Do language change rates depend on population size?

An earlier study (Nettle 1999b) concluded, based on computer simulations and some inferences from empirical data, that languages will change the more slowly the larger the population gets. We replicate this study using a more complete language model for simulations (the Schulze model combined with a Barabasi-Albert net- work) and a richer empirical dataset (the World Atlas of Language Structures edited by Haspelmath et al. 2005). Our simulations show either a weak or stronger dependence of language change on population sizes depending on the parameter settings, and empirical data, like some of the simulations, show a weak dependence.Comment: 20 pages including all figures for a linguistic journa

Population Size and Rates of Language Change

Previous empirical studies of population size and language change have produced equivocal results. We therefore address the question with a new set of lexical data from nearly one-half of the world’s languages. We first show that relative population sizes of modern languages can be extrapolated to ancestral languages, albeit with diminishing accuracy, up to several thousand years into the past. We then test for an effect of population against the null hypothesis that the ultrametric inequality is satisfied by lexical distance among triples of related languages. The test shows mainly negligible effects of population, the exception being an apparently faster rate of change in the larger of two closely related variants. A possible explanation for the exception may be the influence on emerging standard (or cross-regional) variants from speakers who shift from different dialects to the standard. Our results strongly indicate that the sizes of speaker populations do not in and of themselves determine rates of language change. Comparison of this empirical finding with previously published computer simulations suggests that the most plausible model for language change is one in which changes propagate on a local level in a type of network in which the individuals have different degrees of connectivity

Crystal structure of Li3Ga(BO3)2

The crystal structure of trilithium gallium bis(orthoborate), Li3Ga(BO3)2, is isotypic with Li3Al(BO3)2 in a triclinic cell in space-group type P1. The three Li and the unique Ga atom are coordinated by four O atoms each in tetrahedra, and the two B atoms are coordinated by three O atoms in orthoborate triangles. Chains with composition [Ga2(BO3)4] 6 extend along the a axis. The Li atoms interleave these chains in tetrahedral interstices. A comparison is made between the structure model of the title compound and that of a previously reported model for a compound with the same composition [Abdullaev & Mamedov (1972). Zh. Strukt. Khim. 13, 943–946.

Transit Timing Observations from Kepler: III. Confirmation of 4 Multiple Planet Systems by a Fourier-Domain Study of Anti-correlated Transit Timing Variations

We present a method to confirm the planetary nature of objects in systems with multiple transiting exoplanet candidates. This method involves a Fourier-Domain analysis of the deviations in the transit times from a constant period that result from dynamical interactions within the system. The combination of observed anti-correlations in the transit times and mass constraints from dynamical stability allow us to claim the discovery of four planetary systems Kepler-25, Kepler-26, Kepler-27, and Kepler-28, containing eight planets and one additional planet candidate.Comment: Accepted to MNRA

A First Comparison of Kepler Planet Candidates in Single and Multiple Systems

In this letter we present an overview of the rich population of systems with multiple candidate transiting planets found in the first four months of Kepler data. The census of multiples includes 115 targets that show 2 candidate planets, 45 with 3, 8 with 4, and 1 each with 5 and 6, for a total of 170 systems with 408 candidates. When compared to the 827 systems with only one candidate, the multiples account for 17 percent of the total number of systems, and a third of all the planet candidates. We compare the characteristics of candidates found in multiples with those found in singles. False positives due to eclipsing binaries are much less common for the multiples, as expected. Singles and multiples are both dominated by planets smaller than Neptune; 69 +2/-3 percent for singles and 86 +2/-5 percent for multiples. This result, that systems with multiple transiting planets are less likely to include a transiting giant planet, suggests that close-in giant planets tend to disrupt the orbital inclinations of small planets in flat systems, or maybe even to prevent the formation of such systems in the first place.Comment: 13 pages, 13 figures, submitted to ApJ Letter

Modeling Kepler transit light curves as false positives: Rejection of blend scenarios for Kepler-9, and validation of Kepler-9d, a super-Earth-size planet in a multiple system

Light curves from the Kepler Mission contain valuable information on the nature of the phenomena producing the transit-like signals. To assist in exploring the possibility that they are due to an astrophysical false positive, we describe a procedure (BLENDER) to model the photometry in terms of a "blend" rather than a planet orbiting a star. A blend may consist of a background or foreground eclipsing binary (or star-planet pair) whose eclipses are attenuated by the light of the candidate and possibly other stars within the photometric aperture. We apply BLENDER to the case of Kepler-9, a target harboring two previously confirmed Saturn-size planets (Kepler-9b and Kepler-9c) showing transit timing variations, and an additional shallower signal with a 1.59-day period suggesting the presence of a super-Earth-size planet. Using BLENDER together with constraints from other follow-up observations we are able to rule out all blends for the two deeper signals, and provide independent validation of their planetary nature. For the shallower signal we rule out a large fraction of the false positives that might mimic the transits. The false alarm rate for remaining blends depends in part (and inversely) on the unknown frequency of small-size planets. Based on several realistic estimates of this frequency we conclude with very high confidence that this small signal is due to a super-Earth-size planet (Kepler-9d) in a multiple system, rather than a false positive. The radius is determined to be 1.64 (+0.19/-0.14) R(Earth), and current spectroscopic observations are as yet insufficient to establish its mass.Comment: 20 pages in emulateapj format, including 8 tables and 16 figures. To appear in ApJ, 1 January 2010. Accepted versio

The Transit Ingress and the Tilted Orbit of the Extraordinarily Eccentric Exoplanet HD 80606b

We present the results of a transcontinental campaign to observe the 2009 June 5 transit of the exoplanet HD 80606b. We report the first detection of the transit ingress, revealing the transit duration to be 11.64 +/- 0.25 hr and allowing more robust determinations of the system parameters. Keck spectra obtained at midtransit exhibit an anomalous blueshift, giving definitive evidence that the stellar spin axis and planetary orbital axis are misaligned. The Keck data show that the projected spin-orbit angle is between 32-87 deg with 68.3% confidence and between 14-142 deg with 99.73% confidence. Thus the orbit of this planet is not only highly eccentric (e=0.93), but is also tilted away from the equatorial plane of its parent star. A large tilt had been predicted, based on the idea that the planet's eccentric orbit was caused by the Kozai mechanism. Independently of the theory, it is noteworthy that all 3 exoplanetary systems with known spin-orbit misalignments have massive planets on eccentric orbits, suggesting that those systems migrate differently than lower-mass planets on circular orbits.Comment: ApJ, in press [13 pg

Alignment of the stellar spin with the orbits of a three-planet system

The Sun’s equator and the planets’ orbital planes are nearly aligned, which is presumably a consequence of their formation from a single spinning gaseous disk. For exoplanetary systems this well-aligned configuration is not guaranteed: dynamical interactions may tilt planetary orbits, or stars may be misaligned with the protoplanetary disk through chaotic accretion1 , magnetic interactions[superscript 2] or torques from neighbouring stars. Indeed, isolated ‘hot Jupiters’ are often misaligned and even orbiting retrograde[superscript 3, 4]. Here we report an analysis of transits of planets over starspots[superscript 5, 6, 7] on the Sun-like star Kepler-30 (ref. 8), and show that the orbits of its three planets are aligned with the stellar equator. Furthermore, the orbits are aligned with one another to within a few degrees. This configuration is similar to that of our Solar System, and contrasts with the isolated hot Jupiters. The orderly alignment seen in the Kepler-30 system suggests that high obliquities are confined to systems that experienced disruptive dynamical interactions. Should this be corroborated by observations of other coplanar multi-planet systems, then star–disk misalignments would be ruled out as the explanation for the high obliquities of hot Jupiters, and dynamical interactions would be implicated as the origin of hot Jupiters.United States. National Aeronautics and Space Administration (Science MissionDirectorate