Confusion noise from LISA capture sources

Captures of compact objects (COs) by massive black holes (MBHs) in galactic nuclei will be an important source for LISA, the proposed space-based gravitational wave (GW) detector. However, a large fraction of captures will not be individually resolvable---either because they are too distant, have unfavorable orientation, or have too many years to go before final plunge---and so will constitute a source of ``confusion noise, '' obscuring other types of sources. In this paper we estimate the shape and overall magnitude of the GW background energy spectrum generated by CO captures. This energy spectrum immediately translates to a spectral density S₇^capt (f) for the amplitude of capture-generated GWs registered by LISA. The overall magnitude of S₇^capt (f) is linear in the CO capture rates, which are rather uncertain; therefore we present results for a plausible range of rates. S₇^capt (f) includes the contributions from both resolvable and unresolvable captures, and thus represents an upper limit on the confusion noise level. We then estimate what fraction of S₇^capt (f) is due to unresolvable sources and hence constitutes confusion noise. We find that almost all of the contribution to S₇^capt (f) coming from white dwarf and neutron star captures, and at least 30% of the contribution from black hole captures, is from sources that cannot be individually resolved. Nevertheless, we show that the impact of capture confusion noise on the total LISA noise curve ranges from insignificant to modest, depending on the rates. Capture rates at the high end of estimated ranges would raise LISA's overall (effective) noise level fS₇^eff (f) ^1/2 by at most a factor 2 in the frequency range 1--10 mHz, where LISA is most sensitive. While this slightly elevated noise level would somewhat decrease LISA's sensitivity to other classes of sources, we argue that, overall, this would be a pleasant problem for LISA to have: It would also imply that detection rates for CO captures were at nearly their maximum possible levels (given LISA's baseline design and the level of confusion noise from galactic white dwarf binaries). This paper also contains, as intermediate steps, several results that should be useful in further studies of LISA capture sources, including (i) a calculation of the total GW energy output from generic inspirals of COs into Kerr MBHs, (ii) an approximate GW energy spectrum for a typical capture, and (iii) an estimate showing that in the population of detected capture sources, roughly half the white dwarfs and a third of the neutron stars will be detected when they still have 10 years to go before final plunge.