On Eta-Einstein Sasakian Geometry

We study eta-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem for Sasakian geometry to prove the existence of eta-Einstein structures on many different compact manifolds, including exotic spheres. We also relate these results to the existence of Einstein-Weyl structures.Comment: 31 pages, minor changes made, to appear in Commun. Math. Phy

The structure of the space of affine Kaehler curvature tensors as a complex module

We use results of Matzeu and Nikcevic to decompose the space of affine Kaehler curvature tensors as a direct sum of irreducible modules in the complex settin

Evidence for a clumpy disc-wind in the star forming Seyfert\,2 galaxy MCG--03--58--007

We report the results of a detailed analysis of a deep simultaneous $130\,\rm ks$ \textit{XMM-Newton & NuSTAR} observation of the nearby ($z=0.0315$) and bright ($L_{\rm bol}\sim3\times10^{45}\,\rm erg\,s^{-1}$) starburst-AGN Seyfert\,2 system: MCG--03--58--007. From the broadband fitting we show that most of the obscuration needs to be modeled with a toroidal type reprocessor such as \texttt{MYTorus} \citep{MurphyYaqoob09}. Nonetheless the signature of a powerful disc-wind is still apparent at higher energies and the observed rapid short-term X-ray spectral variability is more likely caused by a variable zone of highly ionized fast wind rather than by a neutral clumpy medium. We also detect X-ray emission from larger scale gas as seen from the presence of several soft narrow emission lines in the RGS, originating from a contribution of a weak star forming activity together with a dominant photoionized component from the AGN.Comment: 16 pages, 9 figures, accepted for publication in MNRA

Multiplicity of Positive Solutions for an Obstacle Problem in R

In this paper we establish the existence of two positive solutions for the obstacle problem \displaystyle \int_{\Re}\left[u'(v-u)'+(1+\lambda V(x))u(v-u)\right] \geq \displaystyle \int_{\Re} f(u)(v-u), \forall v\in \Ka where $f$ is a continuous function verifying some technical conditions and \Ka is the convex set given by \Ka =\left\{v\in H^{1}(\Re); v \geq \varphi \right\}, with $\varphi \in H^{1}(\Re)$ having nontrivial positive part with compact support in $\Re$. \vspace{0.2cm} \noindent \emph{2000 Mathematics Subject Classification} : 34B18, 35A15, 46E39. \noindent \emph{Key words}: Obstacle problem, Variational methods, Positive solutions.Comment: To appear in Progress in Nonlinear Differential Equations and their Application

A new powerful and highly variable disk wind in an AGN-star forming galaxy, the case of MCG-03-58-007

We present the discovery of a new candidate for a fast disk wind, in the nearby Seyfert 2 galaxy MCG-03-58-007. This wind is discovered in a deep Suzaku observation that was performed in 2010. Overall the X-ray spectrum of MCG-03-58-007 is highly absorbed by a neutral column density of NH~10^23 cm^-2, in agreement with the optical classification as a type 2 AGN. In addition, this observation unveiled the presence of two deep absorption troughs at E = 7.4 +- 0.1 keV and E = 8.5 +- 0.2 keV. If associated with blue-shifted FeXXVI, these features can be explained with the presence of two highly ionised (log \xi/(erg cm/s)~ 5.5) and high column density (NH~5-8 x 10^23cm^-2) outflowing absorbers with v_out1~ -0.1c and v_out2~ -0.2c. The disk wind detected during this observation is most likely launched from within a few hundreds gravitational radii from the central black and has a kinetic output that matches the prescription for significant feedback. The presence of the lower velocity component of the disk wind is independently confirmed by the analysis of a follow-up XMM-Newton & NuSTAR observation. A faster (v_out~ -0.35 c) component of the wind is also seen in this second observation. During this observation we also witnessed an occultation event lasting \Delta t ~ 120 ksec, which we ascribe to an increase of the opacity of the disk wind (\Delta NH~1.4x10^24 cm^-2). Our interpretation is that the slow zone (v_out~ -0.1c) of the wind is the most stable but inhomogeneous component, while the faster zones could be associated with two different inner streamlines of the wind.Comment: 12 pages, 10 figures, 3 tables. Accepted for publication in MNRA

Swift data hint at a binary Super Massive Black Hole candidate at sub-parsec separation

Dual/binary Supermassive Black Hole (SMBH) systems are the inevitable consequence of the current Lambda Cold Dark Matter cosmological paradigm. In this context, we discuss here the properties of MCG+11-11-032, a local (z=0.0362) Seyfert 2 galaxy. This source was proposed as a dual AGN candidate on the basis of the presence of double-peaked [OIII] emission lines in its optical spectrum. MCG+11-11-032 is also an X-ray variable source and was observed several times by the Swift X-ray Telescope (XRT) on time scales from days to years. In this work, we analyze the SDSS-DR13 spectrum and find evidence for double-peaked profiles in all the strongest narrow emission lines. We also study the XRT light curve and unveil the presence of an alternating behavior of the intrinsic 0.3-10 keV flux, while the 123-month Swift BAT light curve supports the presence of almost regular peaks and dips almost every 25 months. In addition, the XRT spectrum suggests for the presence of two narrow emission lines with rest-frame energies of E~6.16 keV and E~6.56 keV. Although by considering only the optical emission lines, different physical mechanisms may be invoked to explain the kinematical properties, the X-ray results are most naturally explained by the presence of a binary SMBH in the center of this source. In particular, we evidence a remarkable agreement between the putative SMBH pair orbital velocity derived from the BAT light curve and the velocity offset derived by the rest-frame Delta_E between the two X-ray line peaks in the XRT spectrum (i.e. Delta_v~0.06c).Comment: 11 pages, 9 figures, 3 tables. Accepted for publication in MNRA

The flaring X-ray corona in the quasar PDS 456

New Swift monitoring observations of the variable, radio-quiet quasar, PDS 456, are presented. A bright X-ray flare was captured in 2018 September, the flux increasing by a factor of 4 and with a doubling time-scale of 2 d. From the light crossing argument, the coronal size is inferred to be ≲30 gravitational radii for a black hole mass of 109 M⊙ and the total flare energy exceeds 1051 erg. A hardening of the X-ray emission accompanied the flare, with the photon index decreasing from Γ = 2.2 to Γ = 1.7 and back again. The flare is produced in the X-ray corona, the lack of any optical or UV variability being consistent with a constant accretion rate. Simultaneous XMM-Newton and NuSTAR observations were performed, 1-3 d after the flare peak and during the decline phase. These caught PDS 456 in a bright, bare state, where no disc wind absorption features are apparent. The hard X-ray spectrum shows a high energy roll-over, with an e-folding energy of $E_{\rm fold}=51^{+11}_{-8}$ keV. The deduced coronal temperature, of kT = 13 keV, is one of the coolest measured in any AGN and PDS 456 lies well below the predicted pair annihilation line in X-ray corona. The spectral variability, becoming softer when fainter following the flare, is consistent with models of cooling X-ray coronae. Alternatively, an increase in a non-thermal component could contribute towards the hard X-ray flare spectrum

Unveiling Sub-Pc supermassive black hole binary candidates in active galactic nuclei

The elusive supermassive black hole binaries (SMBHBs) are thought to be the penultimate stage of galaxy mergers, preceding a final coalescence phase. SMBHBs are sources of continuous gravitational waves, possibly detectable by pulsar timing arrays; the identification of candidates could help in performing targeted gravitational wave searches. Due to SMBHBs\u2019 origin in the innermost parts of active galactic nuclei (AGN), X-rays are a promising tool for unveiling their presence, by means of either double Fe K\u3b1 emission lines or periodicity in their light curve. Here we report on a new method for selecting SMBHBs by means of the presence of a periodic signal in their Swift Burst Alert Telescope (BAT) 105 month light curves. Our technique is based on Fisher\u2019s exact g-test and takes into account the possible presence of colored noise. Among the 553 AGN selected for our investigation, only the Seyfert 1.5 galaxy Mrk 915 emerges as a candidate SMBHB; from subsequent analysis of its light curve we find a period P0 = 35 \ub1 2 months, and the null hypothesis is rejected at the 3.7\u3c3 confidence level. We also present a detailed analysis of the BAT light curve of the only previously X-ray-selected binary candidate source in the literature, the Seyfert 2 galaxy MCG+11-11-032. We find P0 = 26.3 \ub1 0.6 months, consistent with the one inferred from previously reported double Fe K\u3b1 emission lines

Coordinated X-ray and UV absorption within the accretion disk wind of the active galactic nucleus PG 1126-041

Accretion disk winds launched close to supermassive black holes (SMBHs) are a viable mechanism to provide feedback between the SMBH and the host galaxy. We aim to characterize the X-ray properties of the inner accretion disk wind of the nearby active galactic nucleus (AGN) PG 1126-041, and to study its connection with the ultraviolet (UV)-absorbing wind. We perform spectroscopic analysis of eight XMM-Newton observations of PG 1126-041 taken between 2004 and 2015, using both phenomenological models and the most advanced accretion disk wind models available. For half of the dataset, we can compare the X-ray analysis results with the results of quasi-simultaneous, high-resolution spectroscopic UV observations taken with the Cosmic Origins Spectrograph (COS) on board the Hubble Space Telescope. The X-ray spectra of PG 1126-041 are complex and absorbed by ionized material which is highly variable on multiple time scales, sometimes as short as 11 days. Accretion disk wind models can account for most of the X-ray spectral complexity of PG 1126-041, with the addition of massive clumps, represented by a partially covering absorber. Variations in column density ($N_H \sim 5-20 \times 10^{22}$ cm$^{-2}$) of the partially covering absorber drive the observed X-ray spectral variability of PG 1126-041. The absorption from the X-ray partially covering gas and from the blueshifted C IV troughs appear to vary in a coordinated way. The line of sight toward PG 1126-041 offers a privileged view through a highly dynamic nuclear wind originating on inner accretion disk scales, making the source a very promising candidate for future detailed studies of the physics of accretion disk winds around SMBHs.Comment: 24 pages, 13 figures, accepted for publication in Astronomy & Astrophysic

A new emulated Monte Carlo radiative transfer disc-wind model: X-Ray Accretion Disc-wind Emulator - XRADE

We present a new X-Ray Accretion Disc-wind Emulator (xrade) based on the 2.5D Monte Carlo radiative transfer code that provides a physically motivated, self-consistent treatment of both absorption and emission from a disc wind by computing the local ionization state and velocity field within the flow. xrade is then implemented through a process that combines X-ray tracing with supervised machine learning. We develop a novel emulation method consisting in training, validating, and testing the simulated disc-wind spectra into a purposely built artificial neural network. The trained emulator can generate a single synthetic spectrum for a particular parameter set in a fraction of a second, in contrast to the few hours required by a standard Monte Carlo radiative transfer pipeline. The emulator does not suffer from interpolation issues with multidimensional spaces that are typically faced by traditional X-ray fitting packages such as xspec. xrade will be suitable to a wide number of sources across the black hole mass, ionizing luminosity, and accretion rate scales. As an example, we demonstrate the applicability of xrade to the physical interpretation of the X-ray spectra of the bright quasar PDS 456, which hosts the best-established accretion disc wind observed to date. We anticipate that our emulation method will be an indispensable tool for the development of high-resolution theoretical models, with the necessary flexibility to be optimized for the next generation microcalorimeters onboard future missions, like X-Ray Imaging and Spectroscopy Mission (XRISM)/Resolve and Athena/X-ray Integral Field Unit (X-IFU). This tool can also be implemented across a wide variety of X-ray spectral models and beyond