Resolving the obscuring torus in NGC 1068 with the power of infrared interferometry: Revealing the inner funnel of dust

We present new interferometric data obtained with MIDI (MID infrared Interferometric instrument) for the Seyfert II galaxy NGC 1068, with an extensive coverage of sixteen uv points. These observations resolve the nuclear mid-infrared emission from NGC 1068 in unprecedented detail with a maximum resolution of 7 mas. For the first time, sufficient uv points have been obtained, allowing us to generate an image of the source using maximum entropy image reconstruction. The features of the image are similar to those obtained by modelling. We find that the mid-infrared emission can be represented by two components, each with a Gaussian brightness distribution. The first, identified as the inner funnel of the obscuring torus, is hot (800K), 1.35 parsec long, and 0.45 parsec thick in FWHM at a PA=-42 degrees (from north to east). It has an absorption profile different than standard interstellar dust and with evidence for clumpiness. The second component is 3 by 4 pc in FWHM with T=300K, and we identify it with the cooler body of the torus. The compact component is tilted by 45 degrees with respect to the radio jet and has similar size and orientation to the observed water maser distribution. We show how the dust distribution relates to other observables within a few parsecs of the core of the galaxy such as the nuclear masers, the radio jet, and the ionization cone. We compare our findings to a similar study of the Circinus galaxy and other relevant studies. Our findings shed new light on the relation between the different parsec-scale components in NGC 1068 and the obscuring torus.Comment: Accepted to MNRA

Resolving the nucleus of Centaurus A at mid-IR wavelengths

We have observed Centaurus A with the MID-infrared Interferometric instrument (MIDI) at the Very Large Telescope Interferometer (VLTI) at resolutions of 7 - 15 mas (at 12.5 micron) and filled gaps in the (u,v) coverage in comparison to earlier measurements. We are now able to describe the nuclear emission in terms of geometric components and derive their parameters by fitting models to the interferometric data. With simple geometrical models, the best fit is achieved for an elongated disk with flat intensity profile with diameter 76 +/- 9 mas x 35 +/- 2 mas (1.41 +/- 0.17 pc x 0.65 +/- 0.03 pc) whose major axis is oriented at a position angle (PA) of 10.1 +/- 2.2 degrees east of north. A point source contributes 47 +/- 11 % of the nuclear emission at 12.5 micron. There is also evidence that neither such a uniform nor a Gaussian disk are good fits to the data. This indicates that we are resolving more complicated small-scale structure in AGNs with MIDI, as has been seen in Seyfert galaxies previously observed with MIDI. The PA and inferred inclination i = 62.6 +2.1/-2.6 degrees of the dust emission are compared with observations of gas and dust at larger scales.Comment: Accepted for the PASA special issue on Centaurus

Influence of near-surface stratigraphy on coastal landslides at Sleeping Bear Dunes National Lakeshore, Lake Michigan, USA

This paper is not subject to U.S. copyright. The definitive version was published in Journal of Coastal Research 20 (2004): 510-522, doi:10.2112/1551-5036(2004)020[0510:IONSOC]2.0.CO;2.Lake-level change and landslides are primary controls on the development of coastal environments along the coast of northeastern Lake Michigan. The late Quaternary geology of Sleeping Bear Dunes National Lakeshore was examined with high-resolution seismic reflection profiles, ground-penetrating radar (GPR), and boreholes. Based on sequence-stratigraphic principles, this study recognizes ten stratigraphic units and three major unconformities that were formed by late Pleistocene glaciation and postglacial lake-level changes. Locally high sediment supply, and reworking by two regressions and a transgression have produced a complex stratigraphy that is prone to episodic failure. In 1995, a large landslide deposited approximately 1 million m3 of sediment on the lake floor. The highly deformed landslide deposits, up to 18 m thick, extend 3–4 km offshore and unconformably overlie well-stratified glacial and lacustrine sediment. The landslide-prone bluff is underlain by channel-fill deposits that are oriented nearly perpendicular to the shoreline. The paleochannels are at least 10 m deep and 400 m wide and probably represent stream incision during a lake-level lowstand about 10.3 ka B.P. The channels filled with sediment during the subsequent transgression and lake-level highstand, which climaxed about 4.5 ka B.P. As lake level fell from the highstand, the formation of beach ridges and sand dunes sealed off the channel and isolated a small inland lake (Glen Lake), which lies 5 m above the level of Lake Michigan and may be a source of piped groundwater. Our hypothesis is that the paleochannels act as conduits for pore water flow, and thereby locally reduce soil strength and promote slope failure.Generous support for this project was provided by Max Holden and Steve Yancho of Sleeping Bear Dunes National Lakeshore

Large stellar disks in small elliptical galaxies

We present the rotation velocities V and velocity dispersions sigma along the principal axes of seven elliptical galaxies less luminous than M_B= -19.5. These kinematics extend beyond the half-light radii for all systems in this photometrically selected sample. At large radii the kinematics not only confirm that rotation and "diskiness" are important in faint ellipticals, as was previously known, but also demonstrate that in most sample galaxies the stars at large galactocentric distances have (V/sigma)_max of about 2, similar to the disks in bona-fide S0 galaxies. Comparing this high degree of ordered stellar motion in all sample galaxies with numerical simulations of dissipationless mergers argues against mergers with mass ratios <=3:1 as an important mechanism in the final shaping of low-luminosity ellipticals, and favors instead the dissipative formation of a disk.Comment: 11 pages LaTex with 4 Postscript figure

A diversity of dusty AGN tori: Data release for the VLTI/MIDI AGN Large Program and first results for 23 galaxies

The AGN-heated dust distribution (the "torus") is increasingly recognized not only as the absorber required in unifying models, but as a tracer for the reservoir that feeds the nuclear Super-Massive Black Hole. Yet, even its most basic structural properties (such as its extent, geometry and elongation) are unknown for all but a few archetypal objects. Since most AGNs are unresolved in the mid-infrared, we utilize the MID-infrared interferometric Instrument (MIDI) at the Very Large Telescope Interferometer (VLTI) that is sensitive to structures as small as a few milli-arcseconds (mas). We present here an extensive amount of new interferometric observations from the MIDI AGN Large Program (2009 - 2011) and add data from the archive to give a complete view of the existing MIDI observations of AGNs. Additionally, we have obtained high-quality mid-infrared spectra from VLT/VISIR. We present correlated and total flux spectra for 23 AGNs and derive flux and size estimates at 12 micron using simple axisymmetric geometrical models. Perhaps the most surprising result is the relatively high level of unresolved flux and its large scatter: The median "point source fraction" is 70 % for type 1 and 47 % for type 2 AGNs meaning that a large part of the flux is concentrated on scales smaller than about 5 mas (0.1 - 10 pc). Among sources observed with similar spatial resolution, it varies from 20 % - 100 %. For 18 of the sources, two nuclear components can be distinguished in the radial fits. While these models provide good fits to all but the brightest sources, significant elongations are detected in eight sources. The half-light radii of the fainter sources are smaller than expected from the size ~ L^0.5 scaling of the bright sources and show a large scatter, especially when compared to the relatively tight size--luminosity relation in the near-infrared.Comment: A&A in press; 93 pages, 63 figures, 39 tables; data available only via CD

WFPC2 Images of the Central Regions of Early-Type Galaxies - I. The Data

We present high resolution R-band images of the central regions of 67 early-type galaxies obtained with the Wide Field and Planetary Camera 2 (WFPC2) aboard the Hubble Space Telescope (HST). Our sample strikingly confirms the complex morphologies of the central regions of early-type galaxies. In particular, we detect dust in 43 percent of all galaxies, and evidence for embedded stellar disks in a remarkably large fraction of 51 percent. In 14 of those galaxies the disk-like structures are misaligned with the main galaxy, suggesting that they correspond to stellar bars in S0 galaxies. We analyze the luminosity profiles of the galaxies in our sample, and classify galaxies according to their central cusp slope. To a large extent we confirm the clear dichotomy found in previous HST surveys: bright, boxy ellipticals with shallow inner cusps (`core' galaxies) on one hand and faint, disky ellipticals with steep central cusps (`power-law' galaxies) on the other hand. The advantages and shortcomings of classification schemes utilizing the extrapolated central cusp slope are discussed, and it is shown that this cusp slope might be an inadequate representation for galaxies whose luminosity profile slope changes smoothly with radius rather than resembling a broken power-law. In fact, we find evidence for an `intermediate' class of galaxies, that cannot unambiguously be classified as either core or power-law galaxies, and which have central cusp slopes and absolute magnitudes intermediate between those of core and power-law galaxies.Comment: 44 pages, 7 Postscript figures. Accepted for publication in the Astronomical Journal. The associated Appendix with figures of luminosity profiles, contour plots and isophotal parameters for all galaxies is available at http://www.astro.washington.edu/rest/centralpro

Second harmonic generation and birefringence of some ternary pnictide semiconductors

A first-principles study of the birefringence and the frequency dependent second harmonic generation (SHG) coefficients of the ternary pnictide semiconductors with formula ABC$_2$ (A = Zn, Cd; B = Si, Ge; C = As, P) with the chalcopyrite structures was carried out. We show that a simple empirical observation that a smaller value of the gap is correlated with larger value of SHG is qualitatively true. However, simple inverse power scaling laws between gaps and SHG were not found. Instead, the real value of the nonlinear response is a result of a very delicate balance between different intraband and interband terms.Comment: 13 pages, 12 figure

Static Interactions of non-Abelian Vortices

Interactions between non-BPS non-Abelian vortices are studied in non-Abelian U(1) x SU(N) extensions of the Abelian-Higgs model in four dimensions. The distinctive feature of a non-Abelian vortex is the presence of an internal CP^{N-1} space of orientational degrees of freedom. For fine-tuned values of the couplings, the vortices are BPS and there is no net force between two static parallel vortices at arbitrary distance. On the other hand, for generic values of the couplings the interactions between two vortices depend non-trivially on their relative internal orientations. We discuss the problem both with a numerical approach (valid for small deviations from the BPS limit) and in a semi-analytical way (valid at large vortex separations). The interactions can be classified with respect to their asymptotic property at large vortex separation. In a simpler fine-tuned model, we find two regimes which are quite similar to the usual type I/II Abelian superconductors. In the generic model we find other two new regimes: type I*/II*. Unlike the type I (type II) case, where the interaction is always attractive (repulsive), the type I* and II* have both attractive and repulsive interactions depending on the relative orientation. We have found a rich variety of interactions at small vortex separations. For some values of the couplings, a bound state of two static vortices at a non-zero distance exists.Comment: 36 pages, 13 figures; v2 a small comment and a reference adde

The dusty heart of Circinus II. Scrutinizing the LM-band dust morphology using MATISSE

In this paper we present the first-ever $L$- and $M$-band interferometric observations of Circinus, building upon a recent $N$-band analysis. We used these observations to reconstruct images and fit Gaussian models to the $L$ and $M$ bands. Our findings reveal a thin edge-on disk whose width is marginally resolved and is the spectral continuation of the disk imaged in the $N$ band to shorter wavelengths. Additionally, we find a point-like source in the $L$ and $M$ bands that, based on the $LMN$-band spectral energy distribution fit, corresponds to the $N$-band point source. We also demonstrate that there is no trace of direct sightlines to hot dust surfaces in the circumnuclear dust structure of Circinus. By assuming the dust is present, we find that obscuration of A$_{\rm V} \gtrsim 250$ mag is necessary to reproduce the measured fluxes. Hence, the imaged disk could play the role of the obscuring "torus" in the unified scheme of active galactic nuclei. Furthermore, we explored the parameter space of the disk + hyperbolic cone radiative transfer models and identify a simple modification at the base of the cone. Adding a cluster of clumps just above the disk and inside the base of the hyperbolic cone provides a much better match to the observed temperature distribution in the central aperture. This aligns well with the radiation-driven fountain models that have recently emerged. Only the unique combination of sensitivity and spatial resolution of the VLTI allows such models to be scrutinized and constrained in detail. We plan to test the applicability of this detailed dust structure to other MATISSE-observed active galactic nuclei in the future.Comment: Main article: 12 pages, 6 figures. Accepted for publication in A&A. arXiv admin note: text overlap with arXiv:2205.0157

On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on manifolds. When $F(t)=t, \frac 1p(2t)^{\frac p2}, \sqrt{1+2t} -1,$ and $1-\sqrt{1-2t},$ the $F$-Yang-Mills field becomes an ordinary Yang-Mills field, $p$-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a manifold respectively. We also introduce the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) and derive the first variational formula of the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) with applications. In a more general frame, we use a unified method to study the stress-energy tensors that arise from calculating the rate of change of various functionals when the metric of the domain or base manifold is changed. These stress-energy tensors, linked to $F$-conservation laws yield monotonicity formulae. A "macroscopic" version of these monotonicity inequalities enables us to derive some Liouville type results and vanishing theorems for $p-$forms with values in vector bundles, and to investigate constant Dirichlet boundary value problems for 1-forms. In particular, we obtain Liouville theorems for $F-$harmonic maps (e.g. $p$-harmonic maps), and $F-$Yang-Mills fields (e.g. generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain generalized Chern type results for constant mean curvature type equations for $p-$forms on $\Bbb{R}^m$ and on manifolds $M$ with the global doubling property by a different approach. The case $p=0$ and $M=\mathbb{R}^m$ is due to Chern.Comment: 1. This is a revised version with several new sections and an appendix that will appear in Communications in Mathematical Physics. 2. A "microscopic" approach to some of these monotonicity formulae leads to celebrated blow-up techniques and regularity theory in geometric measure theory. 3. Our unique solution of the Dirichlet problems generalizes the work of Karcher and Wood on harmonic map