1. Yong Zhang Department of Astronomy, Peking University
Using Hydrogen Recombination Spectrum to Probe Nebular Physical Conditions
Yong Zhang
Department of Astronomy, Peking University
Collaborators:
X.-W. Liu (PKU)
R. Wesson (UCL)
P. J. Storey (UCL)
Y. Liu (PKU)
I. J. Danziger (OAT)
astro-ph/

2. Motivations
Electron temperature and density are fundamental parameters for the derivation of all other physical and chemical quantities of nebulae.
To further understand the known BJ/CEL temperature discrepancy and the ORL/CEL abundance disparity requires more tools to probe nebular physical conditions.

3. The method Same density (Ne=104 cm-3) Different temperatures
Same temperature
(Te=104K)
Different densities
Ne=105cm-3
Ne=103cm-3

4. Advantages H I recombination spectra are observable in all PNe.
H I transitions have very high critical densities (permitted lines), so can be used to probe high-density regions.
The comparison of the results derived from H I recombination spectra with those derived from CELs enables us to quantify Te and Ne variations.

5. Fitting observed spectrum
We have analysed 48 PNe
Model:
H I, He I and He II continua; He I lines; H I and He II lines (n=1--500); stellar contribution
slope (Ne)
Neb. Cont.
jump (Te)
Stellar

6. Comparison of densities
Nc([O III] 52um) = 3500 cm-3
Nc([O III] 88um) = 1500 cm-3
Ne(H I) > Ne([O III])
The discrepancy increases with increasing density.
Explanation: condensations are ubiquitous in PNe.
log Ne([O III]52um/88um) (cm-3)
log Ne(H I) (cm-3)

7. Te([O III]λ4959/λ4363) vs. Te(H I)20
Te([O III]) > Te(H I)
Parts of Te difference can be accounted by temperature fluctuations.
Temperature fluctuations cannot account for the cases in some extreme PNe, as labeled.
variable source ? 15
Te([O III] λ4959/λ4363) (103K)
shock heating ? 10
M 1-42 5
Te(H I) (103K)

8. Te([O III](52um+88um)/λ4959) vs. Te(H I)
Nc([O III] 52um,88um) < 4×103 cm-3
Nc([O III] λ4959) = 7×105 cm-3
For Te([O III]fn) vs. Te(H I), the discrepancy Is larger. This is attributed to density variations since [O III] 52um,88um lines have much lower critical densities than [O III] λ4959.
Te([O III] (52um+88um)/λ4959) (K)
0.10
0.06
0.02 t2
Te(H I) (K)

9. Te([O III] λ4959/λ4363) vs. Te([O III](52um+88um)/λ4959)
temperature variations
density variations t
0.1
0.5
1.0
2.0
u2w 5 10 15 20
Temperature and density variations are generally present within PNe.
Using a two-density-component model and assuming that the condensations have a density of 105cm-3, we find that the condensations have a filling factor of about
10-4—10-5.
Te([O III] λ4959/λ4363) (10-3K)
Te([O III](52um+88um)/λ4959) (10-3K)

10. Te(OIII)-Te(Bal) vs. Ne
Large old PNe have higher temperature discrepancies.
Te([O III] λ4959/λ4363) –Te(H I) (K)
log Ne([S III]) (cm-3)

11. Conclusions
We present observational evidence suggesting that both temperature and density variations are generally present in PNe.
They lead to different temperatures and densities derived from different diagnostics.
Part of the known temperature discrepancy could be accounted for by temperature and density variations, but not all.