Toric degenerations of Gelfand-Cetlin systems and potential functions

We define a toric degeneration of an integrable system on a projective manifold, and prove the existence of a toric degeneration of the Gelfand-Cetlin system on the flag manifold of type A. As an application, we calculate the potential function for a Lagrangian torus fiber of the Gelfand-Cetlin system.Comment: 54 pages, 8 figures. v2: added section 4, revised section 9, and minor changes here and ther

Suzaku View of the Swift/BAT Active Galactic Nuclei. V. Torus Structure of Two Luminous Radio-loud AGNs (3C 206 and PKS 0707-35)

We present the results from broad-band X-ray spectral analysis of 3C 206 and PKS 0707-35 with Suzaku and Swift/BAT, two of the most luminous unobscured and obscured radio-loud active galactic nuclei with hard X-ray luminosities of 10^{45.5} erg s^{-1} and 10^{44.9} erg s^{-1} (14--195 keV), respectively. Based on the radio core luminosity, we estimate that the X-ray spectrum of 3C 206 contains a significant (~ 60% in the 14--195 keV band) contribution from the jet, while it is negligible in PKS 0707-35. We can successfully model the spectra with the jet component (for 3C 206), the transmitted emission, and two reflection components from the torus and the accretion disk. The reflection strengths from the torus are found to be R_{torus} (= \Omega/2\pi) = 0.29 +- 0.18 and 0.41 +- 0.18 for 3C 206 and PKS 0707-35, respectively, which are smaller than those in typical Seyfert galaxies. Utilizing the torus model by Ikeda et al. (2009), we quantify the relation between the half opening angle of a torus (\theta_{oa}) and the equivalent width of an iron-K line. The observed equivalent width of 3C 206, < 71 eV, constrain the column density in the equatorial plane to N_{H}^{eq} < 10^{23} cm^{-2}, or the half opening angle to \theta_{oa} > 80^\circ if N_{H}^{eq} = 10^{24} cm^{-2} is assumed. That of PKS 0707-35, 72 +- 36 eV, is consistent with N_{H}^{eq} ~ 10^{23} cm^{-2}. Our results suggest that the tori in luminous radio-loud AGNs are only poorly developed. The trend is similar to that seen in radio-quiet AGNs, implying that the torus structure is not different between AGNs with jets and without jets.Comment: 12 pages, 8 figures, accepted for publication in the Astrophysical Journa

Suzaku View of the Swift/BAT Active Galactic Nuclei (I): Spectral Analysis of Six AGNs and Evidence for Two Types of Obscured Population

We present a systematic spectral analysis with Suzaku of six AGNs detected in the Swift/BAT hard X-ray (15--200 keV) survey, Swift J0138.6-4001, J0255.2-0011, J0350.1-5019, J0505.7-2348, J0601.9-8636, and J1628.1-5145. This is considered to be a representative sample of new AGNs without X-ray spectral information before the BAT survey. We find that the 0.5--200 keV spectra of these sources can be uniformly fit with a base model consisting of heavily absorbed (log $N_{\rm{H}} > 23.5 \rm{cm}^{-2}$) transmitted components, scattered lights, a reflection component, and an iron-K emission line. There are two distinct groups, three "new type" AGNs (including the two sources reported by \citealt{Ueda2007}) with an extremely small scattered fraction ($f_{\rm{scat}} < 0.5$) and strong reflection component ($R = \Omega / 2 \pi \gtrsim 0.8$ where $\Omega$ is the solid angle of the reflector), and three "classical type" ones with $f_{\rm{scat}} > 0.5$ and $R \lesssim 0.8$. The spectral parameters suggest that the new type has an optically thick torus for Thomson scattering ($N_{\rm{H}} \sim 10^{25} \rm{cm}^{-2}$) with a small opening angle $\theta \sim 20^{\circ}$ viewed in a rather face-on geometry, while the classical type has a thin torus ($N_{\rm{H}} \sim 10^{23-24} \ \rm{cm}^{-2}$) with$\theta \gtrsim 30^{\circ}$. We infer that a significant number of new type AGNs with an edge-on view is missing in the current all-sky hard X-ray surveys.Comment: 11 pages, 6 figures, accepted for publication in The Astrophysical Journa

Study of Swift/BAT Selected Low-luminosity Active Galactic Nuclei Observed with Suzaku

We systematically analyze the broadband (0.5--200 keV) X-ray spectra of hard X-ray ($>10$ keV) selected local low-luminosity active galactic nuclei (LLAGNs) observed with {\it Suzaku} and {\it Swift}/BAT. The sample consists of ten LLAGNs detected with {\it Swift}/BAT with intrinsic 14--195 keV luminosities smaller than $10^{42}$ erg s$^{-1}$ available in the {\it Suzaku} archive, covering a wide range of the Eddington ratio from $10^{-5}$ to $10^{-2}$. The overall spectra can be reproduced with an absorbed cut-off power law, often accompanied by reflection components from distant cold matter, and/or optically-thin thermal emission from the host galaxy. In all objects, relativistic reflection components from the innermost disk are not required. Eight objects show a significant narrow iron-K$\alpha$ emission line. Comparing their observed equivalent widths with the predictions from the Monte-Carlo based torus model by \cite{Ike09}, we constrain the column density in the equatorial plane to be $\log N^{\rm eq}_{\rm H} > 22.7$ or the torus half opening angle $\theta_{\rm oa} < 70^\circ$. We infer that the Eddington ratio ($\lambda_{\rm Edd}$) is a key parameter that determines the torus structure of LLAGNs: the torus becomes large at $\lambda_{\rm Edd} \gtrsim 2\times10^{-4}$, whereas at lower accretion rates it is little developed. The luminosity correlation between the hard X-ray and mid-infrared (MIR) bands of the LLAGNs follows the same one as for more luminous AGNs. This implies that other mechanisms than AGN-heated dust are responsible for the MIR emission in low Eddington ratio LLAGNs.Comment: 16 pages, 55 figures, accepted for publication in Ap