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

557 GHz Observations of Water Vapor Outflows from VY CMa and W Hydrae

We report the first detection of thermal water vapor emission in the 557 GHz, $1_{10} - 1_{01}$ ground state transition of ortho-H$_2$O toward VY Canis Majoris. In observations obtained with the Submillimeter Wave Astronomy Satellite (SWAS), we measured a flux of $\sim 450$Jy, in a spectrally resolved line centered on a velocity $v_{LSR} = 25$km s$^{-1}$ with a full width half maximum of $\sim 35$ km s$^{-1}$, somewhat dependent on the assumed line shape. We analyze the line shape in the context of three different radial outflow models for which we provide analytical expressions. We also detected a weaker 557 GHz emission line from W Hydrae. We find that these and other H$_2$O emission line strengths scale as suggested by Zubko and Elitzur (2000).Comment: Astrophysical Journal Letters, accepte

Variability Tests for Intrinsic Absorption Lines in Quasar Spectra

Quasar spectra have a variety of absorption lines whose origins range from energetic winds expelled from the central engines to unrelated, intergalactic clouds. We present multi-epoch, medium resolution spectra of eight quasars at z~2 that have narrow ``associated'' absorption lines (AALs, within $\pm$5000 km s^{-1} of the emission redshift). Two of these quasars were also known previously to have high-velocity mini-broad absorption lines (mini-BALs). We use these data, spanning ~17 years in the observed frame with two to four observations per object, to search for line strength variations as an identifier of absorption that occurs physically near (``intrinsic'' to) the central AGN. Our main results are the following: Two out of the eight quasars with narrow AALs exhibit variable AAL strengths. Two out of two quasars with high-velocity mini-BALs exhibit variable mini-BAL strengths. We also marginally detect variability in a high-velocity narrow absorption line (NAL) system, blueshifted \~32,900 km s^{-1}$ with respect to the emission lines. No other absorption lines in these quasars appeared to vary. The outflow velocities of the variable AALs are 3140 km s^{-1} and 1490 km s^{-1}. The two mini-BALs identify much higher velocity outflows of ~28,400 km s^{-1} and ~52,000 km s^{-1}. Our temporal sampling yields upper limits on the variation time scales from 0.28 to 6.1 years in the quasar rest frames. The corresponding minimum electron densities in the variable absorbers, based on the recombination time scale, are \~40,000 cm^{-3} to ~1900 cm^{-3}. The maximum distances of the absorbers from the continuum source, assuming photoionization with no spectral shielding, range from ~1.8 kpc to ~7 kpc.Comment: 16 pages, 4 figures, ApJ, accepte

Unravelling the chemical inhomogeneity of PNe with VLT FLAMES integral-field unit spectroscopy

Recent weak emission-line long-slit surveys and modelling studies of PNe have convincingly argued in favour of the existence of an unknown component in the planetary nebula plasma consisting of cold, hydrogen-deficient gas, as an explanation for the long-standing recombination-line versus forbidden-line temperature and abundance discrepancy problems. Here we describe the rationale and initial results from a detailed spectroscopic study of three Galactic PNe undertaken with the VLT FLAMES integral-field unit spectrograph, which advances our knowledge about the small-scale physical properties, chemical abundances and velocity structure of these objects across a two-dimensional field of view, and opens up for exploration an uncharted territory in the study and modelling of PNe and photoionized nebulae in general.Comment: 4 pages; 3 figures; invited paper to appear in proceedings of IAU Symp. No. 234, 2006, Planetary Nebulae in our Galaxy and Beyond (held in Hawaii, April 2006

Transition density of diffusion on Sierpinski gasket and extension of Flory's formula

Some problems related to the transition density u(t,x) of the diffusion on the Sierpinski gasket are considerd, based on recent rigorous results and detailed numerical calculations. The main contents are an extension of Flory's formula for the end-to-end distance exponent of self-avoiding walks on the fractal spaces, and an evidence of the oscillatory behavior of u(t,x) on the Sierpinski gasket.Comment: 11 pages, REVTEX, 2 postscript figure

Biased tomography schemes: an objective approach

We report on an intrinsic relationship between the maximum-likelihood quantum-state estimation and the representation of the signal. A quantum analogy of the transfer function determines the space where the reconstruction should be done without the need for any ad hoc truncations of the Hilbert space. An illustration of this method is provided by a simple yet practically important tomography of an optical signal registered by realistic binary detectors.Comment: 4 pages, 3 figures, accepted in PR