This document analyzes plasma diagnostics for planetary nebulae and H II regions using optical recombination lines of N II and O II. It calculates effective recombination coefficients over ranges of electron temperature and density. It fits observed line intensities of several nebulae against theoretical predictions to determine optimal temperature and density. Comparisons with other diagnostics confirm a two-abundance model with a cold, metal-rich component.

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 0
3125 1934 2180 337 1304 980
4.0 4.0 4.0 4.0 4.0 4.0
2344
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 Te
1563 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 and
N (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 0
1222 656 3343 1161 1232 1953
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