B. Scott Gaudi

ACHIEVING BETTER THAN 1 MINUTE ACCURACY IN THE HELIOCENTRIC AND BARYCENTRIC JULIAN DATES

As the quality and quantity of astrophysical data continue to improve, the precision with which certain astrophysical events can be timed becomes limited not by the data themselves, but by the manner, standard, and uniformity with which time itself is referenced. While some areas of astronomy (most notably pulsar studies) have required absolute time stamps with precisions of considerably better than 1 minute for many decades, recently new areas have crossed into this regime. In particular, in the exoplanet community, we have found that the (typically unspecified) time standards adopted by various groups can differ by as much as a minute. Left uncorrected, this ambiguity may be mistaken for transit timing variations and bias eccentricity measurements. We argue that, since the commonly-used Julian Date, as well as its heliocentric and barycentric counterparts, can be specified in several time standards, it is imperative that their time standards always be reported when accuracies of 1 minute are required. We summarize the rationale behind our recommendation to quote the site arrival time, in addition to using BJDTDB, the Barycentric Julian Date in the Barycentric Dynamical Time standard for any astrophysical event. The BJDTDB is the most practical absolute time stamp for extraterrestrial phenomena, and is ultimately limited by the properties of the target system. We compile a general summary of factors that must be considered in order to achieve timing precisions ranging from 15 minutes to 1 μs. Finally, we provide software tools that, in principal, allow one to calculate BJDTDB to a precision of 1 μs for any target from anywhere on Earth or from any spacecraft.

EXOFAST: A Fast Exoplanetary Fitting Suite in IDL

We present EXOFAST, a fast, robust suite of routines written in IDL that is designed to fit exoplanetary transits and radial velocity variations simultaneously or separately and characterize the parameter uncertainties and covariances with a differential evolution Markov chain Monte Carlo method. We describe how our code incorporates both data sets to derive simultaneously stellar parameters along with the transit and RV parameters, resulting in more self-consistent results on an example fit of the discovery data of HAT-P-3b that is well-mixed in under 5 minutes on a standard desktop computer. We describe in detail how our code works and outline ways in which the code can be extended to include additional effects or generalized for the characterization of other data sets—including non-planetary data sets. We discuss the pros and cons of several common ways to parameterize eccentricity, highlight a subtle mistake in the implementation of MCMC that could bias the inferred eccentricity of intrinsically circular orbits to significantly non-zero results, discuss a problem with IDLs built-in random number generator in its application to large MCMC fits, and derive a method to analytically fit the linear and quadratic limb darkening coefficients of a planetary transit. Finally, we explain how we achieved improved accuracy and over a factor of 100 improvement in the execution time of the transit model calculation. Our entire source code, along with an easy-to-use online interface for several basic features of our transit and radial velocity fitting, are available online at http://astroutils.astronomy.ohio-state.edu/exofast.

Prospects for the Characterization and Confirmation of Transiting Exoplanets via the Rossiter-McLaughlin Effect

The Rossiter-McLaughlin (RM) effect is the distortion of stellar spectral lines that occurs during eclipses or transits, due to stellar rotation. We assess the future prospects for using the RM effect to measure the alignment of planetary orbits with the spin axes of their parent stars, and to confirm exoplanetary transits. We compute the achievable accuracy for the parameters of interest, in general and for the five known cases of transiting exoplanets with bright host stars. We determine the requirements for detecting the effects of differential rotation. For transiting planets with small masses or long periods (as will be detected by forthcoming satellite missions), the velocity anomaly produced by the RM effect can be much larger than the orbital velocity of the star. For a terrestrial planet in the habitable zone of a Sunlike star found by the Kepler mission, it will be difficult to use the RM effect to confirm transits with current instruments, but it still may be easier than measuring the spectroscopic orbit.

Analytic Approximations for Transit Light-Curve Observables, Uncertainties, and Covariances

The light curve of an exoplanetary transit can be used to estimate the planetary radius and other parameters of interest. Because accurate parameter estimation is a nonanalytic and computationally intensive problem, it is often useful to have analytic approximations for the parameters as well as their uncertainties and covariances. Here, we give such formulae, for the case of an exoplanet transiting a star with a uniform brightness distribution. We also assess the advantages of some relatively uncorrelated parameter sets for fitting actual data. When limb darkening is significant, our parameter sets are still useful, although our analytic formulae underpredict the covariances and uncertainties.

Periodic Flux Variability of Stars due to the Reflex Doppler Effect Induced by Planetary Companions

Upcoming space-based photometric satellites offer the possibility of detecting continuum flux variability at the micromagnitude (μmag) level. We show that the Doppler flux variability induced by the reflex motion of stars due to planetary companions has an amplitude of (3 - α)K/c, where K is the reflex radial velocity amplitude and α ≈ is the logarithmic slope of the source spectral flux in the observed frequency band. For many of the known close-in planetary systems with periods P 0.2 yr, the periodic Doppler variability, (μmag), is significant relative to the variability caused by reflected light from the planetary companion. For companions with P 0.2 yr, the Doppler signal is larger than the reflected light signal. We show that the future photometric satellites should reach the sensitivity to detect this Doppler variability. In particular, the Kepler satellite should have the photon noise sensitivity to detect at a signal-to-noise ratio 5 all planets with minimum mass Mp sin i 5MJ and P 0.1 yr around the ~104 main-sequence stars with spectral types A-K and apparent magnitude V < 12 in its field of view.

Identifying lenses with small-scale structure. II. Fold lenses

When the source in a four-image gravitational lens system lies sufficiently close to a fold caustic, two of the lensed images lie very close together. If the lens potential is smooth on the scale of the separation between the two close images, the difference between their fluxes should approximately vanish, Rfold ≡ (F+ - F-)/(F+ + F-) ≈ 0. (The subscript indicates the image parity.) Violations of this fold relation in observed lenses are thought to indicate the presence of structure on scales smaller than the separation between the close images. We present a detailed study of the fold relation in realistic smooth lenses, finding it to be more subtle and rich than was previously realized. The degree to which Rfold can differ from zero for smooth lenses depends not only on the distance of the source from the caustic, but also on its location along the caustic, and then on the angular structure of the lens potential (ellipticity, multipole modes, and external shear). Since the source position is unobservable, it is impossible to say from Rfold alone whether the flux ratios in an observed lens are anomalous or not. Instead, we must consider the full distribution of Rfold values that can be obtained from smooth lens potentials that reproduce the separation d1 between the two close images and the distance d2 to the next nearest image. (By reducing the image configuration to these two numbers, we limit our model dependence and obtain a generic analysis.) We show that the generic features of this distribution can be understood, which means that the fold relation provides a robust probe of small-scale structure in lens galaxies. We then compute the full distribution using Monte Carlo simulations of realistic smooth lenses. Comparing these predictions with the data, we find that five of the 12 known lenses with fold configurations have flux ratio anomalies: B0712+472, SDSS 0924+0219, PG 1115+080, B1555+375, and B1933+503. Combining this with our previous analysis revealing anomalies in three of the four known lenses with cusp configurations, we conclude that at least half (8/16) of all four-image lenses that admit generic, local analyses exhibit flux ratio anomalies. The fold and cusp relations do not reveal the nature of the implied small-scale structure, but do provide the formal foundation for substructure studies, and also indicate which lenses deserve further study. Although our focus is on close pairs of images, we show that the fold relation can be used—with great care—to analyze all image pairs in all 22 known four-image lenses and reveal lenses with some sort of interesting structure.

Planet Parameters in Microlensing Events

A planetary microlensing event occurs when a planet perturbs one of the two images created in a point-mass microlensing event, causing a deviation from the standard Paczynski curve. Determination of the two physical parameters that can be extracted from a planetary microlensing event, the planet/star mass ratio q, and the planet/star separation in units of the stellar Einstein ring, yp, is hampered by several types of degeneracies. There are two distinct and qualitatively different classes of planetary events: major and minor image perturbations. For major image perturbations, there is a potentially crippling continuous degeneracy in q which is of order δ -->−1d, where δd is the maximum fractional deviation of the planetary perturbation. Since the threshold of detection is expected to be δd ~ 5%, this degeneracy in q can be a factor of ~20. For minor image perturbations, the continuous degeneracy in q is considerably less severe, and is typically less than a factor of 4. We show that these degeneracies can be resolved by observations from dedicated telescopes on several continents together with optical/infrared photometry from one of these sites. There also exists a class of discrete degeneracies. These are typically easy to resolve given good temporal coverage of the planetary event. Unambiguous interpretation of planetary microlensing events requires the resolution of both types of degeneracy. We describe the degeneracies in detail and specify the situations in which they are problematic. We also describe how individual planet masses and physical projected separations can be measured.

Survey for Transiting Extrasolar Planets in Stellar Systems. III. A Limit on the Fraction of Stars with Planets in the Open Cluster NGC 1245

We analyze a 19 night photometric search for transiting extrasolar planets in the open cluster NGC 1245. An automated transit search algorithm with quantitative selection criteria finds six transit candidates; none are bona fide planetary transits. We characterize the survey detection probability via Monte Carlo injection and recovery of realistic limb-darkened transits. We use this to derive upper limits on the fraction of cluster members with close-in Jupiter radii, RJ, companions. The survey sample contains ~870 cluster members, and we calculate 95% confidence upper limits on the fraction of these stars with planets by assuming that the planets have an even logarithmic distribution in semimajor axis over the Hot Jupiter (HJ; 3.0 < P day-1 < 9.0) and Very Hot Jupiter (VHJ; 1.0 < P day-1 < 3.0) period ranges. For 1.5RJ companions we limit the fraction of cluster members with companions to <6.4% and <52% for VHJ and HJ companions, respectively. For 1.0RJ companions we find that <24% have VHJ companions. We do not reach the sensitivity to place any meaningful constraints on 1.0RJ HJ companions. From a careful analysis of the random and systematic errors of the calculation, we show that the derived upper limits contain a +13%/ - 7% relative error. For photometric noise and weather properties similar to those of this survey, observing NGC 1245 twice as long results in a tighter constraint on HJ companions than observing an additional cluster of richness similar to that of NGC 1245 for the same length of time as this survey. If 1% of stars have 1.5RJ HJ companions (as measured in radial velocity surveys), we expect to detect one planet for every 5000 dwarf stars observed for a month. To reach an ~2% upper limit on the fraction of stars with 1.5RJ companions in the 3.0 < P day-1 < 9.0 range, we conclude that a total sample size of ~7400 dwarf stars observed for at least a month will be needed. Results for 1.0RJ companions, without substantial improvement in the photometric precision, will require a small factor larger sample size.

State of the Field: Extreme Precision Radial Velocities*

The Second Workshop on Extreme Precision Radial Velocities defined circa 2015 the state of the art Doppler precision and identified the critical path challenges for reaching 10 cm s^(−1) measurement precision. The presentations and discussion of key issues for instrumentation and data analysis and the workshop recommendations for achieving this bold precision are summarized here. Beginning with the High Accuracy Radial Velocity Planet Searcher spectrograph, technological advances for precision radial velocity (RV) measurements have focused on building extremely stable instruments. To reach still higher precision, future spectrometers will need to improve upon the state of the art, producing even higher fidelity spectra. This should be possible with improved environmental control, greater stability in the illumination of the spectrometer optics, better detectors, more precise wavelength calibration, and broader bandwidth spectra. Key data analysis challenges for the precision RV community include distinguishing center of mass (COM) Keplerian motion from photospheric velocities (time correlated noise) and the proper treatment of telluric contamination. Success here is coupled to the instrument design, but also requires the implementation of robust statistical and modeling techniques. COM velocities produce Doppler shifts that affect every line identically, while photospheric velocities produce line profile asymmetries with wavelength and temporal dependencies that are different from Keplerian signals. Exoplanets are an important subfield of astronomy and there has been an impressive rate of discovery over the past two decades. However, higher precision RV measurements are required to serve as a discovery technique for potentially habitable worlds, to confirm and characterize detections from transit missions, and to provide mass measurements for other space-based missions. The future of exoplanet science has very different trajectories depending on the precision that can ultimately be achieved with Doppler measurements.

Characterization of Gravitational Microlensing Planetary Host Stars

The gravitational microlensing light curves that reveal the presence of extrasolar planets generally yield the planet-star mass ratio and separation in units of the Einstein ring radius. The microlensing method does not require the detection of light from the planetary host star. This allows the detection of planets orbiting very faint stars, but it also makes it difficult to convert the planet-star mass ratio to a value for the planet mass. We show that in many cases, the lens stars are readily detectable with high-resolution space-based follow-up observations in a single passband. When the lens star is detected, the lens-source relative proper motion can also be measured, and this allows the masses of the planet and its host star to be determined and the star-planet separation to be converted to physical units. Observations in multiple passbands provide redundant information, which can be used to confirm this interpretation. For the recently detected super-Earth planet, OGLE-2005-BLG-169Lb, we show that the lens star will definitely be detectable with observations by the Hubble Space Telescope (HST) unless it is a stellar remnant. Finally, we show that most planets detected by a space-based microlensing survey are likely to orbit host stars that will be detected and characterized by the same survey.