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tokens: 6.4 Quadrupole artefacts In Fig. 13 , we display the quadrupole for all the multiple quality configuration for the GM and NN:Uniform algorithms, respectively. At the same time we show the samples including only the misidentification shift along the line of sight (dashed lines) and the samples including also the shift due to peculiar galaxy velocities (solid lines). In general, we find similar trends to the monopole. In particular, the lower the quality of a given set of line profiles, the larger is the clustering suppression along the line of sight (and the more positive the quadrupole becomes). However, the quadrupole appears to be more sensitive to the quality of the observed line profiles. In fact, for a given algorithm and quality configuration, similarly to the ideal case, the suppression in the quadrupole extents to larger scales than in the monopole. Figure 13. Quadrupole of LAE samples with (solid) and without (dashed) the peculiar motion of galaxies. The plot structure is the same as Fig. 12 . Here the black dashed line indicates zero. This corresponds to the analysis of the snapshot at redshift 3.0 using the Thin Shell. In detail, the quadrupole of the LAE samples for GM (Fig. 13 ) exhibits a significant suppression of the clustering along the line of sight, which increases its amplitude. As well as in the monopole, the quadrupole of LAE samples using the GM algorithm is only slightly affected by the quality of the line profile. In fact, for most of the {Δλ pix , , } combinations, the quadrupole remains almost unchanged. Although, for the worst combination of Δλ pix and studied here, the amplitude of the quadrupole correlates with on scales smaller than . Moreover, NN:Uniform (Fig. 13 ) exhibits the best performance over most of the {Δλ pix , , } volume covered here. In contrast to the monopole, where the NN:Uniform algorithm provided a measurement without a suppression above for , the quadrupole convergence scale for this is extended to in general. In agreement with the monopole, the clustering suppression along the line of sight in this algorithm depends strongly in the quality of the line. In this way, the suppression gets larger as the quality gets lower. 7 DISCUSSION 7.1 Relation between <inline-formula><tex-math id="TM0456" notation="LaTeX"></tex-math></inline-formula> stack line profile and galaxy properties As studied in Section 3 , our model reproduces the trends observed between Δλ and different galaxy properties. Observational studies have split the stacked line profile as function of several galaxy properties. For example, Guaita et al. ( 2017 ) studied the stacked spectrum of LAEs with spectroscopic observations from VIMOS ULTRA-DEEP SURVEY (VUDS; Le Fèvre et al. 2015 ; Tasca et al. 2017 ). Their sample consisted on 76 galaxies between redshifts z = 2 and z = 4, exhibiting both and C iii ] (1908 Å) as emission lines. The galaxy systemic redshifts were determined by the observed wavelength of the C iii ] lines. Then,