tokens: Like black holes, this distribution is relatively flat. Figure 6. Distribution of periods for NSLC binaries detectable by Gaia . Blue is the fiducial model, orange is low αλ, green is the kick model with the same momentum as neutron stars, and red is kicks with the same velocity. For completeness we have also included in Appendix C the distribution of distances from earth (Fig. C1 ), apparent magnitudes of the luminous companions (Fig. C2 ), ratios between the semimajor axes and distances (Fig. C3 ), and radial velocity amplitudes (Fig. C4 ). 5 CONCLUSIONS In this work we give some predictions for the detection of binaries with a single luminous companion with Gaia . Similar endeavours exist in the literature, but two novel ideas that we introduce in this paper are that (i) similar methods can be used to detect neutron star luminous companion systems (which are expected to be more numerous) and (ii) the data from Hipparcos can be used to constrains the theoretical models. Our fiducial model predicts a few dozen BHLC detections with Gaia , and about one detections with Hipparcos . The last result is consistent with non-detection by Hipparcos , due to uncertainties in the models and statistical fluctuations. All other variants of the fiducial model have similar properties. The corresponding predictions for NSLC binaries are hundreds to thousands with Gaia and a few with Hipparcos . We emphasize that the numbers reported here only apply to binaries where the Chandrasekhar mass is beyond the dark companion’s mass error margin. One of the challenges in this kind of work is estimating the uncertainty. This is because this work is largely based on poorly understood physics and empirical models calibrated with incomplete data. One way to get an estimate for the uncertainty is to explore the sensitivity of the results to changes in the different model parameters. This was done in Yamaguchi et al. ( 2018 ), and the conclusion was that while the number of BHLC binaries might change by a factor of order unity, the shapes of the distribution functions do not. The results from Gaia , as well as future observations, are necessary to refine these models and improve their precision. To date, there are no reports of quiescent neutron stars (i.e. neither pulsars nor accreting) in binaries. As for BHLC binaries, there is one reported detection of a ≥2.5 M ⊙ mass black hole candidate with a red giant companion (Thompson et al. 2018 ). We note that another isolated black hole candidate with mass of about four solar masses was detected in the globular cluster NGC 3201 (Giesers et al. 2018 ). This discovery is less relevant to this study, because stars in a cluster are thought to have formed in a relatively short period of star formation, whereas we are interested in the case where star formation proceeds continuously. Another important difference is that we neglect gravitational interaction between stars that are not mutually bound, which is justified
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