Prospecting Period Measurements with LSST - Low Mass X-ray Binaries as a Test Case

The Large Synoptic Survey Telescope (LSST) will provide for unbiased sampling of variability properties of objects with $r$ mag $<$ 24. This should allow for those objects whose variations reveal their orbital periods ($P_{orb}$), such as low mass X-ray binaries (LMXBs) and related objects, to be examined in much greater detail and with uniform systematic sampling. However, the baseline LSST observing strategy has temporal sampling that is not optimised for such work in the Galaxy. Here we assess four candidate observing strategies for measurement of $P_{orb}$ in the range 10 minutes to 50 days. We simulate multi-filter quiescent LMXB lightcurves including ellipsoidal modulation and stochastic flaring, and then sample these using LSST's operations simulator (OpSim) over the (mag, $P_{orb}$) parameter space, and over five sightlines sampling a range of possible reddening values. The percentage of simulated parameter space with correctly returned periods ranges from $\sim$23 %, for the current baseline strategy, to $\sim$70 % for the two simulated specialist strategies. Convolving these results with a $P_{orb}$ distribution, a modelled Galactic spatial distribution and reddening maps, we conservatively estimate that the most recent version of the LSST baseline strategy will allow $P_{orb}$ determination for $\sim$18 % of the Milky Way's LMXB population, whereas strategies that do not reduce observations of the Galactic Plane can improve this dramatically to $\sim$32 %. This increase would allow characterisation of the full binary population by breaking degeneracies between suggested $P_{orb}$ distributions in the literature. Our results can be used in the ongoing assessment of the effectiveness of various potential cadencing strategies.