Source Power

We can estimate the radio source parameters based on the presence of the X-ray cavities (Heinz et al. 1998, RHB, Churazov et al. 2000). We use the two-temperature fit of § 2 to estimate the physical parameters of the ICM. Taking the hot emission to arise uniformly in a sphere of 90 radius yields an electron density of $n_{\rm hot}\gtrsim 0.009\,{\rm cm^{-3}}$. Assuming the cold gas is in pressure equilibrium with the hot gas gives an electron density of $n_{\rm cold} \gtrsim 0.031\, {\rm cm^{-3}}$ and a volume filling factor of $5\times 10^{-3}$.

Figure 2: Hardness ratio $h_2$ adaptively binned to reach a signal-to-noise of 5 (after background subtraction) with contours from the $5-6\sigma$ adaptively smoothed X-ray image (contour start from $c_{1}=10^{-8}\,{\rm ergs\,cm^{-2}\,s^{-2}\,pixel^{-1}}$, increasing by a factor of $1.4$ between each contour).

We assume that both X-ray cavities are completely evacuated by the lobes and estimate their size from the smoothed images by approximating them as spheres. While this is clearly a simplification, it will be sufficient for this order of magnitude estimate. A `by eye' fit of the cavities gives bubble radii of $r_{\rm bub} \sim 20\arcsec$ (20 kpc). The pressure in the hot phase is $p_{\rm ICM} \gtrsim 1.1\times 10^{-10}\,{\rm erg\,cm^{-3}}$, relatively close to the minimum energy pressure in the lobes of $p_{\rm ME} \sim 3 - 5\times 10^{-11}{\rm ergs\ cm^{-3}}$ (T94). At a minimum, the radio galaxy has to perform ``pdV'' work against the ICM. Including the internal energy of the plasma within the cavities, this gives an integrated energy output of $E_{\rm tot} \gtrsim 8\times 10^{59}\, {\rm ergs}$.

The radio galaxy had to inject this energy into the bubbles before they floated out of the cluster core. This buoyancy timescale is approximately twice the sound crossing time of the relevant region of the cluster, $\tau\sim 4r_{\rm bub}/c_{\rm s}\sim 8\times 10^{7}{\rm\thinspace yr}$, where we have used the sound speed for a $4{\rm\thinspace keV}$ gas, $c_{\rm s}\sim 1000\hbox{${\rm\thinspace km}{\rm\thinspace s}^{-1}\,$}$. The time-averaged source power needed to produce the cavities is then $L_{\rm kin}\sim E_{\rm b}/\tau\gtrsim 3\times 10^{44}\hbox{${\rm\thinspace erg}{\rm\thinspace s}^{-1}\,$}$.

Alternatively, we can estimate the source age from the ``sonic boom'' arguments of RHB. The hour-glass structure through the cluster center is roughly 50 long (i.e., $25\arcsec \sim 25\,{\rm kpc}$ on either side of the center). Following RHB, we equate this to the distance traveled by a shock/compression wave which moves at least at the sound speed of the hot ICM. This gives a source age of $\tau \lesssim 2.4\times 10^{7}\,{\rm yrs}$ and a time-averaged power of $L_{\rm kin}\gtrsim E_{\rm b}/\tau\sim 10^{45}\hbox{${\rm\thinspace erg}{\rm\thinspace s}^{-1}\,$}$.

A third, X-ray independent way to estimate the source power is based on the radio flux. The flux densities at 5GHz and 8GHz are given by T94 as 76mJy and 34mJy, while the 1.4GHz NVSS flux Condon et al. (1998) is 1.3Jy. The NVSS flux lies a factor of 2 above the extrapolation of the 5-8GHz flux, and the NVSS image suggests spatial extension on arcmin scales (a factor of $\sim 2$ larger than seen at 5-8GHz). This suggests that NVSS is detecting low frequency emission from plasma that is emitting a steep radio spectrum, possibly indicating that it has suffered synchrotron aging. A reasonable upper limit on the current radio power can be derived by taking the 1.4GHz luminosity, and using the arguments of Bicknell et al. (1998) to convert it into a kinetic luminosity. Taking the smallest reasonable value of their conversion parameter, $\kappa_{1.4} > 10^{-12}$, we estimate an upper limit on the current kinetic power of $L_{\rm kin} < 7\times 10^{43}\hbox{${\rm\thinspace erg}{\rm\thinspace s}^{-1}\,$}$.

Comparing the time-averaged source power (derived the X-ray cavities) to that derived from the radio luminosity (which is equivalent to the source power averaged over the synchrotron cooling time of the 1.4GHz electrons, $\tau_{\rm cool} \lesssim 10^7\,{\rm yrs}$), one infers that either this source has faded in kinetic luminosity by an order of magnitude or more, or that the magnetic field in the lobes is considerably out of equipartition. Since the thermal pressure is close to the equipartition pressure estimated by T94, we favor the first possibility. Given the uncertainties in these arguments (especially in $\kappa_{1.4}$, for which we chose a conservative value), the source could easily have faded by more than an order of magnitude. Indeed, the fact that the average power is in the realm of FR-II radio galaxies, while morphology and current radio luminosity qualify it as an FR-I, leads us to speculate that PKS2354-35 is an example of an FR-II source that has faded into an FR-I source on a timescale of less than $10^8{\rm\thinspace yr}$.

The apparent offset between the cluster center and the center of the cavities and the asymmetric brightness distribution through the equatorial regions of the hour-glass structure may be evidence for bulk ICM motions. In particular, the morphology suggests a bulk flow in a NE direction which might further squeeze the outward moving compression wave from the radio galaxy, and sweep back the cavity structure. We note that the SW ridge is rather cool and thus cannot be a strong shock resulting from the interaction of a bulk flow with the radio galaxy. Hydrodynamic simulations are required to investigate this system further.