The Impact of Prior Assumptions on Bayesian Estimates of Inflation Parameters and the Expected Gravitational Waves Signal from Inflation

There has been much recent discussion, and some confusion, regarding the use of existing observational data to estimate the likelihood that next-generation cosmic microwave background (CMB) polarization experiments might detect a nonzero tensor signal, possibly associated with inflation. We examine this issue in detail here in two different ways: (1) first we explore the effect of choice of different parameter priors on the estimation of the tensor-to-scalar ratio r and other parameters describing inflation, and (2) we examine the Bayesian complexity in order to determine how effectively existing data can constrain inflationary parameters. We demonstrate that existing data are not strong enough to render full inflationary parameter estimates in a parametrization- and prior-independent way and that the predicted tensor signal is particularly sensitive to different priors. For parametrizations where the Bayesian complexity is comparable to the number of free parameters we find that a flat prior on the scale of inflation (which is to be distinguished from a flat prior on the tensor-to-scalar ratio) leads us to infer a larger, and in fact slightly nonzero tensor contribution at 68% confidence level. However, no detection is claimed. Our results demonstrate that all that is statistically relevant at the current time is the (slightly enhanced) upper bound on r, and we stress that the data remain consistent with r = 0.Comment: 9 pages, 5 figures. Section added on Bayesian complexity. Matches published versio

Moving inhomogeneous envelopes of stars

Massive stars are extremely luminous and drive strong winds, blowing a large part of their matter into the galactic environment before they finally explode as a supernova. Quantitative knowledge of massive star feedback is required to understand our Universe as we see it. Traditionally, massive stars have been studied under the assumption that their winds are homogeneous and stationary, largely relying on the Sobolev approximation. However, observations with the newest instruments, together with progress in model calculations, ultimately dictate a cardinal change of this paradigm: stellar winds are highly inhomogeneous. Hence, we are now advancing to a new stage in our understanding of stellar winds. Using the foundations laid by V.V. Sobolev and his school, we now update and further develop the stellar spectral analysis techniques. New sophisticated 3-D models of radiation transfer in inhomogeneous expanding media elucidate the physics of stellar winds and improve classical empiric mass-loss rate diagnostics. Applications of these new techniques to multiwavelength observations of massive stars yield consistent and robust stellar wind parameters.Comment: slightly corrected version of the review for the special issue "V.V. Sobolev and his Legacy", Journal of Quantitative Spectroscopy and Radiative Transfe

A Variable PV Broad Absorption Line and Quasar Outflow Energetics

Broad absorption lines (BALs) in quasar spectra identify high velocity outflows that might exist in all quasars and could play a major role in feedback to galaxy evolution. The viability of BAL outflows as a feedback mechanism depends on their kinetic energies, as derived from the outflow velocities, column densities, and distances from the central quasar. We estimate these quantities for the quasar, Q1413+1143 (redshift $z_e = 2.56$), aided by the first detection of PV $\lambda\lambda$1118,1128 BAL variability in a quasar. In particular, PV absorption at velocities where the CIV trough does not reach zero intensity implies that the CIV BAL is saturated and the absorber only partially covers the background continuum source (with characteristic size <0.01 pc). With the assumption of solar abundances, we estimate that the total column density in the BAL outflow is log N_H > 22.3 (cm^-2). Variability in the PV and saturated CIV BALs strongly disfavors changes in the ionization as the cause of the BAL variability, but supports models with high-column density BAL clouds moving across our lines of sight. The observed variability time of 1.6 yr in the quasar rest frame indicates crossing speeds >750 km/s and a radial distance from the central black hole of <3.5 pc, if the crossing speeds are Keplerian. The total outflow mass is ~4100 M_solar, the kinetic energy ~4x10^54 erg, and the ratio of the outflow kinetic energy luminosity to the quasar bolometric luminosity is ~0.02 (at the minimum column density and maximum distance), which might be sufficient for important feedback to the quasar's host galaxy.Comment: 9 pages, 4 figures, accepted for publication in MNRA

Neglecting the porosity of hot-star winds can lead to underestimating mass-loss rates

Context: The mass-loss rate is a key parameter of massive stars. Adequate stellar atmosphere models are required for spectral analyses and mass-loss determinations. Present models can only account for the inhomogeneity of stellar winds in the approximation of small-scale structures that are optically thin. This treatment of ``microclumping'' has led to reducing empirical mass-loss rates by factors of two and more. Aims: Stellar wind clumps can be optically thick in spectral lines. We investigate how this ``macroclumping'' impacts on empirical mass-loss rates. Methods: The Potsdam Wolf-Rayet (PoWR) model atmosphere code is generalized in the ``formal integral'' to account for clumps that are not necessarily optically thin. Results: Optically thick clumps reduce the effective opacity. This has a pronounced effect on the emergent spectrum. Our modeling for the O-type supergiant zeta Puppis reveals that the optically thin H-alpha line is not affected by wind porosity, but that the PV resonance doublet becomes significantly weaker when macroclumping is taken into account. The reported discrepancies between resonance-line and recombination-line diagnostics can be resolved entirely with the macroclumping modeling without downward revision of the mass-loss rate. Conclusions: Mass-loss rates inferred from optically thin emission, such as the H-alpha line in O stars, are not influenced by macroclumping. The strength of optically thick lines, however, is reduced because of the porosity effects. Therefore, neglecting the porosity in stellar wind modeling can lead to underestimating empirical mass-loss rates.Comment: A&A (in press), see full abstract in the tex

High resolution X-ray spectroscopy of bright O type stars

Archival X-ray spectra of the four prominent single, non-magnetic O stars Zeta Pup, Zeta Ori, Ksi Per and Zeta Oph, obtained in high resolution with Chandra HETGS/MEG have been studied. The resolved X-ray emission line profiles provide information about the shocked, hot gas which emits the X-radiation, and about the bulk of comparably cool stellar wind material which partly absorbs this radiation. In this paper, we synthesize X-ray line profiles with a model of a clumpy stellar wind. We find that the geometrical shape of the wind inhomogeneities is important: better agreement with the observations can be achieved with radially compressed clumps than with spherical clumps. The parameters of the model, i.e. chemical abundances, stellar radius, mass-loss rate and terminal wind velocity, are taken from existing analyses of UV and optical spectra of the programme stars. On this basis, we also calculate the continuum-absorption coefficient of the cool-wind material, using the Potsdam Wolf-Rayet (PoWR) model atmosphere code. The radial location of X-ray emitting gas is restricted from analysing the fir line ratios of helium-like ions. The only remaining free parameter of our model is the typical distance between the clumps; here, we assume that at any point in the wind there is one clump passing by per one dynamical time-scale of the wind. The total emission in a model line is scaled to the observation. There is a good agreement between synthetic and observed line profiles. We conclude that the X-ray emission line profiles in O stars can be explained by hot plasma embedded in a cool wind which is highly clumped in the form of radially compressed shell fragments.Comment: a typo corrected, 14 pages, MNRAS, in pres