Coordinates.md

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Coordinates and conventions

VBMicrolensing correspondence: the source-trajectory convention comes from LightCurves.md, the binary lens frame from BinaryLenses.md, and the north/east sky convention from Parallax.md.

Source trajectory

For the examples in this guide,

tau = (t - t0) / tE
y1  = u0 * sin(alpha) - tau * cos(alpha)
y2  = -u0 * cos(alpha) - tau * sin(alpha)

alpha is in radians and is measured from the binary axis. u0 and rho are in Einstein-radius units; t0 and tE use the same time unit as the supplied epoch array.

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

params = {
    "s": 0.9, "q": 0.1, "u0": 0.0, "alpha": 1.0,
    "rho": 0.01, "tE": 30.0, "t0": 7500,
}
t = np.linspace(7470, 7530, 300)
curve = lcbinint.LightCurve(
    options=lcbinint.Options(coordinates="vbm", caustic_bins=600)
)
trajectory = curve.source_trajectory(t, params)
caustics = curve.caustics(params)

# Both methods return coordinates in this curve's lens-plane frame.
# Plot them directly; do not negate either axis.
display_x = np.asarray(trajectory.x)
display_y = np.asarray(trajectory.y)

plt.figure(figsize=(2.8, 2.8))
for x, y in zip(caustics.x, caustics.y):
    plt.plot(x, y, color="tab:red", lw=1.1)
plt.plot(display_x, display_y, color="tab:blue")
plt.xlabel("y1")
plt.ylabel("y2")
plt.axis("equal")
plt.show()

source_trajectory() and caustics() use the same lens-plane frame. No additional display rotation is required.

coordinates option

Value	Intended use
"vbm"	Default for the worked examples and VBMicrolensing-compatible parameter semantics.
"lcbinint"	Original low-level lcbinint lens-frame convention. Useful with direct source coordinates and ImagePlane.
"center_of_mass"	Original trajectory convention with an explicit binary center-of-mass reference.
"vbm_center_of_mass"	VBMicrolensing parameter semantics with the explicit center-of-mass reference.

Do not mix source coordinates calculated in one convention with caustics from another. Set the option once on the reusable LightCurve and obtain both trajectory and geometry from that object.

Sky coordinates and observatory coordinates

sky = lcbinint.obs.SkyCoord("17:59:02.3", "-29:04:15.2")
ground = lcbinint.obs.Site("ground", -29.0, -70.7)

Right ascension and declination define the J2000 target direction. piEN and piEE are the north and east components of the parallax vector. Ground-site latitude and longitude are degrees, with east-positive longitude. Space-site tables use (JD, RA_deg, Dec_deg, distance_AU).

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