# Binary Star Eclipse Light Curve and Rossiter-McLaughlin Radial Velocity Fitter

Fit spectroscopic-binary radial velocities with a Levenberg-Marquardt orbit solver, derive the mass ratio and mass function, analyse eclipse-time O−C residuals, estimate the Rossiter-McLaughlin spin-orbit angle, and preview a geometric eclipse light curve.

> Canonical page: https://elysiatools.com/en/tools/binary-star-eclipse-light-curve-and-rossiter-mclaughlin-radial-velocity-fitter

- **Category:** Astronomy

- **Keywords:** eclipsing binary fitter, radial velocity orbit, levenberg marquardt astronomy, mass function binary, rossiter mclaughlin lambda, o-c eclipse timing, sb1 sb2 spectroscopic binary

## Overview

The model is v(t) = γ + K[cos(ν+ω) + e cos ω] for both components; LM is restarted over a (P × phase × ω × e) grid to defeat phase-wrapped false minima; derived quantities follow the standard mass-function and projected-separation relations; the RM estimate is first-order; the light-curve preview is an exact-circle-overlap uniform-disk model, not a full Wilson-Devinney solution.

## Inputs

- **Primary RV data (time rv err)** (textarea): 2459000.25 -53.10 1.2 2459001.08 -58.39 1.2 …one observation per line, HJD/BJD days and km/s
- **Secondary RV data (optional, enables SB2)** (textarea): 2459000.61 122.65 1.5 …leave empty for single-lined systems
- **Period hint (days)** (number): e.g. 4.3 — strongly recommended
- **Eclipse times for O−C (optional)** (textarea): 2459000.0000 2459004.2775 …one minimum time per line (cycle numbers optional)
- **Primary mass (M☉)** (number): 1.0
- **Inclination (degrees, optional)** (number): e.g. 87 — enables individual masses
- **Radius ratio R2/R1** (number): 0.28
- **Primary v sin i⋆ (km/s, for RM)** (number): e.g. 45
- **Measured RM amplitude (km/s)** (number): e.g. 1.9 — enables the λ estimate
- **Impact parameter b** (number): 0.3

## When to use

- Fitting spectroscopic radial velocity timeseries for SB1 or SB2 systems to determine systemic velocity, semi-amplitudes, period, and eccentricity.
- Analyzing historical or newly observed eclipse minimum timings to detect orbital period changes through O−C residual analysis.
- Estimating the projected spin-orbit alignment angle (λ) from an observed Rossiter-McLaughlin radial velocity anomaly during transit or eclipse.

## How it works

- Parses primary and optional secondary radial velocity observations (time, RV, error) along with optional eclipse timings and stellar parameters.
- Executes a Levenberg-Marquardt orbital fit across a multi-dimensional parameter grid (period, phase, longitude of periastron, and eccentricity) to bypass local phase-wrapped minima.
- Computes derived orbital properties including the mass function, mass ratio (q), semi-major axis projections, minimum companion mass, or absolute masses when inclination and primary mass are provided.
- Generates an interactive HTML summary containing fitted parameters, phase-folded RV and O−C plots, a first-order Rossiter-McLaughlin calculation, and an exact-circle-overlap light-curve preview.

## Use cases

- Determining fundamental stellar parameters and mass ratios for newly discovered double-lined eclipsing binary systems.
- Evaluating minimum companion masses (M2 sin i) for single-lined spectroscopic binaries and exoplanet-hosting stars.
- Assessing stellar spin-orbit obliquity by modeling in-eclipse Rossiter-McLaughlin velocity deviations against rotational broadening.

## Frequently asked questions

### What input format is required for radial velocity data?

Provide whitespace-separated or tabular rows with observation time (HJD/BJD), radial velocity (km/s), and measurement uncertainty (km/s), one per line.

### Can this tool handle both SB1 and SB2 systems?

Yes. Entering data into Primary RV only fits an SB1 orbit; supplying Secondary RV data automatically triggers a coupled double-lined (SB2) fit.

### How does the solver avoid false local minima?

The Levenberg-Marquardt algorithm restarts across a grid of period, phase, argument of periastron (ω), and eccentricity (e) initial guesses.

### What is required to calculate the Rossiter-McLaughlin spin-orbit angle?

You must supply the primary star's projected rotational velocity (v sin i⋆), the measured RM anomaly amplitude in km/s, the radius ratio, and the impact parameter.

### Does the light-curve preview compute full Roche lobe deformation?

No. The preview uses an exact-circle-overlap uniform-disk model for geometric evaluation rather than a full Wilson-Devinney numerical synthesis.

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