The scalar complex potential and the Aharonov-Bohm effect

The Aharonov-Bohm effect is traditionally attributed to the effect of the electromagnetic 4-potential $A$, even in regions where both the electric field $\mathbf{E}$ and the magnetic field $\mathbf{B}$ are zero. The AB effect reveals that multiple-valued functions play a crucial role in the description of an electromagnetic field. We argue that the quantity measured by AB experiments is a difference in values of a multiple-valued complex function, which we call a complex potential or {pre-potential. We show that any electromagnetic field can be described by this pre-potential, and give an explicit expression for the electromagnetic field tensor through this potential. The pre-potential is a modification of the two scalar potential functions.Comment: 10 pages 2 figure

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

Getting Jobs, Keeping Jobs, and Earning a Living Wage: Can Welfare Reform Work?

Most discussions of welfare and work have focused on how demographic characteristics, schooling, training, and work experience limit welfare mothers’ employment and wages, but they have largely ignored factors such as inappropriate workplace behaviors, expectations of discrimination and harassment, depression, alcoholism, and domestic violence, all of which may affect welfare mothers and make employment difficult. In this paper we review the prevalence of these individual-level barriers and argue that they, in combination with an economy which does not pay low-skill workers well, are likely to impede employment and self-sufficiency for a large proportion of welfare mothers. At the end of the review, we summarize the current state of knowledge about barriers to the employment of welfare recipients and suggest several ways in which welfare-to-work programs might address these barriers.

A deep survey of heavy element lines in planetary nebulae -- II. Recombination line abundances and evidence for ultra-cold plasma

[Abridged] Deep optical observations of the spectra of 12 Galactic planetary nebulae (PNe) and 3 Magellanic Cloud PNe were presented in Paper I by Tsamis et al. (2003b), who carried out an abundance analysis using the collisionally excited forbidden lines. Here, the relative intensities of faint optical recombination lines (ORLs) from ions of carbon, nitrogen and oxygen are analysed in order to derive the abundances of these ions relative to hydrogen. We define an abundance discrepancy factor (ADF) as the ratio of the abundance derived for a heavy element ion from its recombination lines to that derived for the same ion from its ultraviolet, optical or infrared collisionally excited lines (CELs). All of the PNe in our sample are found to have ADF's that exceed unity. There is no dependence of the magnitude of the ADF upon the excitation energy of the UV, optical or IR CEL transition used, indicating that classical nebular temperature fluctuations--i.e. in a chemically homogeneous medium--are not the cause of the observed abundance discrepancies. Instead, we conclude that the main cause of the discrepancy is enhanced ORL emission from cold ionized gas located in hydrogen-deficient clumps inside the main body of the nebulae. We have developed a new electron temperature diagnostic, based upon the relative intensities of the OII 4f-3d 4089A and 3p-3s 4649A recombination transitions. For six out of eight PNe for which both transitions are detected, we derive O2+ ORL electron temperatures of <300 K, very much less than the O2+ forbidden-line and Balmer jump temperatures derived for the same nebulae. These results provide direct observational evidence for the presence of H-deficient, cold plasma regions within the nebulae, consistent with gas cooled largely by infrared fine structure and recombination transitions.Comment: 27 pages, 7 figures, submitted to the MNRA

A deep survey of heavy element lines in planetary nebulae - I. Observations and forbidden-line densities, temperatures and abundances

We present spectrophotometry of 12 Galactic and 3 Magellanic Cloud planetary nebulae (PNe). Nine of the Galactic PNe were observed by scanning the slit across the PN. We use the fluxes of collisionally excited lines (CELs) to derive electron densities (D's) and temperatures (T's), and ionic abundances. We find that the D's derived from optical CEL ratios are systematically higher than those derived from the ratios of the IR fine-structure (FS) lines of [OIII], indicating the presence of significant density variations within the PNe. We also compare T's obtained from the ratio of optical nebular to auroral [OIII] lines with those obtained from the ratio of [OIII] optical to IR FS lines. We find that when the latter are derived using D's based on the [OIII] 52um/88um ratio, they yield values that are significantly higher than the optical [OIII] T's. Contrasting this, [OIII] optical/IR T's derived using the higher D's obtained from [ClIII] 5517A/5537A ratios show much closer agreement with optical [OIII] T's, implying that the observed [OIII] optical/IR ratios are significantly weighted by D's in excess of the critical densities of both [OIII] FS lines. Consistent with this, ionic abundances derived from [OIII] and [NIII] FS lines using D's from optical CELs show much better agreement with abundances derived for the same ions from optical and UV CELs than do abundances derived from the FS lines using the lower D's obtained from the 52um/88um ratios. The behaviour of T's obtained making use of the T-insensitive IR FS lines provides no support for significant T-fluctuations within the PNe that could be responsible for derived Balmer jump T's being lower than those obtained from the much more T-sensitive [OIII] optical lines.Comment: 36 pages; 3 figures; to be published in MNRA

Spectral statistics of random geometric graphs

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the spectrum via the nearest neighbour and next nearest neighbour spacing distribution and long range correlations via the spectral rigidity Delta_3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdos-Renyi, Barabasi-Albert and Watts-Strogatz random graph.Comment: 19 pages, 6 figures. Substantially updated from previous versio

Dust Formation and He II 4686 emission in the Dense Shell of the Peculiar Type Ib Supernova 2006jc

We present evidence for the formation of dust grains in an unusual Type Ib SN based on late-time spectra of SN 2006jc. The progenitor suffered an LBV-like outburst just 2 yr earlier, and we propose that the dust formation is a consequence of the SN blast wave overtaking that LBV-like shell. The key evidence for dust formation is (a) the appearance of a red/near-IR continuum source fit by 1600 K graphite grains, and (b) fading of the redshifted sides of He I emission lines, yielding progressively more asymmetric blueshifted lines as dust obscures receding material. This provides the strongest case yet for dust formation in any SN Ib/c. Both developments occurred between 51 and 75 d after peak, while other SNe observed to form dust did so after a few hundred days. Geometric considerations indicate that dust formed in the dense swept-up shell between the forward and reverse shocks, and not in the freely expanding SN ejecta. Rapid cooling leading to dust formation may have been aided by extremely high shell densities, as indicated by He I line ratios. The brief epoch of dust formation is accompanied by He II 4686 emission and enhanced X-ray emission. These clues suggest that the unusual dust formation in this object was not due to properties of the SN itself, but instead -- like most peculiarities of SN 2006jc -- was a consequence of the dense environment created by an LBV-like eruption 2 yr before the SN.Comment: ApJ, accepted. added some discussion and 2 figures, better title, conclusions same as previous version. 12 pages, 4 color fig

Dynamics and Excitation of Radio Galaxy Emission-Line Regions - I. PKS 2356-61

Results are presented from a programme of detailed longslit spectroscopic observations of the extended emission-line region (EELR) associated with the powerful radio galaxy PKS 2356-61. The observations have been used to construct spectroscopic datacubes, which yield detailed information on the spatial variations of emission-line ratios across the EELR, together with its kinematic structure. We present an extensive comparison between the data and results obtained from the MAPPINGS II shock ionization code, and show that the physical properties of the line-emitting gas, including its ionization, excitation, dynamics and overall energy budget, are entirely consistent with a scenario involving auto-ionizing shocks as the dominant ionization mechanism. This has the advantage of accounting for the observed EELR properties by means of a single physical process, thereby requiring less free parameters than the alternative scheme involving photoionization by radiation from the active nucleus. Finally, possible mechanisms of shock formation are considered in the context of the dynamics and origin of the gas, specifically scenarios involving infall or accretion of gas during an interaction between the host radio galaxy and a companion galaxy.Comment: 35 pages, LaTeX, uses aas2pp4.sty file, includes 9 PostScript figures. Two additional colour plates are available from the authors upon request. Accepted for publication in the Astrophysical Journa