ner_tags: O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: for the 77 pairs with r proj > 5 kpc (blue). Primaries with more than one companion were counted more than once. The pairs with r proj r vir are shown in red. In the case of pairs having both their primaries and secondaries in the parent sample, only the most massive companion was considered. Table 1. Uncertainties associated with the use of z grism on the fraction of pairs. Very close pairs with r proj 5 kpc are superimposed in the CANDELS images so it was not possible to identify them as two distinct objects using the 3D-HST photometric catalogue (see example in the last panel of Fig. 5 ). The images of the galaxies in the parent sample were visually inspected to identify such cases. 10 pair candidates were found. Six of them had z spec , so we visually inspected the associated slit data. For three of them, both nuclei were included into the slit width (see Appendix A ) so we considered them as real pairs, which brings the total number of pairs in the parent sample to 80. The seven remaining ones correspond to a possible systematic underestimation of the number of pairs. Correcting factors to the number of pairs related to, e.g. projection effects are discussed in Section 2.2.4 . 2.2.2 Comparing observational and theoretical merger rates The goal of this paper is to compare observational estimates of the (major) merger rate to the predictions of the ΛCDM model. To avoid introducing systematics in the comparison, one therefore needs to adopt consistent definitions and assumptions. Merger rates in simulations can be defined in several ways. One of them consists in defining the merger rate as the rate at which a secondary halo is accreted on to a primary halo and becomes a sub-halo. This halo–halo merger rate then needs to be corrected by an estimate of the extra time needed for the secondary galaxy entering the primary halo to actually merge with the primary galaxy. Estimates based on semi-analytical or semi-empirical models need to explicitly account for such a correction, which can rely on several methods (e.g. based on the dynamical friction time). This can introduce a systematic uncertainty of a factor of ∼2 on the expected merger rate (see extensive discussion on these aspects in, e.g. section 2.4 of Hopkins et al. 2010a ). Using cosmological simulations, one can directly estimate the resulting galaxy–galaxy merger rate by intrinsically accounting for this delay. However, they are not immune to other uncertainties such as how and when the mass ratio and infall time are defined (Rodriguez-Gomez et al. 2016 ). In this paper, we choose to rely on the semi-empirical approach in which dark matter haloes are populated with realistic galaxies using the halo occupation distribution and empirical scaling relations that are relatively well constrained in the redshift and mass ranges considered in this study. 2.2.3 Identifying merging pairs Since the halo–halo merger rate is the most direct predictions of semi-empirical models, we designed a method