Geometry of integrable dynamical systems on 2-dimensional surfaces

This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous invariants involved in this classification are the left equivalence classes of period or monodromy functions, and the cohomology classes of period cocycles, which can be expressed in terms of Puiseux series. We also study the problem of Hamiltonianization of these integrable vector fields by a compatible symplectic or Poisson structure.Comment: 31 pages, 12 figures, submitted to a special issue of Acta Mathematica Vietnamic

Detection and Preliminary Characterisation of Polluted White Dwarfs from Gaia EDR3 and LAMOST

We present a catalogue of 62 polluted white dwarfs observed by the 9th Low-Resolution Data Release of the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST LRS DR9v1; R$\approx$1,800) and the Early Data Release 3 (EDR3) of the Gaia Mission. Among these stellar remnants, 30 are new discoveries with previously unknown traces of calcium pollution. To generate our catalogue, we used a database of 4,324 unique Gaia EDR3 white dwarf candidates with LAMOST LRS DR9v1 observations, many of which have been spectroscopically confirmed by other telescopes. For these stars, we developed a quantitative method to detect calcium absorption in their spectra between 3,900-4,000$\mathring {\mathrm A}$, which we then validated through visual inspection and multiple literature cross-checks. Our catalogue provides the astrometric and photometric properties of the white dwarf candidates, incorporates supplementary data (e.g. Montreal White Dwarf Database, MWDD; PanSTARRS; the Hubble Space Telescope), and indicates the possibility of calcium pollution in their atmospheres. For our final sample of polluted white dwarfs, we also determine the main atmospheric properties of 23 sources with effective temperatures $T_{\rm eff}$$\leq$25,000K and no existing calcium abundances in the MWDD. Our analysis represents a first step towards measuring the full atmospheric composition of these stars and learning about the bulk properties of their accreted material. As we venture into the era of wide-field spectroscopic surveys, our work highlights the importance of combining large-scale databases for identifying and characterising new polluted white dwarfs.Comment: 29 pages, 14 figures (+3 in the Appendix), 5 tables (+5 in the Appendix). Accepted for publication in MNRA

Energy deposition by heavy ions: Additivity of kinetic and potential energy contributions in hillock formation on CaF2

The formation of nano-hillocks on CaF2 crystal surfaces by individual ion impact has been studied using medium energy (3 and 5 MeV) highly charged ions (Xe19+ to Xe30+) as well as swift (kinetic energies between 12 and 58 MeV) heavy ions. For very slow highly charged ions the appearance of hillocks is known to be linked to a threshold in potential energy while for swift heavy ions a minimum electronic energy loss is necessary. With our results we bridge the gap between these two extreme cases and demonstrate, that with increasing energy deposition via electronic energy loss the potential energy threshold for hillock production can be substantially lowered. Surprisingly, both mechanisms of energy deposition in the target surface seem to contribute in an additive way, as demonstrated when plotting the results in a phase diagram. We show that the inelastic thermal spike model, originally developed to describe such material modifications for swift heavy ions, can be extended to case where kinetic and potential energies are deposited into the surface.Comment: 12 pages, 4 figure

Temperature Variations from \u3cem\u3eHubble Space Telescope\u3c/em\u3e Spectroscopy of the Orion Nebula

We present Hubble Space Telescope (HST)/STIS long-slit spectroscopy of NGC 1976. Our goal is to measure the intrinsic line ratio [O III] 4364/5008 and thereby evaluate the electron temperature (Te) and the fractional mean-square Te variation (t2A)across the nebula. We also measure the intrinsic line ratio [N II] 5756/6585 in order to estimate Te and t2A in the N+region. The interpretation of the [N II] data is not as clear cut as the [O III] data because of a higher sensitivity to knowledge of the electron density as well as a possible contribution to the [N II] 5756 emission by recombination (and cascading). We present results from binning the data along the various slits into tiles that are 0.5 arcsec square (matching the slit width). The average [O III] temperature for our four HST/STIS slits varies from 7678 K to 8358 K; t2A varies from 0.00682 to at most 0.0176. For our preferred solution, the average [N II] temperature for each of the four slits varies from 9133 to 10 232 K; t2A varies from 0.00584 to 0.0175. The measurements of Te reported here are an average along each line of sight. Therefore, despite finding remarkably low t2A, we cannot rule out significantly larger temperature fluctuations along the line of sight. The result that the average [N II]Te exceeds the average [O III]Te confirms what has been previously found for Orion and what is expected on theoretical grounds. Observations of the proplyd P159-350 indicate: large local extinction associated; ionization stratification consistent with external ionization by θ1 Ori C; and indirectly, evidence of high electron density

Infrared optical properties of Pr2CuO4

The ab-plane reflectance of a Pr2CuO4 single crystal has been measured over a wide frequency range at a variety of temperatures, and the optical properties determined from a Kramers-Kronig analysis. Above ~ 250 K, the low frequency conductivity increases quickly with temperature; the resistivity follows the form e^(E_a/k_BT), where E_a ~ 0.17 eV is much less than the inferred optical gap of ~ 1.2 eV. Transport measurements show that at low temperature the resistivity deviates from activated behavior and follows the form e^[(T_0/T)^1/4], indicating that the dc transport in this material is due to variable-range hopping between localized states in the gap. The four infrared-active Eu modes dominate the infrared optical properties. Below ~ 200 K, a striking new feature appears near the low-frequency Eu mode, and there is additional new fine structure at high frequency. A normal coordinate analysis has been performed and the detailed nature of the zone-center vibrations determined. Only the low-frequency Eu mode has a significant Pr-Cu interaction. Several possible mechanisms related to the antiferromagnetism in this material are proposed to explain the sudden appearance of this and other new spectral features at low temperature.Comment: 11 pages, 7 embedded EPS figures, REVTeX

Assessing rotation/curvature corrections to eddy-viscosity models in the calculations of centrifugal-compressor flows

Rotation and curvature (RC) effects on turbulence are expected to impact losses and flow structure in turbomachines. This paper examines two recent eddy-viscosity-model corrections devised to account for these effects: the Spalart and Shur (1997, "On the Sensitization of Turbulence Models to Rotation and Curvature," Aerosp. Sci. Technol., 1(5), pp. 297–302) correction to the model of Spalart and Allmaras (1994, "A One-Equation Turbulence Model for Aerodynamic Flows," Rech. Aerosp., 1, pp. 5–21) and the correction of Cazalbou et al. (2005, "Two-Equation Modeling of Turbulent Rotating Flows," Phys. Fluids., 17, p. 055110) to the (k,epsilon) model. The method of verification and validation is applied to assess the impact of these corrections on the computation of a centrifugal-compressor test case. First, a review of RC effects on turbulence as they apply to centrifugal compressors is made. The two corrected models are then presented. Second,the Radiver open test case (Ziegler K. U., Gallus, H. E., and Niehuis R., 2003, "A Study on Impeller Diffuser Interaction Part 1: Influence on the Performance," ASME J. Turbomach, 125, pp. 173–182) is used as a basis for the assessment of the two corrections. After a physical-consistency analysis, the Richardson extrapolation is applied to quantify the numerical errors involved in all the calculations. Finally, experimental data are used to perform validation for both global and local predictions. The consistency analysis shows that both corrections lead to significant changes in the turbulent field, in perfect agreement with the underlying theoretical considerations. The uncertainty analysis shows that the predictions of the global performances are more sensitive to grid refinement than they are to RC turbulence modeling. However, the opposite conclusion is drawn with regard to the prediction of some local flow properties: Improvements are obtained with the RC corrections, the best results being observed for the RC-corrected (k,epsilon) model

Heavy elements in Galactic and Magellanic Cloud HII regions: recombination-line versus forbidden-line abundances

We have obtained deep optical, long-slit spectrophotometry of the Galactic HII regions M 17, NGC 3576 and of the Magellanic Cloud HII regions 30 Doradus, LMC N11B and SMC N66, recording the optical recombination lines (ORLs) of CII, NII and OII. Temperature-insensitive ORL C2+/O2+ and N2+/O2 ratios are obtained for all nebulae except SMC N66. The ORL C2+/O2+ ratios show remarkable agreement within each galactic system, while also being in agreement with the corresponding CEL ratios. For all five nebulae, the O2+/H+ abundance derived from multiple OII ORLs is found to be higher than the corresponding value derived from the strong [OIII] 4959, 5007A CELs, by factors of 1.8--2.7 for four of the nebulae. The LMC N11B nebula exhibits a more extreme discrepancy factor for the O2+ ion, ~5. Thus these HII regions exhibit ORL/CEL abundance discrepancy factors that are similar to those previously encountered amongst planetary nebulae. Our optical CEL O2+/H+ abundances agree to within 20-30 per cent with published O2+/H+ abundances that were obtained from observations of infrared fine-structure lines. Since the low excitation energies of the latter make them insensitive to variations about typical nebular temperatures, fluctuations in temperature are ruled out as the cause of the observed ORL/CEL O2+ abundance discrepancies. We present evidence that the observed OII ORLs from these HII regions originate from gas of very similar density (<3500 cm-3) to that emitting the observed heavy-element optical and infrared CELs, ruling out models that employ high-density ionized inclusions in order to explain the abundance discrepancy. We consider a scenario whereby much of the heavy-element ORL emission originates from cold (<=500 K) metal-rich ionized regions.Comment: 24 pages; 9 figures; accepted by Monthly Notices of the Royal Astronomical Societ

Temperature Variations from HST Imagery and Spectroscopy of NGC 7009

We present new HST/WFPC2 imagery and STIS long-slit spectroscopy of the planetary nebula NGC 7009. The primary goal was to obtain high spatial resolution of the intrinsic line ratio [O III] 4364/5008 and thereby evaluate the electron temperature (T_e) and the fractional mean-square T_e variation (t_A^2) across the nebula. The WFPC2 T_e map is rather uniform; almost all values are between 9000 - 11,000 K, with the higher T_e's closely coinciding with the inner He^++-zone. The results indicate very small values - <~ 0.01 - for t_A^2 throughout. Our STIS data allow an even more direct determination of T_e and t_A^2, albeit for a much smaller area than with WFPC2. We present results from binning the data along the slit into tiles that are 0.5'' square (matching the slit width). The average [O III] temperature using 45 tiles (excluding the central star and STIS fiducial bars) is 10,139 K; t_A^2 is 0.0035. The measurements of T_e reported here are an average along each line of sight. Therefore, despite finding remarkably low t_A^2, we cannot completely rule out temperature fluctuations along the line of sight as the cause of the large abundance discrepancy between heavy element abundances inferred from collisionally excited emission lines compared to those derived from recombination lines.Comment: MNRAS accepted: 26 pages, 4 Figures, 1 Tabl

[Fe III] emission lines in the planetary nebula NGC 2392

NGC 2392 is a young double-shell planetary nebula (PN). Its intrinsic structure and shaping mechanism are still not fully understood. In this paper we present new spectroscopic observations of NGC 2392. The slits were placed at two different locations to obtain the spectra of the inner and outer regions. Several [Fe III] lines are clearly detected in the inner region. We infer that NGC 2392 might have an intrinsic structure similar to the bipolar nebula Mz 3, which also exhibits a number of [Fe III}] lines arising from the central regions. In this scenario, the inner and outer regions of NGC 2392 correspond to the inner lobes and the outer outflows of Mz 3, respectively. We construct a three-dimensional morpho-kinematic model to examine our hypothesis. We also compare the physical conditions and chemical composition of the inner and outer regions, and discuss the implications on the formation of this type of PN.Comment: 41 pages, 13 figures, Accepted for publication in Ap