Sound wave generation by a spherically symmetric outburst and AGN
  feedback in galaxy clusters II: impact of thermal conduction
  We analyze the impact of thermal conduction on the appearance of a
shock-heated gas shell which is produced when a spherically symmetric outburst
of a supermassive black hole inflates bubbles of relativistic plasma at the
center of a galaxy cluster. The presence of the hot and low-density shell can
be used as an ancillary indicator for a high rate of energy release during the
outburst, which is required to drive strong shocks into the gas. Here we show
that conduction can effectively erase such shell, unless the diffusion of
electrons is heavily suppressed. We conclude that a more robust proxy to the
energy release rate is the ratio between the shock radius and bubble radius. We
also revisited the issue of sound waves dissipation induced by thermal
conduction in a scenario, where characteristic wavelength of the sound wave is
set by the total energy of the outburst. For a fiducial short outburst model,
the dissipation length does not exceed the cooling radius in a typical cluster,
provided that the conduction is suppressed by a factor not larger than
$\sim$100. For quasi-continuous energy injection neither the shock-heated shell
nor the outgoing sound wave are important and the role of conduction is
subdominant.
