The structure of cluster merger shocks: turbulent width and the electron
  heating timescale
  We present a new 2 Ms Chandra observation of the cluster merger Abell 2146,
which hosts two huge M~2 shock fronts each ~500 kpc across. For the first time,
we resolve and measure the width of cluster merger shocks. The best-fit width
for the bow shock is 17+/-1 kpc and for the upstream shock is 10.7+/-0.3 kpc. A
narrow collisionless shock will appear broader in projection if its smooth
shape is warped by local gas motions. We show that both shock widths are
consistent with collisionless shocks blurred by local gas motions of 290+/-30
km/s. The upstream shock forms later on in the merger than the bow shock and is
therefore expected to be significantly narrower. From the electron temperature
profile behind the bow shock, we measure the timescale for the electrons and
ions to come back into thermal equilibrium. We rule out rapid thermal
equilibration of the electrons with the shock-heated ions at the 6 sigma level.
The observed temperature profile instead favours collisional equilibration. For
these cluster merger shocks, which have low sonic Mach numbers and propagate
through a high $\beta$ plasma, we find no evidence for electron heating over
that produced by adiabatic compression. Our findings are expected to be valid
for collisionless shocks with similar parameters in other environments and
support the existing picture from the solar wind and supernova remnants. The
upstream shock is consistent with this result but has a more complex structure,
including a ~2 keV increase in temperature ~50 kpc ahead of the shock.
