Herschel-PACS Measurements of Nitrogen Enrichment in Nebulae around Wolf-Rayet Stars

For three nebulae that have early-WN Wolf-Rayet exciting stars, NGC 6888, WR 8 and Abell 48, we have obtained Herschel-PACS line scans of the [N III] 57 um and [O III] 88 micron lines, along with the 122 and 205 micron lines of [N II]. From the former two lines we have derived N$^{2+}$/O$^{2+}$ abundance ratios, equal to the overall N/O ratio under a wide range of nebular conditions. We find that all of the nebulae observed possess significant nitrogen enrichment, with derived N/O ratios greater than solar. The two nebulae with massive Wolf-Rayet exciting stars, NGC 6888 and WR8 are found to have N/O ratios that are enhanced by factors of 7 - 10 relative to the solar N/O ratio, consistent with an origin as material ejected just before the onset of the Wolf-Rayet phase. The other nebula, Abell 48, has recently been reclassified as a member of the rare class of three planetary nebulae that have early-WN central stars and are not of Peimbert Type I. We derive a nebular N/O ratio for it that is a factor of 4 enhanced relative to solar and slightly above the range of N/O values that have been measured for the other three members of its [WN] planetary nebula class.Comment: 11 pages, 5 figures, MNRAS accepte

OH+^+ emission from cometary knots in planetary nebulae

We model the molecular emission from cometary knots in planetary nebulae (PNe) using a combination of photoionization and photodissociation region (PDR) codes, for a range of central star properties and gas densities. Without the inclusion of ionizing extreme ultraviolet (EUV) radiation, our models require central star temperatures $T_*$ to be near the upper limit of the range investigated in order to match observed H$_2$ and OH$^+$ surface brightnesses consistent with observations - with the addition of EUV flux, our models reproduce observed OH$^+$ surface brightnesses for $T_* \ge 100 \, {\rm kK}$. For $T_* < 80 \, {\rm kK}$, the predicted OH$^+$ surface brightness is much lower, consistent with the non-detection of this molecule in PNe with such central star temperatures. Our predicted level of H$_2$ emission is somewhat weaker than commonly observed in PNe, which may be resolved by the inclusion of shock heating or fluorescence due to UV photons. Some of our models also predict ArH$^+$ and HeH$^+$ rotational line emission above detection thresholds, despite neither molecule having been detected in PNe, although the inclusion of photodissociation by EUV photons, which is neglected by our models, would be expected to reduce their detectability.Comment: Accepted by MNRAS, 11 pages, 15 figures. Author accepted manuscript. Accepted on 24/04/18. Deposited on 27/04/1

Modelling the ArH+^+ emission from the Crab Nebula

We have performed combined photoionization and photodissociation region (PDR) modelling of a Crab Nebula filament subjected to the synchrotron radiation from the central pulsar wind nebula, and to a high flux of charged particles; a greatly enhanced cosmic ray ionization rate over the standard interstellar value, $\zeta_0$, is required to account for the lack of detected [C I] emission in published Herschel SPIRE FTS observations of the Crab Nebula. The observed line surface brightness ratios of the OH$^+$ and ArH$^+$ transitions seen in the SPIRE FTS frequency range can only be explained with both a high cosmic ray ionization rate and a reduced ArH$^+$ dissociative recombination rate compared to that used by previous authors, although consistent with experimental upper limits. We find that the ArH$^+$/OH$^+$ line strengths and the observed H$_2$ vibration-rotation emission can be reproduced by model filaments with $n_{\rm{H}} = 2 \times 10^4$ cm$^{-3}$, $\zeta = 10^7 \zeta_0$ and visual extinctions within the range found for dusty globules in the Crab Nebula, although far-infrared emission from [O I] and [C II] is higher than the observational constraints. Models with $n_{\rm{H}} = 1900$ cm$^{-3}$ underpredict the H$_2$ surface brightness, but agree with the ArH$^+$ and OH$^+$ surface brightnesses and predict [O I] and [C II] line ratios consistent with observations. These models predict HeH$^+$ rotational emission above detection thresholds, but consideration of the formation timescale suggests that the abundance of this molecule in the Crab Nebula should be lower than the equilibrium values obtained in our analysis.Comment: Accepted by MNRAS. Author accepted manuscript. Accepted on 05/09/2017. Deposited on 05/09/1

PLTTER user's guide

The PLTTER graphics system, which is part of CDDMS is discussed. CDDMS is a comprehensive system for data basing and subsequent plotting of data acquired during wind tunnel tests or from computational flow analyses. The PLTTER is a system which creates report-quality plots of data which is stored on a CDDMS data base. The Requests file system allows plot-controlling information to be arranged in the way which is most appropriate for any application. The PLTTER system features many capabilities which are especially useful when plotting wind tunnel data. The PLTTER offers a variety of page formats, different grid options and parametric curve fitting algorithms, and a powerful legend capability to identify relevant information about individual curves. One or more plots on a page can be suppressed if desired so that an established page format can be maintained. Final plot output may be standard Versatec plots, QMS Laser printer plots, or microfiche

Structured total least norm and approximate GCDs of inexact polynomials

The determination of an approximate greatest common divisor (GCD) of two inexact polynomials f=f(y) and g=g(y) arises in several applications, including signal processing and control. This approximate GCD can be obtained by computing a structured low rank approximation S*(f,g) of the Sylvester resultant matrix S(f,g). In this paper, the method of structured total least norm (STLN) is used to compute a low rank approximation of S(f,g), and it is shown that important issues that have a considerable effect on the approximate GCD have not been considered. For example, the established works only yield one matrix S*(f,g), and therefore one approximate GCD, but it is shown in this paper that a family of structured low rank approximations can be computed, each member of which yields a different approximate GCD. Examples that illustrate the importance of these and other issues are presented