It is a well-known conjecture (or maybe just a question) that all hyperbolic groups are residually finite. What happens if we weaken the conclusion; in particular


Are all hyperbolic groups residually amenable?


What is known in this direction? 



Are Hyperbolic Groups Residually Amenable
[Proposition 7 of this paper](http://www.mat.univie.ac.at/~arjantseva/Abs/asymptotic.pdf) establishes that every hyperbolic group is residually amenable iff every hyperbolic group is residually finite.


