Abstract

The gravitational-wave signal of a compact binary carries the imprint of its environment. In a galactic nucleus, the tidal field of the central supermassive black hole (SMBH) drives Kozai--Lidov (KL) oscillations in the eccentricity of an orbiting binary, modulating the emitted signal. As a proof of concept, previous work showed that for an IMBH--stellar-mass black hole binary, this modulation is detectable with LISA out to about a megaparsec (Deme et al. 2020). This detectability depends on the parameters of the triple; among them, the outer eccentricity plays a special role: it switches on the octupole order of the secular approximation, and with it qualitatively stronger and aperiodic oscillations. In this thesis, we ask how the outer eccentricity changes the detectability of this modulation, integrating the secular equations of motion to octupole order, including 1PN pericenter precession and gravitational-wave emission. We quantify detectability through the change in signal-to-noise ratio (ΔSNR) between consecutive LISA observation windows, at a source distance of 1~Mpc.  We find that the outer eccentricity shifts the detectable region of parameter space, expanding it at one end and shrinking it at the other; its effect depends on the binary's orbital parameters. Across our cases, the inner separation ranges from  2 to 7~AU. Where relativistic precession dominates, it suppresses the oscillations; a larger outer eccentricity resists this suppression and can lift a modulation that a circular outer orbit would otherwise leave below LISA's detection threshold into detectability. Where precession is too slow to interfere, the outer eccentricity amplifies the oscillations, driving the eccentricity to higher peaks and strengthening the modulation. In the wide binaries, the eccentricity peaks grow so high that gravitational-wave emission drives the orbit to merger within the mission lifetime. Thus, an eccentric outer orbit reshapes both the strength and the character of the KL imprint that LISA would observe.

Publication Date

8-2026

Document Type

Thesis

Student Type

Graduate

Degree Name

Astrophysical Sciences and Technology (MS)

Department, Program, or Center

Physics and Astronomy, School of

College

College of Science

Advisor

Richard O’Shaughnessy

Advisor/Committee Member

Yosef Zlochower

Advisor/Committee Member

Joshua Faber

Campus

RIT – Main Campus

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