Galaxies form and reside within a large-scale structure primarily composed of dark matter. This spatial clustering is shaped by gravitational forces acting on initially small perturbations present in the very early universe. As structure grows hierarchically through gravitational instability, the tidal fields associated with the evolving matter density are expected to induce subtle effects on the shapes, spins, and orientations of galaxies and dark matter haloes. These correlations are broadly known as "Intrinsic Alignments" (IA). Generally, elliptical galaxies and haloes display a linear relationship with the large-scale tidal field, where long axes are aligned with its stretching direction. For a pedagogical introduction to IA, see Lamman et al. (2023a) and for comprehensive reviews, see Joachimi et al. (2015) and Troxel & Ishak (2015). IA are most commonly studied as a contaminant of cosmological probes, such as weak lensing and redshift-space distortions (RSD), but in principle they can also be used to trace any cosmological effect which is imprinted in the large-scale density field (Chisari & Dvorkin 2013). Compared to traditional two-point clustering statistics, IA have the advantage of capturing both the magnitude and polarization of tidal shear, as is done with weak lensing. While weak lensing traces all foreground matter, IA from spectroscopic data contain additional information along the line-of-sight. However, the effect is subtle and requires large samples and high-quality imaging. IA have been explored as a probe of primordial non-gaussianity (Akitsu et al. 2021; Kurita & Takada 2023), Baryon Acoustic Oscillations (Okumura et al. 2019; Xu et al. 2023), Redshift-space Distortions (Okumura & Taruya 2023), and cosmic B-modes (Georgiou et al. 2023; Akitsu et al. 2023; Saga et al. 2024). In some cases it is advantageous to study the alignment of galaxy ensembles: groups and clusters as opposed to individuals. The determined shapes of galaxy ensembles are unaffected by the myriad of systematic effects which arise from imaging, and are associated with the shape of their host haloes, which display stronger tidal alignment (Smargon et al. 2012; Fortuna et al. 2021; Lee et al. 2023). Clusters of Luminous Red Galaxies (LRGs) in the Sloan Digital Sky Survey display similar but stronger alignment compared to single galaxies (Smargon et al. 2012; van Uitert & Joachimi 2017). These correlations were found to be lower than predicted by N-body simulations, which may be due to hydrodynamic or projection effects, which create misidentification of cluster members (Shi et al. 2024). There are also concerns of orientation bias in identifying clusters, particularly for photometric surveys (Sunayama 2023).In this work we explore the potential of using galaxy “multiplets”: small sets of galaxies, mostly consisting of 2-4 members within 1 ℎ −1Mpc of each other (Fig. 1). We expect these tiny ensembles to still preserve information from the large-scale tidal field, while being more abundant than larger groups. Multiplets are not necessarily virialized systems, but can be understood in the IA framework as they are well within the nonlinear regime of gravitational evolution. Like galaxy shapes and haloes, their orbital structure carries a memory of the initial tidal field. The alignment of galaxy multiplets may be a better estimator than individual galaxies when: imaging is poor, the sample is especially dense, or the sample displays little or no individual alignment, as is the case for spiral (or “blue”) galaxies. The latter of these applies to most available spectroscopic samples beyond redshift 1. Understanding the redshift evolution of IA is an important component of fully utilising forthcoming cosmic shear surveys (Dark Energy Survey and Kilo-Degree Survey Collaboration et al. 2023). However the redshift evolution of IA is unclear and there is no direct IA detection beyond redshift 1 with traditional estimators.We describe and model this estimator from the perspective of IA, but this work is also related to the fields of both galaxy groups and higher-order clustering. Although multiplets are not galaxy groups, which are virialized systems and typically describe more complete sets of galaxies (Oppenheimer et al. 2021), multiplets exist on similar scales. They can overlap group catalogues, especially when multiplets are identified in dense samples. Furthermore, the nonlinear dynamics within groups directly affect the amplitude of multiplet alignment. Since, in most cases, we are measuring the orientation of close galaxy pairs relative to a distant tracer, this estimator can also be thought of as a squeezed three-point correlation function. Previous work has explored 3-point and higher-order correlations in spectroscopic data (Slepian & Eisenstein 2015; Philcox et al. 2022), including detecting evidence of the tidal field (Slepian et al. 2017) and investigating the squeezed 3-point function (Yuan et al. 2017). These describe correlations that arise from larger scales than multiplets, but are a similar framing of our estimator. As a spectroscopic survey of over 40 million galaxies, the DESI Survey (Dark Energy Spectroscopic Instrument), is well-suited to probing subtle, higher-order clustering effects in three dimensions (Levi et al. 2013; DESI Collaboration et al. 2016a,b, 2022, 2023a; Miller et al. 2023). To explore the potential of multiplet IA, we measure the tidal alignment of multiplets in DESI’s Year 1 survey (DESI Collaboration et al. 2024a,b,c). We use three galaxy samples: bright galaxies (BGS), luminous red galaxies (LRG), and emissionline galaxies (ELG), ranging from redshifts 0.1 – 1.5. As a proofof-concept for interpreting this estimator, we develop modelling for the catalogue which displays the highest galaxy bias and alignment signal, LRGs. Section 2 describes the DESI data and mock catalogues used. Section 3 outlines our methodology for identifying galaxy multiplets and measuring their alignment. Section 4 presents a comparison to mock catalogues and an analytic model of the alignment signal. Section 5 summarizes key results and discusses prospects for utilising future datasets. Throughout the paper we assume the cosmological parameters of 𝐻0 = 69.6, Ω𝑚,0 = 0.286, ΩΛ,0 = 0.714.

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