7.2.1 Single Transit Detection - Improved Automation
Efforts to detect K2 candidates (on both short- and long-periods) have, for the most part, re- lied on manual eye-balling. However, a fully computational technique using the techniques
touched on in Chapter 4 should be implemented. Thestevecode, developed in Chapter
4 for detecting single transits from ground-based surveys, should be directly applied to all eleven K2 campaigns in order to detect more candidates in a less time-intensive manner. If a suitable unbiased selection of K2 target stars are selected, such a method could also be used to infer occurrence rates for this long-period regime, thereby comparing with past Kepler occurrences and those of RV, Microlensing, etc. Other data sets would seem equally amenable to such an analysis, including the four years of CoRoT photometry.
This detection technique would benefit from multiple improvements. The first would be to add distinct categories for eclipsing binaries, and known false positives (e.g. from flux drops common to multiple stars). This would vastly decrease the current FP ra- tios, therefore reducing both the amount of human inspection of candidates and increasing the number of detectable planets. Current detectability calculations, which used equivalent binning techniques along multiple parameters, could be improved by using smoothly vary- ing multivariate kernel density estimations, thereby allowing the recoverability of injections and detectability of transits (and the change in these numbers as a function of multiple pa- rameters) to be studied on a sub-bin basis.
7.2.2 Single Transit Candidates - Follow-up Campaigns
The list of candidates detected in ground-based data (e.g.. WASP and NGTS) requires more thorough vetting to provide a short list of potential events. The full season of photometry can be used to search for the potential planetary period, by anchoring the phase fold at the candidate detection and phase-folding the data. In the case of WASP, although the data from past seasons is not as stable or with as rapid cadence as stare fields, it can contribute data for candidate objects that may help constrain potential periods. Such a technique will de- tect potential other dips that could give orbital periods, or provide a probabilistic minimum likely period from the data. For the best candidates, two or three low-resolution observa- tions spaced at the minimum period may be able to rule out eclipsing binary scenarios. This would then pave the way for high-resolution RVs, which may enable an orbital period to be determined, and a transit reobserved.
In the case of K2, the near-continuous phase coverage means a minimum period is already known accurately. Many of the single transit candidates detected in K2 offer ex- cellent opportunities for RV follow-up and eventually the mass measurement, confirmation, and transit re-observation of long-period planets. These could contribute to our understand- ing of planetary bulk compositions, planetary migration & evolution and even occurrence rates. Hence a programme of RV observations on these targets may prove extremely valu- able to the field. In both cases, the precise RV strategy, given a period estimate (or at least minimum period constraint), could also be developed.
For PDS 110, the presence of two events mean the predicted eclipse is constrained to within a few weeks. Photometric observations in September will confirm or rule out the periodic nature of the eclipses. In the former case, multiband photometry over many weeks will allow the dust grain size to be constrained and allow the sub-structure of the object to be studied in more detail. High-resolution spectroscopy out-of-eclipse will enable an estimate (or upper limit) on the mass of any secondary, and multiple such observations during eclipse may even enable the dust gradients to be crudely imaged through their effect on the shape of absorption lines in the star.
For all cases, extensive long-duration photometry of known candidates would be useful, and may allow further transits without radial velocities. A full catalogue of candidate transits could also be compiled across all transit surveys (ground and space-based) which, with the upcoming all-sky TESS mission, may enable their reobservation and confirmation. Proposals for TESS short-cadence data are possible, and should be attempted for these objects.
7.2.3 Long-Period Planets from Future Missions TESS
The Transiting Exoplanet Survey Satellite (TESS Ricker et al., 2015) will monitor 200,000 stars on 2min cadence over 26 different 28-day observing windows. Studies of TESS planet yield suggest more than 100 single transits could be detected above a noise threshold of 7.3σ(Sullivan et al., 2015).
To assess this figure, a similar study of the TESS input catalogue was performed. Using the noise profile from Ricker et al. (2015) combined with the mass-radius-temperature formulations of Boyajian et al. (2012), we reproduce a plausible TESS input catalogue for the 200,000 stars to be observed with 2 minute cadence.
To determine the likely number of planets detectable, we modify the occurrence rates from Fressin et al. (2013), extending them beyond 85d with a trend flat in log period space. A random number was assigned to each radius and period bin for each target and, in the cases where this was below the occurrence rate of that bin, a planet was generated at random inclination and phase. To smooth the distribution we produced a (linearly) random period and radius within each bin. For each inserted planet, we gave it a random field duration according to the proportions of targets in multiple fields given in Ricker et al. (2015) and calculated whether its orbit crossed the stellar disc. We then estimated the transit signal and light curve noise from the planetary characteristics and the stellar magnitude, and calculated whether the planet would transit multiple times during the observations, or just once. All planets with SNR>7.0 were assumed to be detectable.
In total, we found that∼4500 multi-transiting planets may be detectable in the two years of TESS operations, more than triple the estimate of Sullivan et al. (2015) (1700), and far more than expected from the past two years of K2. However, the number of expected single transiting planets (750) was nearly seven times that of Sullivan et al. (2015) (110).
While some of the difference may be from the more complicated analysis of systematic
variability and blending performed in that study, these effects should modify the detectable ratio of multi- and single- transiting systems equally. The previous study did not simulate planets with occurrence rates >1 year, which may have somewhat influenced the single transit yield. Therefore we suggest that Sullivan et al. (2015) may have significantly un- derestimated the number of single transiting exoplanets detectable with TESS, which could increase the planet yield by up to 17%.
Added to this, nearly the entire sky (including up to 20 million stars and galaxies brighter than I=15) will also be observed with 30 minute cadence in the full frame images. Although the fainter objects with lower SNR and the lack of pre-vetting will increase blend- ing and therefore FP ratio, many hundreds more single transits may also be discovered in
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Exoplanet detections with TESS
Multi Transits
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Figure 7.1: Likely number transits (detectable to> 7σ found in TESS as a function of orbital period, magnitude and planetary radius (marker size). In red are multi-transiting planets detectable through "classical" means, and in green are single transiting candidates.
this sample. The search techniques developed here, combined with analysis withNamaste, will prove important tools in the detection and follow up of these planets.
PLATO
Initial observing plans for the PLAnetary Transits and Oscillation of Stars (PLATO) mis- sion suggest 6 fields could be observed on 2-5 month campaigns, yielding 60,000 bright stars (Vmag < 12) with 30s cadence and hundreds of thousands of fainter stars (12 <
Vmag < 16) with 10-minute cadence (Rauer et al., 2014). The potential combination of asteroseismology-derived densities (accurate to 10%) with high-cadence, high-precision photometric data could produce dozens of validated long-period planets. As the period prediction is primarily a function of density and light curve photometric accuracy, PLATO could enable period estimates with 10% precision. This could hugely reduce the follow-up time necessary to confirm such planets.
Another combination possible with PLATO may be to detect long-period planets from a single transit during the ongoing observations. This could then allowing simulta- neous radial velocities with continuous space-based photometry, which can help improve RV precision by tracking stellar variation (Haywood et al., 2014). The improved precision and brighter stars also means that PLATO may be capable of reaching the terrestrial planet
regime from a single transit. If, as expected, a 10th magnitude star produces only 20ppm/hr of photon noise, an earth-radius planet with a 6-hour transit across a G-type star would be detectable to 10-σin a single transit.
Gaia and Direct Imaging
On their long orbits, single transiting exoplanets found in our search of K2, as well as those found in subsequent transit campaigns, could prove the first bridges between the close-in transit regime, and the far-out regime studied by radial velocities (which are already being utilised in follow-up), astrometry and direct imaging.
Gaia has the capability to detect tens of thousands of giant planets on 1 to 4 year orbits (Dzigan and Zucker, 2012). However, due to their long orbits, only∼3 in every 1000 will transit, producing on the order of 10-40 transiting planets (Perryman et al., 2014). However, the precision to confirm (or rule out) a long-period planet may be less than that required to detect the initial orbit, providing a new mechanism for follow-up, therefore transiting gas giants on these orbits found by TESS, PLATO or from the ground stand a good chance of being confirmed by Gaia astrometry. Gaia’s precision photometry of 1 billion stars will also enable the detection of long-period eclipsing binaries on both foreground and background sources which are currently a source of false positives. In the coming decades, only exoplanets on long orbits, and therefore only those detected by single transits, will allow the first overlaps between the realms of transiting and astrometric exoplanet astronomy.
We also computed the likelihood of detecting single transiting planets capable of follow-up by detecting with direct imaging. Assuming average orbits from 1 to 4 years and an occurrence rate of 10% for FGK stars, we used Gaia stellar information for nearby main sequence stars (Michalik et al., 2015) to compute the likely distribution of nearby transiting giant planets. We find that approximately one in every 250 of the nearest FGK stars would contain transiting giant planets, with the closest transiting giant planets likely
∼ 25 parsecs away, with the brightest such case typically around a∼ 6th magnitude star. The largest angular distance of the sample is typically 55mas, more than ten times the current resolution of Sphere (5mas; Beuzit et al., 2008b), although likely far below the necessary contrast level of∼ 108. This level of angular separation and contrast would be easily achievable by the next generation of telescopes, however, including E-ELT EPICS (Kasper et al., 2010), TMT-PFI (Macintosh et al., 2006) and WFIRST-AFTA (Zhao, 2014). As such, single transiting giant exoplanets could allow the first comparison of plan- etary characterisation via the full suite of transit, RVs, astrometry and direct imaging. Such a fleet of resources to characterise an extrasolar world would likely also be necessary for the detailed characterisation of solar-system analogues and earth-like planets in the near future.
With future transit missions, the detection and analysis of single events as detailed in this thesis may allow transiting exoplanet science to push beyond the hot inner regions of planetary systems. This will probe new parameter spaces, including the internal structure and atmospheric compositions of cool worlds. Markers of formation such as eccentricity and spin-orbit angle may also be more pronounced in "Warm" planets, and measurements of these effects allowing insights into formation and evolution of extrasolar systems. The occurrence rates of such worlds may bridge the gulf between transit surveys and those from other methods (RVs, Astrometry and Microlensing) PLATO, for example, will pro- vide long-period planet candidates in abundance around bright and nearby K or G dwarfs, including of solar system analogues such as cold gas giants and exo-Earths.