Intertwining operator for AG2AG_2 Calogero-Moser-Sutherland system

We consider generalised Calogero-Moser-Sutherland quantum Hamiltonian $H$ associated with a configuration of vectors $AG_2$ on the plane which is a union of $A_2$ and $G_2$ root systems. The Hamiltonian $H$ depends on one parameter. We find an intertwining operator between $H$ and the Calogero-Moser-Sutherland Hamiltonian for the root system $G_2$. This gives a quantum integral for $H$ of order 6 in an explicit form thus establishing integrability of $H$.Comment: 24 page

On the Escape of Ionizing Radiation from Starbursts

Far-ultraviolet spectra obtained with $FUSE$ show that the strong $CII\lambda$1036 interstellar absorption-line is essentially black in five of the UV-brightest local starburst galaxies. Since the opacity of the neutral ISM below the Lyman-edge will be significantly larger than in the $CII$ line, these data provide strong constraints on the escape of ionizing radiation from these starbursts. Interpreted as a a uniform absorbing slab, the implied optical depth at the Lyman edge is huge ($\tau_0 \geq 10^2$). Alternatively, the areal covering factor of opaque material is typically $\geq$ 94%. Thus, the fraction of ionizing stellar photons that escape the ISM of each galaxy is small: our conservative estimates typically yield $f_{esc} \leq 6$. Inclusion of extinction due to dust will further decrease $f_{esc}$. An analogous analysis of the rest-UV spectrum of the star-forming galaxy $MS 1512-CB58$ at $z$ =2.7 leads to similar constraints on $f_{esc}$. These new results agree with the constraints provided by direct observations below the Lyman edge in a few other local starbursts. However, they differ from the recently reported properties of star-forming galaxies at $z \geq$ 3. We assess the idea that the strong galactic winds seen in many powerful starbursts clear channels through their neutral ISM. We show empirically that such outflows may be a necessary - but not sufficient - part of the process for creating a relatively porous ISM. We note that observations will soon document the cosmic evolution in the contribution of star-forming galaxies to the metagalactic ionizing background, with important implications for the evolution of the IGM.Comment: 17 pages; ApJ, in pres

Extended trigonometric Cherednik algebras and nonstationary Schr\"odinger equations with delta-potentials

We realize an extended version of the trigonometric Cherednik algebra as affine Dunkl operators involving Heaviside functions. We use the quadratic Casimir element of the extended trigonometric Cherednik algebra to define an explicit nonstationary Schr\"odinger equation with delta-potential. We use coordinate Bethe ansatz methods to construct solutions of the nonstationary Schr\"odinger equation in terms of generalized Bethe wave functions. It is shown that the generalized Bethe wave functions satisfy affine difference Knizhnik-Zamolodchikov equations in their spectral parameter. The relation to the vector valued root system analogs of the quantum Bose gas on the circle with pairwise delta-function interactions is indicated.Comment: 23 pages; Version 2: expanded introduction and misprints correcte

The Spatial Clustering of Low Luminosity AGN

We present the first multi-parameter analysis of the narrow line AGN clustering properties. Estimates of the two-point correlation function (CF) based on SDSS DR2 data reveal that Seyferts are clearly less clustered than normal galaxies, while the clustering amplitude (r_0) of LINERs is consistent with that of the parent galaxy population. The similarities in the host properties (color and concentration index) of Seyferts and LINERs suggest that the difference in their r_0 is not driven by the morphology-density relation. We find that the luminosity of [O I] emission shows the strongest influence on AGN clustering, with low L([O I]) sources having the highest r_0. This trend is much stronger than the previously detected dependence on L([O III]), which we confirm. There is a strong correspondence between the clustering patterns of objects of given spectral type and their physical properties. LINERs, which exhibit high r_0, show the lowest luminosities and obscuration levels, and relatively low gas densities (n_e), suggesting that these objects harbor black holes that are relatively massive yet weakly active or inefficient in their accretion, probably due to the insufficiency of their fuel supply. Seyferts, which have low r_0, are luminous and show large n_e, suggesting that their black holes are less massive but accrete quickly and efficiently enough to clearly dominate the ionization. The low r_0 of the H II galaxies can be understood as a consequence of both the morphology-density and star formation rate-density relations, however, their spectral properties suggest that their centers hide amidst large amounts of obscuring material black holes of generally low mass whose activity remains relatively feeble. Our own Milky Way may be a typical such case.[abridged]Comment: 27 pages, color figures, some are severely degraded in resolution, emulateapj. See http://www.physics.drexel.edu/~constant/work/agnclustering.ps for high resolution version. Accepted to Ap

Optical Spectroscopy of the IRAS 1-Jy Sample of Ultraluminous Infrared Galaxies

This paper discusses the optical spectroscopic properties of the IRAS 1-Jy sample of ultraluminous infrared galaxies (ULIGs). One hundred and eight of the 118 1-Jy ULIGs have been observed at dlambda = 8.3 AA resolution over the wavelength range ~4500 A -- 8900 A. These data are combined with large, previously published sets of optical spectroscopic data of lower luminosity infrared galaxies to look for systematic trends with infrared luminosity over the luminosity range L_ir ~ 10^{10.5}-10^{13} L_sun. As found in previous studies, the fraction of Seyfert galaxies among luminous infrared galaxies increases abruptly above L_ir ~ 10^{12.3} L_sun --- about 50% of the galaxies with L_ir > 10^{12.3} L_sun present Seyfert characteristics. Many of the optical and infrared spectroscopic properties of the Seyfert galaxies are consistent with the presence of a genuine active galactic nucleus (AGN). About 30% of these galaxies are Seyfert 1s with broad-line regions similar to those of optical quasars. The percentage of Seyfert 1 ULIGs increases with infrared luminosity, contrary to the predictions of the standard unification model for Seyfert galaxies. Comparisons of the broad-line luminosities of optical and obscured Seyfert 1 ULIGs with those of optically selected quasars of comparable bolometric luminosity suggest that the dominant energy source in most of these ULIGs is the same as in optical quasars, namely mass accretion onto a supermassive black hole, rather than a starburst. These results are consistent with recently published ISO, ASCA, and VLBI data. (abridged)Comment: Text and 23 figures (45 pages), Tables 1 - 6 (16 pages

Properties of H II Regions in the Centers of Nearby Galaxies

As part of an optical spectroscopic survey of nearby, bright galaxies, we have identified a sample of over 200 emission-line nuclei having optical spectra resembling those of giant extragalactic H II regions. Such "H II nuclei," powered by young, massive stars, are found in a substantial fraction of nearby galaxies, especially those of late Hubble type. This paper summarizes the observational characteristics of H II nuclei, contrasts the variation of their properties with Hubble type, and compares the nuclear H II regions with those found in galaxy disks. Similarities and differences between H II nuclei and luminous starburst nuclei are additionally noted.Comment: To appear in the Astrophysical Journal. LaTex, 37 pages including 15 postscript figures. AAStex macros include

T-Branes and Monodromy

We introduce T-branes, or "triangular branes," which are novel non-abelian bound states of branes characterized by the condition that on some loci, their matrix of normal deformations, or Higgs field, is upper triangular. These configurations refine the notion of monodromic branes which have recently played a key role in F-theory phenomenology. We show how localized matter living on complex codimension one subspaces emerge, and explain how to compute their Yukawa couplings, which are localized in complex codimension two. Not only do T-branes clarify what is meant by brane monodromy, they also open up a vast array of new possibilities both for phenomenological constructions and for purely theoretical applications. We show that for a general T-brane, the eigenvalues of the Higgs field can fail to capture the spectrum of localized modes. In particular, this provides a method for evading some constraints on F-theory GUTs which have assumed that the spectral equation for the Higgs field completely determines a local model.Comment: 110 pages, 5 figure

Radio Sources in Low-Luminosity Active Galactic Nuclei. I. VLA Detections of Compact, Flat-Spectrum Cores

We report a 0.2" resolution, 15 GHz survey of a sample of 48 low-luminosity active galactic nuclei with the Very Large Array. Compact radio emission has been detected in 57% (17 of 30) of LINERs and low-luminosity Seyferts, at least 15 of which have a flat to inverted radio spectrum (alpha > -0.3). The compact radio cores are found in both type 1 (i.e. with broad Halpha) and type 2 (without broad Halpha) nuclei. The 2 cm radio power is significantly correlated with the emission-line ([OI] lambda6300) luminosity. While the present observations are consistent with the radio emission originating in star-forming regions, higher resolution radio observations of 10 of the detected sources, reported in a companion paper (Falcke et al. 2000), show that the cores are very compact (= 10^8K) and probably synchrotron self-absorbed, ruling out a starburst origin. Thus, our results suggest that at least 50% of low-luminosity Seyferts and LINERs in the sample are accretion powered, with the radio emission presumably coming from jets or advection-dominated accretion flows. We have detected only 1 of 18 `transition' (i.e. LINER + HII) nuclei observed, indicating their radio cores are significantly weaker than those of `pure' LINERs.Comment: To appear in the Astrophysical Journal, October 20, 200

The Influence of Bars on Nuclear Activity

We test ideas on fueling of galactic nuclei by bar-driven inflow by comparing the detection rate and intensity of nuclear H II regions and AGNs among barred and unbarred galaxies in a sample of over 300 spirals selected from our recent optical spectroscopic survey of nearby galaxies. Among late-type spirals (Sc-Sm), but not early-type (S0/a-Sbc), we observe in the barred group a very marginal increase in the detection rate of H II nuclei and a corresponding decrease in the incidence of AGNs. The minor differences in the detection rates, however, are statistically insignificant, most likely stemming from selection effects and not from a genuine influence from the bar. The presence of a bar seems to have no noticeable impact on the likelihood of a galaxy to host either nuclear star formation or an AGN. The nuclei of early-type barred spirals do exhibit measurably higher star-formation rates than their unbarred counterparts, as indicated by either the luminosity or the equivalent width of H-alpha emission. By contrast, late-type spirals do not show such an effect. Bars have a negligible effect on the strength of the AGNs in our sample, regardless of the Hubble type of the host galaxy. This result confirms similar conclusions reached by other studies based on much smaller samples.Comment: To appear in the Astrophysical Journal. LaTex, 31 pages including 6 postscript figures and 3 tables. AAStex macros include