On the O II ground configuration energy levels

The most accurate way to measure the energy levels for the O II 2p^3 ground configuration has been from the forbidden lines in planetary nebulae. We present an analysis of modern planetary nebula data that nicely constrain the splitting within the ^2D term and the separation of this term from the ground ^4S_{3/2} level. We extend this method to H II regions using high-resolution spectroscopy of the Orion nebula, covering all six visible transitions within the ground configuration. These data confirm the splitting of the ^2D term while additionally constraining the splitting of the ^2P term. The energies of the ^2P and ^2D terms relative to the ground (^4S) term are constrained by requiring that all six lines give the same radial velocity, consistent with independent limits placed on the motion of the O+ gas and the planetary nebula data.Comment: 20 pages, 3 figures. To be published in Ap

Getting Super-Excited with Modified Dispersion Relations

We demonstrate that in some regions of parameter space, modified dispersion relations can lead to highly populated excited states, which we dub as "super-excited" states. In order to prepare such super-excited states, we invoke dispersion relations that have negative slope in an interim sub-horizon phase at high momenta. This behaviour of quantum fluctuations can lead to large corrections relative to the Bunch-Davies power spectrum, which mimics highly excited initial conditions. We identify the Bogolyubov coefficients that can yield these power spectra. In the course of this computation, we also point out the shortcomings of the gluing method for evaluating the power spectrum and the Bogolyubov coefficients. As we discuss, there are other regions of parameter space, where the power spectrum does not get modified. Therefore, modified dispersion relations can also lead to so-called "calm excited states" as well. We conclude by commenting on the possibility of obtaining these modified dispersion relations within the Effective Field Theory of Inflation.Comment: 1+19 pages, 4 figure

Nonuniqueness for the kinetic Fokker-Planck equation with inelastic boundary conditions

We describe the structure of solutions of the kinetic Fokker-Planck equations in domains with boundaries near the singular set in one-space dimension. We study in particular the behaviour of the solutions of this equation for inelastic boundary conditions which are characterized by means of a coefficient $r$ describing the amount of energy lost in the collisions of the particles with the boundaries of the domain. A peculiar feature of this problem is the onset of a critical exponent rc which follows from the analysis of McKean (cf. [26]) of the properties of the stochastic process associated to the Fokker-Planck equation under consideration. In this paper, we prove rigorously that the solutions of the considered problem are nonunique if $r < r_c$ and unique if $r_{c}<r\leq 1$. In particular, this nonuniqueness explains the different behaviours found in the physics literature for numerical simulations of the stochastic differential equation associated to the Fokker-Planck equation. In the proof of the results of this paper we use several asymptotic formulas and computations in the companion paper [16].Comment: 64 pages, 1 figure. Previous version has been split into tw

Fluorescent Excitation of Spectral Lines in Planetary Nebulae

Fluorescent excitation of spectral lines is demonstrated as a function of temperature-luminosity and the distance of the emitting region from the central stars of planetary nebulae. The electron densities and temperatures are determined, and the method is exemplified through a detailed analysis of spectral observations of a high excitation PN, NGC 6741, observed by Hyung and Aller(1997). Fluorescence should also be important in the determination of element abundances. It is suggested that the method could be generally applied to determine or constrain the luminosity and the region of spectral emission in other intensively radiative sources such as novae, supernovae, and active galactic nuclei.Comment: 5 pages, 4 figures (fig.4 in color), ApJ (in press

Trajectory of test particle around a slowly rotating relativistic star emitting isotropic radiation

We explored the motion of test particles near slowly rotating relativistic star having a uniform luminosity. In order to derive the test particle's equations of motion, we made use of the radiation stress-energy tensor first constructed by Miller and Lamb \cite{ML96}. From the particle's trajectory obtained through the numerical integration of the equations of motion, it is found that for sufficiently high luminosity, "suspension orbit" exists, where the test particle hovers around at uniform angular velocity in the same direction as the star's spin. Interestingly, it turned out that the radial position of the "suspension orbit" was determined by the luminosity and the angular momentum of the star alone and was independent of the initial positions and the specific angular momentum of the particle. Also found is that there exist not only the radiation drag but also "radiation counter-drag" which depends on the stellar radius and the angular momentum and it is this radiation counter-drag that makes the test particle in the "suspension orbit" to hover around at uniform angular velocity which is greater than that induced by the Lense-Thirring effect (i.e., general relativistic dragging of inertial frame).Comment: 23 pages, 7 figures, to appear in Phys. Rev. D

A Reexamination of Electron Density Diagnostics for Ionized Gaseous Nebulae

We present a comparison of electron densities derived from optical forbidden line diagnostic ratios for a sample of over a hundred nebulae. We consider four density indicators, the [O II] $\lambda3729/\lambda3726$, [S II] $\lambda6716/\lambda6731$, [Cl III] $\lambda5517/\lambda5537$ and [Ar IV] $\lambda4711/\lambda4740$ doublet ratios. Except for a few H II regions for which data from the literature were used, diagnostic line ratios were derived from our own high quality spectra. For the [O II] doublet ratio, we find that our default atomic data set, consisting of transition probabilities (Aij) from Zeippen (1982} and collision strengths from Pradhan (1976), fit the observations well, although at high electron densities, the [O II]doublet ratio yields densities systematically lower than those given by the [S II] doublet ratio, suggesting that the ratio of Aij of the [O II] doublet,$A(\lambda3729)/A(\lambda3726)$, given by Zeippen (1982) may need to be revised upwards by ~6%. Our analysis also shows that the more recent calculations of [O II] A value by Zeippen (1987a) and collision strengths by McLaughlin & Bell (1998) are inconsistent with the observations at the high and low density limits, respectively, and can therefore be ruled out. We confirm the earlier result of Copetti & Writzl (2002) that the [O II] A values calculated by Wiese et al. (1996) yield electron densities systematically lower than those deduced from the [S II] doublet ratio and that the discrepancy is most likely caused by errors in the A values calculated by Wiese et al. Using our default atomic data set for [\ion{O}{ii}], we find that N_{\rm e}([\ion{O}{ii}]) \la N_{\rm e}([\ion{S}{ii}]) \approx N_{\rm e}([\ion{Cl}{iii}])< N_{\rm e}([\ion{Ar} {iv}]).Comment: 15 pages, 13 figures, 7 tables, accepted for publication in A&

Extended Effective Field Theory of Inflation

We present a general framework where the effective field theory of single field inflation is extended by the inclusion of operators with mass dimension 3 and 4 in the unitary gauge. These higher dimensional operators introduce quartic and sextic corrections to the dispersion relation. We study the regime of validity of this extended effective field theory of inflation and the effect of these higher dimensional operators on CMB observables associated with scalar perturbations, such as the speed of sound, the amplitude of the power spectrum and the tensor-to-scalar ratio. Tensor perturbations remain instead, unaltered.Comment: new version matches the published version, includes adding few citations and correcting few typo