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We present an analytic model of nonlinear correlators of galaxy/haloellipticities in redshift space. The three-dimensional ellipticity field is notaffected by the redshift-space distortion (RSD) at linear order, but by thenonlinear one, known as the Finger-of-God effect, caused by the coordinatetransformation from real to redshift space. Adopting a simple Gaussian dampingfunction to describe the nonlinear RSD effect and the nonlinear alignment modelfor the relation between the observed ellipticity and underlying tidal fields,we derive analytic formulas for the multipole moments of the power spectra ofthe ellipticity field in redshift space expanded in not only the associatedLegendre basis, a natural basis for the projected galaxy shape field, but alsothe standard Legendre basis, conventionally used in literature. The multipolesof the corresponding correlation functions of the galaxy shape field are shownto be expressed by a simple Hankel transform, as is the case for those of theconventional galaxy density correlations. We measure these multipoles of thepower spectra and correlation functions of the halo ellipticity field usinglarge-volume N-body simulations. We then show that the measured alignmentsignals can be better predicted by our nonlinear model than the existing linearalignment model. The formulas derived here have already been used to placecosmological constraints using from the redshift-space correlation functions ofthe galaxy shape field measured from the Sloan Digital Sky Survey (Okumura andTaruya, 2023).

Nonlinear redshift space distortion in halo ellipticity correlations: Analytical model and N-body simulations