MESS: Multi-Epoch Spectroscopic Solver for Detecting Double-Lined Systems

TL;DR

MESS extends TODCOR to a multi-epoch framework that jointly optimizes two synthetic templates across a continuous parameter space to identify and characterize SB1 and SB2 systems from large spectroscopic surveys. It uses a multi-epoch correlation score $S^2$ and an effective-sample-size–based BIC for model selection, augmented by Wilson-plot diagnostics and rule-based overrides to robustly classify targets as $\mathcal{S}1$, $\mathcal{SB}1$, or $\mathcal{SB}2$ and to infer per-epoch RVs and, for SB2s, mass ratios and systemic velocities. Validation on 1500 simulated, LAMOST-like systems achieves about 95% accuracy, with SB2 detections remaining reliable down to flux ratios $\alpha \sim 0.1$ and primary+secondary RV-amplitudes above ~$70\ \mathrm{km\,s^{-1}}$, illustrating robustness even when individual spectra are only moderately resolved. The authors demonstrate real-data outputs for several LAMOST MRS targets, including a faint SB2 and a well-studied SB1, and discuss implications for large surveys and binary-star science, including mass-ratio distributions and binary evolution. The approach is computationally efficient (a few seconds per system on multi-core hardware) and ready for survey-scale deployment, with a companion paper detailing DR11 catalogs.

Abstract

We present MESS, a fully automated algorithm for identifying and characterizing double-lined spectroscopic binaries (SB2) in large databases 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 (SB1) and single stars (S1) are handled within the same framework by fitting one optimized template, with either epoch-dependent RVs (SB1) or a single shared RV (S1). Model selection among S1/SB1/SB2 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 (SNR=50), with primary RV semi-amplitudes predominantly below the instrumental resolution, achieving an overall classification accuracy of ~95%. We also derive full orbital solutions for two SB2 systems detected in our LAMOST analysis, including a faint-secondary case with flux ratio ~0.1, and present example outputs for one SB1 and three constant-velocity stars. A companion paper will report the survey-wide application to LAMOST DR11 and the resulting SB1/SB2 catalogs.

Figures (10)

• Figure 1: Single-epoch spectrum and 1D cross-correlation for J1145. Upper: normalized observed spectrum (blue) at a representative epoch and the best-fitting primary template (red; vertically offset by $-0.5$ in normalized flux for clarity) obtained from a 1D grid search over $(T_{\rm eff},\log g,Z,V\sin{i})$. Lower: the corresponding 1D cross-correlation function (CCF) used to select both the template and the Doppler shift, showing a maximum at $v=-8\pm6 \,\mathrm{km\,s^{-1}}$.
• Figure 2: Two-dimensional TODCOR surface and orthogonal cuts for J1145 (same target as in figure \ref{['fig:todcor1D']}). Left: the 2D correlation surface $R_\alpha(\rm{v}_1,\rm{v}_2)$; the magenta star marks the global maximum and red dashed lines indicate the orthogonal 1D sections. Right/bottom: 1D cuts through the peak along the $\rm{v}_1$ and $\rm{v}_2$ axes, respectively, illustrating the ridge orientation and blend-driven covariance. Best-fit orbital parameters and derived quantities are listed in table \ref{['tab:J1145_orbit']}.
• Figure 3: MESS results of $500$ simulated $\mathcal{SB}2$ systems in $\alpha$--$(K_1+K_2)$ space (flux ratio vs. the sum of the RV semi-amplitudes). Points are colored by their final label: black---correctly classified as $\mathcal{SB}2$; red---misclassified as $\mathcal{SB}1$; magenta---misclassified as $\mathcal{S}1$. Occurrence rates by outcome are summarized in table \ref{['tab:confusion_sim']} (row $\mathcal{SB}2$). The simulated set concentrates on primary RV semi-amplitudes below the instrumental resolution; the dashed vertical line marks the LAMOST MRS resolution, $\simeq 40\,\mathrm{km\,s^{-1}}$ ($R\!\approx\!7500$).
• Figure 4: Wilson plot for J1145. Points show per-epoch radial-velocity pairs $(\rm{v}_{1,m},\rm{v}_{2,m})$ for $35$ observed epochs; the solid line is the best linear fit, from which the mass ratio $q$ and the systemic velocity $\gamma$ are derived.
• Figure 5: $\mathcal{SB}2$ Keplerian solution for J1145, based on 35 MESS RVs, with reference epoch $T_0 = 57016.7$ days. Upper-left: primary (blue) and secondary (red) velocities versus ${\rm MJD}-T_0$. Note the time gaps in the data, due to LAMOST observational constraints.