A first Chandra view of the cool core cluster A1668: offset cooling and
  AGN feedback cycle
  We present a multi-wavelength analysis of the galaxy cluster A1668, performed
by means of new EVLA and Chandra observations and archival H$\alpha$ data. The
radio images exhibit a small central source ($\sim$14 kpc at 1.4 GHz) with
L$_{\text{1.4 GHz}}$ $\sim$6 $\cdot$ 10$^{23}$ W Hz$^{-1}$. The mean spectral
index between 1.4 GHz and 5 GHz is $\sim$ -1, consistent with the usual indices
found in BCGs. The cooling region extends for 40 kpc, with bolometric X-ray
luminosity L$_{\text{cool}} = 1.9\pm 0.1 \cdot$ 10$^{43}$ erg s$^{-1}$. We
detect an offset of $\sim$ 6 kpc between the cluster BCG and the X-ray peak,
and another offset of $\sim$ 7.6 kpc between the H$\alpha$ and the X-ray peaks.
We discuss possible causes for these offsets, which suggest that the coolest
gas is not condensing directly from the lowest-entropy gas. In particular, we
argue that the cool ICM was drawn out from the core by sloshing, whereas the
H$\alpha$ filaments were pushed aside from the expanding radio galaxy lobes. We
detect two putative X-ray cavities, spatially associated to the west radio lobe
(cavity A) and to the east radio lobe (cavity B). The cavity power and age of
the system are P$_{\text{cav}} \sim$ 9 $\times$10$^{42}$ erg s$^{-1}$ and
t$_{\text{age}} \sim$5.2 Myr, respectively. Evaluating the position of A1668 in
the cooling luminosity-cavity power parameter space, we find that the AGN
energy injection is currently consistent within the scatter of the
relationship, suggesting that offset cooling is likely not breaking the AGN
feedback cycle.
