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We investigate the dependence of the galaxy luminosity function on geometric environment within the Galaxy And Mass Assembly (GAMA) survey. The tidal tensor prescription, based on the Hessian of the pseudo-gravitational potential, is used to classify the cosmic web and define the geometric environments: for a given smoothing scale, we classify every position of the surveyed region, 0.04 < z < 0.26, as either a void, a sheet, a filament or a knot. We consider how to choose appropriate thresholds in the eigenvalues of the Hessian in order to partition the galaxies approximately evenly between environments. We find a significant variation in the luminosity function of galaxies between different geometric environments; the normalization, characterized by φ* in a Schechter function fit, increases by an order of magnitude from voids to knots. The turnover magnitude, characterized by M*, brightens by approximately 0.5 mag from voids to knots. However, we show that the observed modulation can be entirely attributed to the indirect local-density dependence. We therefore find no evidence of a direct influence of the cosmic web on the galaxy luminosity function.
Eardley et al. (Fri,) studied this question.