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Abstract

We present first-order models for tilt-to-length (TTL) coupling in LISA, both
for the individual interferometers as well as in the time-delay interferometry
(TDI) Michelson observables. These models include the noise contributions from
angular and lateral jitter coupling of the six test masses, six movable optical
subassemblies (MOSAs), and three spacecraft. We briefly discuss which terms are
considered to be dominant and reduce the TTL model for the second-generation
TDI Michelson X observable to these primary noise contributions to estimate the
resulting noise level. We show that the expected TTL noise will initially
violate the entire mission displacement noise budget, resulting in the known
necessity to fit and subtract TTL noise in data post-processing. By comparing
the noise levels for different assumptions prior to subtraction, we show why
noise mitigation by realignment prior to subtraction is favorable. We then
discuss that the TTL coupling in the individual interferometers will have noise
contributions that will not be present in the TDI observables. Models for TTL
coupling noise in TDI and in the individual interferometers are therefore
different, and commonly made assumptions are valid as such only for TDI but not
for the individual interferometers. Finally, we analyze what implications can
be drawn from the presented models for the subsequent fit-and-subtraction in
post-processing. We show that noise contributions from the test mass and
inter-satellite interferometers are indistinguishable, such that only the
combined coefficients can be fit and used for subtraction. However, a
distinction is considered not necessary. Additionally, we show a correlation
between coefficients for transmitter and receiver jitter couplings in each
individual TDI Michelson observable. This full correlation can be resolved by
using all three Michelson observables for fitting the TTL coefficients.