  [Abridged] AGN are thought to be intimately connected with their host
galaxies through feeding and feedback processes. A spatially resolved
multiwavelength survey is required to map the interaction of AGN with their
host galaxies on different spatial scales and different phases of the ISM. The
goal of CARS is to obtain the necessary spatially resolved multiwavelength
observations for an unbiased sample of local unobscured luminous AGN. We
present the overall CARS survey design and the associated wide-field optical
IFU spectroscopy for all 41 CARS targets at z<0.06 randomly selected from the
Hamburg/ESO survey of luminous unobscured AGN. This data set provides the
backbone of CARS and allows us to characterize host galaxy morphologies, AGN
parameters, precise systemic redshifts, and ionized gas distributions including
excitation conditions, kinematics, and metallicities in unprecedented detail.
We focus our study on the size of the ENLR which has been traditionally
connected to AGN luminosity. Given the large scatter in the ENLR
size-luminosity relation, we performed a large parameter search to identify
potentially more fundamental relations. Remarkably, we identified the strongest
correlation between the maximum projected ENLR size and the black hole mass,
consistent with an $R_\mathrm{ENLR,max}\sim M_\mathrm{BH}^{0.5}$ relationship.
We interpret the maximum ENLR size as a timescale indicator of a single BH
radiative-efficient accretion episode for which we inferred log(t_AGN) =
(0.45+- 0.08)log(M_BH)+1.78 using forward modeling. The extrapolation of our
inferred relation toward higher BH masses is consistent with an independent
lifetime estimate from the HeII proximity zones around luminous AGN at z~3.
While our proposed link between the BH mass and AGN lifetime might be a
secondary correlation itself or impacted by unknown biases, it has a few
relevant implications if confirmed.
