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 { \cal S } ^ { capt } _ { h } ( f ) for the amplitude of capture-generated GWs registered by LISA .
The overall magnitude of { \cal S } ^ { capt } _ { h } ( f ) is linear in the CO capture rates , which are rather uncertain ; therefore we present results for a plausible range of rates . { \cal S } ^ { capt } _ { h } ( 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 { \cal S } ^ { capt } _ { h } ( f ) is due to unresolvable sources and hence constitutes confusion noise .
We find that almost all of the contribution to { \cal S } ^ { capt } _ { h } ( f ) coming from white-dwarf and neutron-star captures , and at least \sim 30 \% of the contribution from black hole captures , is from sources that can not 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 [ fS ^ { eff } _ { h } ( f ) ] ^ { 1 / 2 } by at most a factor \sim 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 \mathrel { \hbox { \hbox to 0.0 pt { \hbox { \lower 4.0 pt \hbox { $ \sim$ } } } \hbox { $ > $ } } } 10 years to go before final plunge .