Comparing the full LGRB and SLSN samples to relations that are followed by field star-forming galaxy populations. a) Mass-metallicity relation. Overplotted are the median relations of star-forming galaxies at redshifts (from top to bottom) z = 0.07, 0.7, 2.2, and 3.5 (Mannucci et al. 2009). Data are colour-coded according to their redshift. b) Fundamental metallicity relation (line; Mannucci et al. 2010, 2011) for SLSNe and LGRBs. c) SLSN and LGRB host galaxies in the fundamental metallicity plane (FPZ) for low-mass galaxies (grey; Hunt et al. 2016). The plane plotted is done with [N ii]/Hα metallicity calibration (Pettini & Pagel 2004). Dashed lines in a) and b) show the extrapolations of the relations towards lower masses, where the relations are poorly defined.
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