2,914 research outputs found
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- and Bayesian approaches to parameter estimation. Numerical
experiments with independent realizations of an observed orbit confirm
that the and 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&
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