My research is broadly focused on studying population statistics of exoplanetary systems.  Some of the projects I have led or helped to lead to are briefly described below.  Please note that this may not be up-to-date; for my most current research, check out my publications list.

Large-scale Adaptive Optics Imaging of Kepler Candidate Host Stars  [Law, Morton, et al. (2014)]

High-resolution imaging, such as delivered by adaptive optics (AO) systems, is one of the most important follow-up observations for a transiting planet candidate.  It can identify previously unresolved companion stars, which might be a potential source of a false positive signal, a physically bound companion, or just simply innocently blending flux that changes the implied radius of the planet.  The AO systems that provide these important measurements have traditionally been complex-to-operate systems installed on large telescopes.  The result is that each AO observation is very expensive, since time on these telescopes is scarce, and also because the observational overheads are often large, making a large AO survey (e.g., on the order of ~1000 targets) preventatively difficult. 

The new Robo-AO system at Palomar Observatory is a fully autonomous laser-guide-star AO system on a 60" telescope, and I am helping lead a project to use it to observe every Kepler candidate host star.  The first results from this survey (consisting of 715 targets from one observing season's data) have been submitted for publication, already making this project by far the largest AO survey ever undertaken.  This image shows the 53 candidate host stars that were resolved into multiple stars.  We plan to complete this survey (over 2000 stars in total) in the summer of 2014.

Demographics of Exoplanets around Cool Stars  [Morton & Swift (2014)]

The Kepler mission is surveying >150,000 stars for transiting planets; most of these are selected to be stars similar to the Sun.  However, about ~3900 of the Kepler target stars are so-called "red dwarf" stars with temperatures cooler than ~4000 K.  These targets are optimal for learning about the distribution of small planets for several reasons: first, they are much more numerous than Sun-like stars, and thus are representative of most of the stars in the Galaxy; secondly, they have smaller radii so smaller planets are more readily detectable around them.

Divining the true properties of the underlying population of planets from a survey, even from such a great survey as Kepler, is a subtle exercise: for each detected planet there are many planets that have evaded detection, yet must still be counted somehow ("exoplanets are like cockroaches," as my thesis adviser so eloquently put it).  The precise details of how to do this correction properly are important if we want to learn as much from Kepler as possible.  

There are two kinds of "missed planets" that need to be corrected for: planets that are not observed to transit because of unfavorable orbital geometry, and planets that actually do transit but whose transits are note identified by the detection pipeline.  The first of these corrections is easy; the second---completeness correction---is more challenging to get right.  In Morton & Swift (2013), we carefully correct for this so-called "detection incompleteness," and derive the empirical shape of the radius distribution of small planets around these cool stars.

Estimating the true underlying shape of the distribution of some exoplanet property---such as planet radius---given a set of discrete samples is another subtle exercise: in Morton & Swift (2013), we used a modified kernel density estimator, which is just like traditional kernel density estimation except for that each data point gets a normalization appropriate to its individual detection efficiency.  That is, the less likely Kepler was to find any particular planet, the more it contributes to the distribution.  The figure on the right illustrates the final result, which provides a benchmark for theories of planetary system formation and evolution.

The radius distribution of small planets around cool stars, as calculated by Morton & Swift (2013).  There are three notable features of this distribution.  First, we are able to detect a turnover in the radius function below about 1 Earth radius, even correcting for incompleteness.  Secondly, there appears to be an overabundance of planets between about 2 and 2.5 Earth radii, potentially indicative of a population of planets with significant H/He atmospheres.  And finally, there are simply many more planets smaller than ~2.5-3 Earth radii, which is about the detection threshold of some of the leading current ground-based surveys.  Many more planets will be found as surveys continue to get more sensitive!

Transit Candidate False Positive Probabilities [Morton & Johnson (2011b); Morton (2012)]

The idea behind these false positive probability calculations is simple: planets and false positives are different colored marbles in a box.  Planets are green and false positives are blue.  If you pick a marble at random from the box and all you know is the relative numbers of marbles of different colors (e.g. the "prior"), then you'd say you have a 4/12 = 1/3 chance of the marble being green.  If, however, you happened to have more information available, such that you knew that 3/4 of green marbles are large and only 1/4 of blue marbles are large, and you pick out a large marble, then you'd recalculate the chances of it being green to be 3/5---this is incorporating "likelihood" information, or the knowledge that different models predict different distributions of observables. As an exact analogy to this, the probability that a transit signal is a real planet is the equation below, where 'TP' stands for "transiting planet" and 'FP' for "false positive." The whole analysis then rests on carefully calculating these prior and likelihood factors for each model.

When a survey looking for transiting planets finds a source that periodically dims in the manner characteristic of a planet transit signal, it might be a real planet, or it might be an astrophysical false positive---usually some configuration of eclipsing binary star.  Ground-based transit surveys (the only ones around until the CoRoT and Kepler missions) have had a difficult time with false positives, with only a small fraction (~10%) of candidates turning out to be planets.  As a result, the way that transit surveys have historically distinguished between false positives and planets is by a lengthy process of follow-up observations to rule out false positive scenarios, culminating in radial velocity (RV) measurements to determine the mass of the planet.

The Kepler mission presents several challenges to this traditional transit follow-up scheme.  First of all, most of the stars being searched by Kepler are much fainter than typical RV targets, making RV observations costly.  Secondly, most of the planet candidates are so small that even their predicted RV amplitudes are undetectable with current instruments. And finally, there is simply an overwhelming quantity of candidates emerging from Kepler data: over 2300 with the last public release, with that number set to swell to well over 3000.  As a result, the fruit of the Kepler survey is thousands of planet candidates, with little prospect of confirming most of them by traditional methods.

In order to make sense of what this candidate population implies about the true planet population (which is, after all, the ultimate goal of the Kepler mission), it is crucial to have a statistical understanding of the false positive problem.  In Morton & Johnson (2011b), we argued that by taking a careful census of expected false positives and combining that with the level of photometric vetting that should be possible with Kepler data, that fewer than 10% of well-vetted Kepler candidates are likely to turn out to be false positives. 

In Morton (2012) I have expanded this false positive analysis to be capable of statistically validating individual candidates.  I demonstrate that by combining more detailed information about the shape of the transit with a priori information about the expected population of potential false positives, that many planets can be confirmed with just two single-epoch follow-up observations: a spectrum to characterize the host star, and an adaptive optics image to constrain the presence of nearby blended companions.  We intend to use this analysis to statistically validate large numbers of Kepler candidates in the near future.

We start by modeling light curves as trapezoids:

Then we see how well the shape of the signal (as parametrized by the trapezoidal shape) matches with typical shapes of the various possible scenarios:

And then combine the information from all the models to calculate the total false positive probability! 

The false positive scenarios I consider in Morton (2012) are hierarchical eclipsing binaries (HEB), eclipsing binaries (EB), background[/foreground] eclipsing binaries (BGEB), and transiting planets around background[/foreground] stars; in Morton & Johnson (2011b) we only considered HEBs and BGEBs. 

Discerning Exoplanet Migration Mechanisms Using Spin-Orbit Alignment [Morton & Johnson 2011a

Explaining the existence of "hot Jupiters"---gas giant planets orbiting very close to their host stars---is one of the first puzzles of exoplanet science and remains an active area of research.  As it is clear that these planets could not have formed where we see them today, we conclude that they must have originally formed on larger orbits and then somehow traveled ("migrated") to their present-day locations.   

The "spin-orbit angle" of a exoplanet system---the angle between the planet's orbital angular momentum vector and the stellar spin angular momentum---is a fossil record of the system's dynamical history.  That is, if planets originally form from a disc rotating in the same plane as the star, then any misalignment is likely a result of the planet's migration.  Consequently, the ensemble of measured spin-orbit angles provides clues as to what migration mechanisms might have acted over the history of these systems.

Proposed mechanisms fall into two basic categories: disk migration, which preserves low orbital inclincation; and multi-body interactions, which can result in highly inclined orbits.  In Morton & Johnson (2011a), inspired by the earlier work of Fabrycky and Winn (2007), we investigated the observed distribution of measured spin-orbit angles as a tracer of orbital inclination and ask two questions:
  1. Does current spin-orbit data support the idea that multiple migration mechanisms might be at work? 
  2. Is there enough spin-orbit data to distinguish between different multi-body-interaction migration models? 
Using two specific model predictions (figure, right), one for migration via the Kozai effect (Fabrycky & Tremaine 2007) and one via planet-planet scattering (Nagasawa et al. 2008), we determined that the scenario that explains the available data best is about a 50-50 split between disk migration (producing small spin-orbit angles) and planet-planet scattering (producing a wide range of angles).

Other recent work on this subject:
  • Albrecht et al. (2012) suggests a different origin of the observed distribution of spin-orbit angles: that the inclinations of all close-in planets begin as isotropically distributed and that the observed well-aligned systems are a result of tidal interactions between the planet and star that result in tidal re-alignment of the star's spin after migration occurs.  There is good evidence supporting this hypothesis; however, whether the details of the actual migration mechanisms can still be discerned within this paradigm is an open question.  That is, is a particular migration mechanism favored? Does disk migration still play a role?
  • Naoz et al. (2012) propose an updated version of the predictions of hot Jupiter formation via the Kozai effect.  By incorporating higher-order terms into the dynamical equations that were neglected in previous Kozai calculations, they are able to better explain the misaligned population of close-in planets than the previous Kozai predictions.  

The probability distributions for the true and projected spin-orbit angles for the "Kozai cycles plus tidal friction" and "planet-planet scattering plus tidal friction" models (above).  The 32 spin-orbit measurements used for the Morton and Johnson (2011a) analysis are illustrated in gray in the bottom panel.  We determined that the most likely scenario is one in which about half of close-in planets migrate via disk migration (maintaining a small spin-orbit angle) and half via planet-planet scattering (below).  It should be noted that these conclusions assume that these three models are an exhaustive choice of all possible models, which is of course unlikely.  However, it does demonstrate that Kozai migration (as predicted in Fabrycky & Tremaine (2007)) on its own does not sufficiently explain the observed distribution of spin-orbit angles.