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Abell 1201 is a massive galaxy cluster at z=0.169 with a brightest clustergalaxy (BCG) that acts as a gravitational lens to a background source atz=0.451. The lensing configuration is unusual, with a single bright arc formedat small radius $\sim$2 arcsec), where stars and dark matter are both expectedto contribute substantially to the total lensing mass. Here, we present deepspectroscopic observations of the Abell 1201 BCG with MUSE, which revealemission lines from a faint counter-image, opposite to the main arc, at aradius of 0.6 arcsec. We explore models in which the lensing mass is describedby a combination of stellar mass and a standard dark-matter halo. Thecounter-image is not predicted in such models, unless the dark-matter componentis negligible, which would imply an extremely heavy stellar initial massfunction (IMF) in this galaxy. We consider two modifications to the model whichcan produce the observed configuration without resorting to extreme IMFs.Imposing a radial gradient in the stellar mass-to-light ratio, $\Upsilon$, cangenerate a counter-image close to the observed position if $\Upsilon$ increasesby $\gtrsim$60 per cent within the inner $\sim$1 arcsec (e.g. variation from aMilky-Way-like to a Salpeter-like IMF). Alternatively, the counter-image can beproduced by introducing a central super-massive black hole. The required massis $M_{\rm BH}$ = (1.3$\pm$0.6)$\times$10$^{10}$ M$_\odot$, which is comparableto the largest black holes known to date, several of which are also hosted byBCGs. We comment on future observations which promise to distinguish betweenthese alternatives.

A counter-image to the gravitational arc in Abell 1201: Evidence for IMF variations, or a $10^{10}$M$_{\odot}$ black hole?