Electron temperatures and densities of planetary nebulae determined from the nebular hydrogen recombination spectrum and temperature and density variations

Abstract

A method is presented to derive electron temperatures and densities of planetary nebulae (PNe) simultaneously, using the observed hydrogen recombination spectrum, which includes continuum and line emission. By matching theoretical spectra to observed spectra around the Balmer jump at about 3646 Å, we determine electron temperatures and densities for 48 Galactic PNe. The electron temperatures based on this method – hereafter Te(Bal) – are found to be systematically lower than those derived from [O iii]λ4959/λ4363 and [O iii](88 μm + 52 μm)/λ4959 ratios – hereafter Te([O iii]na) and Te([O iii]fn). The electron densities based on this method are found to be systematically higher than those derived from [O ii]λ3729/λ3726, [S ii]λ6731/λ6716, [Cl iii]λ5537/λ5517, [Ar iv]λ4740/λ4711 and [O iii]88 μm/52 μm ratios. These results suggest that temperature and density fluctuations are generally present within nebulae. The comparison of Te([O iii]na) and Te(Bal) suggests that the fractional mean‐square temperature variation (t2) has a representative value of 0.031. A majority of temperatures derived from the Te([O iii]fn) ratio are found to be higher than those of Te([O iii]na), which is attributed to the existence of dense clumps in nebulae – those [O iii] infrared fine‐structure lines are suppressed by collisional de‐excitation in the clumps. By comparing Te([O iii]fn), Te([O iii]na) and Te(Bal) and assuming a simple two‐density‐component model, we find that the filling factor of dense clumps has a representative value of 7 × 10−5. The discrepancies between Te([O iii]na) and Te(Bal) are found to be anticorrelated with electron densities derived from various density indicators; high‐density nebulae have the smallest temperature discrepancies. This suggests that temperature discrepancy is related to nebular evolution. In addition, He/H abundances of PNe are found to be positively correlated with the difference between Te([O iii]na) and Te(Bal), suggesting that He/H abundances might have been overestimated generally because of the possible existence of H‐deficient knots. Electron temperatures and densities deduced from spectra around the Paschen jump regions at 8250 Å are also obtained for four PNe: NGC 7027, NGC 6153, M 1–42 and NGC 7009. Electron densities derived from spectra around the Paschen jump regions are in good agreement with the corresponding values derived from spectra around the Balmer jump, whereas temperatures deduced from the spectra around the Paschen jump are found to be lower than the corresponding values derived from spectra around the Balmer jump for all the four cases. The reason remains unclear.

A pilot study of the radio‐continuum emission from MASH planetary nebulae

“…A possible explanation for this discrepancy could be strong temperature gradients within the nebula (Peimbert 1967), or inner, hydrogen deficient clumps embedded in the diffuse nebula (Zhang et al 2009). The electron density determined from the hydrogen recombination spectrum near the Balmer jump region of n e ≈400 cm −3 (Zhang et al 2004) is a factor of two larger than our radio-continuum determined value.…”

The extinction and dust-to-gas structure of the planetary nebula NGC 7009 observed with MUSE

“…In the case of NGC 7009, the Balmer and Paschen jump temperatures were determined as 7200 K and 5800 K, respectively (Zhang et al 2004); thus 3000−4000 K lower than from the forbidden line temperatures ([O III] and [S III]). The region sampled by the spectra used to fit the Balmer and Paschen jumps is not explicitly specified, but appears to correspond to the bright main shell.…”

“…The region sampled by the spectra used to fit the Balmer and Paschen jumps is not explicitly specified, but appears to correspond to the bright main shell. Although it cannot be stated with certainty that there is no temperature impulse at the main shell rim applicable to H and coincident with the extinction trough, this appears unlikely given that the majority of PNe (cf., Zhang et al 2004) show T e (Bal) < T e [O III].…”

“…From studies of the H temperature from the Balmer (and Paschen) jump in PNe (Zhang et al 2004;Liu & Danziger 1993), it was found that T e (Bal) is generally systematically lower than T e determined from [O III] 5007/4363 Å. In the case of NGC 7009, the Balmer and Paschen jump temperatures were determined as 7200 K and 5800 K, respectively (Zhang et al 2004); thus 3000−4000 K lower than from the forbidden line temperatures ([O III] and [S III]).…”

Significant new planetary nebula discoveries as powerful probes of the LMC

“…The method applied was the temperature equation provided by Osterbrock & Ferland (2006) High T e between 20,000 and 30,000 K are due to both the high T of the PN and high electron densities in PNe, compared to H ii regions as well as low Z in the LMC. Some of the large dispersion is also due to physical differences in the nebulae and may also be related to nebula evolution (e.g., Zhang et al 2004). 108 PNe or 43% of the [O iii] T e sample are above 15,000 K (generally the highest T e for H ii regions (Osterbrock & Ferland 2006)).…”