Mass estimates for visual binaries with incomplete orbits

The problem of estimating the total mass of a visual binary when its orbit is incomplete is treated with Bayesian methods. The posterior mean of a mass estimator is approximated by a triple integral over orbital period, time of periastron and orbital eccentricity. This reduction to 3-D from the 7-D space defined by the conventional Campbell parameters is achieved by adopting the Thiele-Innes elements and exploiting the linearity with respect to the four Thiele-Innes constants. The formalism is tested on synthetic observational data covering a variable fraction of a model binary's orbit. The posterior mean of the mass estimator is numerically found to be unbiased when the data cover > 40% of the orbit.Comment: 12 pages, 13 figures. Revised version accepted by Astronomy and Astrophysic

Frequentist tests for Bayesian models

Analogues of the frequentist chi-square and F tests are proposed for testing goodness-of-fit and consistency for Bayesian models. Simple examples exhibit these tests' detection of inconsistency between consecutive experiments with identical parameters, when the first experiment provides the prior for the second. In a related analysis, a quantitative measure is derived for judging the degree of tension between two different experiments with partially overlapping parameter vectors.Comment: 8 pages, 4 figures. Section 8 rewritten. Additional references. Accepted by Astronomy & Astrophysic

Analysing weak orbital signals in Gaia data

Anomalous orbits are found when minimum-chi^{2} estimation is applied to synthetic Gaia data for orbits with astrometric signatures comparable to the single-scan measurement error (Pourbaix 2002). These orbits are nearly parabolic, edge-on, and their major axes align with the line-of-sight to the observer. Such orbits violate the Copernican principle (CPr) and as such could be rejected. However, the preferred alternative is to develop a statistical technique that incorporates the CPr as a fundamental postulate. This can be achieved in a Bayesian context by defining a Copernican prior. Pourbaix's anomalous orbits then no longer arise. Instead, the selected orbits have a somewhat higher chi^{2} but do not violate the CPr. The problem of detecting a weak additional orbit in an astrometric binary with a well-determined orbit is also treated.Comment: 9 pages, 12 figures. Matches published version. Accepted by A&

Spectroscopic binaries with components of similar mass

The assertion that there is an intrinsic excess of binaries with mass ratios q \simeq 1 - the twin hypothesis - is investigated. A strong version of this hypothesis (H_s), due to Lucy & Ricco (1979) and Tokovinin (2000), refers to a narrow peak in the distribution function psi(q) for q \ga 0.95. A weak version (H_w), due to Halbwachs et al. (2003), refers to a broad peak for q \ga 0.8. Current data on SB2's is analysed and H_s is found to be statistically significant for a sample restricted to orbits of high precision. But claims that H_s is significant for binaries with special characteristics are not confirmed since the sample sizes are well below the minimum required for a reliable test. With regard to H_w, additional observational evidence is not presented, but evidence to the contrary in the form of Hogeveen's (1992b) model of biased sampling with psi \propto q^{-2} is criticized. Specifically, his success in thus fitting catalogued data depends on implausible assumptions about the research methodologies of binary-star spectroscopists.Comment: 8 pages, 8 figures. Accepted by Astronomy & astrophysic

Frequentist confidence intervals for orbits

The problem of efficiently computing the orbital elements of a visual binary while still deriving confidence intervals with frequentist properties is treated. When formulated in terms of the Thiele-Innes elements, the known distribution of probability in Thiele-Innes space allows efficient grid-search plus Monte-Carlo-sampling schemes to be constructed for both the minimum-$\!\chi^{2}$ and Bayesian approaches to parameter estimation. Numerical experiments with $10^{4}$ independent realizations of an observed orbit confirm that the $1-$ and $2\sigma$ confidence and credibility intervals have coverage fractions close to their frequentist values. \keywords{binaries: visual - stars: fundamental parameters - methods:statistical}Comment: 7 pages, 2 figures. Minor changes. Accepted by Astronomy and Astrophysic

O-star mass-loss rates at low metallicity

Mass fluxes J are computed for the extragalactic O stars investigated by Tramper et al. (2011; TSKK). For one early-type O star, computed and observed rates agree within errors. However, for two late-type O stars, theoretical mass-loss rates underpredict observed rates by ~ 1.6 dex, far exceeding observational errors. A likely cause of the discrepancy is overestimated observed rates due to the neglect of wind-clumping. A less likely but intriguing possibility is that, in observing O stars with Z/Z_sun ~ 1/7, TSKK have serendipitously discovered an additional mass-loss mechanism not evident in the spectra of Galactic O stars with powerful radiation-driven winds. Constraints on this unknown mechanism are discussed. In establishing that the discrepancies, if real, are inescapable for purely radiation-driven winds, failed searches for high-J solutions are reported and the importance of a numerical technique that cannot spuriously create or destroy momentum stressed. The Z-dependences of the computed rates for Z/Z_sun in the interval (1/30, 2) show significant departures from a single power law, and these are attributed to curve-of-growth effects in the differentially-expanding reversing layers. The best-fitting power-law exponents range from 0.68-0.97.Comment: 6 pages, 2 figure

The structure of line-driven winds

Following procedures pioneered by Castor, Abbott & Klein (1975, [CAK]), spherically-symmetric supersonic winds for O stars are computed for matching to plane-parallel moving reversing layers (RL's) from Paper I (Lucy 2007). In contrast to a CAK wind, each of these solutions is singularity-free, thus allowing its mass-loss rate to be fixed by the regularity condition at the sonic point within the RL. Moreover, information propagation in these winds by radiative-acoustic waves is everywhere outwardly-directed, justifying the implicit assumption in Paper I that transonic flows are unaffected by inwardly-directed wave motions.Comment: Accepted by A&A; 7 pages, 1 table, 4 figure

Bayesian inference for orbital eccentricities

Highest posterior density intervals (HPDI's) are derived for the true eccentricities of spectroscopic binaries with measured values e ~ 0. These yield upper limits when e is below the detection threshold e_th and seamlessly transform to upper and lower bounds when e > e_th. In the main text, HPDI's are computed with an informative eccentricity prior representing orbital decay due to tidal dissipation. In an appendix, the corresponding HPDI's are computed with a uniform prior and are the basis for a revised version of the Lucy-Sweeney test, with the previous outcome e = 0 now replaced by an upper limit. Sampling experiments with known prior confirm the validity of the HPDI's.Comment: 7 pages, 6 figures. Error in terminology corrected. Results unchanged. Accepted by Astronomy & Astrophysic

Spectroscopic binaries with elliptical orbits

The radial velocity curves of many spectroscopic binaries (SBs) are perturbed by gas streams or proximity effects. For SBs with circular orbits, these perturbations can give rise to spurious orbital eccentricities of high statistical significance. But tests to identify such anomalous orbits can be constructed since perturbed velocity curves are in general no longer Keplerian. The derived tests are applied both to synthetic and to observed velocity curves.Comment: 9pages,3figures,accepted by A&