Today we put out a paper investigating bodies orbiting Sgr A* as a possible source of gravitational waves for LISA. It just so happens that the 4.1 million solar masses of Sgr A* places the gravitational wave (GW) frequency for bodies on a circular orbit in the strong-field right in the sweet spot for LISA. Our paper then addresses two questions: i) what sort of objects can get close enough to Sgr A* without being tidally disrupted and ii) for objects that are not tidally disrupted what would the resulting GWs and signal-to-noise (SNR) look like in LISA.
For the first question, clear candidates (from EMRI research) are stellar mass black holes, neutron stars and white dwarfs all of which can cross the innermost stable circular orbit (ISCO) without being tidal disrupted. We also investigate the Roche limit for planets (rocky and gaseous), low mass stars, red dwarfs and brown dwarfs. These results are nicely summarised in Fig. 1 of the paper:
This shows that detecting Jupiter-like or rocky planets is unlikely but low-mass stars or brown dwarves seems possible. We then go on to show that such object are all detectable in one year of LISA data with a signal-to-noise ratio above 10. We do not in this work attempt any estimate of event rates for these objects to be in the LISA band but hopefully it helps to motivate those who know how to calculate these things to look into this!
Lots more details can be found in our paper at: arXiv:1903.02049 where we also consider sources from another nearby massive black hole in M32 (see appendix C).