Detecting New Planets in Transiting Systems

I present an initial investigation into a new planet detection technique that uses the transit timing of a known, transiting planet. The transits of a solitary planet orbiting a star occur at equally spaced intervals in time. If a second planet is present, dynamical interactions within the system will cause the time interval between transits to vary. These transit time variations can be used to infer the orbital elements of the unseen, perturbing planet. I show analytic expressions for the amplitude of the transit time variations in several limiting cases. Under certain conditions the transit time variations can be comparable to the period of the transiting planet. I also present the application of this planet detection technique to existing transit observations of the TrES-1 and HD209458 systems. While no convincing evidence for a second planet in either system was found from those data, I constrain the mass that a perturbing planet could have as a function of the semi-major axis ratio of the two planets and the eccentricity of the perturbing planet. Near low-order, mean-motion resonances (within about 1% fractional deviation), I find that a secondary planet must generally have a mass comparable to or less than the mass of the Earth--showing that these data are the first to have sensitivity to sub Earth-mass planets orbiting main sequence stars. These results show that TTV will be an important tool in the detection and characterization of extrasolar planetary systems.Comment: Ph.D. dissertation (2006). 108 page

Kepler's Missing Planets

We investigate the distributions of the orbital period ratios of adjacent planets in high multiplicity \kepler\ systems (four or more planets) and low multiplicity systems (two planets). Modeling the low multiplicity sample as essentially equivalent to the high multiplicity sample, but with unobserved intermediate planets, we find some evidence for an excess of planet pairs between the 2:1 and 3:1 Mean Motion Resonances in the low multiplicity sample. This possible excess may be the result of strong dynamical interactions near these or other resonances or it may be a byproduct of other evolutionary events or processes such as planetary collisions. Three planet systems show a significant excess of planets near the 2:1 Mean Motion Resonance that is not as prominent in either of the other samples. This observation may imply a correlation between strong dynamical interactions and observed planet number---perhaps a relationship between resonance pairs and the inclinations or orbital periods of additional planets. The period ratio distributions can also be used to identify targets to search for missing planets in the each of the samples, the presence or absence of which would have strong implications for planet formation and dynamical evolution models.Comment: Accepted to MNRA

The CHASE laboratory search for chameleon dark energy

A scalar field is a favorite candidate for the particle responsible for dark energy. However, few theoretical means exist that can simultaneously explain the observed acceleration of the Universe and evade tests of gravity. The chameleon mechanism, whereby the properties of a particle depend upon the local environment, is one possible avenue. We present the results of the Chameleon Afterglow Search (CHASE) experiment, a laboratory probe for chameleon dark energy. CHASE marks a significant improvement other searches for chameleons both in terms of its sensitivity to the photon/chameleon coupling as well as its sensitivity to the classes of chameleon dark energy models and standard power-law models. Since chameleon dark energy is virtually indistinguishable from a cosmological constant, CHASE tests dark energy models in a manner not accessible to astronomical surveys.Comment: Version 2 is the submission to IDM 2010 conference proceedings, Montpellier, France (slightly longer and two more figures), Version 1 is the submission to ICHEP 2010 conference proceedings, Paris, France (6 pages, four figures

Dark Matter And The Habitability of Planets

In many models, dark matter particles can elastically scatter with nuclei in planets, causing those particles to become gravitationally bound. While the energy expected to be released through the subsequent annihilations of dark matter particles in the interior of the Earth is negligibly small (a few megawatts in the most optimistic models), larger planets that reside in regions with higher densities of slow moving dark matter could plausibly capture and annihilate dark matter at a rate high enough to maintain liquid water on their surfaces, even in the absence of additional energy from starlight or other sources. On these rare planets, it may be dark matter rather than light from a host star that makes it possible for life to emerge, evolve, and survive.Comment: 9 pages, 3 figures, updated calculations with a larger velocity dispersion for the central portion of the Milky Wa

Spectral gene set enrichment (SGSE)

Motivation: Gene set testing is typically performed in a supervised context to quantify the association between groups of genes and a clinical phenotype. In many cases, however, a gene set-based interpretation of genomic data is desired in the absence of a phenotype variable. Although methods exist for unsupervised gene set testing, they predominantly compute enrichment relative to clusters of the genomic variables with performance strongly dependent on the clustering algorithm and number of clusters. Results: We propose a novel method, spectral gene set enrichment (SGSE), for unsupervised competitive testing of the association between gene sets and empirical data sources. SGSE first computes the statistical association between gene sets and principal components (PCs) using our principal component gene set enrichment (PCGSE) method. The overall statistical association between each gene set and the spectral structure of the data is then computed by combining the PC-level p-values using the weighted Z-method with weights set to the PC variance scaled by Tracey-Widom test p-values. Using simulated data, we show that the SGSE algorithm can accurately recover spectral features from noisy data. To illustrate the utility of our method on real data, we demonstrate the superior performance of the SGSE method relative to standard cluster-based techniques for testing the association between MSigDB gene sets and the variance structure of microarray gene expression data. Availability: http://cran.r-project.org/web/packages/PCGSE/index.html Contact: [email protected] or [email protected]

Principal component gene set enrichment (PCGSE)

Motivation: Although principal component analysis (PCA) is widely used for the dimensional reduction of biomedical data, interpretation of PCA results remains daunting. Most existing methods attempt to explain each principal component (PC) in terms of a small number of variables by generating approximate PCs with few non-zero loadings. Although useful when just a few variables dominate the population PCs, these methods are often inadequate for characterizing the PCs of high-dimensional genomic data. For genomic data, reproducible and biologically meaningful PC interpretation requires methods based on the combined signal of functionally related sets of genes. While gene set testing methods have been widely used in supervised settings to quantify the association of groups of genes with clinical outcomes, these methods have seen only limited application for testing the enrichment of gene sets relative to sample PCs. Results: We describe a novel approach, principal component gene set enrichment (PCGSE), for computing the statistical association between gene sets and the PCs of genomic data. The PCGSE method performs a two-stage competitive gene set test using the correlation between each gene and each PC as the gene-level test statistic with flexible choice of both the gene set test statistic and the method used to compute the null distribution of the gene set statistic. Using simulated data with simulated gene sets and real gene expression data with curated gene sets, we demonstrate that biologically meaningful and computationally efficient results can be obtained from a simple parametric version of the PCGSE method that performs a correlation-adjusted two-sample t-test between the gene-level test statistics for gene set members and genes not in the set. Availability: http://cran.r-project.org/web/packages/PCGSE/index.html Contact: [email protected] or [email protected]