Progress in extra-solar planet detection

Progress in extra-solar planet detection is reviewed. The following subject areas are covered: (1) the definition of a planet; (2) the weakness of planet signals; (3) direct techniques - imaging and spectral detection; and (4) indirect techniques - reflex motion and occultations

New Completeness Methods for Estimating Exoplanet Discoveries by Direct Detection

We report new methods for evaluating realistic observing programs that search stars for planets by direct imaging, where observations are selected from an optimized star list, and where stars can be observed multiple times. We show how these methods bring critical insight into the design of the mission & its instruments. These methods provide an estimate of the outcome of the observing program: the probability distribution of discoveries (detection and/or characterization), & an estimate of the occurrence rate of planets (eta). We show that these parameters can be accurately estimated from a single mission simulation, without the need for a complete Monte Carlo mission simulation, & we prove the accuracy of this new approach. Our methods provide the tools to define a mission for a particular science goal, for example defined by the expected number of discoveries and its confidence level. We detail how an optimized star list can be built & how successive observations can be selected. Our approach also provides other critical mission attributes, such as the number of stars expected to be searched, & the probability of zero discoveries. Because these attributes depend strongly on the mission scale, our methods are directly applicable to the design of such future missions & provide guidance to the mission & instrument design based on scientific performance. We illustrate our new methods with practical calculations & exploratory design reference missions for JWST operating with a distant starshade to reduce scattered and diffracted starlight on the focal plane. We estimate that 5 habitable Earth-mass planets would be discovered & characterized with spectroscopy, with a probability of 0 discoveries of 0.004, assuming a small fraction of JWST observing time (7%), eta=0.3, and 70 observing visits, limited by starshade fuel.Comment: 27 pages, 4 figures, 6 tables, accepted for publication by Ap

On the Completeness of Reflex Astrometry on Extrasolar Planets near the Sensitivity Limit

We provide a preliminary estimate of the performance of reflex astrometry on Earth-like planets in the habitable zones of nearby stars. In Monte Carlo experiments, we analyze large samples of astrometric data sets with low to moderate signal-to-noise ratios. We treat the idealized case of a single planet orbiting a single star, and assume there are no non-Keplerian complications or uncertainties. The real case can only be more difficult. We use periodograms for discovery and least-squares fits for estimating the Keplerian parameters. We find a completeness for detection compatible with estimates in the literature. We find mass estimation by least squares to be biased, as has been found for noisy radial-velocity data sets; this bias degrades the completeness of accurate mass estimation. When we compare the true planetary position with the position predicted from the fitted orbital parameters, at future times, we find low completeness for an accuracy goal of 0.3 times the semimajor axis of the planet, even with no delay following the end of astrometric observations. Our findings suggest that the recommendation of the ExoPlanet Task Force (Lunine et al. 2008) for "the capability to measure convincingly wobble semi-amplitudes down to 0.2 $\mu$as integrated over the mission lifetime," may not be satisfied by an instrument characterized by the noise floor of the Space Interferometry Mission, $\sigma_\mathrm{floor}\approx0.035\mu$as. An important, unsolved, strategic challenge for the exoplanetary science program is figuring out how to predict the future position of an Earth-like planet with accuracy sufficient to ensure the efficiency and success of the science operations for follow-on spectroscopy, which would search for biologically significant molecules in the atmosphere.Comment: v2: 16 pages, 4 figures; ApJ accepte

HEALTH AND SAFETY REGULATION OF SMALL, HIGH-RISK SUBPOPULATIONS

The choice of decision framework used to set regulatory tolerance levels for hazardous substances can be divided into rigid and flexible tolerance levels. Rigid decision frameworks include zero or deminimis that fix risk levels for some subpopulation. and/or highly tolerances The accelerating identification of highly sensitive exposed individuals and the division of the population into ever smaller subpopulations at higher risk could prove to be tremendously burdensome on regulatory systems, particularly for rigid decision frameworks. Rigid tolerance levels, philosophically based on "rights" to zero or arbitrarily low excess risks for individuals, do not contain sufficient flexibility to account for small high-risk subpopulations. Furthermore, the equal protection for all such groups is an illusion, mainly because of the potentially large number of such subgroups and the relatively fixed regulatory resources. Thus, deminimis regulation is seen as a minimal but inadequate improvement over zero risk regulation. with improved measures of the heterogeneous demand for risk reduction by various high-risk subpopulations, augmented cost-benefit analyses leading to flexible tolEr2.nces could provide a richer analytic framework for more efficient regulatory decisions. Additionally, it may be useful to attempt to c2.tegorize hazards and subpopulations on the basis of the ability to self-protect.De minimis, sensitive, decision framework, cost benefit, Food Consumption/Nutrition/Food Safety, Health Economics and Policy,

From Baking a Cake to Solving the Schrodinger Equation

The primary emphasis of this study has been to explain how modifying a cake recipe by changing either the dimensions of the cake or the amount of cake batter alters the baking time. Restricting our consideration to the genoise, one of the basic cakes of classic French cuisine, we have obtained a semi-empirical formula for its baking time as a function of oven temperature, initial temperature of the cake batter, and dimensions of the unbaked cake. The formula, which is based on the Diffusion equation, has three adjustable parameters whose values are estimated from data obtained by baking genoises in cylindrical pans of various diameters. The resulting formula for the baking time exhibits the scaling behavior typical of diffusion processes, i.e. the baking time is proportional to the (characteristic length scale)^2 of the cake. It also takes account of evaporation of moisture at the top surface of the cake, which appears to be a dominant factor affecting the baking time of a cake. In solving this problem we have obtained solutions of the Diffusion equation which are interpreted naturally and straightforwardly in the context of heat transfer; however, when interpreted in the context of the Schrodinger equation, they are somewhat peculiar. The solutions describe a system whose mass assumes different values in two different regions of space. Furthermore, the solutions exhibit characteristics similar to the evanescent modes associated with light waves propagating in a wave guide. When we consider the Schrodinger equation as a non-relativistic limit of the Klein-Gordon equation so that it includes a mass term, these are no longer solutions.Comment: 23 pages, 10 Postscript figure