Regularity of a kind of marginal functions in Hilbert spaces

We study well-posedness of some mathematical programming problem depending on a parameter that generalizes in a certain sense the metric projection onto a closed nonconvex set. We are interested in regularity of the set of minimizers as well as of the value function, which can be seen, on one hand, as the viscosity solution to a Hamilton-Jacobi equation, while, on the other, as the minimal time in some related optimal time control problem. The regularity includes both the Fréchet differentiability of the value function and the Hölder continuity of its (Fréchet) gradient

The Close AGN Reference Survey (CARS): Locating the [O III] wing component in luminous local Type 1 AGN

Context. The strong asymmetry in the optical [O III] λ5007 emission line is one of the best signatures of active galactic nuclei (AGN) driven warm (∼104 K) ionized gas outflows on host galaxy scales. While large spectroscopic surveys such as the sloan digital sky survey (SDSS) have characterized the kinematics of [O III] for large samples of AGN, estimating the associated energetics requires spatially resolving these outflows with, for example, integral field unit (IFU) studies. Aims. As part of the Close AGN Reference Survey, we obtained spatially resolved IFU spectroscopy for a representative sample of 39 luminous type 1 AGN at 0.01  80% of the flux associated with a point-like source. We measured < 100 pc offsets in the spatial location of the outflow from the AGN nucleus using the spectro-astrometry technique for these sources. For the other 13 AGN, the [O III] wing emission is resolved and possibly extended on several kiloparsec scales. Conclusions. We conclude that [O III] wing emission can be compact or extended in an unbiased luminous AGN sample, where both cases are likely to appear. Electron density in the compact [O III] wing regions (median ne ∼ 1900 cm−3) is nearly a magnitude higher than in the extended ones (median ne ∼ 500 cm−3). The presence of spatially extended and compact [O III] wing emission is unrelated to the AGN bolometric luminosity and to inclination effects, which means other features such as time delays, or mechanical feedback (radio jets) may shape the ionized gas outflow properties

The Close AGN Reference Survey (CARS): IFU survey data and the BH mass dependence of long-term AGN variability

Context. Active galactic nuclei (AGN) are thought to be intimately connected with their host galaxies through feeding and feedback processes. A strong coupling is predicted and supported by cosmological simulations of galaxy formation, but the details of the physical mechanisms are still observationally unconstrained. Aims. Galaxies are complex systems of stars and a multiphase interstellar medium (ISM). 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 the Close AGN Reference Survey (CARS) is to obtain the necessary spatially resolved multiwavelength observations for an unbiased sample of local unobscured luminous AGN. Methods. We present the overall CARS survey design and the associated wide-field optical integral-field unit (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 the CARS survey 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. Results. We focus our study on the size of the extended narrow-line region (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 RENLR,max ∼ MBH0.5 relationship. We interpret the maximum ENLR size as a timescale indicator of a single black hole (BH) radiative-efficient accretion episode for which we inferred 〈log(tAGN/[yr])〉 = (0.45 ± 0.08)log(MBH/[M⊙]) + 1.78−0.67+0.54 using forward modeling. The extrapolation of our inferred relation toward higher BH masses is consistent with an independent lifetime estimate from the He II proximity zones around luminous AGN at z ∼ 3. Conclusions. 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. For example, the famous AGN Eigenvector 1 parameter space may be partially explained by the range in AGN lifetimes. Also, the lack of observational evidence for negative AGN feedback on star formation can be explained by such timescale effects. Further observational tests are required to confirm or rule out our BH mass dependent AGN lifetime hypothesis