A Bayesian Periodogram Finds Evidence for Three Planets in 47 Ursae Majoris

A Bayesian analysis of 47 Ursae Majoris (47 UMa) radial velocity data confirms and refines the properties of two previously reported planets with periods of 1079 and 2325 days and finds evidence for an additional long period planet with a period of approximately 10000 days. The three planet model is found to be 10^5 times more probable than the next most probable model which is a two planet model. The nonlinear model fitting is accomplished with a new hybrid Markov chain Monte Carlo (HMCMC) algorithm which incorporates parallel tempering, simulated annealing and genetic crossover operations. Each of these features facilitate the detection of a global minimum in chi-squared. By combining all three, the HMCMC greatly increases the probability of realizing this goal. When applied to the Kepler problem it acts as a powerful multi-planet Kepler periodogram. The measured periods are 1078 \pm 2, 2391{+100}{-87}, and 14002{+4018}{-5095}d, and the corresponding eccentricities are 0.032 \pm 0.014, 0.098{+.047}{-.096}, and 0.16{+.09}{-.16}. The results favor low eccentricity orbits for all three. Assuming the three signals (each one consistent with a Keplerian orbit) are caused by planets, the corresponding limits on planetary mass (M sin i) and semi-major axis are (2.53{+.07}{-.06}MJ, 2.10\pm0.02au), (0.54\pm0.07MJ, 3.6\pm0.1au), and (1.6{+0.3}{-0.5}MJ, 11.6{+2.1}{-2.9}au), respectively. We have also characterized a noise induced eccentricity bias and designed a correction filter that can be used as an alternate prior for eccentricity, to enhance the detection of planetary orbits of low or moderate eccentricity

An orbital window into the ancient Sun's mass

Models of the Sun's long-term evolution suggest that its luminosity was substantially reduced 2-4 billion years ago, which is inconsistent with substantial evidence for warm and wet conditions in the geological records of both ancient Earth and Mars. Typical solutions to this so-called "faint young Sun paradox" consider changes in the atmospheric composition of Earth and Mars, and while attractive, geological verification of these ideas is generally lacking-particularly for Mars. One possible underexplored solution to the faint young Sun paradox is that the Sun has simply lost a few percent of its mass during its lifetime. If correct, this would slow, or potentially even offset the increase in luminosity expected from a constant-mass model. However, this hypothesis is challenging to test. Here, we propose a novel observational proxy of the Sun's ancient mass that may be readily measured from accumulation patterns in sedimentary rocks on Earth and Mars. We show that the orbital parameters of the Solar system planets undergo quasi-cyclic oscillations at a frequency, given by secular mode g_2-g_5, that scales approximately linearly with the Sun's mass. Thus by examining the cadence of sediment accumulation in ancient basins, it is possible distinguish between the cases of a constant mass Sun and a more massive ancient Sun to a precision of greater than about 1 per cent. This approach provides an avenue toward verification, or of falsification, of the massive early Sun hypothesis.Comment: 7 pages, 4 Figures. Accepted to The Astrophysical Journal Letter

Bayesian analysis of the radial velocities of HD 11506 reveals another planetary companion

We aim to demonstrate the efficiency of a Bayesian approach in analysing radial velocity data by reanalysing a set of radial velocity measurements. We present Bayesian analysis of a recently published set of radial velocity measurements known to contain the signal of one extrasolar planetary candidate, namely, HD 11506. The analysis is conducted using the Markov chain Monte Carlo method and the resulting distributions of orbital parameters are tested by performing direct integration of randomly selected samples with the Bulirsch-Stoer method. The magnitude of the stellar radial velocity variability, known as jitter, is treated as a free parameter with no assumptions about its magnitude. We show that the orbital parameters of the planet known to be present in the data correspond to a different solution when the jitter is allowed to be a free parameter. We also show evidence of an additional candidate, a 0.8 MJup planet with period of about 0.5 yr in orbit around HD 11506. This second planet is inferred to be present with a high level of confidence.Comment: 4 pages, 5 figures, to appear in A&

A determination of the spin-orbit alignment of the anomalously dense planet orbiting HD 149026

We report 35 radial velocity measurements of HD 149026 taken with the Keck Telescope. Of these measurements, 15 were made during the transit of the companion planet HD 149026b, which occurred on 2005 June 25. These velocities provide a high-cadence observation of the Rossiter-McLaughlin effect, the shifting of photospheric line profiles that occurs when a planet occults a portion of the rotating stellar surface. We combine these radial velocities with previously published radial velocity and photometric data sets and derive a composite best-fit model for the star-planet system. This model confirms and improves previously published orbital parameters, including the remarkably small planetary radius, the planetary mass, and the orbital inclination, found to be Rp/RJup = 0.718 ± 0.065, Mp/MJup = 0.352 ± 0.025, and I = 86.1° ± 1.4°, respectively. Together the planetary mass and radius determinations imply a mean planetary density of 1.18(-0.30)(+0.38)g cm(-3). The new data also allow for the determination of the angle between the apparent stellar equator and the orbital plane, which we constrain to be λ = -12° ± 15°

The catch-22 of external validity in the context of constraints to firm growth

We document the presence of multiple and varied constraints to small and medium firm growth. This presents both a practical problem for business training programs and a challenge to academic economists trying to identify mechanisms though which these programs may affect outcomes. External validity needs theory. This pushes researchers to narrowly defined and highly selected sample frames, which limits the potential for clear, generalizable policy prescriptions. Ultimately, larger samples, multi-arm evaluations, process documentation, and narrowly-focused, theory-supported empirical work are all needed, but the complexity of the problem limits what we learn from any single study

Managing atrial fibrillation in the elderly: critical appraisal of dronedarone

Atrial fibrillation is the most commonly seen arrhythmia in the geriatric population and is associated with increased cardiovascular morbidity and mortality. Treatment of the elderly with atrial fibrillation remains challenging for physicians, because this unique subpopulation is characterized by multiple comorbidities requiring chronic use of numerous medications, which can potentially lead to severe drug interactions. Furthermore, age-related changes in the cardiovascular system as well as other physiological changes result in altered drug pharmacokinetics. Dronedarone is a new drug recently approved for the treatment of arrhythmias, such as atrial fibrillation and/or atrial flutter. Dronedarone is a benzofuran amiodarone analog which lacks the iodine moiety and contains a methane sulfonyl group that decreases its lipophilicity. These differences in chemical structure are responsible for making dronedarone less toxic than amiodarone which, in turn, results in fewer side effects. Adverse events for dronedarone include gastrointestinal side effects and rash. No dosage adjustments are required for patients with renal impairment. However, the use of dronedarone is contraindicated in the presence of severe hepatic dysfunction

Keeping it simple: financial literacy and rules of thumb

Micro-entrepreneurs often lack the financial literacy required to make important financial decisions. We conducted a randomized evaluation with a bank in the Dominican Republic to compare the impact of two distinct programs: standard accounting training versus a simplified, rule-of-thumb training that taught basic financial heuristics. The rule-of-thumb training significantly improved firms' financial practices, objective reporting quality, and revenues. For micro-entrepreneurs with lower skills or poor initial financial practices, the impact of the rule-of-thumb training was significantly larger than that of the standard accounting training, suggesting that simplifying training programs might improve their effectiveness for less sophisticated individuals