Multi-Epoch Spectroscopic Solver for detecting double-lined systems

ABSTRACT We present Multi-Epoch Spectroscopic Solver (MESS), a fully automated algorithm for identifying and characterizing double-lined spectroscopic binaries ($\mathcal {SB}2$) in large data bases of multi-epoch spectra. MESS extends the two-dimensional TODCOR approach to a global multi-epoch formalism, deriving the radial velocities (RVs) of both components at each epoch while optimizing the templates jointly across all observations. Template optimization searches a continuous synthetic-spectra manifold spanning an eight-dimensional parameter space: effective temperature, surface gravity, and rotational broadening for each star, together with a common metallicity and the flux ratio. Single-lined spectroscopic binaries ($\mathcal {SB}1$) and single stars ($\mathcal {S}1$) are handled within the same framework by fitting one optimized template, with either epoch-dependent RVs ($\mathcal {SB}1$) or a single shared RV ($\mathcal {S}1$). Model selection among $\mathcal {S}1/\mathcal {SB}1/\mathcal {SB}2$ uses the Bayesian information criterion with an effective sample size that accounts for intra-spectrum correlations, and is complemented by the Wilson relation between the two RVs to infer the mass ratio and systemic velocity without a full orbital solution. We validate MESS on 1500 simulated LAMOST MRS systems (signal-to-noise ratio $=50$), with primary RV semi-amplitudes predominantly below the instrumental resolution, achieving an overall classification accuracy of $\sim 95~{{\ \rm per\ cent}}$. We also derive full orbital solutions for two $\mathcal {SB}2$ systems detected in our LAMOST analysis, including a faint-secondary case with flux ratio $\sim 0.1$, and present example outputs for one $\mathcal {SB}1$ and three constant-velocity stars. A companion paper will report the survey-wide application to LAMOST DR11 and the resulting $\mathcal {SB}1/\mathcal {SB}2$ catalogues.