Independent Emission and Absorption Abundances for Planetary Nebulae
Robert Williams, Edward B. Jenkins, Jack A. Baldwin, Yong Zhang, Brian Sharpee, Eric Pellegrini, Mark Phillips
aa r X i v : . [ a s t r o - ph ] J a n The Astrophysical Journal, in press, vol. 677, No. 2 (20 April 2008)
Preprint typeset using L A TEX style emulateapj v. 12/01/06
INDEPENDENT EMISSION AND ABSORPTION ABUNDANCES FOR PLANETARY NEBULAE ∗ Robert Williams , Edward B. Jenkins , Jack A. Baldwin , Yong Zhang , Brian Sharpee , Eric Pellegrini , andMark Phillips The Astrophysical Journal, in press, vol. 677, No. 2 (20 April 2008)
ABSTRACTEmission-line abundances have been uncertain for more than a decade due to unexplained discrep-ancies in the relative intensities of the forbidden lines and weak permitted recombination lines inplanetary nebulae (PNe) and H II regions. The observed intensities of forbidden and recombinationlines originating from the same parent ion differ from their theoretical values by factors of more thanan order of magnitude in some of these nebulae. In this study we observe UV resonance line ab-sorption in the central stars of PNe produced by the nebular gas, and from the same ions that emitoptical forbidden lines. We then compare the derived absorption column densities with the emissionmeasures determined from ground-based observations of the nebular forbidden lines. We find for oursample of PNe that the collisionally excited forbidden lines yield column densities that are in basicagreement with the column densities derived for the same ions from the UV absorption lines. A similarcomparison involving recombination line column densities produces poorer agreement, although nearthe limits of the formal uncertainties of the analyses. An additional sample of objects with largerabundance discrepancy factors will need to be studied before a stronger statement can be made thatrecombination line abundances are not correct.
Subject headings: planetary nebulae: general -- planetary nebulae: individual (He2-138, NGC 246,NGC 6543, Tc 1) — ISM: abundances — ultraviolet: ISM INTRODUCTIONThe analysis of emission line intensities has been usedto determine nebular abundances for a wide range ofobjects. Standard procedures have been developed inwhich the collisionally excited forbidden lines and high-level permitted recombination lines of ions are usedto determine abundances (Dopita & Sutherland 2003;Osterbrock & Ferland 2006). For most objects heavy el-ement abundances are derived from the forbidden linesbecause of their greater strengths compared to thefainter recombination lines, which are frequently onlymarginally stronger than the continuum intensity. Forsome of the higher surface brightness gaseous nebulaeboth types of lines have been used to determine the heavyelement CNO abundances, and they have produced dis-crepant results of more than an order of magnitude insome objects.Each of the two types of lines have certain advantagesfor abundance determinations. The forbidden lines arestrong, so they are detected from many more ions thanthe recombination lines. The collisional excitation of low-lying levels dominates other competing population pro-cesses such as fluorescence excitation, charge exchange, ∗ BASED ON OBSERVATIONS WITH THE NASA/ESA HUB-BLE SPACE TELESCOPE OBTAINED AT THE SPACE TELE-SCOPE SCIENCE INSTITUTE, WHICH IS OPERATED BYAURA, INC. UNDER NASA CONTRACT NAS5-26555. Space Telescope Science Institute, 3700 San Martin Drive, Bal-timore, MD 21218. Princeton University Observatory, Princeton, NJ 08544. Department of Physics & Astronomy, Michigan State Univer-sity, East Lansing, MI 48824. Department of Physics, University of Hong Kong, Hong Kong,China. Molecular Physics Laboratory, SRI International, 333Ravenswood Avenue, Menlo Park, CA 94025. Las Campanas Observatory, Carnegie Observatories, Casilla601, La Serena, Chile. and dielectronic recombination. Furthermore, collisionstrengths coupling most of the lower bound levels of ionsare known to better than 30% accuracy. The largestuncertainty in using forbidden line intensities for abun-dances is their sensitivity to kinetic temperature thatresults from excitation by electron impact.Direct electron recapture populates the higher levels ofions and this process has relatively small cross sections.Thus, recombination lines tend not to be strong exceptfor H and He by virtue of their dominant abundances,but they are observable in nebulae from ions of CNOand Ne. They have the advantage that recombinationline intensity ratios are insensitive to temperature anddensity, and the relevant cross sections are believed tobe known reasonably well. Because recombination crosssections are small, however, other excitation processescompete with electron recapture in populating the higherlevels from which these lines are observed. Thus, therecan be greater uncertainty in the excitation processesthat are responsible for specific high level permitted lines.Electron temperatures and densities are determineddirectly from the relative intensities of forbidden linesoriginating on different levels of the same ion with theresult that emission spectra have been a major source ofour knowledge of element abundances of every type ofemission-line object. The relatively high surface bright-nesses of planetary nebulae and a few of the brighter HII regions enable the recombination lines of CNO to beobserved, and in the past decade ion abundances havebeen determined for a number of PNe using both theforbidden lines (FL) and the recombination lines (RL)from the same ions. Surprisingly, the two types of lineshave not yielded the same abundances. The differencesbetween the RL and FL abundances vary from object toobject and span the range from 15 percent, i.e., relativelygood agreement, to factors of 50 and more (Tsamis et al. Williams et al.
TABLE 1Ions with UV Resonance and Optical Forbidden Lines
Ion UV Resonance Transition λ (˚A) a Optical Forbidden Line λ (˚A)C I II I II II I I II III a Single and double asterisks indicate transitions arising from the first and second fine-structure excited level of ground-stateterm, respectively.
TABLE 2Journal of Observations for HST UV Spectroscopy
Object He2-138 NGC 246 NGC 6543 Tc 1Central star (V) 10.9 11.9 11.1 11.4Shell surface brightness, S(H β )(erg cm − s − arcsec ) 5.1 × − × − × − × − Diameter of Central NebularEmission (arcsec) 7 245 20 10Radial velocity, heliocentric (km s − ) -47 -46 -66 -83Exposure times (sec): 1150–1330˚A 7 × × × × · · · × · · · × · · · × × λλ Fig. 1.—
A montage of UV absorption line profiles fromHST/STIS spectra of the central star of He2-138. The foregroundISM absorption is centered around velocity = -10 km s − , and thePN shell absorption is centered around velocity = -60 km s − , asindicated by the vertical dashed line. nebular emission lines. For each ion the column densityand emission measure differ only by the multiplicativefactor of the electron density in the emission measure.Since standard nebular diagnostics provide a direct de-termination of the density appropriate for each ion de-pending upon its ionization level, a direct comparison canbe made between the absorption column density of theion and its emission measure as derived from the differentemission lines. This procedure should demonstrate whichemission lines, forbidden or permitted, yield abundancesmost consistent with those from the UV absorption lines.An initial study of abundances determined from UVabsorption lines in the central star vs. those found fromnebular emission line intensities for the PN IC 418 wasattempted by Williams et al. (2003). For the four ionsS +2 , S + , Ni + , and Fe + , and netural oxygen O o , for whichrelative abundances could be determined independentlyfrom both methods, rough agreement was found. How-ever, the uncertainties were too large for meaningful con-clusions to be drawn.We report here on an observing program which at-tempts to resolve the discrepancies between the forbid-den and permitted emission line intensities by making a Fig. 2.—
A montage of UV absorption line profiles from thestar of NGC 246 from the HST/STIS data. The ISM absorption iscentered near velocity = 0, and the PN shell absorption is centeredaround velocity = -80 km s − , as indicated by the vertical dashedline. The broad N V absorption trough is indicative of an outflow-ing wind from the central star, which has a heliocentric velocity ofv* = -46 km s − . UV absorption line analysis that independently serves tovalidate emission line results. We have obtained highresolution UV spectra of four PNe central stars withHST/STIS, and visible spectra of three of the associ-ated nebular shells from Las Campanas and KPNO. TheUV observations and absorption analysis are describedin §
3, and the optical emission spectra and analysis arepresented in §
4. The relative column densities from thetwo methods are compared and interpreted in § OBJECT SAMPLE AND OBSERVING PROGRAMColumn densities determined from absorption linesare most reliable when the lines are well-resolved andhave ample signal-to-noise to define the continuum, thusbrighter central stars are advantageous. Absorptionlines originating in nebular gas are frequently seriouslyblended with and obliterated by stronger absorption fromthe same transitions caused by intervening ISM gas alongthe same line of sight. Unambiguous measurement of ab-sorption from the nebular gas therefore requires a neb-ular radial velocity differing by at least 50 km s − fromthat of the Local Standard of Rest to shift the nebular Williams et al. Fig. 3.—
Same as Figure 1 except for the central star NGC 6543.The three vertical dashed lines represent distinct absorption com-ponents from the nebular shell. absorption out of the corresponding stronger ISM com-ponent. Optimal candidates for emission study are pref-erentially high surface brightness objects, thus favoringPNe over the lower surface brightness H II regions. Itwould be advantageous to include in our sample somePNe for which the largest FL and RL abundance dis-crepancies have been determined, however the few PNethat have been established to have differences of morethan a factor of ten either have (a) central stars that aretoo faint in the UV, (b) very low surface brightnesses,or (c) radial velocities that are not sufficiently differentfrom the LSR to avoid confusion between the nebularshell and ISM absorption lines.The sample of known PNe satisfying the optimal cri-teria for study is given in Williams et al. (2003), andis not large. We identified four PNe that satisfy thesecriteria and which seem well suited for a combined UV-visible study, viz., He2-138, NGC 246, NGC 6543, &Tc 1, whose central stars are sufficiently bright that UVobservations with HST at high spectral resolution wouldproduce acceptable spectra in reasonable exposure times.We acquired spectra of the central stars of these PNe inthe UV with HST/STIS and then subsequently observedthe nebular shells along adjacent sight lines in the visiblewith ground-based telescopes to obtain line intensities forthe emission-line analysis. ABSORPTION-LINE ANALYSIS3.1.
STIS Observations
HST/STIS was used to obtain spectra of the centralstars of He2-138, NGC 246, NGC 6543, and Tc 1 in thehigh resolution mode, i.e., grating E140H with a resolu-tion of 3 km s − , in three separate settings that coveredthe wavelength region 1150–1690 ˚A. Exposure times thatproduced a continuum signal-to-noise level of S/N ≈ Fig. 4.—
Same as Figure 1, except for the central star of Tc 1. over the entire wavelength regime for each grating set-ting were adopted. The observations were made in 2005(Cycle 12), and the relevant properties of our targetsand the journal of the STIS observations is given in Ta-ble 2. Regrettably, STIS failed and became inoperativebefore our observing program could be completed, thuswe did not succeed in executing all of our planned obser-vations. Only partial data exist for each of the centralstars. The spectra were reduced using the most recentversion of CALSTIS procedures and algorithms (Lindler1998), and a montage of resonance line profiles from thefinal reduced spectra that include ions for which we alsosubsequently observed nebular forbidden emission linesis shown in Figures 1-4 for the four PNe.3.2.
UV Line Measurements
Table 3 lists the absorption lines that we measured inthe central star spectra of the four planetary nebulae.Following the name of each target in the subheaders ofthe table, we list the radial velocity of the central star v ∗ and the velocity interval that covers the strongest ab-sorption features that we identify as arising from theplanetary nebula shell. Weaker features often spannedsmaller velocity intervals and the measurements of theselines, along with those undetected, were taken over themore restricted ranges.We defined the continuum levels by fitting Legendrepolynomials to the fluxes on either side of each line, usingthe methods refined by Sembach & Savage (1992). InFigure 5 we present a portion of the UV spectrum of theHe2-138 central star which shows the final continuumfit, together with the envelope defined by 1 σ excursionsfrom the fit, used in the determination of the absorptionintensities in the apparent optical depth analysis of theNi II λ Fig. 5.—
A segment of the STIS spectrum that covers the Ni II line at 1317.217 ˚A for the central star in He2-138. The large featurecentered at 1317.15 ˚A arises from foreground interstellar material.The small feature centered 1316.96 ˚A is the one that is relevant toour study, since it arises from the nebula. The adopted continuumlevel is shown by a curved line with a cross-hatched overlay thatshows the 1 σ uncertainty in its placement. continuum fitting there is an acceptable range for the re-constructed intensity levels, and limits for this range de-fined the errors in the line measurements attributable tocontinuum uncertainties. For both the equivalent widthmeasurements and the evaluations of column densitiesusing the apparent optical depth (AOD) method ( § § II , only the strongest line appeared above the noise;for such cases we could not measure the weaker line. Us-ing the same methods as for lines that were visible inour spectra, we evaluated intensity upper limits withinthe wavelength intervals where certain lines of interestmight be expected, but which were either marginally de-tectable or not visible at all. Sometimes these measure-ments yielded negative equivalent widths, although withmagnitudes comparable to or much less than the errors,and these determinations are ultimately useful in provid-ing upper limits for the column densities (see footnote bto Table 3).3.3. Absorption Column Densities
Column densities N were derived by integratingover velocity the apparent optical depths τ a ( v ) =ln[ I cont ( v ) /I ( v )] and evaluating the quantity N ≡ Z n dℓ = m e c/ ( πe f λ ) Z τ a ( v ) dv , (1)where n is the density of the ion in the lower level, andthe numerical value for the expression in front of the inte-gral is 3 . × cm − (km s − ) − (Savage & Sembach1991; Jenkins 1996). The results for all of the ions withreliable determinations are given in Table 3, and it shouldbe emphasized that the column densities refer only tothose ions that occupy the lower level of the transition.Errors in the column densities may arise from three dif-ferent sources: (a) photon-counting noise, (b) errors inthe definition of the continuum level, and (c) errors inthe adopted zero intensity level. If the random devia-tions of intensity arising from statistical fluctuations inphoton counts are expressed as σ I ( v ) , an approximationfor the error in τ a ( v ) is simply σ τ a ( v ) = σ I ( v ) I cont ( v ) /I ( v ) , (2)which is reasonably accurate as long as the quantity ismuch less than unity. Jenkins & Tripp (2001) found thatfor a signal-to-noise ratio of about 20 at the continuum(which applies to nearly all of our spectral lines) and aGaussian error distribution, the approximation expressedin equation 2 is good as long as I ( v ) /I cont ( v ) ≥ .
15. Wehave indicated which lines appearing in Table 3 violatethis condition at the maximum level of absorption. Forthese cases, the upper error bounds may need to be in-creased to somewhat larger values than those listed.The errors in optical depth σ τ a ( v ) that arise from pho-ton counting are uncorrelated from one spectral elementto the next, while the systematic error arising from amisplacement of the continuum is an effect that is usu-ally coherent over the extent of an absorption feature.For this reason, the noise errors for successive spectralelements were added together in quadrature before theywere combined as a group with the global uncertainty inline strength caused by inaccuracies in the definition ofthe continuum level. Since the errors arising from photoncounting and continuum misplacement are uncorrelated,it is appropriate to add them together in quadrature. Atthe bottoms of severely saturated lines, we found thatthe intensities deviate from zero by less than 1% of thecontinuum intensity. Thus, anomalies arising from errorsin zero corrections are insignificant compared to short-comings of the approximation in equation 2.Except for some strong lines of Si II and Si II * in thespectrum of NGC 6543, the values of N obtained for linesof different strength generally agreed with each other. Inthis exception, the fact that the stronger lines yieldedlower column densities than the weaker ones for thesetwo ground state levels indicates that there are some un-resolved saturated absorptions that make all of the eval-uations of N using equation 1 underestimate slightly thetrue value of N for Si II (Jenkins 1996). EMISSION-LINE ANALYSIS4.1.
Optical Spectroscopy
The four PNe studied here were observed in the visi-ble with ground-based telescopes to measure intensities Williams et al.
TABLE 3Equivalent Widths and Column Densities λ a log fλ a Species W λ b log N b (˚A) (m˚A) (cm − ) He2-138 ( v ∗ = −
47 km s − ; − < v PN < −
40 km s − )1656.928 2.392 C I 28 . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . c . ± . . , − . c . ± . . , − . c . ± . . , − . . ± . . , − . . ± . . , − . c,d . ± . . , − . c,d e . ± . . , − . f e . ± . . , − . f . ± . . , − . f . ± . . , − . . ± . . , − . . ± . < . . ± . . , − . c . ± . . , − . c . ± . . , − . f . ± . . , − . f . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . f . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . NGC 246 ( v ∗ = −
46 km s − ; − < v PN < −
60 km s − )1277.245 2.037 C I 0 . ± . < . . ± . . , − . . ± . . , − . . ± . . , − . − . ± . < . . ± . . , − . g . ± . < . g − . ± . < . . ± . . , − . − . ± . < . . ± . . , − . . ± . . , − . f . ± . . , − . . ± . . , − . . ± . . , − . − . ± . < . . ± . . , − . − . ± . < . NGC 6543 ( v ∗ = −
66 km s − ; − < v PN < −
74 km s − )1277.245 2.037 C I 1 . ± . < . . ± . . , − . . ± . . , − . − . ± . < . − . ± . < . . ± . . , − . . ± . . , − . c . ± . . , − . . ± . . , − . . ± . . , − . c ndependent Emission and Absorption Abundances 7 TABLE 3(continued) λ a log fλ a Species W λ b log N b (˚A) (m˚A) (cm − ) NGC 6543 ( v ∗ = −
66 km s − ; − < v PN < −
74 km s − )1533.432 2.307 Si II* 43 . ± . . , − . . ± . . , − . . ± . . , − . . ± . < . . ± . . , − . . ± . . , − . . ± . . , − . c . ± . . , − . f . ± . . , − . f . ± . < . . ± . < . . ± . < . − . ± . < . − . ± . < . Tc 1 ( v ∗ = −
83 km s − ; − < v PN < −
86 km s − )1560.309 2.082 C I − . ± . < . − . ± . < . − . ± . < . . ± . . , − . h . ± . < . . ± . < . . ± . . , − . . ± . . , − . . ± . . , − . c,d . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . c . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . . ± . . , − . − . ± . < . . ± . < . − . ± . < . − . ± . < . . ± . . , − . a Wavelengths and line strengths from Morton (2000, 2003), except for the f -values of Ni II , forwhich we have adopted the values measured by Jenkins & Tripp (2001). Transitions for individualspecies are arranged according to decreasing line strength. This was done in order to make it easyto identify trends (strong lines indicating smaller N than weak ones) that signify possible unresolvedsaturated components that could lead to underestimates of column density using the AOD method(Savage & Sembach 1991; Jenkins 1996). Duplicate entries signify independent measurements made indifferent echelle orders. b Listed errors represent ± σ deviations and include uncertainties caused by both photoevent statisticalfluctuations and continuum uncertainties, combined in quadrature. When a measurement of W λ yieldsa value that is below the calculated 1 σ error in W λ , we state the formal measurement of W λ and itserror, but then we follow with an evaluation of a 2 σ upper confidence bound for the real W λ using themethod of Marshall (1992) for interpreting marginal detections (or nondetections) of quantities thatare known not to ever be negative. The listed upper limit for N is calculated from this W λ limit usingthe formula for weak lines (i.e., the linear part of the curve of growth). c The line is strongly saturated (central optical depth τ & τ a ( v ) that exceeded 5.0 were simplyset to equal to 5.0. d The right-hand portion of the profile is partly blended with the left-hand portion of the absorptionarising from foreground material in the general interstellar medium. Thus, the errors could be somewhatlarger than those derived formally (and stated here). e Si II * was also recorded at 1533.4 ˚A, but this line is strong enough to have a small portion of its profilestrongly saturated. Since our recording of the 1309.3 ˚A feature is of excellent quality (and appeared intwo orders), we decided not to measure the stronger line. Williams et al.
TABLE 3(continued) f At the bottom of the line, the intensity relative to the continuum is less than 0.15. For our representa-tive
S/N = 20 (at the continuum), the approximation given in equation 2 starts to become inaccurate.For this reason, the upper bound for log N should be increased slightly beyond the value listed here. g Absorption by the 1301.874 ˚A transition of P II caused by foreground gas interferes with the O I feature. However, we could compensate for this by dividing the spectrum by the P II profile at1152.818 ˚A after its strength had been reduced to reflect the fact that the 1301.874 ˚A line is weaker.(All intensities in the strong profile were taken to a power equal to the ratio of the lines’ values of fλ .) h The right-hand portion of this profile is partly blended with the left-hand side of an absorption arisingfrom the 1301.874 ˚A transition of P II created by the foreground gas. Fig. 6.—
Images of program PNe showing locations, orientations, and size of slits for (a) He2-138, (b) Tc1, and (c) NGC 6543. In allfigures North is up and East is to left. Panels (a) and (c) are HST images. The shell emission sampled by our spectra would be representedby these images convolved with a 1–1.3 arcsec PSF. of the nebular emission lines. The lower surface bright-nesses of the nebular shells compared with the centralstars dictated that the nebular spectra sight lines be po-sitioned no closer than 2 arcsec from the central star inorder to avoid unacceptable levels of contamination byscattered light from the brighter star. However, our goalwas to estimate the intensity directly along the line ofsight to the central star since this is the position of thegas that produces the absorption lines. Our approachwas to take spectra in two positions symmetrically placedon either side of the central star and to then averagetogether the two spectra after they had been flux cali-brated. The flux average serves to compensate for sur-face brightness fluctuations, but does not represent theflux along the sight line to the central star if there is a ra-dial gradient in surface brightness away from the centralstar due to the three-dimensional structure of the shell.Initially, a reconnaissance was carried out in 2004 atlow spectral resolution (300–500 km s − FWHM) usingthe Gold Spectrograph on the 2.1m telescope at KittPeak National Observatory (KPNO) to observe NGC 246and NGC 6543, and the Wide Field CCD (WFCCD)camera on the du Pont 2.5m telescope at Las CampanasObservatory (LCO) to observe He2-138, NGC 246, andTc 1. We found that the emission lines in NGC 246 aremuch too faint for accurate spectrophotometric measure-ments of any of the weaker emission lines; only a few ofthe very strongest lines such as [O
III ] λ − FWHM resolution echelle spectra in 2005 with the echellespectrographs on the 4m Mayall Telescope at KPNO andthe 2.5m du Pont Telescope at LCO.4.1.1.
Observations at LCO
The LCO echelle spectrograph uses a prism as across disperser and covers the wavelength range λλ λ × Fig. 7.—
Nebular emission line profiles from the LCO echellespectrum of He2-138. The panels show the forbidden emissionlines listed in Table 7 that were used to determine forbidden lineabundances. The corresponding lines are shown at zero velocity ineach panel. The linear vertical scale is F λ in units of erg cm − s − ˚A − with the bottom abscissa of each panel corresponding to zeroflux and the top corresponding to the value of F λ printed insidethe panel. Fig. 8.—
Emission line profiles from the KPNO echelle spec-trum of NGC 6543. The panels and scaling are as in Figure 7,except that the right-hand column shows four of the stronger O II recombination lines from Table 10. The stronger red [O I ] emissioncomponents at +70 km s − are atmospheric airglow lines. tracking and seeing caused the intensity to vary amongthe exposures. These variations make our determinationsof the emission measure for this object considerably lesscertain than for the other two PNe. The spectral res-olution was 15 km s − FWHM over most of the range,but degraded to 20 km s − at the extreme ends. Weextracted spectra from each position, and after applyingthe proper flux calibration averaged the two extractedspectra together. We added together seven 1200 sec ex-posures at each slit position over two nights to measurethe weak lines, and used pairs of 30 or 60 sec exposures ateach position to measure the strong emission lines whichwould otherwise be saturated.Only the second night was photometric so we used ob-servations of the standard stars HR 4468, HR 4963 andHR 5501 (Hamuy et al. 1994) made through a 8 × Fig. 9.—
Emission line profiles from the LCO echelle spectrumof Tc 1. The panels and scaling are as in Figure 7, with the narrow[O I ] components at +100 km s − again due to atmospheric [O I ]emisison. was to properly flux calibrate a single long exposure ineach slit position on the photometric night using the cor-rect airmass. Finally, we measured the fluxes of the sameintermediate strength emission lines in both spectra, andused the flux ratios to correct the high S/N spectrum tomatch the flux scale of the single well-calibrated spec-trum. This procedure provides the best calibration forour observing circumstances and results in absolute spec-trophotometry accurate to better than 8 percent over thewhole wavelength range.4.1.2. Observations at KPNO
The KPNO echelle spectra of NGC 6543 were takenover the three nights 18-20 June 2005 UT. We usedthe UV camera on the 4m Mayall Telescope Cassegrainechelle spectrograph with echelle grating 79-63 and crossdisperser 226-1 with two different setups, each giving 20km s − resolution. The blue setup, used for the first twonights, covered the wavelength range λλ order separating filter. We then switched to a red setupcovering the range λλ o , as shown in Figure 6. As with Tc 1 these slit posi-tions are well inside the outer regions of the nebula. Thecombined exposure times at each slit position for eachgrating setting were of order 60 min. We flux calibratedthe NGC 6543 spectra and then averaged together thetwo slit positions to get a final spectrum interpolated forthe line of sight to the central star in the same way aswas done with the LCO spectra. We determine the ab-solute spectrophotometry of our calibration to have anaccuracy of better than 7 percent. In Figures 7-9 we0 Williams et al. TABLE 4Optical Forbidden Emission Line Fluxes
He2-138 NGC 6543 Tc 1Species λ (˚A) F a,b F c c F F c F F c H I I · · · · · · · · · · · · C I · · · · · · < < I · · · · · · · · · · · · C I · · · · · · · · · · · · < < I I II II II I · · · · · · I I II II II II III < < III
III II < < · · · · · · < < II · · · · · · < < I < < · · · · · · < < I · · · · · · · · · · · · < < II II II II III
III
III
III
III · · · · · ·
III
III IV · · · · · · · · · · · · Ar IV · · · · · · · · · · · · Fe II < < < < II < < II · · · · · · · · · · · · Fe II · · · · · · < < II II · · · · · · < < a In units of erg s − cm − , numbers in parentheses are exponents, colons after values indicates uncertain detections. b Observed flux. c Extinction-corrected flux. show portions of the nebular spectra of the three PNethat were used in the analysis of the emission lines andwhich show both the strong diagnostic forbidden linesand the weaker recombination lines of O II .4.2. Nebular Emission Line Intensities
The emission line fluxes have been measured from thefinal co-added and averaged spectra using the IRAF splot routine. The measurements were straightforward be-cause few of the lines of interest showed evidence of sig-nificant blending. The resultant observed intensities forHe2-138, NGC 6543, and Tc 1 are given in Table 4 forlines that can be used to obtain T e , n e , and extinctionalong the lines of sight. The observed intensities havebeen corrected for extinction by taking the flux ratios ofmultiple unblended Balmer and Paschen line pairs fromthe same upper levels and determining the logarithmic extinction at H β , c Hβ , from the expression c Hβ = [ X Hβ / ( X − X )] × log ( A F λ /A F λ ) , (3)where A , , λ , , and F , are the spontaneous emissioncoefficients, wavelengths, and observed fluxes for a spe-cific Balmer and Paschen line pair, and X , ,Hβ are thegalactic extinction law values fitted by Howarth (1983)at the wavelengths of the lines and H β respectively (as-suming R = 3 . F c ( λ ) = 10 c Hβ X ( λ ) /X Hβ F ( λ ) , (4)where F c is the corrected flux. Taking the average of val-ues obtained from multiple line pairs for our lines of sightwe derive values of c Hβ = 0.56, 0.14, and 0.33 for He2-138, NGC 6543, and Tc 1. These values are in goodagreement with those of Cahn, Kaler, & Stanghellini(1992), who obtained global values of 0.40, 0.12, and 0.28ndependent Emission and Absorption Abundances 11 Fig. 10.—
Diagnostic diagram for He2-138. Dashed lines indicate n e diagnostic curves and solid lines T e diagnostics curves derivedfrom emission line intensities listed in Table 4 input into the ratioslisted in Table 6. Fig. 11.—
Diagnostic diagram for Tc 1. Dashed lines indicate n e diagnostic curves and solid lines T e diagnostics curves derivedfrom corresponding emission line intensities listed in Table 4 inputinto the ratios listed in Table 6. for the three PNe. The extinction corrected fluxes, F c ,are listed in column 4 of Table 4, including the upper lim-its to fluxes of undetected lines, which have been takento be the 3 σ rms flux of the noise of the neighboringcontinuum.4.3. Plasma Diagnostics and Emission Measures
Emission measures and relative abundances of ions arenormally determined from their forbidden line intensi-ties, which have a sensitive dependence upon the ki-netic temperature and density of the gas. Electron tem-peratures T e have been determined for regions of dif-ferent ionization primarily from the ratio of auroral tonebular line intensities of [O I ], [S II ], [N II ], [O II ],[O III ], [S
III ], and [Ar
III ] using complete radiativeand collisional multi-level calculations similar to thosein the IRAF nebular package (Shaw & Dufour 1995), asdescribed by Sharpee et al. (2007) in their study of s -process elements in PNe. Similarly, electron densities n e are sensitive to certain line ratios such as [O II ] λ II ] λ III ] λ IV ] λ T e and n e inFigures 10–12. The resulting values of T e and n e are Fig. 12.—
Diagnostic diagram for NGC 6543. Dashed lines in-dicate n e diagnostic curves and solid lines T e diagnostics curvesderived from corresponding emission line intensities listed in Ta-ble 4 input into the ratios listed in Table 6. listed in Table 6 with their formal uncertainties. Thedensities and temperatures derived from the differentlines are generally consistent with each other with theexception of the [N I ] for NGC 6543 and Tc1, and the[S II ] density for He2-138, as is evident from the plotsin Figures 10–12. The disparate densities deduced forHe2-138 from the different lines could be real; the resultof inhomogeneities. The [N I ] lines, on the other hand,are very weak and thus the densities from that doubletare very uncertain.In order to properly account for all relevant physi-cal processes when converting the observed emission lineflux F c into the emission measure we consider here thefull definition of the emission measure. The extinction-corrected flux of an optically thin emission line along aline of sight is F c = θ o [ hν o / (4 π )] Z n u A ul dℓ , (5)where θ o is the angular area of the gas being observed,and A ul and n u are the line transition probability andnumber density of the upper level. The stronger forbid-den transitions normally have direct collisional excitationfrom the ground state as the predominant mechanismexciting the line, therefore it is convenient to write theequation of statistical equilibrium governing the popula-tion of the upper level in terms of the ion and electrondensities as n u X ku n k A ku + n e X k> ,k = u n k q ku TABLE 5Atomic Data References
Species Transition Probabilities Collision StrengthsC I Nussbaumer & Rusca (1979) Pequignot & Aldrovandi (1976)Froese Fischer & Saha (1985) Thomas & Nesbet (1975)Johnson, Burke, & Kingston (1987)N I Zeippen (1982) Berrington & Burke (1981)Froese Fischer & Tachiev (2004) Dopita, Mason, & Robb (1976)N II Nussbaumer & Rusca (1979) Stafford et al. (1994)Wiese, Fuhr, & Deters (1996) Saraph, Seaton, & Shemming (1969)Lennon & Burke (1994)O I Baluja & Zeippen (1988) Berrington & Burke (1981)Mendoza (1983) Berrington (1988)LeDourneuf & Nesbet (1976)O II Zeippen (1982) Pradhan (1976)Wiese, Fuhr, & Deters (1996) McLaughlin & Bell (1993)O III Nussbaumer & Storey (1981) Aggarwal (1983)Wiese, Fuhr, & Deters (1996) Aggarwal, Baluja, & Tully (1982)Baluja, Burke, & Kingston (1980)Baluja, Burke, & Kingston (1981)Lennon & Burke (1994)P II Kaufman & Sugar (1986) Tayal (2004)Mendoza & Zeippen (1982b) Kruger & Czyzak (1970)S II Mendoza & Zeippen (1982a) Keenan et al. (1996)Keenan et al. (1993) Mendoza (1982)Verner, Verner, & Ferland (1996)S III Mendoza & Zeippen (1982b) Mendoza (1982)Heise, Smith, & Calamai (1995)LaJohn & Luke (1993)Cl III Mendoza & Zeippen (1982a) Butler & Zeippen (1989)Ar III Mendoza & Zeippen (1983) Johnson & Kingston (1990)Kruger & Czyzak (1970)Ar IV Mendoza & Zeippen (1982a) Zeippen, Le Borlot, & Butler (1987)Kaufman & Sugar (1986)Fe II Nussbaumer & Storey (1988) Zhang & Pradhan (1995)(159 levels) Garstang (1962) Bautista & Pradhan (1996)Nahar (1995) Bautista & Kallman (2001)Schnabel, Schultz-Johanning, & Kock (2004)Bautista & Kallman (2001)Ni II Nussbaumer & Storey (1982) Bautista (2004)(76 levels) Kurucz (1992)
TABLE 6Electron Temperatures and Densities
Diagnostic He2-138 NGC 6543 Tc 1Density (cm − )[N I ] λ λ + ∞− +900 − − [S II ] λ λ +17000 − +3800 − [O II ] λ λ +9000 − +2400 − +800 − [Cl III ] λ λ +10000 − +2100 − +1800 − [Ar IV ] λ λ · · · +1100 − · · · Temperature (K)[O I ] ( λ λ λ +1200 − · · · +2300 − [S II ] ( λ λ λ λ +7000 − +5000 − [O II ] ( λ λ λ λ +3000 − +3000 − +2700 − [N II ] ( λ λ λ +600 − +800 − +600 − [S III ] λ λ +500 − +500 − +700 − [Ar III ] ( λ λ λ · · · +400 − +800 − [O III ] ( λ λ λ · · · +200 − +500 − ndependent Emission and Absorption Abundances 13 − n e n u X k = u q uk + X k = u n k J ku B ku − n u X k = u J uk B uk + n e n i +1 α u . (7)Here, J ku and B ku are the mean intensity and Einstein B coefficient for radiative (de-)excitation from level k tolevel u , and α u is the effective recombination coefficientinto level u .For most strong forbidden lines direct excitation fromthe ground states predominates, and ξ ≪
1. How-ever, for certain ions, e.g., Fe II and Ni II (Lucy 1995;Bautista, Peng, & Pradhan 1996; Bautista & Pradhan1996; Bautista 2004), and certain transitions of CNO(Grandi 1975) other processes such as radiative exci-tation and strong coupling between other excited levelscontribute to some of the stronger forbidden transitions,such that ξ > n e n , and it is important to treat their ex-citation via detailed multi-level calculations that involvethe radiation field.We have used detailed calculations of the relevant levelpopulations for all of the ions using the values of T e , n e ,and J ν appropriate for the level of ionization and aug-mented by incorporation of additional levels and pro-cesses for the ions, to determine the emission coefficients q u ( T e ) and ξ ( n e , T e , J ν ) for all of the lines listed in Ta-ble 4. The radiation fields J ν for our slit positions havebeen taken from observations of the central stars by IUEand FUSE for frequencies below the Lyman limit. Forfrequencies above the Lyman limit we have extrapolatedthe observed stellar continua by assuming a black bodyflux at the appropriate temperature for the central stars.The dilution factors at our slit positions were rather smallso that radiative excitation by the stellar continua wasnot competitive in the population of any level that weconsidered. For Fe II and Ni II we have used the ex-plicit multi-level population processes and cross sectionsof Bautista, Pradhan, and collaborators to calculate linestrengths for these ions. All known processes that mightmake significant contributions to the line intensities havebeen included in the above calculations, and correspond-ing values of T e and n e have been used that are appro-priate for the ionization state for each line. Reddeningcorrected fluxes have then been used to compute groundstate emission measures EM i for those ions for which UVabsorption was also observed.Combining equations 5-7 produces the following ex-pression for the emission measure of an ion i , EM i ≡ Z n e n dℓ = 4 πF c X k
Species λ (˚A) EM i (cm − pc)He2-138C I II < II II I II III I I II III I II III the various lines for our sample of PNe. The resultingemission measures are presented in Table 7. COMPARATIVE COLUMN DENSITIES FROMEMISSION AND ABSORPTION5.1.
Correction for Different Lines of Sight
In order to compare directly the results of the absorp-tion and emission abundance analyses the emission mea-sures have to be converted to effective column densities,or vice versa, by dividing the emission measures by theelectron density appropriate for each ion. If we designate
A schematic indicating the relevant angles discussedin the text that apply the derivations of the volume and shell cor-rection factors ζ vol and ζ shell , assuming that the nebula is a perfectsphere. i , the equivalent emission column density for theion can be written as N em = EM i / ( ζ
Nebular IdentificationQuantity a He2-138 NGC 6543 Tc1 θ r θ θ b θ y ζ vol ζ shell a Angles given in arc seconds. b One side of the slit extended beyond the edgeof the nebula ( θ = 4 . θ is set to θ r . for the volume-filled nebula, we compute the area A of aprojection of the slit on the surface of the sphere, underthe condition that it is long enough to cover the entirechord, A = 2 πθ r ( θ − θ ) . (15)In this case, the normalization box has the dimensions θ x θ y multiplied by the thickness of the shell. Since theappropriate path length for equation 5 in this case is theshell thickness, this thickness cancels out in the equationfor shell correction factor ζ shell , , leaving us with the ex-pression ζ shell , = Aθ x θ y = 2 πθ r ( θ − θ ) θ x θ y (16)The reduction factor F shell for θ y < θ z is given by F shell = 2 π sin − (cid:18) θ y θ z (cid:19) (17)and this factor reverts to unity for θ y ≥ θ z . As before, ζ shell = F shell ζ shell , (18)Values for the angles and correction factors ζ vol and ζ shell are given in Table 8, and are based upon nebulardiameters taken from the literature, as discussed below.Both values of ζ for NGC 6543 and Tc 1 are not very farfrom 2 because the slit heights were only about half thenebular diameters and the slits were positioned ratherclose to the central stars. The relative change in goingfrom ζ vol to ζ shell is large for He2-138 because the slitsize was comparable to the nebular diameter, and it waspositioned near the nebula’s edge.The images of He2-138, NGC 6543, and Tc 1 in Fig-ure 6 show that all three PNe possess a degree of sphericalsymmetry for the overall structure, but also have embed-ded asymmetrical, inhomogeneous features, e.g., clumpsand possible bipolar structure. Differences between theemission and absorption lines of sight therefore dependnot just on the footprint of the spectrograph slit on thenebulae and whether the nebulae can be represented asfilled shells or thin rings, but also upon small-scale inho-mogeneities that lie along one line of sight but not theother. Small-scale structure could well be the dominantcause of differences between the separate lines of sight,and such structure commonly depends on the level ofionization.Our emission spectra provide information on the ex-tent of both large-scale geometrical and small-scale in-homogeneity effects from the intensity variations of thendependent Emission and Absorption Abundances 15 TABLE 9Comparitive Column Densities from Emission and Absorption Lines
Species log N abs EM i < n e > i log N em a log N abs − log N em a (cm − ) (cm − pc) (cm − ) (cm − )He2-138 ( ζ vol = 0 . ζ shell = 4 . I ± .
16 0.404 7000 (14.26, 13.64) ± .
31 (-0.33, 0.29) ± . II ± . < < (13.05, 12.43) ± . > (0.53, 1.15) ± . II ± .
14 0.61 7000 (14.44, 13.82) ± .
64 (-0.07, 0.55) ± . II ± .
17 0.0124 7000 (12.74, 12.12) ± .
21 (0.03, 0.65) ± . I > ± .
37 12.8 7000 (15.76, 15.14) ± . > (-0.28, 0.34) ± II > ± .
09 12.3 10000 (15.58, 14.96) ± . > (-0.09, 0.53) ± . III ± ± .
11 (-0.10, 0.52) ± . ζ vol = 1 . ζ shell = 2 . I ± .
51 0.23 5000 (13.89, 13.80) ± .
25 (-0.41, -0.32) ± . I ± .
25 0.030 4000 (13.10, 13.01) ± .
21 (-0.81, -0.72) ± . II ± .
07 0.20 5000 (13.83, 13.74) ± .
14 (-0.19, -0.10) ± . III ± .
14 5.56 5000 (15.27, 15.18) ± .
04 (-0.05, 0.04) ± . ζ vol = 1 . ζ shell = 2 . I ± .
06 0.064 2000 (13.82, 13.57) ± .
26 (-0.15, 0.10) ± . II ± .
09 0.137 3000 (13.98, 13.73) ± .
14 (-0.31, -0.06) ± . III ± .
07 0.92 3000 (14.80, 14.55) ± .
04 (0.13, 0.38) ± . a Numbers in parentheses show the outcomes for ζ vol and ζ shell , respectively. These are followed by the error limitsarising from measurement uncertainties. emission lines along the slit length. The slit lengths weused were 4 and 10 arcsec with a spatial resolution of1 arcsec along the slit, so we have relatively few inde-pendent spatial resolution elements. Nevertheless, therange in distance of the slit from the central star over itslength is comparable to the offset of the slit center fromthe central star. Thus, variations of intensity along theslit due to the overall geometry of the nebulae should becomparable to the intensity differences due to the differ-ent path lengths of the absorption and emission sight-lines. We have measured the variations in intensity ofthe [S III ] and [O I ] lines, representing our highest andlowest ionization species, along the slit in the three PNe.We find for Tc 1 that both the [S III ] and [O I ] lineshave a very uniform distribution of intensity throughoutthe full slit, and with no measurable differences betweenthe two slit positions. Thus, for Tc 1 the measurementsindicate that the emission and absorption lines of sightare likely to be very similar.For He2-138 the [S III ] and [O I ] lines have virtuallyidentical, smooth intensity distributions where the inten-sity peaks at the center and decreases outward toward theends of the slit where it falls off rapidly near the ends.The intensity profile is more characteristic of a filled vol-ume than a thin shell distribution of gas, but the smallersize of this nebula causes it to fill only 3 arcsec of the4 arcsec slit length so the geometrical factor zeta repre-sents an important correction for this object. Since thereis no indication of differences in the spatial distributionof the ions based on their ionization level the geometricalnormalization factor zeta is the same for all of the lines.The fact that the emission spectra sampled the outeredge of the nebula makes the corresponding geometricalcorrection for this PN rather uncertain, as was explainedin § III ] completely fills the slits with a uniform inten-sity for one of the slit positions, but shows variations of ∼
25 percent in the other position. The [O I ] completelyfills the slits also, but shows large variations along the slitnear the center. Thus, the lowest ionization species inthis PN display a pronounced small-scale structure thatmay cause the emission and absorption lines of sight tobe quite different for the lowest ionization lines. Basedon the intensity variations one must admit the possibilityof differences in the column densities along different linesof sight for the neutral species to be as large as factorsof 3 for this object - an uncertainty that compromises itsusefulness for the neutral species [O I ] and [N I ].If the stellar absorption and nebular emission spec-troscopy are obtained at sufficiently high resolution onecan use radial velocity information from resolved line pro-files to match velocity components of optical emissionwith the corresponding UV absorption produced in thesame velocity intervals. A comparison of these quanti-ties within the same velocity interval of the gas provides amore accurate assessment of the comparative abundancesthan comparing the total emission measure and columndensity integrated over the full profiles. Local values ofthe emission column density can be determined for spe-cific kinematic regions within the nebulae. Averagingthese values over the full velocity range for the nebu-lar shell will produce the global emission column densityfor the ion, and also information on its fluctuations asa function of velocity. Since thermal and expansion ve-locities of nebulae are of order 10–20 km s − a spectralresolution less than 10 km s − is optimal to perform theanalysis this way. Our emission spectra lack the neces-sary spectral resolution to perform such an analysis, andtherefore we work with the integrated (over wavelength)emission measures and column densities.5.2. Comparison of Absorption & Emission ColumnDensities
The absorption column densities obtained from UVresonance lines refer specifically to those ions occupyingthe lower level of the transition. In order to obtain thetotal column density of the ion the column densities for6 Williams et al.all the individual fine-structure levels of the ground statemust be summed together. In our STIS spectra someions had blended absorption profiles for one or more ofthe transitions from the ground state fine-structure levelsthat prevented us from deriving the column densities forthose levels. We have determined the column densities ofions in those levels by taking values of T e and n e obtainedfrom the emission lines for that ion to solve for the levelpopulations relative to the levels for which column den-sities were determined. Additionally, when more thanone resonance multiplet of an ion has yielded a columndensity we have computed the mean value for the ionby weighting individual values according to the inversesquare of their uncertainties. These calculations, whichhave been applied to the absorption column densities inTable 3, yield the total ion column densities, N abs , tothe central star, and these are listed in Table 9 togetherwith the formal errors that result from the quantifiableuncertainties that are discussed below.Emission measures for the same ions that have been ob-served in absorption, and which appear in Table 7 for oursample of PNe, are also presented in Table 9. For ionswhere more than one forbidden line yields an emissionmeasure we have determined the average of the values,with stronger weight being given to the lines of higherintensity and lower Boltzmann factor. Using the corre-sponding values of the electron density for each of theions the resulting emission column densities, N em , havebeen determined from the emission measures from equa-tion 9. These are given in the penultimate column ofTable 9 together with the combined errors, having beennormalized to the absorption path length by dividing bythe geometrical factor ζ .A comparison of the values of N abs and N em for thedifferent ions from the two completely independent abun-dance analyses shows moderately good agreement, withthe exceptions of P II in He2-138 and N I in NGC 6543.Absolute abundances determined from the forbiddenemission lines and UV absorption lines give the sameresults within ± σ errors in the column densities derived fromthe analyses represent the uncertainties that are quan-tifiable. There are also systematic errors that arise fromassumptions rather than measurement uncertainties, andboth sources of error affect the accuracy of our compari-son of forbidden and recombination line column densities.The primary sources of error for the absorption col-umn densities are (a) the determination of the propercontinuum level, (b) the low S/N of the intensities ofweak absorption lines, (c) the insensitivity of intensityto column density for saturated lines, and (d) the deter-mination of total ground state column density for stateswith fine-structure levels when absorption from one ormore of the levels is either not observed or saturated.The main sources of error for the emission column den-sities are uncertainties in (a) the flux calibration of theechelle spectra, which are at the 5–10 percent level, (b)collision strengths for some of the forbidden lines, and (c)the correct values of T e and n e that correspond to each ofthe transitions, as assigned to the various ions from thediagnostics shown in Figures 10–12. The atomic datafor most of the forbidden lines that we have used for di-agnostics and the determination of column densities are believed to be known to better than 30 percent accu-racy. With the exception of the [P II ] line the currentvalues for most of the forbidden line collision strengthsand transition probabilities are the result of calculationsby independent methods over the past three decades thathave converged on values that are in good agreement witheach other and that have changed little over the past fiveyears. Thus, the atomic data are not likely to be majorsources of error. Rather, the largest sources of formalerrors in the emission column densities are uncertaintiesin the values of temperature and density. Because lineintensities depend upon these two parameters, errors in T e and n e translate to errors in the column density. Mostof the lines are in the low density limit and therefore theemission measures are rather insensitive to density. How-ever, because of the Boltzmann factor the line intensitiesare sensitive to T e . The errors caused by uncertaintiesin the temperature, together with uncertainties in inten-sity measurement and flux calibration, form the basis forthe combined error that is presented in Table 9 for eachemission column density. To these uncertainties mustbe added the unknown errors in collision strengths andthose differences that small-scale inhomogeneities maycause between the lines of sight.Several features of Table 9 merit comment. First, dueto a combination of weak, saturated, or strongly blendedUV absorption lines coupled with the failure of our nebu-lar spectra to detect forbidden lines from some ions, thereare relatively few ions for which we were able to deriveindependent abundances from both UV absorption andforbidden emission lines. Even with the relatively longslit used to sample substantial portions of the PNe shellswe were not successful in detecting weak emission linesfrom a number of the ions for which column densities hadbeen measured from the STIS spectra.Second, with the exception of S +2 all of the ion specieslisted in Tables 7 and 9 are the lowest ionization stagesthat have ionization potentials greater than 13.6 eV. Thismeans that some fraction of most of the ions we havemeasured could exist in cold, neutral gas residing eitherwithin dense clumps embedded inside the nebula or ina foreground shell of material around the nebula. Suchgas would complicate our analysis by increasing the ab-sorption column density without having any effect onthe emission lines, leading to legitimate differences be-tween the emission and absorption column densities. For-tunately, we can test for this possibility by comparing N abs (O I ) with N abs (S II ). The ionization fraction of Ois closely coupled to that of H through a charge exchangereaction that has a large rate constant (Field & Steigman1971; Chambaud et al. 1980), which guarantees that theamount of O I in the ionized gas is quite low and thatpractically all of the O is neutral in H I gas. By contrast,in an H II region a reasonable fraction of the S will bein the form of S + since its ionization potential is high(23.3 eV). Furthermore, in an H I region nearly all of theS should also be singly ionized. Therefore, from H I gaswe expect to find the ratio N abs (O I )/ N abs (S II ) to beapproximately equal to the solar value of [O/S] = 1.46,assuming that neither of the elements are significantlycondensed onto dust grains nor are they enriched or de-pleted by nuclear processes within the AGB progenitor ofthe central star. A ratio smaller than this value signifiesprogressively less contribution to the column densitiesndependent Emission and Absorption Abundances 17from neutral gas.For Tc 1 we have found that N abs (O I ) ≈ N abs (S II ),which indicates that any contribution from neutral ma-terial must be so small that it can be neglected forour study. The situation for NGC 6543 is not quite sostraightforward because our inferred value of N abs (O I )for the nebula is based on the marginal detection of O I *.Our ability to directly measure O I in the ground fine-structure level is compromised by possible P II λ − , which appears at the same wavelength asthe velocity-shifted O I λ I column density for the nebula from this fea-ture, which has equivalent width EW = 10 m˚A, by as-suming the foreground P II absorption to be negligible.When we do this, we derive a value log N (O I ) = 13.2,an amount that is above the lower bound for our calcu-lated log N abs (O I ) that is listed in Table 9. However,this value is still substantially lower than our measure-ment of N abs (S II ), so once again we are assured thatcontamination of the column densities from neutral gasis negligible for NGC 6543.We are unable to make any assertion about N abs (O I )/ N abs (S II ) toward He2-138 because both col-umn densities were recorded as lower limits (the lines arestrongly saturated; see footnote c in Table 3). However,in the spectrum of the central star for this nebula we seeabsorption features from excited H at v = -62 km s − ,which is a strong indication that we are viewing a pho-todissociation region at the inner edge of a neutral shellsurrounding the nebula. Thus, it is possible for this oneobject that N abs for ions that can exist within H I regionscould add to the contributions from the ionized nebula.This may explain why N abs (P II ) ≫ N em (P II ) for thisPN, although it is then puzzling why the discrepanciesfor Fe II and Ni II are not nearly as large unless both ofthem are condensed onto grains.Finally, we point out that heavy element recombina-tion lines for the ion species that we studied by UV ab-sorption, and which are substantially weaker than theforbidden lines, remained under the detection thresholdof our spectra. This limits our ability to make a directcomparison of abundances determined from recombina-tion lines for our PNe. However, although our spectradid not detect recombination lines originating from anyof the ions in Tables 7 and 9 from which UV resonanceabsorption was observed, we did observe C II , N II , andO II recombination lines. Any information that can beobtained from an analysis of these recombination lines ispotentially useful. Of the above ions only the O II re-combination lines originate from a parent ion for whichforbidden lines were observed, viz., O +2 , so the columndensities inferred from these lines are considered in thefollowing section.5.3. Recombination Line Column Densities
The results of Table 9 show that the absorption andforbidden emission column densities agree within the un-certainties of measurement error, inaccuracies in the val-ues of temperature and density, and inhomogeneities thatcause the adjacent lines of sight to sample different com-ponents of the nebulae. This agreement indicates thatnebular analyses based upon forbidden emission lines
TABLE 10Recombination Line Abundances
Line(Multiplet) F a ADF(erg cm − s − )NGC 6543O II λ λ λ λ λ λ λ λ λ λ λ λ ± . II λ λ λ λ λ λ λ λ λ ± . a Number in parentheses in an exponent. yield heavy element abundances that are the same asthose derived from absorption lines-the key result fromthis study. That said, what conclusions can be drawnfrom our sample of PNe about nebular abundances basedon recombination lines? Do our objects show the samediscrepancies exhibited by other PNe?We have detected a number of the same O II recom-bination lines from NGC 6543 and Tc 1 that have beenstudied extensively in PNe over the past decade and usedto determine relative O +2 abundances (Liu et al. 2000;Robertson-Tessi & Garnett 2005). Since the [O III ] for-bidden lines are strong in both objects it is straightfor-ward to determine the abundance of O +2 as derived fromthe two types of lines. No recombination lines were ob-served in the spectrum of the very low ionization nebulaHe2-138.The permitted O II lines from multiplets 1, 2, 10, 19,and 20 have been shown to be populated by recombi-nation and to yield, among themselves, consistent val-ues of the O +2 abundance in H II regions and PNe(Tsamis et al. 2003; Wesson, Liu, & Barlow 2005). Wehave used the extinction-corrected intensities of theselines, the observed intensities of which are shown in Ta-ble 10, to compute the O +2 abundance relative to thatdetermined from the [O III ] λλ II lines,and these are listed in the last column of Table 10.The resulting mean values of the ADFs for NGC 6543and Tc 1 are 2.8 and 2.5 (0.45 and 0.40 dex), re-spectively. The mean ADF of 2.8 found here for8 Williams et al.NGC 6543 is consistent with the previous determinationsof ADF = 3.0 and 3.8 from other lines of sight throughthis same nebula (Kingsburgh, Lopez, & Peimbert 1996;Wesson & Liu 2004). Thus, at least two of our objectsshow the same discrepancies between the recombinationand forbidden line abundances for O +2 that are typicalof PNe, and we have not by chance studied nebulae forwhich the ADFs are close to unity.Since there is good agreement between the absorp-tion and forbidden line column densities in our objects,one can infer from the above results that recombinationlines are likely to produce emission column densities thatare significantly higher than those derived from absorp-tion lines. The final column of Table 9 shows that themean of the forbidden emission line column densities ismarginally larger than that of the absorption columndensities for each of the PNe. The recombination line col-umn densities would produce a larger discrepancy. How-ever, because the ADFs for NGC 6543 and Tc 1 are ofthe same size as the uncertainties in the column den-sities, a larger sample of PNe is needed, especially in-cluding some objects with relatively large ADFs, beforea definitive statement can be made that recombinationabundances are not correct. Given that we do not de-tect any recombination lines from parent ions for whichwe measured UV absorption lines, a direct comparison ofabsorption and recombination line column densities forthe same ions is likely to remain elusive. Realistically, theonly ions in Tables 7 and 9 that are likely to be parentions of detectable recombination lines are S + and S +2 .With deeper spectra it should be possible to observe theS II recombination lines in our PNe, however the rele-vant recombination coefficients are not known and arevery difficult to calculate with any accuracy (P. Storey,private communication).Emission line analysis of a large number of PNe hasshown that recombination lines originating from C +2 ,N +2 , O +2 , and Ne +2 ions all yield roughly the samerelative abundances among themselves as do the col-lisionally excited forbidden and intercombination linesfrom these same ions, and that the recombinationlines consistently indicate higher abundances with re-spect to H and He (Robertson-Tessi & Garnett 2005;Wesson, Liu, & Barlow 2005; Liu et al. 2006). The dis-crepancies do not appear to arise from problems withthe atomic data, rather they seem to be linked to char-acteristics that are specific to the nebulae. Thus, theADFs for doubly ionized CNONe tend to be approxi-mately the same in individual objects, and they vary instep with each other from one nebula to the next al-though there are exceptions to this rule, e.g., NGC 6720(Garnett & Dinerstein 2001).If the agreement among the CNONe ADFs also ap-plied to S +2 one could use the ADFs we have derivedfrom the O II lines in NGC 6543 and Tc 1 to infer therecombination line column density for S +2 , based on the[S III ] emission measure. However, the ADFs for ele-ments in the 3rd row of the periodic table, including sul-fur, are virtually unknown because so few recombinationlines are detected and the relevant cross sections are notknown (Barlow et al. 2003). The only 3rd row ion forwhich a recombination abundance has been determinedis Mg +2 , from Mg II lines having been measured in tenPNe by Barlow et al. (2003). They found the Mg +2 /H + abundances for their objects to show little evidence forenhancement over the solar value, contrary to the largeO +2 /H + enhancements derived from the O II recombi-nation lines in the same PNe. They conclude that the re-combination line abundance discrepancies may be a phe-nomenon restricted to ions of the 2nd row of the periodictable, viz., C, N, O, and Ne, and not exhibited by 3rdrow ions.Our current study shows nonetheless that the electrondensities and temperatures deduced from the usual for-bidden line analysis are correct over a range of ionizationzones that should include the regions where C +2 , N +2 ,O +2 , and Ne +2 reside. This means that the large ADFsfor the second row elements cannot be reflecting errors inthe forbidden line abundances due to the use of incorrectvalues of n e or T e . It would be necessary to find anothermechanism that would affect the forbidden line abun-dances derived for C +2 , N +2 , O +2 , and Ne +2 , but notthose found for S + and S +2 . In our opinion this makesfactors affecting the recombination line abundances al-most certainly the cause of the abundance discrepancies. SUMMARYThe results reported here are derived from a limitedsample of PNe and are based upon observations thatmay not be extended in the near future unless STIS isrepaired and put back into service on HST. For this sam-ple we find that the forbidden lines yield absolute abun-dances for C I , Fe II , Ni II , O I , S II , and S III that areconsistent with those derived from their absorption linesalong adjacent sight lines. Within the uncertainties inthe line intensities and calculations, the good agreementbetween the column densities derived from the forbiddenemission lines and the UV absorption lines for the threePNe represents a validation of both types of analysis. Itstrengthens confidence in the abundances derived fromforbidden emission lines in spite of discrepancies with theabundances derived from high level permitted recombi-nation lines from the same ions, and is the primary resultof this investigation.Although recombination lines were detected in onlytwo of the three objects in this study, those two PNedo show factor 2.5-2.8 discrepancies between the O +2 abundances derived from forbidden lines and those fromrecombination lines. This demonstrates that we havestudied PNe in which the abundance discrepancy prob-lem exists. Not being able to independently measure anabundance for O +2 from its UV resonance lines, whichfall outside of the HST wavelength range, we cannotconfirm that the recombination abundances for O +2 areanomalously high. Nor can we use the similarity in theabundance discrepancy factors of C +2 , N +2 , and Ne +2 with that of O +2 to make a comparison of the inferredrecombination abundances of these ions with those froman absorption analysis because their UV resonance linesalso fall outside of the HST wavelength range. The onedoubly ionized ion for which we do have good absorptiondata, S +2 , did not have recombination lines detected inour nebular spectra.We have shown that the electron densities and temper-atures deduced for a wide range of ionization levels dogive correct abundances using the forbidden lines fromions of other elements within the same ionization zone asO +2 (and C +2 , N +2 , and Ne +2 ). In particular, the for-ndependent Emission and Absorption Abundances 19bidden line abundances for S +2 are in good agreementwith the absorption line abundances for S +2 . 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