Can cluster merger shocks reproduce the luminosity and shape distribution of radio relics?

Radio relics in galaxy clusters are believed to trace merger shock fronts. If cosmological structure formation determines the luminosity, size and shape distributions of radio relics then merger shocks need to be lighted up in a homogeneous way. We investigate if a mock relic sample, obtained from zoomed galaxy cluster simulations, is able to match the properties of relics measured in the NRAO VLA Sky Survey (NVSS). We compile a list of all radio relics known to date and homogeneously measure their parameters in all NVSS images and apply the same procedure to relics in our simulations. Number counts in the mock relic sample increase more steeply towards lower relic flux densities, suggesting an incompleteness of NVSS in this regime. Overall, we find that NVSS and mock samples show similar properties. However, large simulated relics tend to be somewhat smaller and closer to the cluster centre than observed ones. Besides this, the mock sample reproduces very well-known correlations for radio relics, in particular those relating the radio luminosity with the largest linear size and the X-ray luminosity. We show that these correlations are largely governed by the sensitivity of the NVSS observations. Mock relics show a similar orientation with respect to the direction to the cluster centre as the NVSS sample. Moreover, we find that their maximum radio luminosity roughly correlates with cluster mass, although displaying a large scatter. The overall good agreement between NVSS and the mock sample suggests that properties of radio relics are indeed governed by merger shock fronts, emitting in a homogeneous fashion. Our study demonstrates that the combination of mock observations and data from upcoming radio surveys will allow to shed light on both the origin of radio relics and the nature of the intracluster medium.