We present adaptive optics-assisted K-band integral field spectroscopy of the central cluster galaxy in 2A 0335+096 ( z=0.0349 ) .
The H _ { 2 } v=1–0 S ( 1 ) emission is concentrated in two peaks within 600 pc of the nucleus and fainter but kinematically-active emission extends towards the nucleus .
The H _ { 2 } is in a rotating structure which aligns with , and appears to have been accreted from , a stream of H \alpha emission extending over 14 kpc towards a companion galaxy .
The projected rotation axis aligns with the 5 GHz radio lobes .

This H _ { 2 } traces the known 1.2 \times 10 ^ { 9 } \thinspace M _ { \odot } CO-emitting reservoir ; limits on the Br \gamma emission confirm that the H _ { 2 } emission is not excited by star formation , which occurs at a rate of less than 1 \hbox { $ \thinspace M _ { \odot } $ } { \thinspace yr } ^ { -1 } in this gas .
If its accretion onto the black hole can be regulated whilst star formation remains suppressed , the reservoir could last for at least 1 Gyr ; the simultaneous accretion of just \sim 5 per cent of the gas could drive a series of AGN outbursts which offset X-ray cooling in the cluster core for the full \sim 1 Gyr .
Alternatively , if the regulation is ineffective and the bulk of the H _ { 2 } accretes within a few orbital periods ( 25–100 Myr ) , the resulting 10 ^ { 62 } erg outburst would be among the most powerful cluster AGN outbursts known .
In either case , these observations further support cold feedback scenarios for AGN heating .