace(7470.0, 7530.0, 300)
parameters = {
"s": 0.9, "q": 0.1, "alpha": 0.7, "tE": 30.0,
"t0": 7500.0, "u0": 0.20,
"rho1": 0.004, "rho2": 0.002, "flux_ratio": 0.4,
"source_mass_ratio": 0.7,
"xi_1": 0.02, "xi_2": -0.01,
"w1": 0.004, "w2": 0.35, "w3": 0.08,
}
binary_curve = lcbinint.LightCurve(
source="binary", xallarap="circular_velocity",
source_orbit_coordinates="xallarap", t_ref=7500.0,
)
components = binary_curve.binary_source_components(times, parameters)plt.figure(figsize=(4.2, 2.7))
plt.plot(times, components.source1.magnification, color="#0173B2", alpha=0.45, lw=1.0, label="source 1")
plt.plot(times, components.source2.magnification, color="#029E73", alpha=0.45, lw=1.0, label="source 2")
plt.plot(times, components.total, color="black", lw=1.5, label="total")
plt.xlabel("Time")
plt.ylabel("Magnification")
plt.legend(loc="upper left", fontsize=8)
plt.show()
caustics = binary_curve.caustics(parameters)
plt.figure(figsize=(3.4, 3.2))
for x, y in zip(caustics.x, caustics.y):
plt.plot(x, y, color="#6C6C6C", lw=1.1)
plt.plot(components.source1.trajectory.x, components.source1.trajectory.y, color="#0173B2", label="source 1")
plt.plot(components.source2.trajectory.x, components.source2.trajectory.y, color="#029E73", label="source 2")
plt.xlabel("Trajectory coordinate 1")
plt.ylabel("Trajectory coordinate 2")
plt.axis("equal")
plt.legend(fontsize=7)
plt.show()
kepler_velocity keeps the direct source-1 coordinates and adds the
line-of-sight state xa_szs and xa_ar.
kepler_parameters = dict(parameters, xa_szs=0.2, xa_ar=1.4)
kepler_curve = lcbinint.LightCurve(
source="binary", xallarap="kepler_velocity",
source_orbit_coordinates="xallarap", t_ref=7500.0,
)
kepler_magnification = kepler_curve(times, kepler_parameters)source_orbit_coordinates="trajectory_offset" accepts the two tangent tracks
at t_ref: t0, u0, t0_2, and u0_2. Use the same binary-source inputs
above. The values below represent the same CoM state and source-1 offset as
the direct example at t_ref.
offset_parameters = dict(parameters)
offset_parameters.pop("xi_1")
offset_parameters.pop("xi_2")
offset_parameters.update({
"t0": 7499.4, "u0": 0.19,
"t0_2": 7500.857142857, "u0_2": 0.214285714,
})
binary_curve = lcbinint.LightCurve(
source="binary", xallarap="circular_velocity",
source_orbit_coordinates="trajectory_offset", t_ref=7500.0,
)
components = binary_curve.binary_source_components(times, offset_parameters)plt.figure(figsize=(4.2, 2.7))
plt.plot(times, components.source1.magnification, color="#0173B2", alpha=0.45, lw=1.0, label="source 1")
plt.plot(times, components.source2.magnification, color="#029E73", alpha=0.45, lw=1.0, label="source 2")
plt.plot(times, components.total, color="black", lw=1.5, label="total")
plt.xlabel("Time")
plt.ylabel("Magnification")
plt.legend(loc="upper left", fontsize=8)
plt.show()
caustics = binary_curve.caustics(offset_parameters)
plt.figure(figsize=(3.4, 3.2))
for x, y in zip(caustics.x, caustics.y):
plt.plot(x, y, color="#6C6C6C", lw=1.1)
plt.plot(components.source1.trajectory.x, components.source1.trajectory.y, color="#0173B2", label="source 1")
plt.plot(components.source2.trajectory.x, components.source2.trajectory.y, color="#029E73", label="source 2")
plt.xlabel("Trajectory coordinate 1")
plt.ylabel("Trajectory coordinate 2")
plt.axis("equal")
plt.legend(fontsize=7)
plt.show()The source trajectories and caustics are the same as the direct-coordinate example above; this is the same physical state expressed with different inputs.
kepler_parameters = dict(offset_parameters, xa_szs=0.2, xa_ar=1.4)
kepler_curve = lcbinint.LightCurve(
source="binary", xallarap="kepler_velocity",
source_orbit_coordinates="trajectory_offset", t_ref=7500.0,
)
kepler_magnification = kepler_curve(times, kepler_parameters)Previous: Xallarap · Documentation home · Next: Combining higher-order effects