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Plasma diagnostics for planetary nebulae and H II regions using N II and O II
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Plasma diagnostics for planetary nebulae and H II regions using N II and O II

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Poster presented by Ian McNabb at the IAU Symposium 283, Planetary Nebulae: an Eye to the Future, 25-29 July 2011, Tenerife, Spain.

Poster presented by Ian McNabb at the IAU Symposium 283, Planetary Nebulae: an Eye to the Future, 25-29 July 2011, Tenerife, Spain.

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  • 1. Plasma Diagnostics for Planetary Nebulae and H II Regions using N II and O II Optical Recombination Lines I. McNabb1, X. Fang1, X.W. Liu1,2, P.J. Storey3 1. Kavli Institute of Astronomy and Astrophysics at Peking University 2. Department of Astronomy at Peking University 3. Department of Physics and Astronomy at University College London 500 500 Abstract -- We carry out plasma diagnostic analysis for a number of planetary nebulae (PNe) and H II regions. We use N II and O II 500 500 Iobs = 0.0652 Iobs = 0.1355 Iobs = 0.6664 Iobs = 0.2174 obs= 0.0043 obs= 0.0065 obs= 0.0089 obs= 0.0140 optical recombination lines (ORLs) with new effective recombination coefficients calculated under the intermediate coupling scheme, 400 Nsim = 10000 Imean = 0.0651 400 Nsim = 10000 Imean = 0.1355 400 Nsim = 10000 Imean = 0.6665 400 Nsim = 10000 Imean = 0.2172 for a range of electron temperatures (Te) and densities (Ne), and fitted against the most reliable measurements. Comparing Te derived 300 mean = 0.0043 Ifit = 0.0652 300 mean = 0.0065 Ifit = 0.1355 300 mean = 0.0088 Ifit = 0.6664 300 mean = 0.0140 Ifit = 0.2173 fit = 0.0043 fit = 0.0066 from ORLs, collisionally excited lines (CELs), the hydrogen Balmer Jump, and/or He I if available, we find the relation Te (ORLs) < fit = 0.0089 fit = 0.0140 # # # # Te (He I) < Te (H I BJ) < Te (CELs), confirming the physical conditions in the two-abundance model postulated by Liu et al. (2000), 200 200 200 200 i.e. the nebula contains another cold, metal-rich and probably H-deficient component. 100 100 100 100 Methodology -- For N II ORLs, the effective recombination coefficients covered a log Te range from 2.1 to 4.3 [K], with a 0.1 0 0.04 0.05 0.06 0.07 0.08 0.09 0 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0 0.62 0.64 0.66 0.68 0.70 0.72 0 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 increment, and a log Ne range from 2 to 6 [cm-3], also with a 0.1 increment. For O II ORLs, the effective recombination coefficients I (V3 5666) I (V3 5679) I (V1 4649) I (V1 4661) covered a log Te range from 2.6 to 4.2 [K], with a 0.2 increment, and a log Ne range from 2 to 5 [cm-3], also with a 0.2 increment, and 500 Iobs = 0.0819 obs= 0.0051 500 Iobs = 0.0371 obs= 0.0071 500 Iobs = 0.2654 obs= 0.0048 500 Iobs = 0.0921 obs= 0.0066 later bilinearly interpolated to a resolution of 0.05 [K] by 0.05 [cm-3]. The location of the minimum χ2 value corresponded to the 400 Nsim = 10000 Imean = 0.0819 400 Nsim = 10000 Imean = 0.0370 400 Nsim = 10000 Imean = 0.2655 400 Nsim = 10000 Imean = 0.0922 mean = 0.0051 mean = 0.0070 optimal Te and Ne for each wavelength combination of the observed intensities. Fig. 1 shows the log χ2-distributions for 8 PNe and 1 H 300 Ifit = 0.0819 fit = 0.0051 300 Ifit = 0.0371 fit = 0.0070 300 mean = 0.0048 Ifit = 0.2654 300 mean = 0.0066 Ifit = 0.0922 fit = 0.0049 fit = 0.0066 II region (Hf 2-2, M 1-42, NGC 6153, and M 2-36, NGC 7009, NGC 6543, IC 4191, M 3-32, and M 42), matching the archived data # # # # 200 200 200 200 for each nebula against the theoretical predictions from each wavelength. Once the optimal Te and Ne were located for each PN, the comparison was also calculated for each combination of simulated 100 100 100 100 intensities within a 1-σ Gaussian distribution confined to the errors of the observed intensities. Fig. 2 shows the Gaussian-distributions 0 0.06 0.07 0.08 0.09 0.10 0.11 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0 0 0.24 0.25 0.26 0.27 0.28 0.29 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 for N II and O II wavelengths within 1-σ of the observed intensities. The optimal Te and Ne locations for each simulation would I (V39b 4041) I (V39a 4035) I (V48a 4089) I (V48c 4087) provide the error estimates of the optimal Te and Ne from the observed intensities. The randomly generated intensities were combined Fig. 2: (left 4 panels) Normal distributions for 10,000 simulations for 4 N II ORLs. (right 4 panels) Same for each simulation and compared with the theoretical predictions based on the effective recombination coefficients for each for 4 O II ORLs. The black curve represents the Gaussian profile from observed intensities and errors. wavelength covering a range of temperatures and densities. Fig. 3 shows the frequencies of the optimal Te and Ne locations derived The blue curve is from the mean intensities and errors. The red curve is created from fitting. from the simulated intensities. a) Hf 2-2 (2as) (XWL06) adf (O2+) = 84: b) M 1-42 (XWL01) adf (O2+) = 22: c) NGC 6153 (XWL00) adf (O2+) = 9.2: a) Hf 2-2 (2as) (XWL06) adf (O2+) = 84: b) M 1-42 (XWL01) adf (O2+) = 22: c) NGC 6153 (XWL00) adf (O2+) = 9.2: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) 5.0 2 log 2 log 2 log 2 log Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2 Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2 1.939 1.011 1.102 1.068 1.393 1.314 4.0 1.654 4.0 0.738 4.0 0.804 4.0 0.731 4.0 1.045 4.0 0.913 [O III] 1.369 0.466 0.507 0.395 0.697 0.512 H I BJ He I ( 7281/ 6678) NGC 6543 1.084 0.193 0.210 0.059 0.348 0.111 3.5 3.5 3.5 O II IC 4191 fixed 0.798 -0.080 -0.088 -0.277 -0.000 -0.290 3.5 3.5 3.5 4.5 N II log Te log Te log Te log Te log Te log Te 0.513 -0.353 -0.385 -0.613 -0.349 -0.692 NGC 7009 NGC 6153 M 42 Hf 2-2 2as 3.0 0.228 3.0 -0.625 3.0 -0.683 -0.950 -0.697 -1.093 M 3-32 M 2-36 M 1-42 -0.057 -0.898 -0.980 -1.286 -1.046 -1.494 3.0 3.0 3.0 2.5 -0.342 2.5 -1.171 2.5 -1.277 -1.622 -1.394 -1.895 -0.627 -1.444 -1.575 -1.958 -1.742 -2.296 2 3 4 log Ne 5 6 -0.912 2 3 4 log Ne 5 6 -1.716 2 3 4 log Ne 5 6 -1.872 2.0 2.5 3.0 3.5 log Ne 4.0 4.5 5.0 -2.294 2.0 2.5 3.0 3.5 log Ne 4.0 4.5 5.0 -2.091 2.0 2.5 3.0 3.5 log Ne 4.0 4.5 5.0 -2.697 4.0 d) M 2-36 (XWL01) adf (O2+) = 6.9: e) NGC 7009 (XF11) adf (O2+) = 4.7: f) NGC 6543 (RW04) adf (O2+) = 4.2: d) M 2-36 (XWL01) adf (O2+) = 6.9: e) NGC 7009 (XF11) adf (O2+) = 4.7: f) NGC 6543 (RW04) adf (O2+) = 4.2: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) log 2 Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) log 2 Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) log 2 Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2 Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2 Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2 1.447 1.251 0.629 1.314 1.337 0.887 log Te [K] 1.075 0.878 0.277 0.926 0.861 0.614 4.0 4.0 4.0 4.0 4.0 4.0 0.703 0.505 -0.076 0.538 0.384 0.342 3.5 0.331 3.5 0.132 3.5 -0.428 0.150 -0.092 0.069 3.5 -0.042 -0.241 -0.780 -0.238 -0.569 -0.204 3.5 3.5 3.5 log Te log Te log Te log Te log Te log Te -0.414 -0.614 -1.133 -0.626 -1.045 -0.476 3.0 -0.786 3.0 -0.987 3.0 -1.485 -1.014 -1.522 -0.749 -1.158 -1.360 -1.838 -1.402 -1.998 -1.022 3.0 3.0 3.0 2.5 -1.531 -1.903 2.5 -1.733 -2.106 2.5 -2.190 -2.542 -1.790 -2.178 -2.475 -2.951 -1.294 -1.567 3.0 -2.275 -2.479 -2.895 -2.566 -3.428 -1.840 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne log Ne log Ne log Ne log Ne log Ne g) IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: h) M 3-32 (WW07) adf (O2+) = 1.15: i) M 42 (CE04) adf (O2+) = 1.02: g) IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: h) M 3-32 (WW07) adf (O2+) = 1.15: i) M 42 (CE04) adf (O2+) = 1.02: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) log 2 Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) log 2 Iobs( 5666) + Iobs( 5679) + Iobs( 4041) log 2 Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2 Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2 Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2 0.543 0.763 0.267 1.318 0.997 0.850 4.0 0.375 0.207 4.0 0.642 0.520 4.0 0.163 0.059 4.0 0.998 0.678 4.0 0.806 0.616 4.0 0.667 0.485 2.5 0.039 0.398 -0.045 0.358 0.426 0.303 3.5 3.5 3.5 -0.130 0.276 -0.149 0.039 0.236 0.120 3.5 3.5 3.5 log Te log Te log Te log Te log Te log Te -0.298 0.154 -0.253 -0.281 0.046 -0.062 3.0 -0.466 3.0 0.033 3.0 -0.356 -0.601 -0.144 -0.245 2.0 -0.634 -0.089 -0.460 -0.921 -0.334 -0.427 2.5 -0.802 2.5 -0.211 2.5 -0.564 3.0 -1.241 3.0 -0.525 3.0 -0.610 0.0 0.5 1.0 1.5 2.0 -0.970 -1.139 -0.333 -0.455 -0.668 -0.772 -1.560 -1.880 -0.715 -0.905 -0.792 -0.975 log adf (O2+) 2 3 4 5 6 2 3 4 5 6 2 3 4 5 6 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne log Ne log Ne log Ne log Ne log Ne Fig. 1: Log χ2-distributions of the effective recombination coefficients for N II (left 9 panels), from Multiplets V3 & V39, and for O II Fig. 4: Te from literature and values derived here vs. adf from [O III] (red open triangles), the Balmer (right 9 panels), from Multiplets M1, M10, & M48, ORLs for the aforementioned PNe and H II regions, comparing observed Jump (orange open circles), He I (yellow open squares) for λ7281/λ6678, O II ORLs (green open intensities with theoretical predictions. The white crosshairs pinpoint the optimal Te and Ne locations for the observed intensities of diamonds), and N II ORLs (blue open stars), for 8 PNe and 1 H II region, each nebula.a) Hf 2-2 (2as) (XWL06) adf (O2+) = 84: b) M 1-42 (XWL01) adf (O2+) = 22: c) NGC 6153 (XWL00) adf (O2+) = 9.2: a) Hf 2-2 (2as) (XWL06) adf (O2+) = 84: b) M 1-42 (XWL01) adf (O2+) = 22: c) NGC 6153 (XWL00) adf (O2+) = 9.2: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035) Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035) Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035) Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087) Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087) Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087) Results -- For all nebulae analyzed here, the mean value of log Te ([O III]) is 4.02 [K]. The mean value of 3000 4000 4000 1000 2000 1500 2500 3000 3000 800 1500 N (Nesim) N (Nesim) N (Nesim) N (Nesim) N (Nesim) N (Nesim) 2000 1000 2000 2000 600 1000 1500 1000 400 500 log Te (H I BJ) is 3.95 [K]. The mean value of log Te (He I λ7281/λ6678) is 3.75 [K]. The mean value of 1000 1000 200 500 500 0 0 0 0 0 03125 1934 2180 337 1304 980 4.0 4.0 4.0 4.0 4.0 4.02344 3.5 1451 3.5 1635 3.5 253 978 735 log Te (O II) is 3.32 [K]. The mean value of log Te (N II) is 3.29 [K]. The mean value of log Ne (O II) is 4.07 [cm−3]. The mean value of log Ne (N II) is 3.14 [cm−3]. The relationship between the mean values of 3.5 3.5 3.5 log Te log Te log Te log Te log Te log Te1563 967 1090 169 652 490 3.0 3.0 3.0 781 2.5 484 2.5 545 2.5 84 3.0 326 3.0 245 3.0 Te is indeed, Te (ORLs) < Te (He I) < Te (H I BJ) < Te (CELs), confirming the physical conditions in the 0 0 0 0 0 0 two-abundance model, showing that the PNe and H II regions contain a secondary cold, metal-rich andN (Nesim,Tesim) 2 3 4 5 0 3000 sim sim 6000 N (Ne ,Te ) 2 3 4 5 0 1250 2500 N (Nesim,Tesim) 2 3 4 5 0 2500 5000 N (Nesim,Tesim) 2.0 2.5 3.0 3.5 4.0 4.5 0 1000 2000 N (Nesim,Tesim) 2.0 2.5 3.0 3.5 4.0 4.5 0 3000 6000 N (Nesim,Tesim) 2.0 2.5 3.0 3.5 4.0 4.5 0 2750 5500 log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim)d) M 2-36 (XWL01) adf (O2+) = 6.9: e) NGC 7009 (XF11) adf (O2+) = 4.7: f) NGC 6543 (RW04) adf (O2+) = 4.2: d) M 2-36 (XWL01) adf (O2+) = 6.9: e) NGC 7009 (XF11) adf (O2+) = 4.7: f) NGC 6543 (RW04) adf (O2+) = 4.2: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035) Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035) Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035) Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087) Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087) Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087) 1000 800 1000 800 3000 2500 1500 2000 1500 2000 probably H-deficient component. N (Nesim) N (Nesim) N (Nesim) N (Nesim) N (Nesim) N (Nesim) 2000 1500 600 600 1000 1500 1000 1000 400 400 1000 500 500 500 200 200 500 0 0 0 0 0 01222 656 3343 1161 1232 1953 REFERENCES 4.0 4.0 4.0 4.0 4.0 4.0 917 492 2507 871 924 1465 3.5 3.5 3.5 3.5 3.5 log Te log Te log Te log Te log Te log Te 3.5 Aller, L.H. & Kaler, J., 1964, ApJS, 139, 1074 Péquignot, D., Petitjean, P., & Boisson, C., 1991, A&A, 251, 680 611 328 1672 581 616 977 3.0 3.0 3.0 306 2.5 164 2.5 836 2.5 290 3.0 308 3.0 488 3.0 Bastin, R.J. & Storey, P.J., 2008, unpublished Robertson-Tessi,. M. & Garnett, D., 2005, ApJS, 157, 371 0 0 0 0 0 0 Ercolano, B., et al., 2004, MNRAS, 354, 558 Otsuka, M., et al., 2010, ApJ., 541, 688N (Nesim,Tesim) 2 N (Nesim,Tesim) 2.0 N (Nesim,Tesim) 2.0 N (Nesim,Tesim) 2.0 Esteban, C. & Rodríguez, M., 2002, ApJ, 581, 241 Ruiz, M.T., et al., 2003, MNRAS, 354, 558 sim sim 3 4 5 0 1550 3100 N (Ne ,Te ) 2 3 4 5 0 1250 2500 N (Nesim,Tesim) 2 3 4 5 0 2250 4500 2.5 3.0 3.5 4.0 4.5 0 3250 6500 2.5 3.0 3.5 4.0 4.5 0 3750 7500 2.5 3.0 3.5 4.0 4.5 0 5000 10000 log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim)g) 4000 IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: Isim( 5666) + Isim( 5679) + Isim( 4041) h) 2500 M 3-32 (WW07) adf (O2+) = 1.15: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035) i) M 42 (CE04) adf (O2+) = 1.02: Isim( 5666) + Isim( 5679) + Isim( 4041) g) 1200 IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087) h) 2000 M 3-32 (WW07) adf (O2+) = 1.15: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087) i) 2500 M 42 (CE04) adf (O2+) = 1.02: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087) Esteban, C., et al., 2004, MNRAS, 355, 229 Ruiz, et al., ApJ, 595, 247 Esteban, C., et al., 2009, ApJ, 700, 654 Schwarz, H.E., Corradi, R.L.M. & Melnick, J., 1992, A&AS, 96, 23 6000 1000 2000 3000 2000 N (Nesim) N (Nesim) N (Nesim) N (Nesim) N (Nesim) N (Nesim) 800 1500 1500 4000 1500 2000 600 1000 1000 Fang, X., Storey, P.J., & Liu, X.-W., 2011, accepted in A&A Sharpee, B., et al., 2004, ApJ., 615, 323 1000 400 1000 2000 500 500 500 200 0 0 0 0 0 04410 1165 4273 721 1509 1954 4.0 4.0 4.0 4.0 4.0 4.0 Fang, X., & Liu, X.-W., 2011, accepted in MNRAS Sharpee, B., et al., 2007, ApJ, 659, 12653308 3.5 874 3.5 3205 3.5 541 1132 1466 García-Rojas, J., et al., 2004, ApJS, 153, 501 Shen, Z.-X., Liu, X.-W., & Danziger, I.J., 2003, A&A, 422, 563 3.5 3.5 García-Rojas, J., et al., 2005, MNRAS, 362, 301 Storey, P.J., 1994, A&A, 282, 999 log Te log Te log Te log Te log Te log Te2205 583 2137 361 755 977 3.5 3.0 3.0 3.0 García-Rojas, J., et al., 2006, MNRAS, 368, 253 Storey., P.J. & Hummer, D.G., 1995, MNRAS, 272, 411103 2.5 291 2.5 1068 2.5 180 3.0 377 3.0 489 3.0 Garnett, D. & Dinerstein, H.L., 2001, ApJ, 558, 145 Tsamis, Y.G., et al., 2003, MNRAS, 338, 687 0N (Nesim,Tesim) 2 3 4 5 0 3300 0 sim sim 6600 N (Ne ,Te ) 2 3 4 5 0 2250 4500 0 N (Nesim,Tesim) 2 3 4 5 0 5000 10000 0 N (Nesim,Tesim) 2.0 2.5 3.0 3.5 4.0 4.5 0 2250 4500 0 N (Nesim,Tesim) 2.0 2.5 3.0 3.5 4.0 4.5 0 2100 4200 0 N (Nesim,Tesim) 2.0 2.5 3.0 3.5 4.0 4.5 0 5000 10000 Kisielius, R. & Storey, P.J., 2001, ApJ, 387, 1135 Tsamis, Y.G., et al., 2003, MNRAS, 345, 186 log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim) log Ne N (Tesim) Liu, X.-W., et al., 1995, MNRAS, 272, 369 Tsamis, Y.G., et al., 2004, MNRAS, 353, 953 Liu, X.-W., et al., 2000, MNRAS, 312, 585 Tsamis, Y.G., et al., 2008, MNRAS, 386, 22 Fig. 3: Frequencies of the optimal Te and Ne for N II (left 9 panels) and O II (right 9 panels). For each nebula, the top panel Liu, X.-W., et al., 2001, MNRAS, 327, 141 Wang, W. & Liu, X.-W., 2007, MNRAS, 381, 669 corresponds to the unique Ne locations, the right panel for the unique Te locations, and the central panel for the 2-dimensional frequency Liu, X.-W., et al., 2006, MNRAS, 368, 1959 Wesson, R., Liu, X.-W., & Barlow, M.J., 2003, MNRAS, 340, 253 Liu, X.-W., et al., 2010, arxiv, 1001.3715L Wesson, R. & Liu, X.-W., 2004, MNRAS, 351, 1021 of both optimal Te and Ne locations. The white-solid contour represents the 1-σ confidence level of the optimal Te and Ne locations for Liu, Y., et al., 2004, MNRAS, 353, 1251 Wesson, R., Liu, X.-W., 2005, MNRAS, 362, 424 the simulated intensities. The white cross-hairs pinpoint the observed Te and Ne values, as above. The light-green error bars represent Nussbaumer, H. & Storey, P.J., 1984, A&AS, 56, 293 Zhang, Y. & Liu, X.-W., 2003, A&A, 404, 545 Peimbert, M., Peimbert, A., & Ruiz, M.T., 2000, ApJ, 541, 688 Zhang, Y. & Liu, X.-W., 2003, A&A, 545, 556 the mean sigma values from the simulated intensities. The blue curve represents the Gaussian profile generated from the same mean Peimbert, A., 2003, ApJ, 584, 735 Zhang, Y., et al., 2005, A&A, 442, 249 values and standard deviations centered on the optimal Te and Ne locations obtained from observed intensities. Peimbert, M., et al., 2004, ApJS, 150, 431