P. J. Storey

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 arbitrary geometry and density distributions, with both the stellar and diffuse radiation fields treated self-consistently. In addition, the code is capable of treating one 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 structure and the 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: at Meudon in 1985 and at Lexington in 1995 and 2000. 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.

The dusty mocassin: fully self-consistent 3D photoionization and dust radiative transfer models

We present the first 3D Monte Carlo (MC) photoionization code to include a fully self-consistent treatment of dust radiative transfer (RT) within a photoionized region. This is the latest development (version 2.0) of the gas-only photoionization code MOCASSIN and employs a stochastic approach to the transport of radiation, allowing both the primary and secondary components of the radiation field to be treated self-consistently, whilst accounting for the scattering of radiation by dust grains mixed with the gas, as well as the absorption and emission of radiation by both the gas and the dust components. An escape probability method is implemented for the transfer of resonance lines that may be absorbed by the grains, thus contributing to their energy balance. The energetics of the co-existing dust and gas components must also take into account the effects of dust‐gas collisions and photoelectric emission from the dust grains, which are dependent on the grain charge. These are included in our code using the average grain potential approximation scheme. A set of rigorous benchmark tests have been carried out for dust-only spherically symmetric geometries and 2D disc configurations. The results of MOCASSIN are found to be in agreement with those obtained by well-established dust-only RT codes that employ various approaches to the solution of the RT problem. A model of the dust and of the photoionized gas components of the planetary nebula NGC 3918 is also presented as a means of testing the correct functioning of the RT procedures in a case where both gas and dust opacities are present. The two components are coupled via the heating of dust grains by the absorption of both UV continuum photons and resonance line photons emitted by the gas. The MOCASSIN results show agreement with those of a 1D dust and gas model of this nebula published previously, showing the reliability of the new code, which can be applied to a variety of astrophysical environments. Ke yw ords: radiative transfer ‐ dust, extinction ‐ H II regions ‐ planetary nebulae: general.

Heavy elements in Galactic and Magellanic Cloud H ii 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.

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

In our Paper 1, we presented deep optical observations of the spectra of 12 Galactic planetary nebulae (PNe) and three Magellanic Cloud PNe, carrying out an abundance analysis using the collisionally excited forbidden lines. Here, we analyse the relative intensities of faint optical recombination lines (ORLs) from ions of carbon, nitrogen and oxygen in order to derive the abundances of these ions relative to hydrogen. The relative intensities of four high-l C II recombination lines with respect to the well-known 3d-4f lambda4267 line are found to be in excellent agreement with the predictions of recombination theory, removing uncertainties about whether the high C2+ abundances derived from the lambda4267 line could be due to non-recombination enhancements of its intensity.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 ADFs that exceed unity. Two of the PNe, NGC 2022 and LMC N66, have O2+ ADFs of 16 and 11, respectively, while the remaining 13 PNe have a mean O2+ ADF of 2.6, with the smallest value being 1.8.Garnett and Dinerstein found that for a sample of about 12 PNe the magnitude of the O2+ ADF was inversely correlated with the nebular Balmer line surface brightness. We have investigated this for a larger sample of 20 PNe, finding weak correlations with decreasing surface brightness for the ADFs of O2+ and C2+. The C2+ ADFs are well correlated with the absolute radii of the nebulae, although no correlation is present for the 021 ADFs. We also find both the C2+ and O2+ ADFs to be strongly correlated with the magnitude of the difference between the nebular [O III] and Balmer jump electron temperatures (DeltaT), corroborating a result of Liu et al. for the O2+ ADF. AT is found to be weakly correlated with decreasing nebular surface brightness and increasing absolute nebular radius.There is no dependence of the magnitude of the ADF upon the excitation energy of the ultraviolet, optical or infrared 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, as first postulated by Liu et al. for the high-ADFPN, NGC 6153. We have developed a new electron temperature diagnostic, based upon the relative intensities of the O II 4f-3d lambda4089 and 3p-3s lambda4649 recombination transitions. For six out of eight PNe for which both transitions are detected, we derive O2+ ORL electron temperatures of less than or equal to300 K, very much less than the O2+ forbidden-line and H+ Balmer jump temperatures derived for the same nebulae. These results provide direct observational evidence for the presence of cold plasma regions within the nebulae, consistent with gas cooled largely by infrared fine-structure transitions; at such low temperatures, recombination transition intensities will be significantly enhanced due to their inverse power-law temperature dependence, while ultraviolet and optical CELs will be significantly suppressed.

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

We present deep optical spectrophotometry of 12 Galactic planetary nebulae (PNe) and three Magellanic Cloud PNe. Nine of the Galactic PNe were observed by scanning the slit of the spectrograph across the nebula, yielding relative line intensities for the entire nebula that are suitable for comparison with integrated nebular fluxes measured in other wavelength regions. In this paper we use the fluxes of collisionally excited lines (CELs) from the nebulae to derive electron densities and temperatures, and ionic abundances. We find that the nebular electron densities derived from optical CEL ratios are systematically higher than those derived from the ratios of the infrared (IR) fine-structure (FS) lines of [O III]. The latter have lower critical densities than the typical nebular electron densities derived from optical CELs, indicating the presence of significant density variations within the nebulae, with the IR CELs being biased towards lower density regions. We find that for several nebulae the electron temperatures obtained from [O II] and [N II] optical CELs are significantly affected by recombination excitation of one or more of the CELs. When allowance is made for recombination excitation, much better agreement is obtained with the electron temperatures obtained from optical [O III] lines. We also compare electron temperatures obtained from the ratio of optical nebular to auroral [O III] lines with temperatures obtained from the ratio of [O III] optical lines to [O III] IR FS lines. We find that when the latter are derived using electron densities based on the [O III ]5 2µm/88 µm line ratio, they yield values that are significantly higher than the optical [O III] electron temperatures. In contrast to this, [O III] optical/IR temperatures derived using the higher electron densities obtained from optical [Cl III] λ5517/λ5537 ratios show much closer agreement with optical [O III] electron temperatures, implying that the observed [O III] optical/IR ratios are significantly weighted by densities in excess of the critical densities of both [O III] FS lines. Consistent with this, ionic abundances derived from [O III] and [N III] FS lines using electron densities from optical CELs show much better agreement with abundances derived for the same ions from optical and ultraviolet CELs than do abundances derived from the FS lines using the lower electron densities obtained from the observed [O III ]5 2µm/88 µm ratios. The behaviour of these electron temperatures, obtained making use of the temperatureinsensitive [O III] IR FS lines, provides no support for significant temperature fluctuations within the nebulae being responsible for derived Balmer jump electron temperatures that are lower than temperatures obtained from the much more temperature sensitive [O III] optical lines.

Chemical abundances for Hf 2-2, a planetary nebula with the strongest-known heavy-element recombination lines

We present high-quality optical spectroscopic observations of the planetary nebula (PN) Hf 2-2. The spectrum exhibits many prominent optical recombination lines (ORLs) from heavy-element ions. Analysis of the H i and He i recombination spectrum yields an electron temperature of ∼900 K, a factor of 10 lower than given by the collisionally excited [O iii] forbidden lines. The ionic abundances of heavy elements relative to hydrogen derived from ORLs are about a factor of 70 higher than those deduced from collisionally excited lines (CELs) from the same ions, the largest abundance discrepancy factor (adf) ever measured for a PN. By comparing the observed O iiλ4089/λ4649 ORL ratio to theoretical value as a function of electron temperature, we show that the O ii ORLs arise from ionized regions with an electron temperature of only ∼630 K. The current observations thus provide the strongest evidence that the nebula contains another previously unknown component of cold, high-metallicity gas, which is too cool to excite any significant optical or ultraviolet CELs and is thus invisible via such lines. The existence of such a plasma component in PNe provides a natural solution to the long-standing dichotomy between nebular plasma diagnostics and abundance determinations using CELs on the one hand and ORLs on the other.

Fast computer evaluation of radiative properties of hydrogenic systems

Abstract Three subroutines are described for the very fast calculation of bound-bound, bound-free, and free-free cross-sections for nonrelativistic hydrogenic systems of arbitrary nuclear charge and reduced mass. The first two are essentially exact, being based on recursion relations which are known to be stable. The third evaluates the thermally-averaged free-free Gaunt factor by means of a two-dimensional Chebyshev expansion calculated by numerical evaluation of the cross-sections expressed as hypergeometric functions, augmented by other analytical approximations.

Electron temperatures and densities of planetary nebulae determined from the nebular hydrogen recombination spectrum and temperature and density variations

A method is presented to derive electron temperatures and densities of planetary nebulae (PNe) simultaneously, using the observed hydrogen recombination spectrum, which includes continuum and line emission. By matching theoretical spectra to observed spectra around the Balmer jump at about 3646 A, we determine electron temperatures and densities for 48 Galactic PNe. The electron temperatures based on this method - hereafter T e (Bal)- are found to be systematically lower than those derived from [O III] λ4959/λ4363 and [O III] (88 μm + 52 μm)/λ4959 ratios- hereafter T e ([O III] na ) and T e ([O III] fn ). The electron densities based on this method are found to be systematically higher than those derived from [O II] λ3729/λ3726, [S II] λ6731/λ6716, [Cl III] λ5537/λ5517, [ArIV] λ4740/λ4711 and [O III] 88 μm/52 μm ratios. These results suggest that temperature and density fluctuations are generally present within nebulae. The comparison of T e ([O III] na ) and T e (Bal) suggests that the fractional mean-square temperature variation (t 2 ) has a representative value of 0.031. A majority of temperatures derived from the T e ([O III] fn ) ratio are found to be higher than those of T e ([O III] na ), which is attributed to the existence of dense clumps in nebulae - those [O III] infrared fine-structure lines are suppressed by collisional de-excitation in the clumps. By comparing T e ([O III] fn ), T e ([O III] na ) and T e (Bal) and assuming a simple two-density-component model, we find that the filling factor of dense clumps has a representative value of 7 x 10 -5 . The discrepancies between T e ([O III] na ) and T e (Bal) are found to be anticorrelated with electron densities derived from various density indicators; high-density nebulae have the smallest temperature discrepancies. This suggests that temperature discrepancy is related to nebular evolution. In addition, He/H abundances of PNe are found to be positively correlated with the difference between T e ([O III] na ) and T e (Bal), suggesting that He/H abundances might have been overestimated generally because of the possible existence of H-deficient knots. Electron temperatures and densities deduced from spectra around the Paschen jump regions at 8250 A are also obtained for four PNe: NGC 7027, NGC 6153, M 1-42 and NGC 7009. Electron densities derived from spectra around the Paschen jump regions are in good agreement with the corresponding values derived from spectra around the Balmer jump, whereas temperatures deduced from the spectra around the Paschen jump are found to be lower than the corresponding values derived from spectra around the Balmer jump for all the four cases. The reason remains unclear.

Theoretical calculations of the H I, He I and He II free-bound continuous emission spectra

We present coefficients for the calculation of the continuous emission spectra of H I, He I and He ii due to electron-ion recombination. Coefficients are given for photon energies from the first ionization threshold for each ion to the n = 20 threshold of hydrogen (36.5 μm), and for temperatures 100 ≤ T < 10 5 K. The emission coefficients for He I are derived from accurate ab initio photoionization data. The coefficients are scaled in such a way that they may be interpolated by a simple scheme with uncertainties less than 1 per cent in the whole temperature and wavelength domain. The data are suitable for incorporation into photoionization/plasma codes and should aid with the interpretation of spectra from the very cold ionized gas phase inferred to exist in a number of gaseous clouds.

Improved He I emissivities in the case B approximation

We update our prior work on the case B collisional-recombination spectrum of He I to incorporate ab initio photoionization cross-sections. This large set of accurate, self-consistent cross-sections represents a significant improvement in He I emissivity calculations because it largely obviates the piecemeal nature that has marked all modern works. A second, more recent set of ab initio cross-sections is also available, but we show that those are less consistent with bound–bound transition probabilities than our adopted set. We compare our new effective recombination coefficients with our prior work and our new emissivities with those by other researchers, and we conclude with brief remarks on the effects of the present work on the He I error budget. Our calculations cover temperatures 5000 ≤ Te ≤ 25 000 K and densities 10 1 ≤ ne ≤ 10 14 cm −3 . Full results are available online (see Supporting Information).