BinarySources.md

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Binary sources

source="binary" describes two luminous source stars magnified by the same lens. It changes the source trajectory and flux model only; it is independent of the lens multiplicity.

The observed magnification is A(t) = (A1(t) + flux_ratio * A2(t)) / (1 + flux_ratio), with flux_ratio = F2 / F1.

Parameter	Meaning
t0, u0, rho1	Closest-approach epoch, impact parameter, and normalized radius of source 1.
t0_2, u0_2, rho2	Corresponding parameters for source 2.
tE, alpha	Shared Einstein timescale and trajectory angle.
flux_ratio	Source flux ratio, F2 / F1.

Both rho1 and rho2 are required. Set either to zero for a point source.

import numpy as np
import matplotlib.pyplot as plt
import lcbinint

options = lcbinint.Options(tol=1e-3, reltol=1e-3)
binary_curve = lcbinint.LightCurve(source="binary", options=options)
parameters = {
    "s": 1.0, "q": 1.0, "alpha": 0.0, "tE": 37.3,
    "t0": 7550.4, "u0": 0.075, "rho1": 0.004,
    "t0_2": 7552.0, "u0_2": -0.04, "rho2": 0.002,
    "flux_ratio": 0.4,
}
times = np.linspace(7550.4 - 37.3, 7550.4 + 37.3, 300)

components = binary_curve.binary_source_components(times, parameters)

plt.figure(figsize=(4.8, 3.0))
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=(2.8, 2.8))
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("X")
plt.ylabel("Y")
plt.axis("equal")
plt.legend(fontsize=7)
plt.show()

For source orbital motion alone, see Xallarap. For a physical binary source with xallarap, see Binary source + xallarap.

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