Physical Structure of Planetary Nebulae. I. The Owl Nebula

The Owl Nebula is a triple-shell planetary nebula with the outermost shell being a faint bow-shaped halo. We have obtained deep narrow-band images and high-dispersion echelle spectra in the H-alpha, [O III], and [N II] emission lines to determine the physical structure of each shell in the nebula. These spatio-kinematic data allow us to rule out hydrodynamic models that can reproduce only the nebular morphology. Our analysis shows that the inner shell of the main nebula is slightly elongated with a bipolar cavity along its major axis, the outer nebula is a filled envelope co-expanding with the inner shell at 40 km/s, and the halo has been braked by the interstellar medium as the Owl Nebula moves through it. To explain the morphology and kinematics of the Owl Nebula, we suggest the following scenario for its formation and evolution. The early mass loss at the TP-AGB phase forms the halo, and the superwind at the end of the AGB phase forms the main nebula. The subsequent fast stellar wind compressed the superwind to form the inner shell and excavated an elongated cavity at the center, but has ceased in the past. At the current old age, the inner shell is backfilling the central cavity.Comment: 10 pages, 6 figures, 1 table, to appear in the Astronomical Journa

PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics

A non-Hermitian Hamiltonian that has an unbroken PT symmetry can be converted by means of a similarity transformation to a physically equivalent Hermitian Hamiltonian. This raises the following question: In which form of the quantum theory, the non-Hermitian or the Hermitian one, is it easier to perform calculations? This paper compares both forms of a non-Hermitian $ix^3$ quantum-mechanical Hamiltonian and demonstrates that it is much harder to perform calculations in the Hermitian theory because the perturbation series for the Hermitian Hamiltonian is constructed from divergent Feynman graphs. For the Hermitian version of the theory, dimensional continuation is used to regulate the divergent graphs that contribute to the ground-state energy and the one-point Green's function. The results that are obtained are identical to those found much more simply and without divergences in the non-Hermitian PT-symmetric Hamiltonian. The $\mathcal{O}(g^4)$ contribution to the ground-state energy of the Hermitian version of the theory involves graphs with overlapping divergences, and these graphs are extremely difficult to regulate. In contrast, the graphs for the non-Hermitian version of the theory are finite to all orders and they are very easy to evaluate.Comment: 13 pages, REVTeX, 10 eps figure

Clusters in the Luminous Giant HII Regions in M101

(Abridged) We have obtained HST WFPC2 observations of three very luminous but morphologically different giant HII regions (GHRs) in M101, NGC5461, NGC5462, and NGC5471, in order to study cluster formation in GHRs. The measured (M_F547M - M_F675W) colors and M_F547M magnitudes are used to determine the ages and masses of the cluster candidates with M_F547M <= -9.0. NGC5461 is dominated by a very luminous core, and has been suggested to host a super-star cluster (SSC). Our observations show that it contains three R136-class clusters superposed on a bright stellar background in a small region. This tight group of clusters may dynamically evolve into an SSC in the future, and may appear unresolved and be identified as an SSC at large distances, but at present NGC5461 has no SSCs. NGC5462 has loosely distributed HII regions and clusters without a prominent core. It has the largest number of cluster candidates among the three GHRs, but most of them are faint and older than 10 Myr. NGC5471 has multiple bright HII regions, and contains a large number of faint clusters younger than 5 Myr. Two of the clusters in NGC5471 are older than R136, but just as luminous; they may be the most massive clusters in the three GHRs. The fraction of stars formed in massive clusters is estimated from the clusters' contribution to the total stellar continuum emission and a comparison of the ionizing power of the clusters to the ionizing requirement of the associated HII regions. Both estimates show that <~ 50% of massive stars are formed in massive clusters. The cluster luminosity functions (CLFs) of the three GHRs show different slopes. NGC5462 has the steepest CLF and the most loosely distributed interstellar gas, qualitatively consistent with the hypothesis that massive clusters are formed in high-pressure interstellar environments.Comment: 36 pages (figures not included), 16 figures (3 of them are color figures). Figures are in JPEG or GIF format with a lower resolution due to the size limit of the file. For a higher resolution version of the paper, please download from http://www.astro.uiuc.edu/~c-chen/clusters.pdf. accepted for ApJ (scheduled for the ApJ 2005 February issue