Filaments as Possible Signatures of Magnetic Field Structure in Planetary Nebulae

We draw attention to the extreme filamentary structures seen in high-resolution optical images of certain planetary nebulae. We determine the physical properties of the filaments in the nebulae IC 418, NGC 3132, and NGC 6537, and based on their large length-to-width ratios, longitudinal coherence, and morphology, we suggest that they may be signatures of the underlying magnetic field. The fields needed for the coherence of the filaments are probably consistent with those measured in the precursor circumstellar envelopes. The filaments suggest that magnetic fields in planetary nebulae may have a localized and thread-like geometry.Comment: 26 pages with 7 figures. To be published in PASP. For full resolution images see http://physics.nyu.edu/~pjh

Gauge Independent Trace Anomaly for Gravitons

We show that the trace anomaly for gravitons calculated using the usual effective action formalism depends on the choice of gauge when the background spacetime is not a solution of the classical equation of motion, that is, when off-shell. We then use the gauge independent Vilkovisky-DeWitt effective action to restore gauge independence to the off-shell case. Additionally we explicitly evaluate trace anomalies for some N-sphere background spacetimes.Comment: 19 pages, additional references and title chang

A CO Survey of Young Planetary Nebulae

We report the results of a sensitive survey of young planetary nebulae in the CO J=2-1 line that significantly increases the available data on warm, dense, molecular gas in the early phases of planetary nebula formation. The observations were made using the IRAM 30 m telescope with the 3 by 3 pixel Heterodyne Receiver Array (HERA). The array provides an effective means of discriminating the CO emission of planetary nebulae in the galactic plane from contaminating emission of interstellar clouds along the line of sight. 110 planetary nebulae were observed in the survey and 40 were detected. The results increase the number of young planetary nebulae with known CO emission by approximately a factor of two. The CO spectra yield radial velocities for the detected nebulae, about half of which have uncertain or no velocity measurements at optical wavelengths. The CO profiles range from parabolic to double-peaked, tracing the evolution of structure in the molecular gas. The line widths are significantly larger than on the Asymptotic Giant Branch, and many of the lines show extended wings, which probably result from the effects on the envelopes of high velocity jets.Comment: 29 pages, 2 figures (with multiple panels), to be published in Astrophysical Journal Supplement Serie

Zeta-Functions for Non-Minimal Operators

We evaluate zeta-functions $\zeta(s)$ at $s=0$ for invariant non-minimal 2nd-order vector and tensor operators defined on maximally symmetric even dimensional spaces. We decompose the operators into their irreducible parts and obtain their corresponding eigenvalues. Using these eigenvalues, we are able to explicitly calculate $\zeta(0)$ for the cases of Euclidean spaces and $N$-spheres. In the $N$-sphere case, we make use of the Euler-Maclaurin formula to develop asymptotic expansions for the required sums. The resulting $\zeta(0)$ values for dimensions 2 to 10 are given in the Appendix.Comment: 26 pages, additional reference

Evaluation of EPIC for Three Minnesota Cropping Systems

The Erosion Productivity Impact Calculator (EPIC) model was tested using four years of field data collected at a site near Lamberton, Minnesota, under three different crop rotations: continuous corn (Zea mays L.) or CC, soybean (Glycine max L.)-corn (SC), continuous alfalfa (Medicago sativa L.) or CA. The model was evaluated by comparing measured versus predicted subsurface drainage flow (tile flow), nitratenitrogen (NO3-N) loss in tile flow, residual NO3-N in the soil profile, crop N uptake, and yield. Initially, EPIC was run using standard Soil Conservation Service (SCS) runoff curve numbers (CN2) suggested for the soil type at the site. Two different SC runs were performed with a nitrogen fixation parameter denoted as parm(7) set at either 1.0 or 0.3, reflecting uncertainty for this parameter. Under this scenario, EPIC accurately tracked monthly CC and SC variations of tile flow (r2 = 0.86 and 0.90) and NO3- N loss (r2 = 0.69 and 0.52 or 0.62). However, average annual CC and SC tile flows were under-predicted by 32 and 34 percent, and corresponding annual NO3-N losses were under-predicted by 11 and 41 or 52 percent. Predicted average annual tile flows and NO3-N losses improved following calibration of the CN2; CC and SC tile flow under-predictions were -9 and -12 percent while NO3-N losses were 0.6 and -54 or -24 percent. In general, EPIC reliably replicated the impacts of different crop management systems on nitrogen fate; e.g., greater N loss under CC and SC than CA, and less residual soil N under CA as compared to the other cropping systems. The simulated CA monthly tile flows and NO3-N losses also compared poorly with observed values (r2 values of 0.27 and 0.19). However, the predicted CA annual drainage volumes and N losses were of similar magnitude to those measured, which is of primary interest when applying models such as EPIC on a regional scale

Massive expanding torus and fast outflow in planetary nebula NGC 6302

We present interferometric observations of $^{12}$CO and $^{13}$CO $J$=2$-$1 emission from the butterfly-shaped, young planetary nebula NGC 6302. The high angular resolution and high sensitivity achieved in our observations allow us to resolve the nebula into two distinct kinematic components: (1) a massive expanding torus seen almost edge-on and oriented in the North-South direction, roughly perpendicular to the optical nebula axis. The torus exhibits very complex and fragmentated structure; (2) high velocity molecular knots moving at high velocity, higher than 20 \kms, and located in the optical bipolar lobes. These knots show a linear position-velocity gradient (Hubble-like flow), which is characteristic of fast molecular outflow in young planetary nebulae. From the low but variable $^{12}$CO/$^{13}$CO $J$=2$-$1 line intensity ratio we conclude that the $^{12}$CO $J$=2$-$1 emission is optically thick over much of the nebula. Using the optically thinner line $^{13}$CO $J$=2$-$1 we estimate a total molecular gas mass of $\sim$ 0.1 M$_\odot$, comparable to the ionized gas mass; the total gas mass of the NGC 6302 nebula, including the massive ionized gas from photon dominated region, is found to be $\sim$ 0.5 M$_\odot$. From radiative transfer modelling we infer that the torus is seen at inclination angle of 75$^\circ$ with respect to the plane of the sky and expanding at velocity of 15 \kms. Comparison with recent observations of molecular gas in NGC 6302 is also discussed.Comment: 24 pages, 7 figures, accepted for publication in Astrophysical Journa

Jets and the shaping of the giant bipolar envelope of the planetary nebula KjPn 8

A hydrodynamic model involving cooling gas in the stagnation region of a collimated outflow is proposed for the formation of the giant parsec-scale bipolar envelope that surrounds the planetary nebula KjPn 8. Analytical calculations and numerical simulations are presented to evaluate the model. The envelope is considered to consist mainly of environmental gas swept-up by shocks driven by an episodic, collimated, bipolar outflow. In this model, which we call the ``free stagnation knot'' mechanism, the swept-up ambient gas located in the stagnation region of the bow-shock cools to produce a high density knot. This knot moves along with the bow-shock. When the central outflow ceases, pressurization of the interior of the envelope stops and its expansion slows down. The stagnation knot, however, has sufficient momentum to propagate freely further along the axis, producing a distinct nose at the end of the lobe. The model is found to successfully reproduce the peculiar shape and global kinematics of the giant bipolar envelope of KjPn 8.Comment: 20 pages + 8 figures (in 1 tar-file 0.67 Mb

Coal Mineral Analysis: A Check on Inter-Laboratory Agreement

Four laboratories co-operated to test repeatibility and reproducibility of the semi-quantitive Coal Mineral Analysis (CMA) method. CMA is an instrumented image analysis method which identifies mineral particles in coal by chemical composition (energy dispersive X-ray spectroscopy) and size (scanning electron microscopy). The repeatability of weight percent data was better than 0.2 relative standard deviation for most minerals constituting more than five percent of all coal minerals. The type of mineral had no effect on repeatability. Errors arising from counting statistics were shown to be the major source of bias at a given instrument setting. Inter-laboratory data for the major minerals agreed to within 0.1 relative standard deviation in about 50% of the cases. For other major minerals the relative standard deviation from the inter-laboratory average varied between 0.1 and 0.3. The weight percentages of kaolinite and mixed silicates showed poorer reproducibility than those of quartz and illite. Differences in detector window thickness may have affected discrimination between light elements and, therefore, inter-laboratory agreement of clay minerals data. Means to compensate window thickness effects are suggested

Radio continuum properties of young planetary nebulae

We have selected a small sample of post-AGB stars in transition towards the planetary nebula and present new Very Large Array multi-frequency high-angular resolution radio observations of them. The multi-frequency data are used to create and model the targets' radio continuum spectra, proving that these stars started their evolution as very young planetary nebulae. In the optically thin range, the slopes are compatible with the expected spectral index (-0.1). Two targets (IRAS 18062+2410 and 17423-1755) seem to be optically thick even at high frequency, as observed in a handful of other post-AGB stars in the literature, while a third one (IRAS 20462+3416) shows a possible contribution from cold dust. In IRAS 18062+2410, where we have three observations spanning a period of four years, we detect an increase in its flux density, similar to that observed in CRL 618. High-angular resolution imaging shows bipolar structures that may be due to circumstellar tori, although a different hypothesis (i.e., jets) could also explain the observations. Further observations and monitoring of these sources will enable us to test the current evolutionary models of planetary nebulae.Comment: 8 pages, 3 figures, accepted for publication in MNRA

One-loop Vilkovisky-DeWitt Counterterms for 2D Gravity plus Scalar Field Theory

The divergent part of the one-loop off-shell effective action is computed for a single scalar field coupled to the Ricci curvature of 2D gravity ($c \phi R$), and self interacting by an arbitrary potential term $V(\phi)$. The Vilkovisky-DeWitt effective action is used to compute gauge-fixing independent results. In our background field/covariant gauge we find that the Liouville theory is finite on shell. Off-shell, we find a large class of renormalizable potentials which include the Liouville potential. We also find that for backgrounds satisfying $R=0$, the Liouville theory is finite off shell, as well.Comment: 19 pages, OKHEP 92-00