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tokens: the fit is repeated; the uncertainty on each RV is taken to be the standard deviation of the best-fitting velocity at each epoch when this procedure is repeated many times. Fitting a Keplerian orbit amounts to simultaneously maximizing the likelihood of the RV curves of the primary and secondary, where the model RV for a given set of orbital parameters is obtained by solving the two-body problem (Murray Correia 2010 ). We use a custom python implementation of the adaptive simulated annealing algorithm (Iglesias-Marzoa, López-Morales Jesús Arévalo Morales 2015 ) to obtain an initial maximum-likelihood estimate of the best-fitting orbital parameters and then sample the parameter space in the vicinity of the maximum likelihood with emcee (Foreman-Mackey et al. 2013 ) to estimate parameter uncertainties. We use non-informative, flat priors throughout. In addition to the seven standard Keplerian orbital parameters, 10 we fit a ‘jitter’ term, s 2 , to allow for the possibility of intrinsic scatter in the RVs due to e.g. stellar pulsation or underestimated RV uncertainties (see e.g. Baluev 2009 ; Price-Whelan et al. 2017 ). The effective total uncertainties in the RVs used in fitting are then , where σ i are the RV uncertainties at each epoch found from bootstrapping. Explicitly, the log-likelihood function isHere, the sum is over N epochs at times t i , represents the predicted RV at time t for a system with orbital parameters (Murray Correia 2010 ), and and are the orbital parameters for each component. For most systems, the best-fitting jitter is small ( s 2 ∼ 0.1 km 2 s − 2 ), indicating that our estimates of σ i are reasonably accurate. However, for stars with large v macro , which indicates significant rotation, jitter is sometimes of order 1 km s − 1 . This suggests that our velocity measurements are less accurate for rapidly rotating stars, which is also supported by our experiments with semi-empirical binary spectra (Appendix B1 ). For some systems with mass ratios near 1, we found that it was initially impossible to obtain a good fit to the measured RVs because the velocity assignments of the two stars were switched in the fits for one or more visits. We attempted to fit these systems by allowing the fitting algorithm to switch the assigned velocities for individual visits if doing so would improve the fit. In most cases, this solved the problem. A few systems (∼5 per cent of those with sufficient coverage) remained with RV curves that could not be well fitted by a Keplerian orbit, even with the possibility of switching the assigned velocities; these systems may have poorly measured RVs or contain an unseen component. Fig. 10 (a) shows an example orbital solution for a system with typical phase coverage, RV errors, and number of epochs. This system has the lowest mass ratio, q = 0.44, of the systems for which we derive orbital solutions. Because of the system’s low mass ratio, the secondary contributes only a small fraction (∼3 per cent)