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.