Three-Dimensional Ionisation, Dust RT and Chemical Modelling of Planetary Nebulae

The assumption of spherical symmetry is not justified for the vast majority of PNe. The interpretation of spatially-resolved observations cannot rely solely on the application of 1D codes, which may yield incorrect abundances determinations resulting in misleading conclusions. The 3D photoionisation code MOCASSIN (Monte CAarlo SimulationS of ionised Nebulae) is designed to remedy these shortcomings. The 3D transfer of both primary and secondary radiation is treated self-consistently without the need of approximations. The code was benchmarked and has been applied to the study of several PNe. The current version includes a fully self-consistent radiative transfer treatment for dust grains mixed within the gas, taking into account the microphysics of dust-gas interactions within the geometry-independent Monte Carlo transfer. The new code provides an excellent tool for the self-consistent analysis of dusty ionised regions showing asymmetries and/or density and chemical inhomogeneities. Work is currently in progress to incorporate the processes that dominate the thermal balance of photo-dissociation regions (PDRs), as well as the formation and destruction processes for all the main molecular species.Comment: 3 pages, to appear in Proc. IAU Symp. 234, Planetary Nebulae in Our Galaxy and Beyond (3-7 Apr 2006), eds. M.J. Barlow & R.H. Mendez (Cambridge Univ. Press

A study of the drooped leading edge airfoil

Wind tunnel tests were conducted to examine various aspects of the drooped-leading edge airfoil which reduces the tendency for an airplane to enter a spin after stall occurs. Three baseline models were used for tests of two dimensional models: NACA 0015, 0014.6, and 0014.2. The 14.6% and 14.2% models were derived from NACA 0015 sections by increasing the chord and matching the profiles aft section. Force, balance data (lift, drag, pitching moment) were obtained for each model at a free-steam Reynold's number of 2.66 x 10 to the 6th power/m. In addition, oil flow visualization tests were performed at various angles of attack. An existing NACA 64 sub 1 A211 airfoil was used in a second series of tests. The leading edge flap was segmented in three parts which allowed various baseline/drooped leading edge configurations to be tested. Force balance and flow visualization tests were completer at chord Renolds numbers of 0.44 x 10 to the 6th power, 1.4 x 10 to the 6th power, and 2.11 x 10 to the 6th power. Test results are included

3D Photoionisation Modelling of NGC 6302

We present a three-dimensional photoionisation and dust radiative transfer model of NGC 6302, an extreme, high-excitation planetary nebula. We use the 3D photoionisation code Mocassin} to model the emission from the gas and dust. We have produced a good fit to the optical emission-line spectrum, from which we derived a density distribution for the nebula. A fit to the infrared coronal lines places strong constraints on the properties of the unseen ionising source. We find the best fit comes from using a 220,000 K hydrogen-deficient central star model atmosphere, indicating that the central star of this PN may have undergone a late thermal pulse. We have also fitted the overall shape of the ISO spectrum of NGC 6302 using a dust model with a shallow power-law size distribution and grains up to 1.0 micron in size. To obtain a good fit to the infrared SED the dust must be sufficiently recessed within the circumstellar disk to prevent large amounts of hot dust at short wavelengths, a region where the ISO spectrum is particularly lacking. These and other discoveries are helping to unveil many properties of this extreme object and trace it's evolutionary history.Comment: 8 pages, 4 figures; for the proceedings of "Asymmetric Planetary Nebuale IV," R. L. M. Corradi, A. Manchado, N. Soker ed

Dust yields in clumpy SN shells: SN 1987A revisited

We present a study of the effects of clumping on the emergent spectral energy distribution (SED) from dusty supernova (SN) shells illuminated by a diffuse radiation source distributed throughout the medium. (...) The fully 3D radiation transport problem is solved using a Monte Carlo code, MOCASSIN, and we present a set of models aimed at investigating the sensitivity of the SEDs to various clumping parameters. We find that, contrary to the predictions of analytical prescriptions, the combination of an optical and IR observational data set is sufficient to constrain dust masses even in the case where optically thick clumps are present. Using both smoothly varying and clumped grain density distributions, we obtain new estimates for the mass of dust condensed by the Type II SN 1987A by fitting the optical and infrared spectrophotometric data of Wooden et al. (1993) at two epochs (day 615 and day 775). (...) From our numerical models we derive dust masses for SN 1987A that are comparable to previous analytic clumped graphite grain mass estimates, and at least two orders of magnitude below the 0.1-0.3 Msol that have been predicted to condense as dust grains in primordial core collapse supernova ejecta. This low condensation efficiency for SN 1987A is in contrast to the case of SN 2003gd, for which a dust condensation efficiency as large as 0.12 has recently been estimated. (Abridged)Comment: accepted for publication in MNRAS. The paper contains 15 figures and 1 tabl

The timing and location of dust formation in the remnant of SN 1987A

The discovery with the {\it Herschel Space Observatory} of bright far infrared and submm emission from the ejecta of the core collapse supernova SN\,1987A has been interpreted as indicating the presence of some 0.4--0.7\,M$_\odot$ of dust. We have constructed radiative transfer models of the ejecta to fit optical to far-infrared observations from the literature at epochs between 615 days and 24 years after the explosion, to determine when and where this unexpectedly large amount of dust formed. We find that the observations by day 1153 are consistent with the presence of 3$\times$10$^{-3}$M$_\odot$ of dust. Although this is a larger amount than has previously been considered possible at this epoch, it is still very small compared to the amount present in the remnant after 24 years, and significantly higher dust masses at the earlier epochs are firmly ruled out by the observations, indicating that the majority of the dust must have formed at very late times. By 8515-9200 days after the explosion, 0.6--0.8\,M$_\odot$ of dust is present, and dust grains with radii greater than 2\,$\mu$m are required to obtain a fit to the observed SED. This suggests that the dust mass increase at late times was caused by accretion onto and coagulation of the dust grains formed at earlier epochs. These findings provide further confirmation that core collapse supernovae can create large quantities of dust, and indicate that the reason for small dust masses being estimated in many cases is that the vast majority of the dust forms long after most supernovae have been detectable at mid-infrared wavelengths.Comment: 13 pages, 16 figures. Accepted for publication in MNRA

Mocassin: A fully three-dimensional Monte Carlo photoionization code

The study of photoionized environments is fundamental to many astrophysical problems. Up to the present most photoionization codes have numerically solved the equations of radiative transfer by making the extreme simplifying assumption of spherical symmetry. Unfortunately very few real astronomical nebulae satisfy this requirement. To remedy these shortcomings, a self-consistent, three-dimensional radiative transfer code has been developed using Monte Carlo techniques. The code, Mocassin, is designed to build realistic models of photoionized nebulae having arbitraries geometry and density distributions with both the stellar and diffuse radiation fields treated self-consistently. In addition, the code is capable of tretating on or more exciting stars located at non-central locations. The gaseous region is approximated by a cuboidal Cartesian grid composed of numerous cells. The physical conditions within each grid cell are determined by solving the thermal equilibrium and ionization balance equations This requires a knowledge of the local primary and secondary radiation fields, which are calculated self-consistently by locally simulating the individual processes of ionization and recombination. The main structure and computational methods used in the Mocassin code are described in this paper. Mocassin has been benchmarked against established one-dimensional spherically symmetric codes for a number of standard cases, as defined by the Lexington/Meudon photoionization workshops (Pequignot et al., 1986; Ferland et al., 1995; Pequignot et al., 2001)\citep{pequignot86,ferland95, pequignot01}. The results obtained for the benchmark cases are satisfactory and are presented in this paper. A performance analysis has also been carried out and is discussed here.Comment: 17 pages, 4 figures, 1 appendix Changes: appendix adde

New accurate measurement of 36ArH+ and 38ArH+ ro-vibrational transitions by high resolution IR absorption spectroscopy

The protonated Argon ion, $^{36}$ArH$^{+}$, has been identified recently in the Crab Nebula (Barlow et al. 2013) from Herschel spectra. Given the atmospheric opacity at the frequency of its $J$=1-0 and $J$=2-1 rotational transitions (617.5 and 1234.6 GHz, respectively), and the current lack of appropriate space observatories after the recent end of the Herschel mission, future studies on this molecule will rely on mid-infrared observations. We report on accurate wavenumber measurements of $^{36}$ArH$^{+}$ and $^{38}$ArH$^{+}$ rotation-vibration transitions in the $v$=1-0 band in the range 4.1-3.7 $\mu$m (2450-2715 cm$^{-1}$). The wavenumbers of the $R$(0) transitions of the $v$=1-0 band are 2612.50135$\pm$0.00033 and 2610.70177$\pm$0.00042 cm$^{-1}$ ($\pm3\sigma$) for $^{36}$ArH$^{+}$ and $^{38}$ArH$^{+}$, respectively. The calculated opacity for a gas thermalized at a temperature of 100 K and a linewidth of 1 km.s$^{-1}$ of the $R$(0) line is $1.6\times10^{-15}\times N$($^{36}$ArH$^+$). For column densities of $^{36}$ArH$^+$ larger than $1\times 10^{13}$ cm$^{-2}$, significant absorption by the $R$(0) line can be expected against bright mid-IR sources

Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true in the examples that have been analyzed in the existing literature

Materials for Biomedical Applications

This paper discusses two ceramic material systems for selective laser sintering (SLS) that are being developed for biomedical applications for use in repair of bone defects. SLS is the preferred method of fabricating ceramic implants that exhibit well defined porous microstructures. Implants fabricated in this. manner have proven effective in-vivo showing excellent biocompatibility as well as considerable osseous integration and remodeling of the imp'ant materialMechanical Engineerin