Parametric modeling of photometric signals

This paper studies a new model for photometric signals under high flux assumption. Photometric signals are modeled by Gaussian autoregressive processes having the same mean and variance denoted Constraint Gaussian Autoregressive Processes (CGARP's). The estimation of the CGARP parameters is discussed. The Cramér Rao lower bounds for these parameters are studied and compared to the estimator mean square errors. The CGARP is intended to model the signal received by a satellite designed for extrasolar planets detection. A transit of a planet in front of a star results in an abrupt change in the mean and variance of the CGARP. The Neyman–Pearson detector for this changepoint detection problem is derived when the abrupt change parameters are known. Closed form expressions for the Receiver Operating Characteristics (ROC) are provided. The Neyman–Pearson detector combined with the maximum likelihood estimator for CGARP parameters allows to study the generalized likelihood ratio detector. ROC curves are then determined using computer simulations

Determining the Mass of Kepler-78b With Nonparametric Gaussian Process Estimation

Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hours. The mass of Kepler-78b has been independently reported by two teams based on radial velocity measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in radial velocity data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the radial velocity datasets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV datasets, giving a Doppler amplitude of 1.86 $\pm$ 0.25 m s$^{-1}$ and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87 $^{+0.27}_{-0.26}$ M$_{\oplus}$ is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0$^{+1.9}_{-1.4}$ g cm$^{-3}$. We estimate that Kepler-78b is 32$\pm$26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.Comment: 10 pages, 5 figures, accepted to ApJ 6/16/201

Precision cluster mass determination from weak lensing

Weak gravitational lensing has been used extensively in the past decade to constrain the masses of galaxy clusters, and is the most promising observational technique for providing the mass calibration necessary for precision cosmology with clusters. There are several challenges in estimating cluster masses, particularly (a) the sensitivity to astrophysical effects and observational systematics that modify the signal relative to the theoretical expectations, and (b) biases that can arise due to assumptions in the mass estimation method, such as the assumed radial profile of the cluster. All of these challenges are more problematic in the inner regions of the cluster, suggesting that their influence would ideally be suppressed for the purpose of mass estimation. However, at any given radius the differential surface density measured by lensing is sensitive to all mass within that radius, and the corrupted signal from the inner parts is spread out to all scales. We develop a new statistic that is ideal for estimation of cluster masses because it completely eliminates mass contributions below a chosen scale (which we suggest should be about 20 per cent of the virial radius), and thus reduces sensitivity to systematic and astrophysical effects. We use simulated and analytical profiles to quantify systematic biases on the estimated masses for several standard methods of mass estimation, finding that these can lead to significant mass biases that range from ten to over fifty per cent. The mass uncertainties when using our new statistic are reduced by up to a factor of ten relative to the standard methods, while only moderately increasing the statistical errors. This new method of mass estimation will enable a higher level of precision in future science work with weak lensing mass estimates for galaxy clusters.Comment: 27 pages, 7 figures, submitted to MNRAS; v2 has expanded explanation for clarity, no change in results or conclusion

Suzaku Observation of Abell 1689: Anisotropic Temperature and Entropy Distributions Associated with the Large-Scale Structure

(Abridged) We present results of Suzaku observations of the intracluster medium (ICM) in Abell 1689, combined with complementary analysis of the SDSS data and weak and strong lensing analysis of Subaru/Suprime-Cam and HST/ACS observations. Faint X-ray emission from the ICM around the virial radius is detected at 4.0 sigma significance. We find anisotropic gas temperature and entropy distributions in cluster outskirts correlated with large-scale structure of galaxies. The high temperature and entropy region in the northeastern (NE) outskirts is connected to an overdense filamentary structure. The outskirt regions in contact with low density void environments have low gas temperatures and entropies, deviating from hydrostatic equilibrium. These results suggest that thermalization of the ICM occurs faster along the filamentary structures than the void regions. A joint X-ray and lensing analysis shows that the hydrostatic mass is $\sim60-90$ of spherical lensing one but comparable to a triaxial halo mass within errors in 0.6r_{2500} \simlt r \simlt 0.8r_{500}, and that it is significantly biased as low as \simlt60% within $0.4r_{2500}$, irrespective of mass models. The thermal gas pressure within $r_{500}$ is, at most, $\sim50$--60% of the total pressure to balance fully the gravity of the spherical lensing mass, and $\sim30$--40% around the virial radius. Although these constitute lower limits when one considers the possible halo triaxiality, these small relative contributions of thermal pressure would require additional sources of pressure, such as bulk and/or turbulent motions.Comment: 24 pages, 15 figures, 9 tables. Accepted for publication in Ap

Discovery of a Ringlike Dark Matter Structure in the Core of the Galaxy Cluster Cl 0024+17

We present a comprehensive mass reconstruction of the rich galaxy cluster Cl 0024+17 at z~0.4 from ACS data, unifying both strong- and weak-lensing constraints. The weak-lensing signal from a dense distribution of background galaxies (~120 per square arcmin) across the cluster enables the derivation of a high-resolution parameter-free mass map. The strongly-lensed objects tightly constrain the mass structure of the cluster inner region on an absolute scale, breaking the mass-sheet degeneracy. The mass reconstruction of Cl 0024+17 obtained in such a way is remarkable. It reveals a ringlike dark matter substructure at r~75" surrounding a soft, dense core at r~50". We interpret this peculiar sub-structure as the result of a high-speed line-of-sight collision of two massive clusters 1-2 Gyr ago. Such an event is also indicated by the cluster velocity distribution. Our numerical simulation with purely collisionless particles demonstrates that such density ripples can arise by radially expanding, decelerating particles that originally comprised the pre-collision cores. Cl 0024+17 can be likened to the bullet cluster 1E0657-56, but viewed $along$ the collision axis at a much later epoch. In addition, we show that the long-standing mass discrepancy for Cl 0024+17 between X-ray and lensing can be resolved by treating the cluster X-ray emission as coming from a superposition of two X-ray systems. The cluster's unusual X-ray surface brightness profile that requires a two isothermal sphere description supports this hypothesis.Comment: To appear in the June 1 issue of The Astrophysical Journa