Exo-Earth/Super-Earth Yield of JWST plus a Starshade External Occulter

We examine the scientific viability of an imaging mission to find exo-Earths combining the James Webb Space Telescope (JWST) with a starshade external occulter under a realistic set of astrophysical assumptions. We define an exo-Earth as a planet of 1 to 10 Earth masses orbiting in the habitable zone (HZ) of a solar-type star. We show that for a survey strategy that relies on a single image to detect an exo-Earth, roughly half of all exo-Earth detections will be false alarms. Here, a false alarm is a mistaken identification of a planet as an exo-Earth. We consider two survey strategies designed to mitigate the false alarm problem. The first is to require that for each potential exo-Earth, a sufficient number of detections are made to measure the orbit. When the orbit is known we can determine if the planet is in the habitable zone. With this strategy, we find that the number of exo-Earths found is on average 0.9, 1.9 and 2.7 for {\eta}_Earth = 0.1, 0.2 and 0.3. Here, {\eta}_Earth is the frequency of exo-Earths orbiting solar-type stars. There is a ~40% probability of finding zero exo-Earths for {\eta}_Earth = 0.1. A second strategy can be employed if a space astrometry mission has identified and measured the orbits and masses of the planets orbiting nearby stars. We find that with prior space-based astrometry from a survey of 60 nearby stars, JWST plus an external occulter can obtain orbital solutions for the majority (70% to 80%) of the exo-Earths orbiting these 60 stars. The exo-Earth yield is approximately five times higher than the yield for the JWST plus occulter mission without prior astrometry. With prior astrometry, the probability that an imaging mission will find zero exo-Earths is reduced to below 1% for the case of {\eta}_Earth = 0.1.Comment: Accepted by PASP. To appear in February 2010 issue. 15 pages, 2 figure

The Synergy of Direct Imaging and Astrometry for Orbit Determination of exo-Earths

The holy grail of exoplanet searches is an exo-Earth, an Earth mass planet in the habitable zone around a nearby star. Mass is the most important parameter of a planet and can only be measured by observing the motion of the star around the planet-star center of mass. A single image of a planet, however, does not provide evidence that the planet is Earth mass or that it is in a habitable zone orbit. The planet's orbit, however, can be measured either by imaging the planet at multiple epochs or by measuring the position of the star at multiple epochs by space-based astrometry. The measurement of an exo-planet's orbit by direct imaging is complicated by a number of factors: (1) the inner working angle (IWA); (2) the apparent brightness of the planet depending on the orbital phase; (3) confusion arising from the presence of multiple planets; and (4) the planet-star contrast. In this paper we address the question: "Can a prior astrometric mission that can identify which stars have Earthlike planets significantly improve the science yield of a mission to image exo-Earths?" We find that the Occulting Ozone Observatory (a small external occulter mission that cannot measure spectra) could confirm the orbits of ~4 to ~5 times as many exo-Earths if an astrometric mission preceded it to identify which stars had such planets. We find that in the case of an internal coronagraph, a survey of the nearest ~60 stars could be done with a telescope of half the size if an astrometric mission had first identified the presence of Earth-like planets in the habitable zone and measured their orbital parameters.Comment: ApJ, in press; 28 pages, 8 figure

Kepler Planet Detection Metrics: Window and One-Sigma Depth Functions for Data Release 25

This document describes the window and one-sigma depth functions relevant to the Transiting Planet Search (TPS) algorithm in the Kepler pipeline (Jenkins 2002; Jenkins et al. 2017). The window function specifies the fraction of unique orbital ephemeris epochs over which three transits are observable as a function of orbital period. In this context, the epoch and orbital period, together, comprise the ephemeris of an orbiting companion, and ephemerides with the same period are considered equivalent if their epochs differ by an integer multiple of the period. The one-sigma depth function specifies the depth of a signal (in ppm) for a given light curve that results in a one-sigma detection of a transit signature as a function of orbital period when averaged over all unique orbital ephemerides. These planet detection metrics quantify the ability of TPS to detect a transiting planet signature on a star-by-star basis. They are uniquely applicable to a specific Kepler data release, since they are dependent on the details of the light curves searched and the functionality of the TPS algorithm used to perform the search. This document describes the window and one-sigma depth functions relevant to Kepler Data Release 25 (DR25), where the data were processed (Thompson et al. 2016) and searched (Twicken et al. 2016) with the SOC 9.3 pipeline. In Section 4, we describe significant differences from those reported in Kepler Data Release 24 (Burke Seader 2016) and document our verification method

Kepler Planet Detection Metrics: Per-Target Flux-Level Transit Injection Tests of TPS for Data Release 25

Quantifying the ability of a transiting planet survey to recover transit signals has commonly been accomplished through Monte-Carlo injection of transit signals into the observed data and subsequent running of the signal search algorithm (Gilliland et al., 2000; Weldrake et al., 2005; Burke et al., 2006). In order to characterize the performance of the Kepler pipeline (Twicken et al., 2016; Jenkins et al., 2017) on a sample of over 200,000 stars, two complementary injection and recovery tests are utilized:1. Injection of a single transit signal per target into the image or pixel-level data, hereafter referred to as pixel-level transit injection (PLTI), with subsequent processing through the Photometric Analysis (PA), Presearch Data Conditioning (PDC), Transiting Planet Search (TPS), and Data Validation (DV) modules of the Kepler pipeline. The PLTI quantification of the Kepler pipeline's completeness has been described previously by Christiansen et al. (2015, 2016); the completeness of the final SOC 9.3 Kepler pipeline acting on the Data Release 25 (DR25) light curves is described by Christiansen (2017).2. Injection of multiple transit signals per target into the normalized flux time series data with a subsequent transit search using a stream-lined version of the Transiting Planet Search (TPS) module. This test, hereafter referred to as flux-level transit injection (FLTI), is the subject of this document. By running a heavily modified version of TPS, FLTI is able to perform many injections on selected targets and determine in some detail which injected signals are recoverable. Significant numerical efficiency gains are enabled by precomputing the data conditioning steps at the onset of TPS and limiting the search parameter space (i.e., orbital period, transit duration, and ephemeris zero-point) to a small region around each injected transit signal.The PLTI test has the advantage that it follows transit signals through all processing steps of the Kepler pipeline, and the recovered signals can be further classified as planet candidates or false positives in the exact same manner as detections from the nominal (i.e., observed) pipeline run (Twicken et al., 2016, Thompson et al., in preparation). To date, the PLTI test has been the standard means of measuring pipeline completeness averaged over large samples of targets (Christiansen et al., 2015, 2016; Christiansen, 2017). However, since the PLTI test uses only one injection per target, it does not elucidate individual-target variations in pipeline completeness due to differences in stellar properties or astrophysical variability. Thus, we developed the FLTI test to provide a numerically efficient way to fully map individual targets and explore the performance of the pipeline in greater detail. The FLTI tests thereby allow a thorough validation of the pipeline completeness models (such as window function (Burke and Catanzarite, 2017a), detection efficiency (Burke Catanzarite, 2017b), etc.) across the spectrum of Kepler targets (i.e., various astrophysical phenomena and differences in instrumental noise). Tests during development of the FLTI capability revealed that there are significant target-to-target variations in the detection efficiency

Astrometric Detection of exo-Earths in the Presence of Stellar Noise

Space astrometry is capable of sub-microarcsecond measurements of star positions. A hundred visits over several years could yield relative astrometric precision of ~0.1 uas, below the astrometric signature (0.3 uas) of a Sun-Earth system at a distance of 10 parsecs. We investigate the impact of starspots on the detectability, via astrometric and radial velocity techniques, of Earthlike planets orbiting Sunlike stars. We find that for nearby stars, although starspot noise imposes severe restrictions on detectability by the radial velocity technique, it does not significantly affect astrometric detectability of habitable zone planets down to below an Earth mass.Comment: 11 pages, 7 figure

Astrometric Detection of Terrestrial Planets in the Habitable Zones of Nearby Stars with SIM PlanetQuest

SIM PlanetQuest (Space Interferometry Mission) is a space-borne Michelson interferometer for precision stellar astrometry, with a nine meter baseline, currently slated for launch in 2015. One of the principal science goals is the astrometric detection and orbit characterization of terrestrial planets in the habitable zones of nearby stars. Differential astrometry of the target star against a set of reference stars lying within a degree will allow measurement of the target star's reflex motion with astrometric accuracy of 1 micro-arcsecond in a single measurement. We assess SIM's capability for detection (as opposed to characterization by orbit determination) of terrestrial planets in the habitable zones of nearby solar-type stars. We compare SIM's performance on target lists optimized for the SIM and Terrestrial Planet Finder Coronograph (TPF-C) missions. Performance is quantified by three metrics: minimum detectable planet mass, number and mass distribution of detected planets, and completeness of detections in each mass range. Finally, we discuss the issue of confidence in detections and non-detections, and show how information from SIM's planet survey can enable TPF to increase its yield of terrestrial planets.Comment: Minor corrections to figures and tables. 46 pages, 27 figures. To appear in PASP (Publications of the Astronomical Society of the Pacific), May 200

The Occurrence Rate of Earth Analog Planets Orbiting Sunlike Stars

Kepler is a space telescope that searches Sun-like stars for planets. Its major goal is to determine {\eta}_Earth, the fraction of Sunlike stars that have planets like Earth. When a planet 'transits' or moves in front of a star, Kepler can measure the concomitant dimming of the starlight. From analysis of the first four months of those measurements for over 150,000 stars, Kepler's science team has determined sizes, surface temperatures, orbit sizes and periods for over a thousand new planet candidates. In this paper, we characterize the period probability distribution function of the super-Earth and Neptune planet candidates with periods up to 132 days, and find three distinct period regimes. For candidates with periods below 3 days the density increases sharply with increasing period; for periods between 3 and 30 days the density rises more gradually with increasing period, and for periods longer than 30 days, the density drops gradually with increasing period. We estimate that 1% to 3% of stars like the Sun are expected to have Earth analog planets, based on the Kepler data release of Feb 2011. This estimate of is based on extrapolation from a fiducial subsample of the Kepler planet candidates that we chose to be nominally 'complete' (i.e., no missed detections) to the realm of the Earth-like planets, by means of simple power law models. The accuracy of the extrapolation will improve as more data from the Kepler mission is folded in. Accurate knowledge of {\eta}_Earth is essential for the planning of future missions that will image and take spectra of Earthlike planets. Our result that Earths are relatively scarce means that a substantial effort will be needed to identify suitable target stars prior to these future missions.Comment: Accepted for publication in the Astrophysical Journal. 19 pages, 8 figures. Minor text revisions, as requested by the scientific editor. Included an additional figure. No changes in the scientific result

Finding Earth clones with SIM: The most promising near-term technique to detect, find masses for, and determine three-dimensional orbits of nearby habitable planets

SIM is a space astrometric interferometer capable of better than one-microarcsecond (µas) single measurement accuracy, providing the capability to detect stellar "wobble" resulting from planets in orbit around nearby stars. While a search for exoplanets can be optimized in a variety of ways, a SIM five-year search optimized to detect Earth analogs (0.3 to 10 Earth masses) in the middle of the habitable zone (HZ) of nearby stars would yield the masses, without M*sin(i) ambiguity, and three-dimensional orbital parameters for planets around ~70 stars, including those in the HZ and further away from those same stars. With >200 known planets outside our solar system, astrophysical theorists have built numerical models of planet formation that match the distribution of Jovian planets discovered to date and those models predict that the number of terrestrial planets (< 10 M_⊕) would far exceed the number of more massive Jovian planets. Even so, not every star will have an Earth analog in the middle of its HZ. This paper describes the relationship between SIM and other planet detection methods, the SIM planet observing program, expected results, and the state of technical readiness for the SIM mission

Measuring Transit Signal Recovery in the Kepler Pipeline II: Detection Efficiency as Calculated in One Year of Data

The Kepler planet sample can only be used to reconstruct the underlying planet occurrence rate if the detection efficiency of the Kepler pipeline is known, here we present the results of a second experiment aimed at characterising this detection efficiency. We inject simulated transiting planet signals into the pixel data of ~10,000 targets, spanning one year of observations, and process the pixels as normal. We compare the set of detections made by the pipeline with the expectation from the set of simulated planets, and construct a sensitivity curve of signal recovery as a function of the signal-to-noise of the simulated transit signal train. The sensitivity curve does not meet the hypothetical maximum detection efficiency, however it is not as pessimistic as some of the published estimates of the detection efficiency. For the FGK stars in our sample, the sensitivity curve is well fit by a gamma function with the coefficients a = 4.35 and b = 1.05. We also find that the pipeline algorithms recover the depths and periods of the injected signals with very high fidelity, especially for periods longer than 10 days. We perform a simplified occurrence rate calculation using the measured detection efficiency compared to previous assumptions of the detection efficiency found in the literature to demonstrate the systematic error introduced into the resulting occurrence rates. The discrepancies in the calculated occurrence rates may go some way towards reconciling some of the inconsistencies found in the literature.Comment: 13 pages, 7 figures, 1 electronic table, accepted by Ap