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 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 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 later bilinearly interpolated to a resolution of 0.05 [K] by 0.05 [cm -3 ]. The location of the minimum χ 2 value corresponded to the optimal Te and Ne for each wavelength combination of the observed intensities. Fig. 1 shows the log χ 2 -distributions for 8 PNe and 1 H 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 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 intensities within a 1-σ Gaussian distribution confined to the errors of the observed intensities. Fig. 2 shows the Gaussian-distributions for N II and O II wavelengths within 1-σ of the observed intensities. The optimal Te and Ne locations for each simulation would provide the error estimates of the optimal Te and Ne from the observed intensities. The randomly generated intensities were combined for each simulation and compared with the theoretical predictions based on the effective recombination coefficients for each wavelength covering a range of temperatures and densities. Fig. 3 shows the frequencies of the optimal Te and Ne locations derived from the simulated intensities. 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 corresponds to the unique Ne locations, the right panel for the unique Te locations, and the central panel for the 2-dimensional frequency 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 the simulated intensities. The white cross-hairs pinpoint the observed Te and Ne values, as above. The light-green error bars represent the mean sigma values from the simulated intensities. The blue curve represents the Gaussian profile generated from the same mean values and standard deviations centered on the optimal Te and Ne locations obtained from observed intensities. Fig. 4 : Te from literature and values derived here vs. adf from [O III] (red open triangles), the Balmer Jump (orange open circles), He I (yellow open squares) for λ7281/λ6678, O II ORLs (green open diamonds), and N II ORLs (blue open stars), for 8 PNe and 1 H II region, Results -- For all nebulae analyzed here, the mean value of log Te ([O III]) is 4.02 [K]. The mean value of 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 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 Te is indeed, T e (ORLs) < T e (He I) < T e (H I BJ) < T e (CELs), confirming the physical conditions in the two-abundance model, showing that the PNe and H II regions contain a secondary cold, metal-rich and probably H-deficient component. 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We use N II and O II optical recombination lines (ORLs) with new effective recombination coefficients calculated under the intermediate coupling scheme, for a range of electron temperatures (Te) and densities (Ne), and fitted against the most reliable measurements. Comparing Te derived from ORLs, collisionally excited lines (CELs), the hydrogen Balmer Jump, and/or He I if available, we find the relation Te (ORLs) < Te (He I) < Te (H I BJ) < Te (CELs), confirming the physical conditions in the two-abundance model postulated by Liu et al. (2000), i.e. the nebula contains another cold, metal-rich and probably H-deficient component. Fig. 1 : Log χ 2 -distributions of the effective recombination coefficients for N II (left 9 panels), from Multiplets V3 & V39, and for O II (right 9 panels), from Multiplets M1, M10, & M48, ORLs for the aforementioned PNe and H II regions, comparing observed intensities with theoretical predictions. The white crosshairs pinpoint the optimal Te and Ne locations for the observed intensities of each nebula. 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 I. McNabb 1 , X. Fang 1 , X.W. Liu 1,2 , P.J. Storey 3 Fig. 2 : (left 4 panels) Normal distributions for 10,000 simulations for 4 N II ORLs. (right 4 panels) Same for 4 O II ORLs. The black curve represents the Gaussian profile from observed intensities and errors. The blue curve is from the mean intensities and errors. The red curve is created from fitting. 0.0 0.5 1.0 1.5 2.0 log adf (O 2+ ) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log T e [K] [O III] H I BJ He I (h7281/h6678) O II N II Hf 2-2 2as M 1-42 NGC 6153 M 2-36 NGC 7009 NGC 6543 IC 4191 fixed M 3-32 M 42 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e -0.912 -0.627 -0.342 -0.057 0.228 0.513 0.798 1.084 1.369 1.654 1.939 -0.912 -0.627 -0.342 -0.057 0.228 0.513 0.798 1.084 1.369 1.654 1.939 Hf 2-2 (2as) (XWL06) adf (O 2+ ) = 84: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) Hf 2-2 (2as) (XWL06) adf (O 2+ ) = 84: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) log r 2 log r 2 a) a) 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e -1.716 -1.444 -1.171 -0.898 -0.625 -0.353 -0.080 0.193 0.466 0.738 1.011 -1.716 -1.444 -1.171 -0.898 -0.625 -0.353 -0.080 0.193 0.466 0.738 1.011 M 1-42 (XWL01) adf (O 2+ ) = 22: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) M 1-42 (XWL01) adf (O 2+ ) = 22: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) log r 2 log r 2 b) b) 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e -1.872 -1.575 -1.277 -0.980 -0.683 -0.385 -0.088 0.210 0.507 0.804 1.102 -1.872 -1.575 -1.277 -0.980 -0.683 -0.385 -0.088 0.210 0.507 0.804 1.102 NGC 6153 (XWL00) adf (O 2+ ) = 9.2: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) NGC 6153 (XWL00) adf (O 2+ ) = 9.2: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) log r 2 log r 2 c) c) 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e -2.275 -1.903 -1.531 -1.158 -0.786 -0.414 -0.042 0.331 0.703 1.075 1.447 -2.275 -1.903 -1.531 -1.158 -0.786 -0.414 -0.042 0.331 0.703 1.075 1.447 M 2-36 (XWL01) adf (O 2+ ) = 6.9: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) M 2-36 (XWL01) adf (O 2+ ) = 6.9: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) log r 2 log r 2 d) d) 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e -2.479 -2.106 -1.733 -1.360 -0.987 -0.614 -0.241 0.132 0.505 0.878 1.251 -2.479 -2.106 -1.733 -1.360 -0.987 -0.614 -0.241 0.132 0.505 0.878 1.251 NGC 7009 (XF11) adf (O 2+ ) = 4.7: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) NGC 7009 (XF11) adf (O 2+ ) = 4.7: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) log r 2 log r 2 e) e) 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e -2.895 -2.542 -2.190 -1.838 -1.485 -1.133 -0.780 -0.428 -0.076 0.277 0.629 -2.895 -2.542 -2.190 -1.838 -1.485 -1.133 -0.780 -0.428 -0.076 0.277 0.629 NGC 6543 (RW04) adf (O 2+ ) = 4.2: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) NGC 6543 (RW04) adf (O 2+ ) = 4.2: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) log r 2 log r 2 f) f) 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e -1.139 -0.970 -0.802 -0.634 -0.466 -0.298 -0.130 0.039 0.207 0.375 0.543 -1.139 -0.970 -0.802 -0.634 -0.466 -0.298 -0.130 0.039 0.207 0.375 0.543 IC 4191 (fixed slit) (YT04) adf (O 2+ ) = 2.4: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) IC 4191 (fixed slit) (YT04) adf (O 2+ ) = 2.4: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) log r 2 log r 2 g) g) 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e -0.455 -0.333 -0.211 -0.089 0.033 0.154 0.276 0.398 0.520 0.642 0.763 -0.455 -0.333 -0.211 -0.089 0.033 0.154 0.276 0.398 0.520 0.642 0.763 M 3-32 (WW07) adf (O 2+ ) = 1.15: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) M 3-32 (WW07) adf (O 2+ ) = 1.15: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) + Iobs(h4035) log r 2 log r 2 h) h) 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 6 log Ne 2.5 3.0 3.5 4.0 log T e -0.772 -0.668 -0.564 -0.460 -0.356 -0.253 -0.149 -0.045 0.059 0.163 0.267 -0.772 -0.668 -0.564 -0.460 -0.356 -0.253 -0.149 -0.045 0.059 0.163 0.267 M 42 (CE04) adf (O 2+ ) = 1.02: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) M 42 (CE04) adf (O 2+ ) = 1.02: Iobs(h5666) + Iobs(h5679) + Iobs(h4041) log r 2 log r 2 i) i) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e -2.294 -1.958 -1.622 -1.286 -0.950 -0.613 -0.277 0.059 0.395 0.731 1.068 -2.294 -1.958 -1.622 -1.286 -0.950 -0.613 -0.277 0.059 0.395 0.731 1.068 Hf 2-2 (2as) (XWL06) adf (O 2+ ) = 84: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) Hf 2-2 (2as) (XWL06) adf (O 2+ ) = 84: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) log r 2 log r 2 a) a) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e -2.091 -1.742 -1.394 -1.046 -0.697 -0.349 -0.000 0.348 0.697 1.045 1.393 -2.091 -1.742 -1.394 -1.046 -0.697 -0.349 -0.000 0.348 0.697 1.045 1.393 M 1-42 (XWL01) adf (O 2+ ) = 22: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) M 1-42 (XWL01) adf (O 2+ ) = 22: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) log r 2 log r 2 b) b) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e -2.697 -2.296 -1.895 -1.494 -1.093 -0.692 -0.290 0.111 0.512 0.913 1.314 -2.697 -2.296 -1.895 -1.494 -1.093 -0.692 -0.290 0.111 0.512 0.913 1.314 NGC 6153 (XWL00) adf (O 2+ ) = 9.2: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) NGC 6153 (XWL00) adf (O 2+ ) = 9.2: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) log r 2 log r 2 c) c) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e -2.566 -2.178 -1.790 -1.402 -1.014 -0.626 -0.238 0.150 0.538 0.926 1.314 -2.566 -2.178 -1.790 -1.402 -1.014 -0.626 -0.238 0.150 0.538 0.926 1.314 M 2-36 (XWL01) adf (O 2+ ) = 6.9: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) M 2-36 (XWL01) adf (O 2+ ) = 6.9: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) log r 2 log r 2 d) d) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e -3.428 -2.951 -2.475 -1.998 -1.522 -1.045 -0.569 -0.092 0.384 0.861 1.337 -3.428 -2.951 -2.475 -1.998 -1.522 -1.045 -0.569 -0.092 0.384 0.861 1.337 NGC 7009 (XF11) adf (O 2+ ) = 4.7: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) NGC 7009 (XF11) adf (O 2+ ) = 4.7: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) log r 2 log r 2 e) e) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e -1.840 -1.567 -1.294 -1.022 -0.749 -0.476 -0.204 0.069 0.342 0.614 0.887 -1.840 -1.567 -1.294 -1.022 -0.749 -0.476 -0.204 0.069 0.342 0.614 0.887 NGC 6543 (RW04) adf (O 2+ ) = 4.2: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) NGC 6543 (RW04) adf (O 2+ ) = 4.2: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) log r 2 log r 2 f) f) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e -1.880 -1.560 -1.241 -0.921 -0.601 -0.281 0.039 0.358 0.678 0.998 1.318 -1.880 -1.560 -1.241 -0.921 -0.601 -0.281 0.039 0.358 0.678 0.998 1.318 IC 4191 (fixed slit) (YT04) adf (O 2+ ) = 2.4: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) IC 4191 (fixed slit) (YT04) adf (O 2+ ) = 2.4: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) log r 2 log r 2 g) g) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e -0.905 -0.715 -0.525 -0.334 -0.144 0.046 0.236 0.426 0.616 0.806 0.997 -0.905 -0.715 -0.525 -0.334 -0.144 0.046 0.236 0.426 0.616 0.806 0.997 M 3-32 (WW07) adf (O 2+ ) = 1.15: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) M 3-32 (WW07) adf (O 2+ ) = 1.15: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) log r 2 log r 2 h) h) 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 5.0 log Ne 3.0 3.5 4.0 log T e -0.975 -0.792 -0.610 -0.427 -0.245 -0.062 0.120 0.303 0.485 0.667 0.850 -0.975 -0.792 -0.610 -0.427 -0.245 -0.062 0.120 0.303 0.485 0.667 0.850 M 42 (CE04) adf (O 2+ ) = 1.02: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) M 42 (CE04) adf (O 2+ ) = 1.02: Iobs(h4649) + Iobs(h4661) + Iobs(h4089) + Iobs(h4087) log r 2 log r 2 i) i) 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 0 84 169 253 337 0 84 169 253 337 Hf 2-2 (2as) (XWL06) adf (O 2+ ) = 84: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) Hf 2-2 (2as) (XWL06) adf (O 2+ ) = 84: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) a) a) 0 200 400 600 800 1000 N (N e sim ) 0 200 400 600 800 1000 N (N e sim ) 0 1000 2000 N (Te sim ) 0 1000 2000 N (Te sim ) 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 0 326 652 978 1304 0 326 652 978 1304 M 1-42 (XWL01) adf (O 2+ ) = 22: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) M 1-42 (XWL01) adf (O 2+ ) = 22: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) b) b) 0 500 1000 1500 2000 N (N e sim ) 0 500 1000 1500 2000 N (N e sim ) 0 3000 6000 N (Te sim ) 0 3000 6000 N (Te sim ) 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 0 245 490 735 980 0 245 490 735 980 NGC 6153 (XWL00) adf (O 2+ ) = 9.2: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) NGC 6153 (XWL00) adf (O 2+ ) = 9.2: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) c) c) 0 500 1000 1500 N (N e sim ) 0 500 1000 1500 N (N e sim ) 0 2750 5500 N (Te sim ) 0 2750 5500 N (Te sim ) 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 0 290 581 871 1161 0 290 581 871 1161 M 2-36 (XWL01) adf (O 2+ ) = 6.9: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) M 2-36 (XWL01) adf (O 2+ ) = 6.9: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) d) d) 0 500 1000 1500 N (N e sim ) 0 500 1000 1500 N (N e sim ) 0 3250 6500 N (Te sim ) 0 3250 6500 N (Te sim ) 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 0 308 616 924 1232 0 308 616 924 1232 NGC 7009 (XF11) adf (O 2+ ) = 4.7: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) NGC 7009 (XF11) adf (O 2+ ) = 4.7: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) e) e) 0 500 1000 1500 2000 N (N e sim ) 0 500 1000 1500 2000 N (N e sim ) 0 3750 7500 N (Te sim ) 0 3750 7500 N (Te sim ) 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 0 488 977 1465 1953 0 488 977 1465 1953 NGC 6543 (RW04) adf (O 2+ ) = 4.2: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) NGC 6543 (RW04) adf (O 2+ ) = 4.2: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) f) f) 0 500 1000 1500 2000 N (N e sim ) 0 500 1000 1500 2000 N (N e sim ) 0 5000 10000 N (Te sim ) 0 5000 10000 N (Te sim ) 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 0 180 361 541 721 0 180 361 541 721 IC 4191 (fixed slit) (YT04) adf (O 2+ ) = 2.4: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) IC 4191 (fixed slit) (YT04) adf (O 2+ ) = 2.4: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) g) g) 0 200 400 600 800 1000 1200 N (N e sim ) 0 200 400 600 800 1000 1200 N (N e sim ) 0 2250 4500 N (Te sim ) 0 2250 4500 N (Te sim ) 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 0 377 755 1132 1509 0 377 755 1132 1509 M 3-32 (WW07) adf (O 2+ ) = 1.15: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) M 3-32 (WW07) adf (O 2+ ) = 1.15: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) h) h) 0 500 1000 1500 2000 N (N e sim ) 0 500 1000 1500 2000 N (N e sim ) 0 2100 4200 N (Te sim ) 0 2100 4200 N (Te sim ) 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 2.0 2.5 3.0 3.5 4.0 4.5 log Ne 3.0 3.5 4.0 log T e 0 489 977 1466 1954 0 489 977 1466 1954 M 42 (CE04) adf (O 2+ ) = 1.02: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) M 42 (CE04) adf (O 2+ ) = 1.02: Isim(h4649) + Isim(h4661) + Isim(h4089) + Isim(h4087) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) i) i) 0 500 1000 1500 2000 2500 N (N e sim ) 0 500 1000 1500 2000 2500 N (N e sim ) 0 5000 10000 N (Te sim ) 0 5000 10000 N (Te sim ) 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e log Ne 2.5 3.0 3.5 4.0 log T e 0 781 1563 2344 3125 0 781 1563 2344 3125 Hf 2-2 (2as) (XWL06) adf (O 2+ ) = 84: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) Hf 2-2 (2as) (XWL06) adf (O 2+ ) = 84: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) a) a) 0 500 1000 1500 2000 2500 3000 N (N e sim ) 0 500 1000 1500 2000 2500 3000 N (N e sim ) 0 3000 6000 N (Te sim ) 0 3000 6000 N (Te sim ) 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e log Ne 2.5 3.0 3.5 4.0 log T e 0 484 967 1451 1934 0 484 967 1451 1934 M 1-42 (XWL01) adf (O 2+ ) = 22: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) M 1-42 (XWL01) adf (O 2+ ) = 22: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) b) b) 0 1000 2000 3000 4000 N (N e sim ) 0 1000 2000 3000 4000 N (N e sim ) 0 1250 2500 N (Te sim ) 0 1250 2500 N (Te sim ) 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e log Ne 2.5 3.0 3.5 4.0 log T e 0 545 1090 1635 2180 0 545 1090 1635 2180 NGC 6153 (XWL00) adf (O 2+ ) = 9.2: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) NGC 6153 (XWL00) adf (O 2+ ) = 9.2: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) c) c) 0 1000 2000 3000 4000 N (N e sim ) 0 1000 2000 3000 4000 N (N e sim ) 0 2500 5000 N (Te sim ) 0 2500 5000 N (Te sim ) 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e log Ne 2.5 3.0 3.5 4.0 log T e 0 306 611 917 1222 0 306 611 917 1222 M 2-36 (XWL01) adf (O 2+ ) = 6.9: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) M 2-36 (XWL01) adf (O 2+ ) = 6.9: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) d) d) 0 200 400 600 800 1000 N (N e sim ) 0 200 400 600 800 1000 N (N e sim ) 0 1550 3100 N (Te sim ) 0 1550 3100 N (Te sim ) 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e log Ne 2.5 3.0 3.5 4.0 log T e 0 164 328 492 656 0 164 328 492 656 NGC 7009 (XF11) adf (O 2+ ) = 4.7: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) NGC 7009 (XF11) adf (O 2+ ) = 4.7: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) e) e) 0 200 400 600 800 1000 N (N e sim ) 0 200 400 600 800 1000 N (N e sim ) 0 1250 2500 N (Te sim ) 0 1250 2500 N (Te sim ) 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e log Ne 2.5 3.0 3.5 4.0 log T e 0 836 1672 2507 3343 0 836 1672 2507 3343 NGC 6543 (RW04) adf (O 2+ ) = 4.2: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) NGC 6543 (RW04) adf (O 2+ ) = 4.2: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) f) f) 0 500 1000 1500 2000 2500 3000 N (N e sim ) 0 500 1000 1500 2000 2500 3000 N (N e sim ) 0 2250 4500 N (Te sim ) 0 2250 4500 N (Te sim ) 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e log Ne 2.5 3.0 3.5 4.0 log T e 0 1103 2205 3308 4410 0 1103 2205 3308 4410 IC 4191 (fixed slit) (YT04) adf (O 2+ ) = 2.4: Isim(h5666) + Isim(h5679) + Isim(h4041) IC 4191 (fixed slit) (YT04) adf (O 2+ ) = 2.4: Isim(h5666) + Isim(h5679) + Isim(h4041) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) g) g) 0 1000 2000 3000 4000 N (N e sim ) 0 1000 2000 3000 4000 N (N e sim ) 0 3300 6600 N (Te sim ) 0 3300 6600 N (Te sim ) 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e log Ne 2.5 3.0 3.5 4.0 log T e 0 291 583 874 1165 0 291 583 874 1165 M 3-32 (WW07) adf (O 2+ ) = 1.15: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) M 3-32 (WW07) adf (O 2+ ) = 1.15: Isim(h5666) + Isim(h5679) + Isim(h4041) + Isim(h4035) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) h) h) 0 500 1000 1500 2000 2500 N (N e sim ) 0 500 1000 1500 2000 2500 N (N e sim ) 0 2250 4500 N (Te sim ) 0 2250 4500 N (Te sim ) 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e 2 3 4 5 log Ne 2.5 3.0 3.5 4.0 log T e log Ne 2.5 3.0 3.5 4.0 log T e 0 1068 2137 3205 4273 0 1068 2137 3205 4273 M 42 (CE04) adf (O 2+ ) = 1.02: Isim(h5666) + Isim(h5679) + Isim(h4041) M 42 (CE04) adf (O 2+ ) = 1.02: Isim(h5666) + Isim(h5679) + Isim(h4041) N (Ne sim ,Te sim ) N (Ne sim ,Te sim ) i) i) 0 2000 4000 6000 N (N e sim ) 0 2000 4000 6000 N (N e sim ) 0 5000 10000 N (Te sim ) 0 5000 10000 N (Te sim ) 0.04 0.05 0.06 0.07 0.08 0.09 I (V3 h5666) 0 100 200 300 400 500 # I obs = 0.0652 m obs = 0.0043 N sim = 10000 I fit = 0.0652 m fit = 0.0043 I mean = 0.0651 m mean = 0.0043 0.11 0.12 0.13 0.14 0.15 0.16 0.17 I (V3 h5679) 0 100 200 300 400 500 # I obs = 0.1355 m obs = 0.0065 N sim = 10000 I fit = 0.1355 m fit = 0.0066 I mean = 0.1355 m mean = 0.0065 0.06 0.07 0.08 0.09 0.10 0.11 I (V39b h4041) 0 100 200 300 400 500 # I obs = 0.0819 m obs = 0.0051 N sim = 10000 I fit = 0.0819 m fit = 0.0051 I mean = 0.0819 m mean = 0.0051 0.01 0.02 0.03 0.04 0.05 0.06 0.07 I (V39a h4035) 0 100 200 300 400 500 # I obs = 0.0371 m obs = 0.0071 N sim = 10000 I fit = 0.0371 m fit = 0.0070 I mean = 0.0370 m mean = 0.0070 0.62 0.64 0.66 0.68 0.70 0.72 I (V1 h4649) 0 100 200 300 400 500 # I obs = 0.6664 m obs = 0.0089 N sim = 10000 I fit = 0.6664 m fit = 0.0089 I mean = 0.6665 m mean = 0.0088 0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28 I (V1 h4661) 0 100 200 300 400 500 # I obs = 0.2174 m obs = 0.0140 N sim = 10000 I fit = 0.2173 m fit = 0.0140 I mean = 0.2172 m mean = 0.0140 0.24 0.25 0.26 0.27 0.28 0.29 I (V48a h4089) 0 100 200 300 400 500 # I obs = 0.2654 m obs = 0.0048 N sim = 10000 I fit = 0.2654 m fit = 0.0049 I mean = 0.2655 m mean = 0.0048 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 I (V48c h4087) 0 100 200 300 400 500 # I obs = 0.0921 m obs = 0.0066 N sim = 10000 I fit = 0.0922 m fit = 0.0066 I mean = 0.0922 m mean = 0.0066 Plasma Diagnostics for Planetary Nebulae and H II Regions using N II and O II Optical Recombination Lines
Plasma diagnostics for planetary nebulae and H II regions using N II and O II
Jun 13, 2015
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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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 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 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 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 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 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 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 intensities within a 1-σ Gaussian distribution confined to the errors of the observed intensities. Fig. 2 shows the Gaussian-distributions for N II and O II wavelengths within 1-σ of the observed intensities. The optimal Te and Ne locations for each simulation would provide the error estimates of the optimal Te and Ne from the observed intensities. The randomly generated intensities were combined for each simulation and compared with the theoretical predictions based on the effective recombination coefficients for each wavelength covering a range of temperatures and densities. Fig. 3 shows the frequencies of the optimal Te and Ne locations derived from the simulated intensities.
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 corresponds to the unique Ne locations, the right panel for the unique Te locations, and the central panel for the 2-dimensional frequency 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 the simulated intensities. The white cross-hairs pinpoint the observed Te and Ne values, as above. The light-green error bars represent the mean sigma values from the simulated intensities. The blue curve represents the Gaussian profile generated from the same mean values and standard deviations centered on the optimal Te and Ne locations obtained from observed intensities.
Fig. 4: Te from literature and values derived here vs. adf from [O III] (red open triangles), the Balmer Jump (orange open circles), He I (yellow open squares) for λ7281/λ6678, O II ORLs (green open diamonds), and N II ORLs (blue open stars), for 8 PNe and 1 H II region,
Results -- For all nebulae analyzed here, the mean value of log Te ([O III]) is 4.02 [K]. The mean value of 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 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 Te is indeed, T
e (ORLs) < T
e (He I) < T
e (H I BJ) < T
e (CELs), confirming the physical conditions in the
two-abundance model, showing that the PNe and H II regions contain a secondary cold, metal-rich and probably H-deficient component.
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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 optical recombination lines (ORLs) with new effective recombination coefficients calculated under the intermediate coupling scheme, for a range of electron temperatures (Te) and densities (Ne), and fitted against the most reliable measurements. Comparing Te derived from ORLs, collisionally excited lines (CELs), the hydrogen Balmer Jump, and/or He I if available, we find the relation Te (ORLs) < Te (He I) < Te (H I BJ) < Te (CELs), confirming the physical conditions in the two-abundance model postulated by Liu et al. (2000), i.e. the nebula contains another cold, metal-rich and probably H-deficient component.
Fig. 1: Log χ2-distributions of the effective recombination coefficients for N II (left 9 panels), from Multiplets V3 & V39, and for O II (right 9 panels), from Multiplets M1, M10, & M48, ORLs for the aforementioned PNe and H II regions, comparing observed intensities with theoretical predictions. The white crosshairs pinpoint the optimal Te and Ne locations for the observed intensities of each nebula.
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
I. McNabb1, X. Fang1, X.W. Liu1,2, P.J. Storey3
Fig. 2: (left 4 panels) Normal distributions for 10,000 simulations for 4 N II ORLs. (right 4 panels) Same for 4 O II ORLs. The black curve represents the Gaussian profile from observed intensities and errors. The blue curve is from the mean intensities and errors. The red curve is created from fitting.
0.0 0.5 1.0 1.5 2.0log adf (O2+)
2.0
2.5
3.0
3.5
4.0
4.5
5.0
log T e
[K]
[O III]H I BJHe I ( 7281/ 6678)O IIN II
Hf 2
-2 2
as
M 1
-42
NGC
6153
M 2
-36
NGC
7009
NGC
6543
IC 4
191
fixed
M 3
-32M
42
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
-0.912
-0.627
-0.342
-0.057
0.228
0.513
0.798
1.084
1.369
1.654
1.939
-0.912
-0.627
-0.342
-0.057
0.228
0.513
0.798
1.084
1.369
1.654
1.939
Hf 2-2 (2as) (XWL06) adf (O2+) = 84: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035)Hf 2-2 (2as) (XWL06) adf (O2+) = 84: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) log 2log 2
a)a)
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
-1.716
-1.444
-1.171
-0.898
-0.625
-0.353
-0.080
0.193
0.466
0.738
1.011
-1.716
-1.444
-1.171
-0.898
-0.625
-0.353
-0.080
0.193
0.466
0.738
1.011
M 1-42 (XWL01) adf (O2+) = 22: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035)M 1-42 (XWL01) adf (O2+) = 22: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) log 2log 2
b)b)
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
-1.872
-1.575
-1.277
-0.980
-0.683
-0.385
-0.088
0.210
0.507
0.804
1.102
-1.872
-1.575
-1.277
-0.980
-0.683
-0.385
-0.088
0.210
0.507
0.804
1.102
NGC 6153 (XWL00) adf (O2+) = 9.2: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035)NGC 6153 (XWL00) adf (O2+) = 9.2: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) log 2log 2
c)c)
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
-2.275
-1.903
-1.531
-1.158
-0.786
-0.414
-0.042
0.331
0.703
1.075
1.447
-2.275
-1.903
-1.531
-1.158
-0.786
-0.414
-0.042
0.331
0.703
1.075
1.447
M 2-36 (XWL01) adf (O2+) = 6.9: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035)M 2-36 (XWL01) adf (O2+) = 6.9: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) log 2log 2
d)d)
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
-2.479
-2.106
-1.733
-1.360
-0.987
-0.614
-0.241
0.132
0.505
0.878
1.251
-2.479
-2.106
-1.733
-1.360
-0.987
-0.614
-0.241
0.132
0.505
0.878
1.251
NGC 7009 (XF11) adf (O2+) = 4.7: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035)NGC 7009 (XF11) adf (O2+) = 4.7: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) log 2log 2
e)e)
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
-2.895
-2.542
-2.190
-1.838
-1.485
-1.133
-0.780
-0.428
-0.076
0.277
0.629
-2.895
-2.542
-2.190
-1.838
-1.485
-1.133
-0.780
-0.428
-0.076
0.277
0.629
NGC 6543 (RW04) adf (O2+) = 4.2: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035)NGC 6543 (RW04) adf (O2+) = 4.2: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) log 2log 2
f)f)
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
-1.139
-0.970
-0.802
-0.634
-0.466
-0.298
-0.130
0.039
0.207
0.375
0.543
-1.139
-0.970
-0.802
-0.634
-0.466
-0.298
-0.130
0.039
0.207
0.375
0.543
IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: Iobs( 5666) + Iobs( 5679) + Iobs( 4041)IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) log 2log 2
g)g)
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
-0.455
-0.333
-0.211
-0.089
0.033
0.154
0.276
0.398
0.520
0.642
0.763
-0.455
-0.333
-0.211
-0.089
0.033
0.154
0.276
0.398
0.520
0.642
0.763
M 3-32 (WW07) adf (O2+) = 1.15: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035)M 3-32 (WW07) adf (O2+) = 1.15: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) + Iobs( 4035) log 2log 2
h)h)
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 6log Ne
2.5
3.0
3.5
4.0
log T e
-0.772
-0.668
-0.564
-0.460
-0.356
-0.253
-0.149
-0.045
0.059
0.163
0.267
-0.772
-0.668
-0.564
-0.460
-0.356
-0.253
-0.149
-0.045
0.059
0.163
0.267
M 42 (CE04) adf (O2+) = 1.02: Iobs( 5666) + Iobs( 5679) + Iobs( 4041)M 42 (CE04) adf (O2+) = 1.02: Iobs( 5666) + Iobs( 5679) + Iobs( 4041) log 2log 2
i)i)
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
-2.294
-1.958
-1.622
-1.286
-0.950
-0.613
-0.277
0.059
0.395
0.731
1.068
-2.294
-1.958
-1.622
-1.286
-0.950
-0.613
-0.277
0.059
0.395
0.731
1.068
Hf 2-2 (2as) (XWL06) adf (O2+) = 84: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087)Hf 2-2 (2as) (XWL06) adf (O2+) = 84: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2log 2
a)a)
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
-2.091
-1.742
-1.394
-1.046
-0.697
-0.349
-0.000
0.348
0.697
1.045
1.393
-2.091
-1.742
-1.394
-1.046
-0.697
-0.349
-0.000
0.348
0.697
1.045
1.393
M 1-42 (XWL01) adf (O2+) = 22: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087)M 1-42 (XWL01) adf (O2+) = 22: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2log 2
b)b)
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
-2.697
-2.296
-1.895
-1.494
-1.093
-0.692
-0.290
0.111
0.512
0.913
1.314
-2.697
-2.296
-1.895
-1.494
-1.093
-0.692
-0.290
0.111
0.512
0.913
1.314
NGC 6153 (XWL00) adf (O2+) = 9.2: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087)NGC 6153 (XWL00) adf (O2+) = 9.2: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2log 2
c)c)
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
-2.566
-2.178
-1.790
-1.402
-1.014
-0.626
-0.238
0.150
0.538
0.926
1.314
-2.566
-2.178
-1.790
-1.402
-1.014
-0.626
-0.238
0.150
0.538
0.926
1.314
M 2-36 (XWL01) adf (O2+) = 6.9: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087)M 2-36 (XWL01) adf (O2+) = 6.9: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2log 2
d)d)
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
-3.428
-2.951
-2.475
-1.998
-1.522
-1.045
-0.569
-0.092
0.384
0.861
1.337
-3.428
-2.951
-2.475
-1.998
-1.522
-1.045
-0.569
-0.092
0.384
0.861
1.337
NGC 7009 (XF11) adf (O2+) = 4.7: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087)NGC 7009 (XF11) adf (O2+) = 4.7: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2log 2
e)e)
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
-1.840
-1.567
-1.294
-1.022
-0.749
-0.476
-0.204
0.069
0.342
0.614
0.887
-1.840
-1.567
-1.294
-1.022
-0.749
-0.476
-0.204
0.069
0.342
0.614
0.887
NGC 6543 (RW04) adf (O2+) = 4.2: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087)NGC 6543 (RW04) adf (O2+) = 4.2: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2log 2
f)f)
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
-1.880
-1.560
-1.241
-0.921
-0.601
-0.281
0.039
0.358
0.678
0.998
1.318
-1.880
-1.560
-1.241
-0.921
-0.601
-0.281
0.039
0.358
0.678
0.998
1.318
IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087)IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2log 2
g)g)
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
-0.905
-0.715
-0.525
-0.334
-0.144
0.046
0.236
0.426
0.616
0.806
0.997
-0.905
-0.715
-0.525
-0.334
-0.144
0.046
0.236
0.426
0.616
0.806
0.997
M 3-32 (WW07) adf (O2+) = 1.15: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087)M 3-32 (WW07) adf (O2+) = 1.15: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2log 2
h)h)
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 5.0log Ne
3.0
3.5
4.0
log T e
-0.975
-0.792
-0.610
-0.427
-0.245
-0.062
0.120
0.303
0.485
0.667
0.850
-0.975
-0.792
-0.610
-0.427
-0.245
-0.062
0.120
0.303
0.485
0.667
0.850
M 42 (CE04) adf (O2+) = 1.02: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087)M 42 (CE04) adf (O2+) = 1.02: Iobs( 4649) + Iobs( 4661) + Iobs( 4089) + Iobs( 4087) log 2log 2
i)i)
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
0
84
169
253
337
0
84
169
253
337
Hf 2-2 (2as) (XWL06) adf (O2+) = 84: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)Hf 2-2 (2as) (XWL06) adf (O2+) = 84: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)
N (Nesim,Te
sim)N (Nesim,Te
sim)
a)a)
0
200400600800
1000
N (N
esim)
0
200400600800
1000
N (N
esim)
0 1000 2000N (Te
sim)
0 1000 2000N (Te
sim)
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
0
326
652
978
1304
0
326
652
978
1304
M 1-42 (XWL01) adf (O2+) = 22: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)M 1-42 (XWL01) adf (O2+) = 22: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)
N (Nesim,Te
sim)N (Nesim,Te
sim)
b)b)
0
500100015002000
N (N
esim)
0
500100015002000
N (N
esim)
0 3000 6000N (Te
sim)
0 3000 6000N (Te
sim)
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
0
245
490
735
980
0
245
490
735
980
NGC 6153 (XWL00) adf (O2+) = 9.2: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)NGC 6153 (XWL00) adf (O2+) = 9.2: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)
N (Nesim,Te
sim)N (Nesim,Te
sim)
c)c)
0
500
1000
1500
N (N
esim)
0
500
1000
1500
N (N
esim)
0 2750 5500N (Te
sim)
0 2750 5500N (Te
sim)
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
0
290
581
871
1161
0
290
581
871
1161
M 2-36 (XWL01) adf (O2+) = 6.9: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)M 2-36 (XWL01) adf (O2+) = 6.9: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)
N (Nesim,Te
sim)N (Nesim,Te
sim)
d)d)
0
500
1000
1500
N (N
esim)
0
500
1000
1500
N (N
esim)
0 3250 6500N (Te
sim)
0 3250 6500N (Te
sim)
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
0
308
616
924
1232
0
308
616
924
1232
NGC 7009 (XF11) adf (O2+) = 4.7: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)NGC 7009 (XF11) adf (O2+) = 4.7: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)
N (Nesim,Te
sim)N (Nesim,Te
sim)
e)e)
0
500100015002000
N (N
esim)
0
500100015002000
N (N
esim)
0 3750 7500N (Te
sim)
0 3750 7500N (Te
sim)
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
0
488
977
1465
1953
0
488
977
1465
1953
NGC 6543 (RW04) adf (O2+) = 4.2: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)NGC 6543 (RW04) adf (O2+) = 4.2: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)
N (Nesim,Te
sim)N (Nesim,Te
sim)
f)f)
0
500100015002000
N (N
esim)
0
500100015002000
N (N
esim)
0 5000 10000N (Te
sim)
0 5000 10000N (Te
sim)
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
0
180
361
541
721
0
180
361
541
721
IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)
N (Nesim,Te
sim)N (Nesim,Te
sim)
g)g)
0
200400600800
10001200
N (N
esim)
0
200400600800
10001200
N (N
esim)
0 2250 4500N (Te
sim)
0 2250 4500N (Te
sim)
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
0
377
755
1132
1509
0
377
755
1132
1509
M 3-32 (WW07) adf (O2+) = 1.15: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)M 3-32 (WW07) adf (O2+) = 1.15: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)
N (Nesim,Te
sim)N (Nesim,Te
sim)
h)h)
0
500100015002000
N (N
esim)
0
500100015002000
N (N
esim)
0 2100 4200N (Te
sim)
0 2100 4200N (Te
sim)
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
2.0 2.5 3.0 3.5 4.0 4.5 log Ne
3.0
3.5
4.0
log T e
0
489
977
1466
1954
0
489
977
1466
1954
M 42 (CE04) adf (O2+) = 1.02: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)M 42 (CE04) adf (O2+) = 1.02: Isim( 4649) + Isim( 4661) + Isim( 4089) + Isim( 4087)
N (Nesim,Te
sim)N (Nesim,Te
sim)
i)i)
0
5001000150020002500
N (N
esim)
0
5001000150020002500
N (N
esim)
0 5000 10000N (Te
sim)
0 5000 10000N (Te
sim)
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
log Ne
2.5
3.0
3.5
4.0
log T e
0
781
1563
2344
3125
0
781
1563
2344
3125
Hf 2-2 (2as) (XWL06) adf (O2+) = 84: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)Hf 2-2 (2as) (XWL06) adf (O2+) = 84: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)
N (Nesim,Te
sim)N (Nesim,Te
sim)
a)a)
0
50010001500200025003000
N (N
esim)
0
50010001500200025003000
N (N
esim)
0 3000 6000N (Te
sim)
0 3000 6000N (Te
sim)
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
log Ne
2.5
3.0
3.5
4.0
log T e
0
484
967
1451
1934
0
484
967
1451
1934
M 1-42 (XWL01) adf (O2+) = 22: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)M 1-42 (XWL01) adf (O2+) = 22: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)
N (Nesim,Te
sim)N (Nesim,Te
sim)
b)b)
0
1000200030004000
N (N
esim)
0
1000200030004000
N (N
esim)
0 1250 2500N (Te
sim)
0 1250 2500N (Te
sim)
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
log Ne
2.5
3.0
3.5
4.0
log T e
0
545
1090
1635
2180
0
545
1090
1635
2180
NGC 6153 (XWL00) adf (O2+) = 9.2: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)NGC 6153 (XWL00) adf (O2+) = 9.2: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)
N (Nesim,Te
sim)N (Nesim,Te
sim)
c)c)
0
1000200030004000
N (N
esim)
0
1000200030004000
N (N
esim)
0 2500 5000N (Te
sim)
0 2500 5000N (Te
sim)
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
log Ne
2.5
3.0
3.5
4.0
log T e
0
306
611
917
1222
0
306
611
917
1222
M 2-36 (XWL01) adf (O2+) = 6.9: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)M 2-36 (XWL01) adf (O2+) = 6.9: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)
N (Nesim,Te
sim)N (Nesim,Te
sim)
d)d)
0
200400600800
1000
N (N
esim)
0
200400600800
1000
N (N
esim)
0 1550 3100N (Te
sim)
0 1550 3100N (Te
sim)
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
log Ne
2.5
3.0
3.5
4.0
log T e
0
164
328
492
656
0
164
328
492
656
NGC 7009 (XF11) adf (O2+) = 4.7: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)NGC 7009 (XF11) adf (O2+) = 4.7: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)
N (Nesim,Te
sim)N (Nesim,Te
sim)
e)e)
0
200400600800
1000
N (N
esim)
0
200400600800
1000
N (N
esim)
0 1250 2500N (Te
sim)
0 1250 2500N (Te
sim)
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
log Ne
2.5
3.0
3.5
4.0
log T e
0
836
1672
2507
3343
0
836
1672
2507
3343
NGC 6543 (RW04) adf (O2+) = 4.2: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)NGC 6543 (RW04) adf (O2+) = 4.2: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)
N (Nesim,Te
sim)N (Nesim,Te
sim)
f)f)
0
50010001500200025003000
N (N
esim)
0
50010001500200025003000
N (N
esim)
0 2250 4500N (Te
sim)
0 2250 4500N (Te
sim)
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
log Ne
2.5
3.0
3.5
4.0
log T e
0
1103
2205
3308
4410
0
1103
2205
3308
4410
IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: Isim( 5666) + Isim( 5679) + Isim( 4041)IC 4191 (fixed slit) (YT04) adf (O2+) = 2.4: Isim( 5666) + Isim( 5679) + Isim( 4041)
N (Nesim,Te
sim)N (Nesim,Te
sim)
g)g)
0
1000200030004000
N (N
esim)
0
1000200030004000
N (N
esim)
0 3300 6600N (Te
sim)
0 3300 6600N (Te
sim)
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
log Ne
2.5
3.0
3.5
4.0
log T e
0
291
583
874
1165
0
291
583
874
1165
M 3-32 (WW07) adf (O2+) = 1.15: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)M 3-32 (WW07) adf (O2+) = 1.15: Isim( 5666) + Isim( 5679) + Isim( 4041) + Isim( 4035)
N (Nesim,Te
sim)N (Nesim,Te
sim)
h)h)
0
5001000150020002500
N (N
esim)
0
5001000150020002500
N (N
esim)
0 2250 4500N (Te
sim)
0 2250 4500N (Te
sim)
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
2 3 4 5 log Ne
2.5
3.0
3.5
4.0
log T e
log Ne
2.5
3.0
3.5
4.0
log T e
0
1068
2137
3205
4273
0
1068
2137
3205
4273
M 42 (CE04) adf (O2+) = 1.02: Isim( 5666) + Isim( 5679) + Isim( 4041)M 42 (CE04) adf (O2+) = 1.02: Isim( 5666) + Isim( 5679) + Isim( 4041)
N (Nesim,Te
sim)N (Nesim,Te
sim)
i)i)
0
2000
4000
6000
N (N
esim)
0
2000
4000
6000
N (N
esim)
0 5000 10000N (Te
sim)
0 5000 10000N (Te
sim)
0.04 0.05 0.06 0.07 0.08 0.09I (V3 5666)
0
100
200
300
400
500
#
Iobs = 0.0652obs= 0.0043
Nsim = 10000
Ifit = 0.0652fit = 0.0043
Imean = 0.0651mean = 0.0043
0.11 0.12 0.13 0.14 0.15 0.16 0.17I (V3 5679)
0
100
200
300
400
500
#
Iobs = 0.1355obs= 0.0065
Nsim = 10000
Ifit = 0.1355fit = 0.0066
Imean = 0.1355mean = 0.0065
0.06 0.07 0.08 0.09 0.10 0.11I (V39b 4041)
0
100
200
300
400
500
#
Iobs = 0.0819obs= 0.0051
Nsim = 10000
Ifit = 0.0819fit = 0.0051
Imean = 0.0819mean = 0.0051
0.01 0.02 0.03 0.04 0.05 0.06 0.07I (V39a 4035)
0
100
200
300
400
500
#
Iobs = 0.0371obs= 0.0071
Nsim = 10000
Ifit = 0.0371fit = 0.0070
Imean = 0.0370mean = 0.0070
0.62 0.64 0.66 0.68 0.70 0.72I (V1 4649)
0
100
200
300
400
500
#
Iobs = 0.6664obs= 0.0089
Nsim = 10000
Ifit = 0.6664fit = 0.0089
Imean = 0.6665mean = 0.0088
0.14 0.16 0.18 0.20 0.22 0.24 0.26 0.28I (V1 4661)
0
100
200
300
400
500
#
Iobs = 0.2174obs= 0.0140
Nsim = 10000
Ifit = 0.2173fit = 0.0140
Imean = 0.2172mean = 0.0140
0.24 0.25 0.26 0.27 0.28 0.29I (V48a 4089)
0
100
200
300
400
500
#
Iobs = 0.2654obs= 0.0048
Nsim = 10000
Ifit = 0.2654fit = 0.0049
Imean = 0.2655mean = 0.0048
0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13I (V48c 4087)
0
100
200
300
400
500
#
Iobs = 0.0921obs= 0.0066
Nsim = 10000
Ifit = 0.0922fit = 0.0066
Imean = 0.0922mean = 0.0066
Plasma Diagnostics for Planetary Nebulae and H II Regions using N II and O II Optical Recombination Lines
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