Syntriod: A Robust Initial Parameter Estimator for Radial Velocity Curve Solutions Beyond Conventional Sampling Limits

Abstract

We present Syntriod, an orbital-phase domain radial velocity (RV) template-based algorithm designed to provide robust initial orbital parameter estimates for spectroscopic binaries across diverse observational sampling conditions. Rather than performing full orbital inference, Syntriod constrains the parameter space with physically consistent solutions to guide subsequent optimization procedures. We evaluate its performance using 10,000 synthetic Keplerian orbits spanning diverse configurations and sampling regimes. For well-sampled datasets ($N_{obs}\ge 8$), Syntriod recovers orbital periods with relative accuracies of order $10^{-3}$. At the theoretical sampling limit ($N_{obs}=6$), the method maintains a ~94% success rate, while classical period-search techniques like Lomb-Scargle become increasingly affected by aliasing. Even below this limit ($N_{obs}=5$), Syntriod recovers the correct orbital solution in ~83% of cases, showing gradual degradation rather than catastrophic failure. We further evaluate the method on 12 real spectroscopic binary systems (HD 160934, Phi Cyg, Capella A, Kepler 16, KIC 3858884, KIC 6867766, KIC 2445134, KIC 3003991, DU Boo, HL Dra, FP Boo, and AK Her) spanning broad orbital periods and eccentricities. Syntriod consistently reproduces literature solutions even when datasets are randomly subsampled to sparse regimes. Where a full Keplerian solution becomes underconstrained ($N_{obs}\le 4$), the algorithm transitions to linear dynamical relations, recovering parameters such as mass ratio ($q$) and systemic velocity ($\gamma$) with success rates exceeding 99%. These results demonstrate that Syntriod provides reliable, computationally efficient initial parameter estimates across well-sampled and sparse regimes, making it a practical pre-solver for modern orbit-fitting pipelines and large spectroscopic surveys.

23 pages, 14 figures and 3 tables. Published in Publications of the Astronomical Society of the Pacific (PASP). Code will be made available on GitHub soon

References in corpus (24)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• The Sloan Digital Sky Survey: Technical Summary
• The Gaia mission
• The Transiting Exoplanet Survey Satellite
• A Survey of Stellar Families: Multiplicity of Solar-Type Stars
• The generalised Lomb-Scargle periodogram. A new formalism for the floating-mean and Keplerian periodograms
• The PLATO 2.0 Mission
• Understanding the Lomb-Scargle Periodogram
• SB9: The Ninth Catalogue of Spectroscopic Binary Orbits
• RadVel: The Radial Velocity Modeling Toolkit
• Juliet: a versatile modelling tool for transiting and non-transiting exoplanetary systems
• Eccentricity distribution of wide binaries
• Variable Stars: which Nyquist Frequency ?
• Radial Velocity Studies of Close Binary Stars. XI
• Statistical properties of exoplanets IV. The period--eccentricity relations of exoplanets and of binary stars
• KIC 3858884: a hybrid δ Sct pulsator in a highly eccentric eclipsing binary
• Radial Velocity Studies of Close Binary Stars.X
• The SDSS-HET Survey of Kepler Eclipsing Binaries: Spectroscopic Dynamical Masses of the Kepler-16 Circumbinary Planet Hosts
• The Dark Energy Spectroscopic Instrument (DESI)
• The APOGEE Spectroscopic Survey of Kepler Planet Hosts: Feasibility, Efficiency, and First Results
• Optimal placement of a limited number of observations for period searches
• Orbits of Six Late-type Active-Chromosphere Binaries
• The SDSS-HET Survey of Kepler Eclipsing Binaries. Description of the Survey and First Results