The Volume of the Past Light-Cone and the Paneitz Operator

We study a conjecture involving the invariant volume of the past light-cone from an arbitrary observation point back to a fixed initial value surface. The conjecture is that a 4th order differential operator which occurs in the theory of conformal anomalies gives $8\pi$ when acted upon the invariant volume of the past light-cone. We show that an extended version of the conjecture is valid for an arbitrary homogeneous and isotropic geometry. First order perturbation theory about flat spacetime reveals a violation of the conjecture which, however, vanishes for any vacuum solution of the Einstein equation. These results may be significant for constructing quantum gravitational observables, for quantifying the back-reaction on spacetime expansion and for alternate gravity models which feature a timelike vector field.Comment: 22 pages, no figures, 5 tables. Version 2 substantially extended to cover nonzero spatial curvature, and with simplified derivation

Chemical abundances in the protoplanetary disk LV2 (Orion): clues to the causes of the abundance anomaly in HII regions

Optical integral field spectroscopy of the archetype protoplanetary disk LV2 in the Orion Nebula is presented, taken with the VLT FLAMES/Argus fibre array. The detection of recombination lines of CII and OII from this class of objects is reported, and the lines are utilized as abundance diagnostics. The study is complemented with the analysis of HST Faint Object Spectrograph ultraviolet and optical spectra of the target contained within the Argus field of view. By subtracting the local nebula background the intrinsic spectrum of the proplyd is obtained and its elemental composition is derived for the first time. The proplyd is found to be overabundant in carbon, oxygen and neon compared to the Orion Nebula and the sun. The simultaneous coverage over LV2 of the CIII] 1908-A and [OIII] 5007-A collisionally excited lines (CELs) and CII and OII recombination lines (RLs) has enabled us to measure the abundances of C++ and O++ for LV2 with both sets of lines. The two methods yield consistent results for the intrinsic proplyd spectrum, but not for the proplyd spectrum contaminated by the generic nebula spectrum, thus providing one example where the long-standing abundance anomaly plaguing metallicity studies of HII regions has been resolved. These results would indicate that the standard forbidden-line methods used in the derivation of light metal abundances in HII regions in our own and other galaxies underestimate the true gas metallicity.Comment: Accepted by MNRAS November 8; 16 pages, 9 figs; typos corrected, error in FWHMs in table 4 corrected in this versio

Endogenous oxygen in the extremely metal-poor planetary nebula PN G135.9+55.9

It is shown that, in contrast to recent claims, oxygen (and helium) may not be extraordinarily underabundant in the new galactic halo planetary nebula (GHPN) PN G135.9+55.9 (hereafter PN G135). Determining elemental abundances in hot, highly ionized objects such as PN G135 depends critically on a proper description of the collisional excitation of the hydrogen Balmer lines, the departure from Case B recombination of hydrogen, the underlying stellar absorption lines, the shape of the primary continuum and the ionization equilibrium of highly ionized species of both oxygen and neon. Conversely, PN G135 provides unique checks of atomic data in unusual conditions: the H I collision strengths obtained by Aggarwal et al. (1991) for 1s - n transitions (3 ≤ n ≤ 5) are too large, while those obtained by Anderson et al. (2002) are acceptable. Empirical collision strengths are presented for n > 5. Photoionization models of PN G135 that fit all available optical data can be demonstrated only for oxygen abundances 12 + log (O/H) > 7.2 (>1/30 solar) and values 0.6 dex larger are possible, depending on the assumed C/O abundance ratio. Plausible variations in the geometry of the nebula, the primary stellar continuum and the atomic data do not alter this conclusion. The C/O ratio is less than 10 by number and Ne/O is at most solar. A satisfactory model for PN G135 can be obtained in which elemental abundances are nearly the same as those of a new detailed model for K 648, the prototypical GHPN in the old globular cluster M 15 (with 12 + log (O/H) = 7.58 ∼ 1/13 solar), although C/O may be smaller. Nonetheless, given the paucity of argon and iron in the nebula, PN G135 is likely to be a more extreme Population II object than K 648, reinforcing the idea of an endogenous origin for part of the oxygen in very metal-poor PNe. Assuming a standard H-burning post-Asymptotic Giant Branch evolution, timescale and spectroscopic considerations lead to an optimal solution, in which the distance to PN G135 is 8 kpc, the effective temperature of the nucleus slightly less than 1.3 × 105 K, its luminosity 1.4 × 1037 erg s-1, its mass 0.59 M⊙, the age of the ionized shell 104 yrs, the ionized mass 0.05 M⊙ and the abundances by number (H:He:C:O:Ne) = (106:81 500:90:30:4.5), with C/H being rather an upper limit and O/H and Ne/H uncertain by ±0.3 and ±0.1 dex respectively. Line intensities that could be used as diagnostics of the nebular elemental abundances are provided. Detailed imaging together with ultraviolet and very deep far-red spectra of PN G135 will be essential to definitely narrow the range of acceptable parameters and help us decide whether this exceptional PN is so oxygen-poor as to possibly influence current views on stellar evolution

The Quantum Gravitationally Induced Stress Tensor

We derive non-perturbative relations between the expectation value of the invariant element in a homogeneous and isotropic state and the quantum gravitationally induced pressure and energy density. By exploiting previously obtained bounds for the maximum possible growth of perturbative corrections to a locally de Sitter background we show that the two loop result dominates all higher orders. We also show that the quantum gravitational slowing of inflation becomes non-perturbatively strong earlier than previously expected.Comment: 13 pages, LaTeX 2 epsilo

Chemical abundances in the protoplanetary disc LV 2 (Orion) - II. High-dispersion VLT observations and microjet properties

Integral field spectroscopy of the LV 2 proplyd is presented taken with the Very Large Telescope (VLT)/FLAMES Argus array at an angular resolution of 0.31 × 0.31 arcsec2 and velocity resolutions down to 2 km s-1 pixel-1. Following subtraction of the local M42 emission, the spectrum of LV 2 is isolated from the surrounding nebula. We measured the heliocentric velocities and widths of a number of lines detected in the intrinsic spectrum of the proplyd, as well as in the adjacent Orion nebula falling within a 6.6 × 4.2 arcsec2 field of view. It is found that far-ultraviolet to optical collisional lines with critical densities, Ncr, ranging from 103 to 109 cm-3 suffer collisional de-excitation near the rest velocity of the proplyd correlating tightly with their critical densities. Lines of low Ncr are suppressed the most. The bipolar jet arising from LV 2 is spectrally and spatially well detected in several emission lines. We compute the [O III] electron temperature profile across LV 2 in velocity space and measure steep temperature variations associated with the red-shifted lobe of the jet, possibly being due to a shock discontinuity. From the velocity-resolved analysis the ionized gas near the rest frame of LV 2 has Te= 9200 ± 800 K and Ne∼ 106 cm-3, while the red-shifted jet lobe has Te≈ 9000–104 K and Ne∼ 106–107 cm-3. The jet flow is highly ionized but contains dense semineutral clumps emitting neutral oxygen lines. The abundances of N+, O2+, Ne2+, Fe2+, S+and S2+ are measured for the strong red-shifted jet lobe. Iron in the core of LV 2 is depleted by 2.54 dex with respect to solar as a result of sedimentation on dust, whereas the efficient destruction of dust grains in the fast microjet raises its Fe abundance to at least 30 per cent solar. Sulphur does not show evidence of significant depletion on dust, but its abundance both in the core and the jet is only about half solar

Computing the Primordial Power Spectra Directly

The tree order power spectra of primordial inflation depend upon the norm-squared of mode functions which oscillate for early times and then freeze in to constant values. We derive simple differential equations for the power spectra, that avoid the need to numerically simulate the physically irrelevant phases of the mode functions. We also derive asymptotic expansions which should be valid until a few e-foldings before first horizon crossing, thereby avoiding the need to evolve mode functions from the ultraviolet over long periods of inflation.Comment: 11 pages, uses LaTex2

Primordial Gravitational Waves Enhancement

We reconsider the enhancement of primordial gravitational waves that arises from a quantum gravitational model of inflation. A distinctive feature of this model is that the end of inflation witnesses a brief phase during which the Hubble parameter oscillates in sign, changing the usual Hubble friction to anti-friction. An earlier analysis of this model was based on numerically evolving the graviton mode functions after guessing their initial conditions near the end of inflation. The current study is based on an equation which directly evolves the normalized square of the magnitude. We are also able to make a very reliable estimate for the initial condition using a rapidly converging expansion for the sub-horizon regime. Results are obtained for the energy density per logarithmic wave number as a fraction of the critical density. These results exhibit how the enhanced signal depends upon the number of oscillatory periods; they also show the resonant effects associated with particular wave numbers.Comment: 25 pages, 14 figure