W. Wang X.-W. Liu, Y. Zhang & M.J. Barlow A Reexamination of Electron Density Diagnostics for Ionized Gaseous Nebulae W. Wang X.-W. Liu, Y. Zhang & M.J. Barlow

Motivations Different tracers 1. To characterize structure of ionized nebulae Different tracers 2. To test the accuracy of calculations of atomic physics Compared with observations 3. To test the result of McLaughlin & Bell 1998 Showing departure from the LS-coupling for [O II]

Tools 2D3/2 2D5/2 4S3/2 [O II] 2P3 Ne >> Nc λ3729 λ3726 (2) Ne >> Nc λ3729 λ3726 2D5/2 2D3/2 4S3/2 38635 Nc 4200 1200 Tex 38606 Test of A values Ne << Nc (3) (LS-coupling) Test of q values M B 1998 show q ratio = 1.93 ? !

The four density indicators Te = 10000 K Line ratios S+,O+,Cl++ are similar in their IPs and Nc, thus should yield consistent densities . Ar3+ has much higher IP and Nc, thus should yield higher densities . Log Ne (cm-3)

Previous work – various conclusions Meatheringham & Dopita 1991 Kingsburgh & English 1992 Copetti & Writzl 2002 Stanghellini & Kaler 1989 Two causes : Intrinsic? Ne variations; ionization stratifications atomic? Adopting different atomic parameters

Z82 P76 Z87 P76 W96 P76 Z87 MB98 Z82, P76 is best fit Z87, W96 can be ruled out by this figure Low Ne limit 1.93 (MB98) Z82 P76 Z87 P76 W96 P76 Z87 MB98 CW02 excludes MB98 using the departure of the pink line from data We argue that it is not sufficient. Because relativistic effects for S II are more serious than O II and easier to fail LS-coupling Key test: whether there are observational ratios in excess of 1.50 None of PNe in my sample has ratio exceeding 1.50

O II literature survey --- no evidence supports MB1998

S II – the best available measurements PN Near Diff. Em. I(6716) I(6731) NGC 3195 1.98:: Fg 1 1.45±0.11 He 2-104 1.71 ±0.21 He 2-141 1.62 ±0.22 He 2-146 1.52 ±0.15 NGC 6072 1.61 ±0.19 Mz 2 1.44 ±0.11 IC 4634 2.14:: IC 4637 1.75:: Our sample: largest ratio : 1.21 ±0.028 KE 1992 : double spectrograph, scanning whole nebulae Among their 57 PNe largest ratio: 1.35 ± 0.038 22 detection for diffuse Galactic emission. See Table

Unexpected .. R(average) = 1.85 Two exceed 1.5 by more than 2 σ Galarza, Walterbos & Braun (1999) have observed H II regions and SNRs in M31 Among their result, some ratios are much larger than 1.5, as listed in the right table R(average) = 1.85 Two exceed 1.5 by more than 2 σ The observation is not very reliable 4 for H II regions and 5 for SNRs in M31 [1] Galarza, Walterbos & Braun (1999)

5 4 3 2 When Ne >> Nc, Testing A value Fit to the data points Log Ne from [S II]6716/6731 A(2D5/2)/A(2D3/2) from Zeippen 1982 needs to be revised upwards by 6% This conclusion is based on the assumption that A values for [S II] are in good shape 2 3 4 5 Log Ne from [O II] 3729/3726

Ne (S II) ~ Ne (Cl III) > Ne (O III) Log Ne from [Cl III]5517/5537 5 4 3 2 2 3 4 5 Log Ne from [O II] 3729/3726 2 3 4 5 Log Ne from [S II] 6716/6731 Ne (S II) ~ Ne (Cl III) > Ne (O III) Confirm that it is A values for [ O II] that need to be revised

Ne (Ar IV) is larger than the others Log Ne from [Ar IV]4711/4740 5 4 3 2 2 3 4 5 Log Ne from [S II] 6716/6731 2 3 4 5 Log Ne from [Cl III] 5517/5537 Ne (Ar IV) is larger than the others The discrepancies become larger as Ne increase. Causes: Inhomogeneities and/ or ionization stratifications

Summary Ne([OII]) ≦Ne([S II]) ≈ Ne([Cl III])< Ne([Ar IV]) 1. For [O II], Ai from Z82,and qij from P76 are the most compatible with observations, yet A(3729)/A(3726) needs a 6% rise 2. More recent calculation of Ai from Z87 and qij from Wiese 96 are ruled out 3. Best observations so far do not support the calculation by MB98 of qij for [O II] However, it is worth further investigation on the validity of LS-coupling 4. Using atomic set of Z82 and P76, we find Ne([OII]) ≦Ne([S II]) ≈ Ne([Cl III])< Ne([Ar IV])