Fast subsumption checks using anti-links

The concept of "anti-link" is defined, and useful equivalence-preserving operations based on anti-links are introduced.These operations eliminate a potentially large number of subsumed paths in a negation normal form formula.Those anti-links that directly indicate the presence of subsumed paths are characterized. The operations have linear time complexity in the size of that part of the formula containing the anti-link. The problem of removing all subsumed paths in an NNF formula is shown to be NP-hard, even though such formulas may be small relative to the size of their path sets. The general problem of determining whether there exists a pair of subsumed paths associated with an arbitrary anti-link is shown to be NP-complete. Additional techniques based on "strictly pure full blocks" are introduced and are also shown to eliminate redundant subsumption checks. The effectiveness of these techniques is examined with respect to some benchmark examples from the literature

Massive Clumps in the NGC 6334 Star Forming Region

We report observations of dust continuum emission at 1.2 mm toward the star forming region NGC 6334 made with the SEST SIMBA bolometer array. The observations cover an area of $\sim 2$ square degrees with approximately uniform noise. We detected 181 clumps spanning almost three orders of magnitude in mass (3\Msun$-6\times10^3$ \Msun) and with sizes in the range 0.1--1.0 pc. We find that the clump mass function $dN/d\log M$ is well fit with a power law of the mass with exponent -0.6 (or equivalently $dN/dM \propto M^{-1.6}$). The derived exponent is similar to those obtained from molecular line emission surveys and is significantly different from that of the stellar initial mass function. We investigated changes in the mass spectrum by changing the assumptions on the temperature distribution of the clumps and on the contribution of free-free emission to the 1.2 mm emission, and found little changes on the exponent. The Cumulative Mass Distribution Function is also analyzed giving consistent results in a mass range excluding the high-mass end where a power-law fit is no longer valid. The masses and sizes of the clumps observed in NGC 6334 indicate that they are not direct progenitors of stars and that the process of fragmentation determines the distribution of masses later on or occurs at smaller spatial scales. The spatial distribution of the clumps in NGC 6334 reveals clustering which is strikingly similar to that exhibited by young stars in other star forming regions. A power law fit to the surface density of companions gives $\Sigma\propto \theta^{-0.62}$.Comment: 16 pages, 11 figures, 4 tables. To appear in the Astrophysical Journa

A dynamic logic for every season

This paper introduces a method to build dynamic logics with a graded semantics. The construction is parametrized by a structure to support both the spaces of truth and of the domain of computations. Possible instantiations of the method range from classical assertional) dynamic logic to less common graded logics suitable to deal with programs whose transitional semantics exhibits fuzzy or weighted behaviour.This leads to the systematic derivation of program logics tailored to specific program classes

Mass-losing accretion discs around supermassive black holes

We study the effects of outflow/wind on the gravitational stability of accretion discs around supermassive black holes using a set of analytical steady-state solutions. Mass-loss rate by the outflow from the disc is assumed to be a power-law of the radial distance and the amount of the energy and the angular momentum which are carried away by the wind are parameterized phenomenologically. We show that the mass of the first clumps at the self-gravitating radius linearly decreases with the total mass-loss rate of the outflow. Except for the case of small viscosity and high accretion rate, generally, the self-gravitating radius increases as the amount of mass-loss by the outflow increases. Our solutions show that as more angular momentum is lost by the outflow, then reduction to the mass of the first clumps is more significant.Comment: Accepted for publication in Astrophysics & Space Scienc

Radio Circular Polarization Produced in Helical Magnetic Fields in Eight Active Galactic Nuclei

Homan & Lister (2006) have recently published circular-polarization (CP) detections for 34 objects in the MOJAVE sample - a set of bright, compact AGN being monitored by the Very Long Baseline Array at 15 GHz. We report the detection of 15-GHz parsec-scale CP in two more AGN (3C345 and 2231+114), and confirm the MOJAVE detection of CP in 1633+382. It is generally believed that the most likely mechanism for the generation of this CP is Faraday conversion of linear polarization to CP. A helical jet magnetic-field (B-field) geometry can facilitate this process - linearly polarized emission from the far side of the jet is converted to CP as it passes through the magnetised plasma at the front side of the jet on its way toward the observer. In this case, the sign of the generated CP is essentially determined by the pitch angle and helicity of the helical B field. We have determined the pitch-angle regimes and helicities of the helical jet B fields in 8 AGN for which parsec-scale CP has been detected, and used them to predict the expected CP signs for these AGN if the CP is generated via conversion in these helical fields. We have obtained the intriguing result that our predictions agree with the observed signs in all eight cases, provided that the longitudinal B-field components in the jets correspond to South magnetic poles. This clearly non-random pattern demonstrates that the observed CP in AGN is directly associated with the presence of helical jet B fields. These results suggest that helical B fields are ubiquitous in AGN jets.Comment: 24 pages, 6 figures, accepted for publication in Monthly Notices of the Royal Astronomical Society (MNRAS

The power output of local obscured and unobscured AGN: crossing the absorption barrier with Swift/BAT and IRAS

The Swift/BAT 9-month catalogue of active galactic nuclei (AGN) provides an unbiased census of local supermassive black hole accretion, and probes to all but the highest levels of absorption in AGN. We explore a method for characterising the bolometric output of both obscured and unobscured AGN by combining the hard X-ray data from Swift/BAT (14-195keV) with the reprocessed IR emission as seen with the IRAS all-sky surveys. This approach bypasses the complex modifications to the SED introduced by absorption in the optical, UV and 0.1-10 keV regimes and provides a long-term, average picture of the bolometric output of these sources. We broadly follow the approach of Pozzi et al. for calculating the bolometric luminosities by adding nuclear IR and hard X-ray luminosities, and consider different approaches for removing non-nuclear contamination in the large-aperture IRAS fluxes. Using mass estimates from the M_BH-L_bulge relation, we present the Eddington ratios \lambda_Edd and 2-10 keV bolometric corrections for a subsample of 63 AGN (35 obscured and 28 unobscured) from the Swift/BAT catalogue, and confirm previous indications of a low Eddington ratio distribution for both samples. Importantly, we find a tendency for low bolometric corrections (typically 10-30) for the obscured AGN in the sample (with a possible rise from ~15 for \lambda_Edd<0.03 to ~32 above this), providing a hitherto unseen window onto accretion processes in this class of AGN. This finding is of key importance in calculating the expected local black hole mass density from the X-ray background since it is composed of emission from a significant population of such obscured AGN. Analogous studies with high resolution IR data and a range of alternative models for the torus emission will form useful future extensions to this work. (Abridged)Comment: 19 pages, 16 figures, 2 tables. Accepted for publication in MNRA

Isotope shift in the dielectronic recombination of three-electron ^{A}Nd^{57+}

Isotope shifts in dielectronic recombination spectra were studied for Li-like ^{A}Nd^{57+} ions with A=142 and A=150. From the displacement of resonance positions energy shifts \delta E^{142,150}(2s-2p_1/2)= 40.2(3)(6) meV (stat)(sys)) and \delta E^{142,150}(2s-2p_3/2) = 42.3(12)(20) meV of 2s-2p_j transitions were deduced. An evaluation of these values within a full QED treatment yields a change in the mean-square charge radius of ^{142,150}\delta = -1.36(1)(3) fm^2. The approach is conceptually new and combines the advantage of a simple atomic structure with high sensitivity to nuclear size.Comment: 10 pages, 3 figures, accepted for publication in Physical Review Letter

Faraday Conversion and Rotation In Uniformly Magnetized Relativistic Plasmas

We provide precise fitting formulae for Faraday conversion and rotation coefficients in uniformly magnetized relativistic plasma. The formulae are immediately applicable to Rotation Measure and Circular Polarization (CP) production in jets and hot accretion flows. We show the recipe and results for arbitrary isotropic particle distributions, in particular thermal and power-law. The exact Faraday conversion coefficient is found to approach zero with the increasing particle energy. The non-linear corrections of Faraday conversion and rotation coefficients are found essential for reliable CP inter- pretation of Sgr A*.Comment: 21 pages, 10 figues, accepted by MNRA