Speeding up low-mass planetary microlensing simulations and modelling: the Caustic Region Of INfluence

Extensive simulations of planetary microlensing are necessary both before and after a survey is conducted: before to design and optimize the survey and after to understand its detection efficiency. The major bottleneck in such computations is the computation of lightcurves. However, for low-mass planets most of these computations are wasteful, as most lightcurves do not contain detectable planetary signatures. In this paper I develop a parameterization of the binary microlens that is conducive to avoiding lightcurve computations. I empirically find analytic expressions describing the limits of the parameter space that contain the vast majority of low-mass planet detections. Through a large scale simulation I measure the (in)completeness of the parameterization and the speed-up it is possible to achieve. For Earth-mass planets in a wide range of orbits it is possible to speed up simulations by a factor of ${\sim} 30$-$125$ (depending on the survey's annual duty-cycle) at the cost of missing ${\sim} 1$ percent of detections (which is actually a smaller loss than for the arbitrary parameter limits typically applied in microlensing simulations). The benefits of the parameterization probably outweigh the costs for planets below $100M_{\oplus}$. For planets at the sensitivity limit of AFTA-WFIRST, simulation speed-ups of a factor ${\sim} 1000$ or more are possible.Comment: 9 pages, 8 figures, 3 table

How fast do Jupiters grow? Signatures of the snowline and growth rate in the distribution of gas giant planets

We present here observational evidence that the snowline plays a significant role in the formation and evolution of gas giant planets. When considering the population of observed exoplanets, we find a boundary in mass-semimajor axis space that suggests planets are preferentially found beyond the snowline prior to undergoing gap-opening inward migration and associated gas accretion. This is consistent with theoretical models suggesting that sudden changes in opacity -- as would occur at the snowline -- can influence core migration. Furthermore, population synthesis modelling suggests that this boundary implies that gas giant planets accrete ~ 70 % of the inward flowing gas, allowing ~ 30$ % through to the inner disc. This is qualitatively consistent with observations of transition discs suggesting the presence of inner holes, despite there being ongoing gas accretion.Comment: 7 pages, 6 figures, accepted for publication in Monthly Notices of the Royal Astronomical Societ

Is the Galactic bulge devoid of planets?

Considering a sample of 31 exoplanetary systems detected by gravitational microlensing, we investigate whether or not the estimated distances to these systems conform to the Galactic distribution of planets expected from models. We derive the expected distribution of distances and relative proper motions from a simulated microlensing survey, correcting for the dominant selection effects that affect the planet detection sensitivity as a function of distance, and compare it to the observed distribution using Anderson-Darling (AD) hypothesis testing. Taking the relative abundance of planets in the bulge to that in the disk, $f_{\rm bulge}$, as a model parameter, we find that our model is only consistent with the observed distribution for $f_{\rm bulge}<0.54$ (for a $p$-value threshold of 0.01) implying that the bulge may be devoid of planets relative to the disk. Allowing for a dependence of planet abundance on metallicity and host mass, or an additional dependence of planet sensitivity on event timescale does not restore consistency for $f_{\rm bulge}=1$. We examine the distance estimates of some events in detail, and conclude that some parallax-based distance estimates could be significantly in error. Only by combining the removal of one problematic event from our sample and the inclusion of strong dependences of planet abundance or detection sensitivity on host mass, metallicity and event timescale are we able to find consistency with the hypothesis that the bulge and disk have equal planet abundance.Comment: Revised following referee's report. 12 pages, 7 figures, 1 tabl

Caustic Structures and Detectability of Circumbinary Planets in Microlensing

Recent discoveries of circumbinary planets in Kepler data show that there is a viable channel of planet formation around binary main sequence stars. Motivated by these discoveries, we have investigated the caustic structures and detectability of circumbinary planets in microlensing events. We have produced a suite of animations of caustics as a function of the projected separation and angle of the binary host to efficiently explore caustic structures over the entire circumbinary parameter space. Aided by these animations, we have derived a semi-empirical analytic expression for the location of planetary caustics, which are displaced in circumbinary lenses relative to those of planets with a single host. We have used this expression to show that the dominant source of caustic motion will be due to the planet's orbital motion and not that of the binary star. Finally, we estimate the fraction of circumbinary microlensing events that are recognizable as such to be significant (5-50 percent) for binary projected separations in the range 0.1-0.5 in units of Einstein radii.Comment: 15 pages, 1 table, 18 figures. Accepted for publication in Ap

3D printed reactors and Kessil lamp holders for flow photochemistry: design and system standardization

A low-cost 3D printed standardized flow-photochemistry setup has been designed and developed for use with a pressure-driven flow system using photochemistry lamps available in most laboratories. In this research, photochemical reactors were 3D printed from polypropylene which facilitated rapid optimization of both reactor geometry and experimental setup of the lamp housing system. To exemplify the rapidity of this approach to optimization, a Kessil LED lamp was used in the bromination of a range of toluenes in the 3D printed reactors in good yields with residence times as low as 27 s. The reaction compared favorably with the batch photochemical procedure and was able to be scaled up to a productivity of 75 mmol h−1

Exploring exoplanetary systems beyond 1AU with WFIRST

The Wide Field InfraRed Survey Telescope (WFIRST) was the top ranked large space mission of the New Worlds, New Horizons Decadal Survey, and is currently under active study by NASA. Its primary instrument will be a large-format high-resolution near-infrared imager and slitless spectrometer. A primary goal of WFIRST will be to perform a high-cadence microlensing survey of the Galactic bulge to search for low-mass exoplanets beyond the ice line. We highlight some of the expected results of the WFIRST exoplanet survey. For example, the survey will probe the abundance of Earth-mass planets from less than 1 AU outwards, including free-floating planets. In its peak sensitivity range of ~2-5 AU, WFIRST will be sensitive to planets with masses lower than Mercury, and even down to the mass of Ganymede. Overall, WFIRST is expected to detect several thousand bound planets, in addition to several thousand free-floating planets. WFIRST will complete the exoplanet census begun by Kepler, enabling an unprecedented understanding of planetary systems and their formation. Copyright © 2013, International Astronomical Union

Measuring the galactic distribution of transiting planets with WFIRST

The WFIRST microlensing mission will measure precise light curves and relative parallaxes for millions of stars, giving it the potential to characterize short-period transiting planets all along the line of sight and into the galactic bulge. These light curves will enable the detection of more than 100,000 transiting planets whose host stars have measured distances. Although most of these planets cannot be followed up, several thousand hot Jupiters can be confirmed directly by detection of their secondary eclipses in the WFIRST data. Additionally, some systems of small planets may be confirmed by detecting transit timing variations over the duration of the WFIRST microlensing survey. Finally, many more planets may be validated by ruling out potential false positives. The combination of WFIRST transits and microlensing will provide a complete picture of planetary system architectures, from the very shortest periods to unbound planets, as a function of galactocentric distance