Poster presented by R. Wesson, D. Stock, P. Scicluna at the IAU Symposium 283, Planetary Nebulae: an Eye to the Future, 25-29 July 2011, Tenerife, Spain.

1. NEAT (Nebular Empirical Analysis Tool): robust uncertainties on nebular abundance estimates
1 1,2 1
R. Wesson , D. Stock , P. Scicluna
1 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
2 Department of Physics and Astronomy, University of Western Ontario, London, Ontario N6A 3K7, Canada
Abstract
Calculations 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 number
of 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 statistical
uncertainties 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 code
calculates meaningful uncertainties using a Monte Carlo technique. We use the code to assess the magnitudes of both statistical and systematic uncertainties.
The code Uncertainties
The code requires as input a list of rest wavelengths, line fluxes, and uncertainties on the fluxes. For each Uncertainty propagation is commonly carried out by means of simple analytic formulae, based on partial
line, it then takes a random number from a Gaussian distribution with a mean of the quoted intensity differential equations and truncated series expansions. These implicitly assume that the input uncertainties
and a standard deviation of the quoted uncertainty. Then, using this randomised line list, it calculates the are normally distributed, and that the magnitude of the uncertainty is small compared to the magnitude
logarithmic extinction at Hβ, c(Hβ), and temperatures and densities from standard collisionally excited of the quantity. These assumptions may be commonly violated in real observations, particularly in spectra
line (CEL) diagnostic ratios. Ionic abundances are then calculated using a three zone model in which the with low signal-to-noise. Thus, the analytic approach breaks down and the estimated uncertainties will be
nebula is divided into low, medium and high ionization zones. Heavy element abundances are calculated unreliable.
both from CELs and from recombination lines (RLs). The Monte Carlo method avoids these pitfalls and when the code is run with sufficient iterations, the
By carrying out this process many times, it is possible to build up an accurate picture of the true distribu- results can well sample the true uncertainty distribution in the calculated variables at each stage of the
tion of statistical uncertainties on chemical abundances resulting from the line flux uncertainties. process. Error propagation in this way is very simple and very reliable. We find that 10,000 iterations are
generally sufficient to well sample the true probability distributions.
Statistical uncertainties
Applying the code to spectra with low signal to noise demonstrates the shortcomings of approximation-
Systematic uncertainties: atomic data
based uncertainty propagation. The figures below show the results of analysis of spectra of the nebula We use the code to investigate the magnitude of systematic uncertainties which may afflict nebular abun-
surrounding the LMC Wolf-Rayet star BAT99-2 (Stock, Barlow & Wesson, MNRAS, submitted). Probability dance determinations. One major possible source of systematic uncertainties is the atomic data which is
distributions emerge for the neon ICF (left) and Ne/H abundance (right), among others, which are double- necessary for all of the calculations. Systematic uncertainties in atomic data can be very difficult to quan-
peaked, when line flux uncertainties lead to different ionisation correction schemes being used depending tify and their corresponding effect on nebular abundance determinations can be large but unknown. By
on the exact line fluxes adopted. The significant probability of a lower abundance of Neon shown here determining nebular abundances using three different compilations of atomic data, we can estimate the
cannot be recovered by approximation-based uncertainty propagation. possible magnitudes of these uncertainties.
The figures below show the results of a reanalysis of observations of NGC 6543 originally presented by
Wesson & Liu (2004, MNRAS, 351, 1026). We analyse the data using three different compilations of atomic
data: a "home made" set compiled from various results in the literature, the CHIANTI 5.2 database, and
the CHIANTI 6 database.
Development A documented error in the data used by CHIANTI for O+ (see Kisielius et al., 2009, MNRAS, 397, 903)
The current alpha version of NEAT is available by request from rwesson@star.ucl.ac.uk, and a beta release has a significant effect on some derived quantities, compared to the analysis using the "home made" set
is planned soon. Future developments will include the inclusion of more interstellar extinction laws, ion- of atomic data. The systematic uncertainty is comparable to or larger than the statistical uncertainties for
isation correction schemes, and routines to account for the known upward bias of line flux measurements some derived temperatures, densities and abundances. The O/H abundance is largely robust against this
at low SNR. All bug reports and development requests will be gratefully received. particular error, but N/H and Ne/H abundances are (statistically) significantly overestimated due to the
error. Other undocumented systematic uncertainties could of course exist.