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Distant quasars (QSOs) in galaxy overdensities are considered key actors in the evolution of the early Universe. In this work, we studied the kinematic and physical properties of the BR1202-0725 system at z=4.7, one of the most overdense fields known in the early Universe, consisting of a QSO, a submillimeter galaxy (SMG), and three Lyman-$\alpha$ emitters. We used data from the JWST/NIRSpec Integral Field Unit (IFU) to analyze the rest-frame optical emission of each source in the system. We estimated a bolometric luminosity of log($L_{\rm bol}/$[erg/s]) = 47.2 $\pm$ 0.4 and a black hole mass of log($M_{\rm BH}/M_\odot$) = 10.1 $\pm$ 0.5 for the QSO, which are consistent with previous measurements obtained with ground-based observations. The NIRSpec spectra of the SMG revealed instead unexpected [OIII] and H$\alpha$+[NII] profiles. The overall [OIII] line profile is blue-shifted by more than 700 km/s relative to the systemic velocity of the galaxy. Additionally, both the [OIII] and H$\alpha$+[NII] lines show prominent broad (1300 km/s), blueshifted wings associated with outflowing ionized gas. The analysis of NIRSpec and X-ray observations indicates that the SMG likely hosts an accreting supermassive black hole as supported by the following results: (i) the excitation diagnostic diagram is consistent with ionization from an active galactic nucleus (AGN); (ii) the X-ray luminosity is higher than $10^{44}$ erg/s; and (iii) it hosts a fast outflow ($v_{\rm out}$ = 5000 km/s), comparable to those observed in luminous QSOs. Therefore, the QSO-SMG pair represents one of the highest-redshift double AGN to date, with a projected separation of 24 kpc. Finally, we investigated the environment of this system and found four new galaxies at the same redshift of the QSO and within a projected distance of 5 kpc from it. This overdense system includes at least ten galaxies in only 980 kpc$^2$., Comment: 21 pages, 19 figures, Submitted to Astronomy & Astrophysics

Studying the distribution and properties of ionised gas in outflows driven by AGN is crucial for understanding the feedback mechanisms at play in extragalactic environments. In this study, we explore the connection between ionised outflows traced by rest-frame UV absorption and optical emission lines in GS133, a Compton thick AGN at z = 3.47. We combine observations from the JWST NIRSpec Integral Field Spectrograph (IFS) with archival VLT VIMOS long-slit spectroscopic data, as part of the GA-NIFS project. We perform a multi-component kinematic decomposition of the UV and optical line profiles to derive the physical properties of the absorbing and emitting gas in GS133. Our kinematic decomposition reveals two distinct components in the optical lines. The first component likely traces a rotating disk with a dynamical mass of 2e10 Msun. The second component corresponds to a galaxy-wide, bi-conical outflow, with a velocity of 1000 km/s and an extension of 3 kpc. The UV absorption lines show two outflow components, with bulk velocities v_out = -900 km/s and -1900 km/s, respectively. This characterises GS133 as a mini-BAL system. Balmer absorption lines with similar velocities are tentatively detected in the NIRSpec spectrum. Both photoionisation models and outflow energetics suggest that the ejected absorbing gas is located at 1-10 kpc from the AGN. We use 3D gas kinematic modelling to infer the orientation of the [O III] bi-conical outflow, and find that a portion of the emitting gas resides along our line of sight, suggesting that [O III] and absorbing gas clouds are partially mixed in the outflow. The derived mass-loading factor (i.e. the mass outflow rate divided by the SFR) of 1-10, and the kinetic coupling efficiency (i.e. the kinetic power divided by LAGN) of 0.1-1% per cent suggest that the outflow in GS133 provides significant feedback on galactic scales., Comment: 18 pages, 13 figures, submitted to Astronomy & Astrophysics. Comments are welcome

In this paper we analyze the asymptotic behaviour of the poles of certain rational solutions of the fifth Painlev\'e equation. These solutions are constructed by relating the corresponding tau function with a Hankel determinant of a certain sequence of moments. This approach was also used by one of the authors and collaborators in the study of the rational solutions of the second Painlev\'e equation. More specifically we study the roots of the corresponding polynomial tau function, whose location corresponds to the poles of the associated rational solution. We show that, upon suitable rescaling, the roots fill a well-defined region bounded by analytic arcs when the degree of the polynomial tau function tends to infinity. Moreover we provide an approximate location of these roots within the region in terms of suitable quantization conditions., Comment: 44 pages, 11 figures

We consider soliton gas solutions of the Focusing Nonlinear Schr\"odinger (NLS) equation, where the point spectrum of the Zakharov-Shabat linear operator condensate in a bounded domain $\mathcal{D}$ in the upper half-plane. We show that the corresponding inverse scattering problem can be formulated as a $\overline{\partial}$-problem on the domain. We prove the existence of the solution of this $\overline{\partial}$-problem by showing that the $\tau$-function of the problem (a Fredholm determinant) does not vanish. We then represent the solution of the NLS equation via the $\tau$ of the $\overline{\partial}$- problem. Finally we show that, when the domain $\mathcal{D}$ is an ellipse and the density of solitons is analytic, the initial datum of the Cauchy problem is asymptotically step-like oscillatory, and it is described by a periodic elliptic function as $x \to - \infty$ while it vanishes exponentially fast as $x \to +\infty$., Comment: 24 pages, 4 figures

The energy released by AGN has the potential to heat or remove the gas of the ISM, thus likely impacting the cold molecular gas reservoir of host galaxies at first, with star formation following on longer timescales. Previous works on high-z galaxies have yielded conflicting results, possibly due to selection biases and other systematics. To provide a reliable benchmark for galaxy evolution models at cosmic noon (z=1-3), two surveys were conceived: SUPER and KASHz, both targeting unbiased X-ray-selected AGN at z>1 that span a wide bolometric luminosity range. In this paper, we assess the effects of AGN feedback on the molecular gas content of host galaxies in a statistically robust, uniformly selected, coherently analyzed sample of AGN at z=1-2.6, drawn from the KASHz and SUPER surveys. By using ALMA data in combination with dedicated SED modeling, we retrieve CO and FIR luminosity as well as $M_*$ of SUPER and KASHz AGN. We selected non-active galaxies from PHIBBS, ASPECS and multiple ALMA/NOEMA surveys of sub-mm galaxies. By matching the samples in z, $M_*$ and $L_{FIR}$, we compared the properties of AGN and non-active galaxies within a Bayesian framework. We find that AGN hosts at given $L_{FIR}$ are on average CO depleted compared to non-active galaxies, confirming what was previously found in the SUPER survey. Moreover, the molecular gas fraction distributions of AGN and non-active galaxies are statistically different, with that of of AGN being skewed to lower values. Our results indicate that AGN can indeed reduce the total cold molecular gas reservoir of their host galaxies. Lastly, by comparing our results with predictions from three cosmological simulations (TNG, Eagle and Simba) filtered to match the observed properties, we confirm already known discrepancies and highlight new ones between observations and simulations.[Abridged], Comment: 26 pages (17 in the main body of the paper and 9 in the appendix), 14 figures (11 in the main body of the paper and 3 in the appendix), 8 tables (2 in the main body of the paper and 6 in the appendix). Accepted for publication in A&A, in press

We detail a numerical algorithm and related code to construct rational quadratic differentials on the Riemann sphere that satisfy the Boutroux condition. These differentials, in special cases, provide solutions of (generalized) Chebotarov problem as well as being instances of Jenkins--Strebel differentials. The algorithm allows to construct Boutroux differentials with prescribed polar part, thus being useful in the theory of weighted capacity and Random Matrices., Comment: 10 pages, 12 figures; version 2: 12 pages, 13 figures, added details on the code and error, added link to source code in GitHub

We present spatially resolved VLT/SINFONI spectroscopy with adaptive optics of type-2 active galactic nuclei (AGN) from the SINFONI Survey for Unveiling the Physics and Effect of Radiative feedback (SUPER), which targeted X-ray bright ($L_{2-10 keV}\gtrsim10^{42}$ erg s$^{-1}$) AGN at Cosmic Noon ($z\sim2$). Our analysis of the rest-frame optical spectra unveils ionised outflows in all seven examined targets, as traced via [OIII]$\lambda$5007 line emission, moving at $v\gtrsim600$ km s$^{-1}$. In six objects these outflows are clearly spatially resolved and extend on 2-4 kpc scales, whereas marginally resolved in the remaining one. Interestingly, these SUPER type-2 AGN are all heavily obscured sources ($N_{H}\gtrsim10^{23}$ cm$^{-2}$) and host faster ionised outflows than their type-1 counterparts within the same range of bolometric luminosity ($L_{bol} \sim 10^{44.8-46.5}$ erg s$^{-1}$). SUPER has hence provided observational evidence that the type-1/type-2 dichotomy at $z\sim2$ might not be driven simply by projection effects, but might reflect two distinct obscuring life stages of active galaxies, as predicted by evolutionary models. Within this picture, SUPER type-2 AGN might be undergoing the 'blow-out' phase, where the large amount of obscuring material efficiently accelerates large-scale outflows via radiation pressure on dust, eventually unveiling the central active nucleus and signal the start of the bright, unobscured type-1 AGN phase. Moreover, the overall population of ionised outflows detected in SUPER has velocities comparable with the escape speed of their dark matter halos, and in general high enough to reach 30-50 kpc distances from the centre. These outflows are hence likely to sweep away the gas (at least) out of the baryonic disk and/or to heat the host gas reservoir, thus reducing and possibly quenching star formation., Comment: 21 pages, 13 figures. Key figure is 8. Accepted for publication in A&A

IRASF11119 is an ultra-luminous IR galaxy with post-merger morphology, hosting a type-1 QSO at z=0.189. Its 2013 Suzaku spectrum shows a prominent Ultra Fast Outflow (UFO) absorption feature (v_out~0.25c). In 2021, we obtained the first XMM-Newton long look of the target, coordinated with a simultaneous NuSTAR observation. The new high-quality data allow us to detect at P>99.8% c.l. multiple absorption features associated with the known UFO. Furthermore, an emission plus absorption feature at 1.1-1.3 keV reveals the presence of a blueshifted P-Cygni profile in the soft band. We associate the hard band features with blends of FeXXV and FeXXVI He$\alpha$-Ly$\alpha$ and He$\beta$-Ly$\beta$ line pairs and infer a large column (N$_H$~$10^{24}$ cm$^{-2}$) of highly ionized (log$\xi$~5) gas outflowing at v_out=0.27c. The 1 keV feature can be associated with a blend of Fe and Ne transitions, produced by a lower column (N$_H$~$10^{21}$ cm$^{-2}$) and ionization (log$\xi$~2.6) gas component outflowing at the same speed. Using a radiative-transfer disk wind model to fit the highly ionized UFO, we derive a large mass outflow rate, comparable with the mass accretion rate (M$_{out}$=4.25 M$_{Sun}$/yr, ~1.6 M$_{acc}$), and kinetic energy and momentum flux among the highest reported in the literature. We measure an extremely low high-energy cut-off (E$_c$~25 keV). Several other cases in the literature suggest that a steep X-ray continuum may be related to the formation of powerful winds. The lack of a significant momentum boost between the nuclear UFO and the different phases of the large-scale outflow, observed in IRASF11119 and in a growing number of sources with powerful UFOs, can be explained by (i) a momentum-driven expansion, (ii) an inefficient coupling of the UFO with the host ISM, or (iii) by repeated energy-driven expansion episodes with low duty-cycle, that average out on long time-scales., Comment: 21 pages, 13 figures, accepted for publication in A&A

We present JWST NIRSpec observations in IFS mode of the galaxy GS5001 at redshift z=3.47, the brightest member of a candidate protocluster in the GOODS-S field. The data cover a field of view (FoV) of 4''$\times$4'' (~$30\times30$~kpc$^2$) and were obtained as part of the GA-NIFS GTO program. The observations include both high (R~2700) and low (R~100) spectral resolution data, spanning the rest-frame wavelength ranges 3700-6780A and 1300-11850A, respectively. We analyse the spatially resolved ionised gas kinematics and interstellar medium properties, including obscuration, gas metallicity, excitation, ionisation parameter, and electron density. In addition to the central galaxy, the NIRSpec FoV covers three components in the south, with velocities blue-shifted by -150 km/s with respect to the main galaxy, and another source in the north redshifted by ~200 km/s. The emission line ratios in the BPT diagram are consistent with star formation for all the sources in the FoV. We measure electron densities of ~500 cm$^{-3}$ in the different sources. The gas-phase metallicity in the main galaxy is 12+log(O/H) $= 8.45\pm0.04$, and slightly lower in the companions (12+log(O/H)$ = 8.34-8.42$), consistent with the mass-metallicity relation at $z\sim3$. We find peculiar line ratios (high log [NII]/H$\alpha$, low log [OIII]/H$\beta$) in the northern part of the main galaxy (GS5001). These could be attributed to either higher metallicity, or to shocks resulting from the interaction of the main galaxy with the northern source. We identify a spatially resolved outflow in the main galaxy, with an extension of about 3 kpc. We find maximum outflow velocities of ~400 km/s, an outflow mass of $(1.7\pm0.4)\times 10^8$ M$_{\odot}$, a mass outflow rate of $23\pm5$ M$_{\odot}$ yr$^{-1}$ and a mass loading factor of 0.23. These properties are compatible with star formation being the driver of the outflow., Comment: Submitted to A&A

JWST is discovering increasing numbers of quiescent galaxies 1--2 billion years after the Big Bang, whose redshift, high mass, and old stellar ages indicate that their formation and quenching were surprisingly rapid. This fast-paced evolution seems to require that feedback from AGN (active galactic nuclei) be faster and/or more efficient than previously expected \citep{Xie24}. We present deep ALMA observations of cold molecular gas (the fuel for star formation) in a massive, fast-rotating, post-starburst galaxy at $z=3.064$. This galaxy hosts an AGN, driving neutral-gas outflows with a mass-outflow rate of $60\pm20$ M$_{\odot}$ yr$^{-1}$, and has a star-formation rate of $<5.6$ M$_{\odot}$ yr$^{-1}$. Our data reveal this system to be the most distant gas-poor galaxy confirmed with direct CO observations (molecular-gas mass $< 10^{9.1}$ M$_{\odot}$; <0.8 % of its stellar mass). Combining ALMA and JWST observations, we estimate the gas-consumption history of this galaxy, showing that it evolved with net zero gas inflow, i.e., gas consumption by star formation matches the amount of gas this galaxy is missing relative to star-forming galaxies. This could arise both from preventive feedback stopping further gas inflow, which would otherwise refuel star formation or, alternatively, from fine-tuned ejective feedback matching precisely gas inflows. Our methods, applied to a larger sample, promise to disentangle ejective vs preventive feedback., Comment: 14 pages, 4 figures

We investigate the X-ray properties of a large sample of 71 broad line and narrow line AGN at 2

The spectral energy distribution (SED) of low-luminosity active galactic nuclei (LLAGN) presents challenges due to their faint emissions and the complexity of their accretion processes. This study introduces a new CIGALE module tailored for LLAGN, combining the empirical $L_X$-$L_{12\mu m}$ relationship with physical models like advection-dominated accretion flows (ADAFs) and truncated accretion disks. This module yields a refined depiction of LLAGN emissions, and a mock analysis shows reliable parameter recovery, with only minor biases. We tested the module on a sample of 50 X-ray-detected local galaxies, including LINERs and Seyferts, where it demonstrated good estimation of bolometric luminosities, even in the presence of significant galaxy contamination. Notably, the previous X-ray module failed to provide AGN solutions for this sample, stressing the need for a novel approach. Comparisons with mid-luminosity AGN confirm the module's robustness and applicability to AGN up to $L_X$ < $10^{45}$ erg/s. We also expanded the X-ray to bolometric correction formula, making it applicable to AGN spanning ten orders of magnitude in luminosity, and revealing lower $k_X$ values than typically assumed. Additionally, our analysis of the $\alpha_{ox}$ index, representing the slope between UV and X-ray emissions, uncovered trends that differ from those observed in high-luminosity AGN, suggesting a shift in accretion physics and photon production mechanisms in low-luminosity regimes. These results underscore the importance of a multiwavelength approach in AGN studies and reveal distinct behaviors in LLAGN compared to quasars. Our findings significantly advance the understanding of LLAGN and offer a comprehensive framework for future research aimed at completing the census of the AGN population., Comment: Acepted for publication (A&A)

An increasing number of observations and simulations suggests that low-power (<10$^{44}$ erg s$^{-1}$) jets may be a significant channel of feedback produced by active galactic nuclei (AGN), but little is known about their actual effect on their host galaxies from the observational point of view. We targeted four luminous type 2 AGN hosting moderately powerful radio emission ($\sim$10$^{44}$ erg s$^{-1}$), two of which and possibly a third are associated with jets, with optical integral field spectroscopy observations from the Multi Unit Spectroscopic Explorer (MUSE) at the Very Large Telescope (VLT) to analyze the properties of their ionized gas as well as the properties and effects of ionized outflows. We combined these observations with Very Large Array (VLA) and e-MERLIN data to investigate the relations and interactions between the radio jets and host galaxies. We detected ionized outflows as traced by the fast bulk motion of the gas. The outflows extended over kiloparsec scales in the direction of the jet, when present. In the two sources with resolved radio jets, we detected a strong enhancement in the emission-line velocity dispersion (up to 1000 km s$^{-1}$) perpendicular to the direction of the radio jets. We also found a correlation between the mass and the energetics of this high-velocity dispersion gas and the radio power, which supports the idea that the radio emission may cause the enhanced turbulence. This phenomenon, which is now being observed in an increasing number of objects, might represent an important channel for AGN feedback on galaxies., Comment: 18 pages, 17 figures

Powerful outflows from active galactic nuclei (AGN) can significantly impact the gas reservoirs of their host galaxies. However, it is still unclear how these outflows can propagate from the very central regions of galaxies to their outskirts, and whether nuclear winds can be driven by and/or be responsible for drastic spectral transitions. In this work we test feedback propagation models on the case test of 2MASS 0918+2117 (2M0918), a z=0.149 X-ray variable AGN, which showed tentative evidence for nuclear ultra-fast outflows (UFOs) in a 2005 XMM-Newton observation. We also investigate whether UFOs can be related to the observed X-ray variability. We observed 2M0918 with XMM-Newton and NuSTAR in 2020 to confirm the presence and characterize the UFOs. We perform a kinematic analysis of the 2005 SDSS optical spectrum to reveal and measure the properties of galaxy-scale ionized outflows. Furthermore, we construct 20-year-long lightcurves of observed flux, line-of-sight column density, and intrinsic accretion rate from the spectra of the first 4 SRG/eROSITA all-sky surveys and archival observations from Chandra and XMM-Newton.We significantly detect UFOs with v$\sim$0.16c and galaxy-scale ionized outflows with velocities of $\sim$ 700 km/s. We also find that the drastic X-ray variability (factors >10) can be explained both in terms of variable obscuration and variable intrinsic luminosity.Comparing the energetics of the two outflow phases, 2M0918 is consistent with momentum-driven wind propagation. 2M0918 expands the sample of AGN with both UFOs and ionized gas winds from 5 to 6, and brings the sample of AGN hosting multiscale outflows to 19, contributing to a clearer picture of feedback physics. From the variations in accretion rate, column density, and ionization level of the obscurer, we propose a scenario that connects obscurers, an accretion enhancement, and the emergence of UFOs, Comment: 18 pages, 18 figures

We present HOMERUN (Highly Optimized Multi-cloud Emission-line Ratios Using photo-ionizatioN), a new approach to modelling emission lines from photoionized gas that can simultaneously reproduce all observed line intensities from a wide range of ionization levels and with high accuracy. Our approach is based on the weighted combination of multiple single-cloud photoionization models and, contrary to previous works, the novelty of our approach consists in using the weights as free parameters of the fit and constraining them with the observed data. One of the main applications of HOMERUN is the accurate determination of gas-phase metallicities and we show that a critical point is to allow for a variation of the N/O and S/O abundance ratios which can significantly improve the quality of the fit and the accuracy of the results. Moreover, our approach provides a major improvement compared to the single-cloud, constant-pressure models commonly used in the literature. By using high-quality literature spectra of H ii regions where 10 to 20 emission lines (including several auroral lines) are detected with high signal-to-noise ratio, we show that all lines are reproduced by the model with an accuracy better than 10%. In particular, the model is able to simultaneously reproduce [O i]6300, 6363, [O ii]3726, 3729, [O iii]4959, 5007, [S ii]6717, 6731, and [S iii]9069, 9532 emission lines which, to our knowledge, is an unprecedented result. Finally, we show that the gas metallicities estimated with our models for HII regions in the Milky Way are in agreement with the stellar metallicities than the estimates based on the Te-method. Overall, our method provides a new accurate tool to estimate the metallicity and the physical conditions of the ionized gas. It can be applied to many different science cases from HII regions to AGN and wherever there are emission lines from photoionized gas., Comment: A&A in press, new version following referee report

Merger events can trigger gas accretion onto supermassive black holes (SMBHs) sitting at the centre of galaxies, and form close pairs of active galactic nuclei (AGN). The fraction of AGN in pairs gives key information to constrain the environmental properties and evolution of SMBHs and their host galaxies. However, the identification of dual AGN is difficult, and only very few have been found in the distant Universe so far. We report the serendipitous discovery of a triple AGN and four dual AGN (one considered as a candidate), with projected separations in the range 3-28 kpc. Their AGN classification is mostly based on classical optical emission line flux ratios, as observed with the Near-InfraRed Spectrograph (NIRSpec) on the James Webb Space Telescope (JWST), and is complemented with additional multi-wavelength diagnostics. The identification of these multiple AGN out of the 17 AGN systems in our GA-NIFS survey (i.e. ~ 20-30%), suggests that they might be more common than expected from the most recent cosmological simulations, which predict a fraction of dual AGN at least one order of magnitude smaller. This work highlights the exceptional capabilities of NIRSpec for detecting distant dual AGN, and prompts new investigations to better constrain their fraction across the cosmic time, and to inform upcoming cosmological simulations., Comment: 40 pages, 7 figures, submitted to Nature, comments welcome!

We develop the theory of integrable operators $\mathcal{K}$ acting on a domain of the complex plane with smooth boundary in analogy with the theory of integrable operators acting on contours of the complex plane. We show how the resolvent operator is obtained from the solution of a $\overline{\partial}$-problem in the complex plane. When such a $\overline{\partial}$-problem depends on auxiliary parameters we define its Malgrange one form in analogy with the theory of isomonodromic problems. We show that the Malgrange one form is closed and coincides with the exterior logarithmic differential of the Hilbert-Carleman determinant of the operator $\mathcal{K}$. With suitable choices of the setup we show that the Hilbert-Carleman determinant is a $\tau$-function of the Kadomtsev-Petviashvili (KP) or nonlinear Schr\"odinger hierarchies., Comment: 25 pages, no figures, misprint corrections, add more tecnical aspect, a new subsection subsubsection and new references has been added. Submitted in Nonlinearity

The novel Gaia Multi Peak (GMP) technique has proven to be able to successfully select dual and lensed AGN candidates at sub-arcsec separations. Both populations are important because dual AGN represent one of the central, still largely untested, predictions of lamdaCDM cosmology, and compact lensed quasars allow to probe the central regions of the lensing galaxies. In this work, we present high spatial resolution spectroscopy of twelve GMP-selected systems. We use the the adaptive-optics assisted integral-field spectrograph MUSE at VLT to resolve each system and study the nature of each component. All the targets reveal the presence of two components confirming the GMP selection. We classify five targets as dual AGN, two as lensed systems, and five as a chance alignment of a star and and AGN. Having separations between 0.30" and 0.86", these dual and lensed systems are, to date, among the most compact ever discovered at z >0.3. This is the largest sample of distant dual AGN with sub-arcsec separations ever presented in a single paper., Comment: 16 pages, 11 figures

We present the broad-band X-ray spectral analysis (0.6-50 keV) of seven Compton-Thick active galactic nuclei (CT-AGN; line-of-sight, l.o.s., column density $>10^{24}$ cm$^{-2}$) candidates selected from the Swift-BAT 100-month catalog, using archival NuSTAR data. This work is in continuation of the on-going research of the Clemson-INAF group to classify CT-AGN candidates at redshift $z<0.05$, using physically-motivated torus models. Our results confirm that three out of seven targets are \textit{bona-fide} CT-AGN. Adding our results to the previously analysed sources using NuSTAR data, we increase the population of bona-fide CT-AGN by $\sim9\%$, bringing the total number to 35 out of 414 AGN. We also performed a comparative study using MyTorus and borus02 on the spectra in our sample, finding that both physical models are strongly consistent in the parameter space of l.o.s. column density and photon index. Furthermore, the clumpiness of the torus clouds is also investigated by separately computing the line-of-sight and average torus column densities, in each of the seven sources. Adding our results to all the previous 48 CT-AGN candidates analysed by the Clemson-INAF research team having NuSTAR observations: we find $78\%$ of the sources are likely to have a clumpy distribution of the obscuring material surrounding the accreting supermassive black hole., Comment: Accepted for publication in the Section 4. Extragalactic astronomy of Astronomy and Astrophysics, 20 pages, 10 figures

We revisit the symplectic aspects of the spectral transform for matrix-valued rational functions with simple poles. We construct eigenvectors of such matrices in terms of the Szeg\H{o} kernel on the spectral curve. Using variational formulas for the Szeg\H{o} kernel we construct a new system of action-angle variables for the canonical symplectic form on the space of such functions. Comparison with previously known action-angle variables shows that the vector of Riemann constants is the gradient of some function on the moduli space of spectral curves; this function is found in the case of matrix dimension 2, when the spectral curve is hyperelliptic.

The Hamiltonian approach to isomonodromic deformation systems is extended to include generic rational covariant derivative operators on the Riemann sphere with irregular singularities of arbitrary Poincar\'e rank. The space of rational connections with given pole degrees carries a natural Poisson structure corresponding to the standard classical rational R-matrix structure on the dual space $L^*gl(r)$ of the loop algebra $Lgl(r)$. Nonautonomous isomonodromic counterparts of the isospectral systems generated by spectral invariants are obtained by identifying the deformation parameters as Casimir functions on the phase space. These are shown to coincide with the higher Birkhoff invariants determining the local asymptotics near to irregular singular points, together with the pole loci. Infinitesimal isomonodromic deformations are shown to be generated by the sum of the Hamiltonian vector field and an explicit derivative vector field that is transversal to the symplectic foliation. The Casimir elements serve as coordinates complementing those along the symplectic leaves, extended by the exponents of formal monodromy, defining a local symplectomorphism between them. The explicit derivative vector fields preserve the Poisson structure and define a flat transversal connection, spanning an integrable distribution whose leaves, locally, may be identified as the orbits of a free abelian group. The projection of the infinitesimal isomonodromic deformations vector fields to the quotient manifold under this action gives the commuting Hamiltonian vector fields corresponding to the spectral invariants dual to the Birkhoff invariants and the pole loci., Comment: V6. 46 pages. To comply with J. Math. Phys. formatting requirements, the abstract was reduced to one paragraph and the table of contents and highlighting of theorems were removed. Comparison comments were added after Theorems 3.2 and 3.3. The summation limits were made more explicit in eqs. (3.15), (3.17). Ref. [19] was corrected

We study the WKB expansion of $2\times 2$ system of linear differential equations with four fuchsian singularities. The main focus is on the generating function of the monodromy symplectomorphism which, according to a recent paper is closely related to the Jimbo-Miwa tau-function. We compute the first three terms of the WKB expansion of the generating function and establish the link to the Bergman tau-function., Comment: 33 pages, 1 figure; v2 minor corrections

In this paper we study the small-$\lambda$ spectral asymptotics of an integral operator $\mathscr{K}$ defined on two multi-intervals $J$ and $E$, when the multi-intervals touch each other (but their interiors are disjoint). The operator $\mathscr{K}$ is closely related to the multi-interval Finite Hilbert Transform (FHT). This case can be viewed as a singular limit of self-adjoint Hilbert-Schmidt integral operators with so-called integrable kernels, where the limiting operator is still bounded, but has a continuous spectral component. The regular case when $\text{dist}(J,E)>0$, and $\mathscr{K}$ is of the Hilbert-Schmidt class, was studied in an earlier paper by the authors. The main assumption in this paper is that $U=J\cup E$ is a single interval. We show that the eigenvalues of $\mathscr{K}$, if they exist, do not accumulate at $\lambda=0$. Combined with the results in an earlier paper by the authors, this implies that $H_p$, the subspace of discontinuity (the span of all eigenfunctions) of $\mathscr{K}$, is finite dimensional and consists of functions that are smooth in the interiors of $J$ and $E$. We also obtain an approximation to the kernel of the unitary transformation that diagonalizes $\mathscr{K}$, and obtain a precise estimate of the exponential instability of inverting $\mathscr{K}$. Our work is based on the method of Riemann-Hilbert problem and the nonlinear steepest-descent method of Deift and Zhou.