NEAT (Nebular Empirical Analysis Tool): robust uncertainties on nebular abundance estimatesR. Wesson1, D. Stock1,2, P. Scicluna1

1Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom

2Department of Physics and Astronomy, University of Western Ontario, London, Ontario N6A 3K7, Canada

AbstractCalculations of the chemical abundances in photoionised nebulae rely either on the construction of a realistic physical model and the comparison of the predicted spectrum with observed, or the application of a numberof simplifying assumptions to derive the abundances from observed emission line ratios. In practice, the second method is far less time consuming and therefore more often used. However, the systematic and statisticaluncertainties in this approach are often difficult to quantify.We have developed a code to calculate the physical conditions and chemical abundances from observed emission line fluxes, from both collisionally excited lined and the much fainter recombination lines. Our codecalculates meaningful uncertainties using a Monte Carlo technique. We use the code to assess the magnitudes of both statistical and systematic uncertainties.

The codeThe code requires as input a list of rest wavelengths, line fluxes, and uncertainties on the fluxes. For eachline, it then takes a random number from a Gaussian distribution with a mean of the quoted intensityand a standard deviation of the quoted uncertainty. Then, using this randomised line list, it calculates thelogarithmic extinction at Hβ, c(Hβ), and temperatures and densities from standard collisionally excitedline (CEL) diagnostic ratios. Ionic abundances are then calculated using a three zone model in which thenebula is divided into low, medium and high ionization zones. Heavy element abundances are calculatedboth from CELs and from recombination lines (RLs).By carrying out this process many times, it is possible to build up an accurate picture of the true distribu-tion of statistical uncertainties on chemical abundances resulting from the line flux uncertainties.

UncertaintiesUncertainty propagation is commonly carried out by means of simple analytic formulae, based on partialdifferential equations and truncated series expansions. These implicitly assume that the input uncertaintiesare normally distributed, and that the magnitude of the uncertainty is small compared to the magnitudeof the quantity. These assumptions may be commonly violated in real observations, particularly in spectrawith low signal-to-noise. Thus, the analytic approach breaks down and the estimated uncertainties will beunreliable.The Monte Carlo method avoids these pitfalls and when the code is run with sufficient iterations, theresults can well sample the true uncertainty distribution in the calculated variables at each stage of theprocess. Error propagation in this way is very simple and very reliable. We find that 10,000 iterations aregenerally sufficient to well sample the true probability distributions.

Systematic uncertainties: atomic dataWe use the code to investigate the magnitude of systematic uncertainties which may afflict nebular abun-dance determinations. One major possible source of systematic uncertainties is the atomic data which isnecessary for all of the calculations. Systematic uncertainties in atomic data can be very difficult to quan-tify and their corresponding effect on nebular abundance determinations can be large but unknown. Bydetermining nebular abundances using three different compilations of atomic data, we can estimate thepossible magnitudes of these uncertainties.The figures below show the results of a reanalysis of observations of NGC 6543 originally presented byWesson & Liu (2004, MNRAS, 351, 1026). We analyse the data using three different compilations of atomicdata: a "home made" set compiled from various results in the literature, the CHIANTI 5.2 database, andthe CHIANTI 6 database.

A documented error in the data used by CHIANTI for O+ (see Kisielius et al., 2009, MNRAS, 397, 903)has a significant effect on some derived quantities, compared to the analysis using the "home made" setof atomic data. The systematic uncertainty is comparable to or larger than the statistical uncertainties forsome derived temperatures, densities and abundances. The O/H abundance is largely robust against thisparticular error, but N/H and Ne/H abundances are (statistically) significantly overestimated due to theerror. Other undocumented systematic uncertainties could of course exist.

Statistical uncertaintiesApplying the code to spectra with low signal to noise demonstrates the shortcomings of approximation-based uncertainty propagation. The figures below show the results of analysis of spectra of the nebulasurrounding the LMC Wolf-Rayet star BAT99-2 (Stock, Barlow & Wesson, MNRAS, submitted). Probabilitydistributions emerge for the neon ICF (left) and Ne/H abundance (right), among others, which are double-peaked, when line flux uncertainties lead to different ionisation correction schemes being used dependingon the exact line fluxes adopted. The significant probability of a lower abundance of Neon shown herecannot be recovered by approximation-based uncertainty propagation.

DevelopmentThe current alpha version of NEAT is available by request from rwesson@star.ucl.ac.uk, and a beta releaseis planned soon. Future developments will include the inclusion of more interstellar extinction laws, ion-isation correction schemes, and routines to account for the known upward bias of line flux measurementsat low SNR. All bug reports and development requests will be gratefully received.

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