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

Binary Star Eclipse Light Curve and Rossiter-McLaughlin Radial Velocity Fitter | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Astronomy
Input types: textarea, number
Output type: html
Sample coverage: 4
API ready: Yes

Overview

The Binary Star Eclipse Light Curve and Rossiter-McLaughlin Radial Velocity Fitter models single-lined (SB1) and double-lined (SB2) spectroscopic binary orbits using a grid-restarted Levenberg-Marquardt solver. It extracts key orbital parameters, computes binary mass functions and mass ratios, analyzes eclipse timing O−C residuals, estimates the Rossiter-McLaughlin spin-orbit alignment angle (λ), and generates a phase-folded geometric eclipse light-curve preview in a single HTML report.

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

1Parses primary and optional secondary radial velocity observations (time, RV, error) along with optional eclipse timings and stellar parameters.
2Executes a Levenberg-Marquardt orbital fit across a multi-dimensional parameter grid (period, phase, longitude of periastron, and eccentricity) to bypass local phase-wrapped minima.
3Computes 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.
4Generates 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.

Examples

1. Double-Lined Eccentric Binary Orbit and Timing Fit

Observational Astrophysicist

Background

A researcher has obtained 20 primary and 12 secondary radial velocity measurements from high-resolution echelle spectra, along with 5 mid-eclipse epochs.

Problem

Determine the eccentric orbital parameters (P, e, ω, γ), compute component semi-amplitudes (K1, K2), evaluate the mass ratio, and check for period drift via O−C timings.

How to use

Paste primary RV data into rv1Data, secondary RV data into rv2Data, input the period hint (4.3 days), paste the 5 eclipse times, and provide primary mass (2.1 M☉) and inclination (87°).

rv1Data: 20 rows (HJD, RV, err)
rv2Data: 12 rows (HJD, RV, err)
periodHintDays: 4.3
eclipseTimes: 5 timestamps
mass1Msun: 2.1
inclinationDeg: 87
radiusRatio: 0.28
vsiniKmS: 45
rmAmplitudeKmS: 1.9
impactParam: 0.3

Outcome

Yields an HTML report with fitted P ≈ 4.29 d, e ≈ 0.21, mass ratio q ≈ 0.81, mass function ≈ 0.25 M☉, corrected ephemeris, and spin-orbit angle λ ≈ 56°.

2. Single-Lined Radial Velocity and Mass Function Fit

Astronomy Graduate Student

Background

An investigator has radial velocity tracking of a candidate binary star where only the primary spectral lines are visible.

Problem

FAQ

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.

rv1Data: 6 rows (HJD, RV, err)
rv2Data: (empty)
periodHintDays: 0.5
mass1Msun: 1.2

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Double-Lined Eccentric Binary Orbit and Timing Fit

2. Single-Lined Radial Velocity and Mass Function Fit

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