Stellar-mass black-hole binaries in LISA: characteristics and complementarity with current-generation interferometers

Stellar-mass black-hole binaries are the most numerous gravitational-wave sources observed to date. Their properties make them suitable for observation both by ground- and space-based detectors. Starting from synthetic catalogues constructed based on observational constraints from ground-based detectors, we explore the detection rates and the characteristic parameters of the stellar-mass black-hole binaries observable by LISA during their inspiral, using signal-to-noise ratio thresholds as a detection criterion. We find that only a handful of these sources will be detectable with signal-to-noise ratio larger than 8: about 5 sources on average in 4 years of mission duration, among which only one or two are multiband ones (i.e. merging in less than 15 years). We find that detectable sources have chirp mass $10 M_\odot\lesssim \mathcal{M}_c\lesssim 100 M_\odot$, residual time-to-coalescence $4\mathrm{yr}\lesssim \tau_c\lesssim 100 \mathrm{yr}$, and redshift $z\lesssim 0.1$, much closer than those observed up to now by ground-based detectors. We also explore correlations between the number of LISA detectable sources and the parameters of the population, suggesting that a joint measurement with the stochastic signal might be informative of the population characteristics. By performing parameter estimation on a subset of sources from the catalogues, we conclude that, even if LISA measurements will not be directly informative on the population due to the low number of resolvable sources, it will characterise a few, low-redshift candidates with great precision. Furthermore, we construct for the first time the LISA waterfall plot for low chirp mass, and demonstrate that LISA will also be able to discriminate and characterize, through very precise parameter estimation, a population of binaries with higher masses, $\mathcal{M}_c\sim \mathcal{O}(10^3) M_\odot$, if it exists.