Bayesians Can Learn From Old Data

In a widely-cited paper, Glymour (Theory and Evidence, Princeton, N. J.: Princeton University Press, 1980, pp. 63-93) claims to show that Bayesians cannot team from old data. His argument contains an elementary error. I explain exactly where Glymour went wrong, and how the problem should be handled correctly. When the problem is fixed, it is seen that Bayesians, just like logicians, can indeed learn from old data.Astronom

Orbital theories of outer planet satellites

An analytical theory of Mimas and Tethys was developed, retaining terms which produce perturbations of the order of + or - 10 km. The theory uses a novel set of variables, and was developed with the Hori-Lie algorithm, using the algebraic manipulation language TRIGMAN. the perturbations were implemented by means of FORTRAN subroutines produced by the computer

Equivalence of the perturbation theories of Hori and Deprit

Equivalence of perturbation theories of Hori and Deprit, based on Poisson brackets, and computer calculations through sixth orde

Vacuum Energy: Cosmological Constant or Quintessence?

For a flat universe presently dominated by smooth energy, either cosmological constant (LCDM) or quintessence (QCDM), we calculate the asymptotic collapsed mass fraction as function of the present ratio of smooth energy to matter energy $\mathcal R_0$. Identifying the normalized collapsed fraction as a conditional probability for habitable galaxies, we observe that the observed present ratio $\mathcal R_0 \sim 2$ is likely in LCDM, but more likely in QCDM. Inverse application of Bayes' Theorem makes the Anthropic Principle a predictive scientific principle: the data implies that the prior probability for $\mathcal R_0$ must be essentially flat over the anthropically allowed range. Interpreting this prior as a distribution over {\em theories} lets us predict that any future theory of initial conditions must be indifferent to $\mathcal R_0$. This application of the Anthropic Principle does not demand the existence of other universes.Comment: 17 pages AAS LATEX, including 2 tables, 3 figures (Postscript

Detection of a Third Planet in the HD 74156 System Using the Hobby-Eberly Telescope

We report the discovery of a third planetary mass companion to the G0 star HD 74156. High precision radial velocity measurements made with the Hobby-Eberly Telescope aided the detection of this object. The best fit triple Keplerian model to all the available velocity data yields an orbital period of 347 days and minimum mass of 0.4 M_Jup for the new planet. We determine revised orbital periods of 51.7 and 2477 days, and minimum masses of 1.9 and 8.0 M_Jup respectively for the previously known planets. Preliminary calculations indicate that the derived orbits are stable, although all three planets have significant orbital eccentricities (e = 0.64, 0.43, and 0.25). With our detection, HD 74156 becomes the eighth normal star known to host three or more planets. Further study of this system's dynamical characteristics will likely give important insight to planet formation and evolutionary processes.Comment: 24 pages, 4 tables, 6 figures. Accepted for publication in ApJ. V2 fixed table 4 page overrun. V3 added reference

Type Ia Supernovae, Evolution, and the Cosmological Constant

We explore the possible role of evolution in the analysis of data on SNe Ia at cosmological distances. First, using a variety of simple sleuthing techniques, we find evidence that the properties of the high and low redshift SNe Ia observed so far differ from one another. Next, we examine the effects of including simple phenomenological models for evolution in the analysis. The result is that cosmological models and evolution are highly degenerate with one another, so that the incorporation of even very simple models for evolution makes it virtually impossible to pin down the values of $\Omega_M$ and $\Omega_\Lambda$, the density parameters for nonrelativistic matter and for the cosmological constant, respectively. Moreover, we show that if SNe Ia evolve with time, but evolution is neglected in analyzing data, then, given enough SNe Ia, the analysis hones in on values of $\Omega_M$ and $\Omega_\Lambda$ which are incorrect. Using Bayesian methods, we show that the probability that the cosmological constant is nonzero (rather than zero) is unchanged by the SNe Ia data when one accounts for the possibility of evolution, provided that we do not discriminate among open, closed and flat cosmologies a priori. The case for nonzero cosmological constant is stronger if the Universe is presumed to be flat, but still depends sensitively on the degree to which the peak luminosities of SNe Ia evolve as a function of redshift. The estimated value of $H_0$, however, is only negligibly affected by accounting for possible evolution.Comment: 45 pages, 15 figures; accepted for publication in The Astrophysical Journal. Minor revisions and clarifications made including addition of recent reference

Bayesian Analysis of Two Stellar Populations in Galactic Globular Clusters II: NGC 5024, NGC 5272, and NGC 6352

We use Cycle 21 Hubble Space Telescope (HST) observations and HST archival ACS Treasury observations of Galactic Globular Clusters to find and characterize two stellar populations in NGC 5024 (M53), NGC 5272 (M3), and NGC 6352. For these three clusters, both single and double-population analyses are used to determine a best fit isochrone(s). We employ a sophisticated Bayesian analysis technique to simultaneously fit the cluster parameters (age, distance, absorption, and metallicity) that characterize each cluster. For the two-population analysis, unique population level helium values are also fit to each distinct population of the cluster and the relative proportions of the populations are determined. We find differences in helium ranging from $\sim$0.05 to 0.11 for these three clusters. Model grids with solar $\alpha$-element abundances ([$\alpha$/Fe] =0.0) and enhanced $\alpha$-elements ([$\alpha$/Fe]=0.4) are adopted.Comment: ApJ, 21 pages, 14 figures, 7 table

An m sin i = 24 Earth Mass Planetary Companion To The Nearby M Dwarf GJ 176

We report the detection of a planetary companion with a minimum mass of m sin i = 0.0771 M_Jup = 24.5 M_Earth to the nearby (d = 9.4 pc) M2.5V star GJ 176. The star was observed as part of our M dwarf planet search at the Hobby-Eberly Telescope (HET). The detection is based on 5 years of high-precision differential radial velocity (RV) measurements using the High-Resolution-Spectrograph (HRS). The orbital period of the planet is 10.24 d. GJ 176 thus joins the small (but increasing) sample of M dwarfs hosting short-periodic planets with minimum masses in the Neptune-mass range. Low mass planets could be relatively common around M dwarfs and the current detections might represent the tip of a rocky planet population.Comment: 13 pages preprint, 3 figures, submitted to Ap

Interferometric Astrometry of Proxima Centauri and Barnard's Star Using Hubble Space Telescope Fine Guidance Sensor 3: Detection Limits for sub-Stellar Companions

We report on a sub-stellar companion search utilizing interferometric fringe-tracking astrometry acquired with Fine Guidance Sensor 3 (FGS 3) on the Hubble Space Telescope. Our targets were Proxima Centauri and Barnard's Star. We obtain absolute parallax values for Proxima Cen pi_{abs} = 0.7687 arcsecond and for Barnard's Star pi_{abs} = 0.5454 arcsecond. Once low-amplitude instrumental systematic errors are identified and removed, our companion detection sensitivity is less than or equal to one Jupiter mass for periods longer than 60 days for Proxima Cen. Between the astrometry and the radial velocity results we exclude all companions with M > 0.8M_{Jup} for the range of periods 1 < P < 1000 days. For Barnard's Star our companion detection sensitivity is less than or equal to one Jupiter mass for periods long er than 150 days. Our null results for Barnard's Star are consistent with those of Gatewood (1995).Comment: 35 pages, 13 figures, to appear in August 1999 A