How to interpret measurements of diffuse light in stacked observations of groups and clusters of galaxies

The diffuse light within galaxy groups and clusters provides valuable insight into the growth of massive cosmic structures. Groups are particularly interesting in this context, because they represent the link between galactic haloes and massive clusters. However, low surface brightness makes their diffuse light extremely challenging to detect individually. Stacking many groups is a promising alternative, but its physical interpretation is complicated by possible systematic variations of diffuse light profiles with other group properties. Another issue is the often ambiguous choice of group centre. We explore these challenges using mock observations for 497 galaxy groups and clusters with halo masses from $\sim 10^{12}$ to $1.5 \times 10^{15}\, \textrm {M}_{\odot }$ at redshift 0.1 from the Hydrangea cosmological hydrodynamic simulations. In 18 per cent of groups with at least five galaxies above $10^{9} \, \mathrm{M}_\odot$ in stellar mass, the r-band brightest galaxy is not the one at the centre of the gravitational potential; line-of-sight projections account for half of these cases. Miscentring does not significantly affect the ensemble average mass density profile or the surface brightness profile for our sample: even within ambiguously centred haloes, different centring choices lead to only a 1 per cent change in the total fraction of diffuse intra-group light, f_IGL. We find strong correlations of f_IGL with the luminosity of the central group galaxy and halo mass. Stacking groups in narrow bins of central galaxy luminosity will therefore make the physical interpretation of the signal more straightforward than combining systems across a wide range of mass.