Sen—Jupiter-sized planets are the easiest type of planets to detect with every one of our current detection methods. Their high mass leads to easier radial velocity and microlensing observations, and their large size and young warmer temperatures lead to easier transiting and direct imaging detections. That is why the first radial velocity planet (51 Peg), the first transiting planet (OGLE-TR-056), the first microlensing planet (OGLE 2003-BLG-235L), and the first directly imaged planet (GQ Lupi b) were all Jupiter-like or larger.
But each detection method has its own pros and cons, and each one preferentially detects planets with certain characteristics. This begs the question of whether all the Jupiter-like planet detections from the different methods are really consistent with each other. This is similar to looking at a dalmatian and a miniature poodle and not knowing whether they both come from the same species. They might look similar, but are they really members of the same larger population?
Two astronomers at The Ohio State University, Christian Clanton and B. Scott Gaudi, have discovered that, yes, all Jupiter-like planets in Jupiter-like orbits do indeed represent the same population of planets. They combined results from five exoplanet surveys that use varying detection methods and were able to show that the number of Jupiter-massed planets at large orbital distances was consistent with a single population of Jupiter-like planets.
Limiting the analysis to Jupiter-sized planets at large orbital distances—two astronomical units (AU) or farther—immediately eliminates hot Jupiters from the problem. The astronomers made this cutoff in order to maximize the overlap between the radial velocity, microlensing, and direct imaging surveys. They did not want any one method to dominate the analysis they were doing to ensure they did not retain any of the observational biases they were trying to overcome.
Unfortunately there were no planets from transit surveys to add to the analysis. When hot Jupiters are excluded, the number of large, transiting, gaseous planets drops to a flat zero. The orbital distance cutoff of two AU immediately reduces the likelihood of any planet transiting altogether. Whether or not a planet transits depends on whether we are looking at the system nearly edge-on (transiting) or from the top-down (not transiting). The range of orientations that lead to transits falls off as orbital distances grow: Small changes in the angle of the planet's orbit become large changes in the apparent position of the planet and star, precluding a transit. Also, collecting enough data to detect a transiting long-orbit planet takes more time than Kepler had on its original field. The few confirmed transiting planets at large orbital distances generally only have two observed transits, rather than the standard three transits needed to confirm, and only one of those (KOI-351 h) is close to Jupiter-sized.
However, the two AU cutoff has an important scientific implication. Out beyond two AU, any Jupiter-sized planets are likely very close to where they actually formed. It is commonly accepted that hot Jupiters must have undergone a dramatic move from the outer parts of their solar systems to their current positions. Since one end goal is to discover how many planets of a certain mass form at a certain distance, they want to remove planets that are no longer in the places in which they formed. The orbital distance cutoff drastically improves the chances that the planets used are appropriate for this analysis.
Clanton and Gaudi included both detected planets and planetary "non-detections" to constrain their analysis. The "non-detections" place upper limits on the number of certain types of planets; that is, if there were any more planets of a certain mass or orbital distance then these surveys would have found them. The combination of radial velocity and imaging follow-up was represented by the California Planet Survey Targeting Benchmark-objects with Doppler Spectroscopy (CPS/TRENDS), a consortium of US-based universities and researchers. Additional direct imaging results were provided by the Gemini Deep Planet Survey (GDPS) out of the Gemini North Observatory in Hawai'i and the Planets Around Low-Mass Stars survey (PALMS) out of Caltech. Lastly, microlensing results from the Microlensing Observations in Astrophysics survey (MOA) of Japan and New Zealand and the Optical Gravitational Lensing Experiment (OGLE) of the University of Warsaw, Poland were included in the study.
They developed the model to report how the total number of planets (detected or not) is dependent on planet mass and orbital distance. They first assume that there is indeed an underlying distribution of planets that can be modelled, and that the distribution has the same shape as most distributions in astronomy: the power law. A power law simply says that smaller objects are much more frequent than larger objects. This relation holds true for stars, for galaxies, and for planets (as we have recently learned). It is a reasonable assumption that a power law can also be applied to this subgroup of planets. After assuming that a single population exists, they test whether their claim is likely true.
To accurately account for planets that exist but that we cannot find, they then had to calculate detection limits and sensitivities for each of the surveys they included. Detection limits refer to the technical specifications of the instrument used, while sensitivity refers to the physical parameters of the planetary system. Detection limits are knowing exactly how small a signal (radial velocity, microlensing, or imaging) can be and still be reliably detected by each instrument. Any signal above detection limits should have been detected if they were there.
Tied into this is the issue of sensitivity, that certain methods are more sensitive to certain masses, orbital distances, or configurations of the system. For example, a planet can only induce an observable radial velocity if it orbits nearly edge-on from our point of view, and that configuration will only induce a detectable signal if the planet is massive enough and close enough to its star.
By combining the detection limits and sensitivities with the list of detected planets and non-detections they are able to discover how many planets are missing from the population simply because we cannot observe them. This is the inferred planet population from radial velocity, microlensing, and direct imaging. They then use the inferred population to inform the specifics of their model population of planets.
The power law model population is dependent on four key parameters: How fast the number of planets changes with planet mass, how fast the number of planets changes with orbital distance, the outer-most orbital distance at which a planet can be detected, and the combination of mass and orbital distance that produces the most planets (the "pivot point"). Each survey can only constrain some combination of these four parameters, but combining each of the constraints lets Clanton and Gaudi narrow in on the most likely set of values.
Approximate regions of sensitivity for the various surveys considered. The solid, black lines bound the region for the OGLE and MOA microlensing surveys. The green region shows the area within which the CPS/TRENDS survey can detect long-term RV trends, while the red regions show the areas within which the GDPS (solid) and the PALMS (dashed) surveys are sensitive to directly imaged planets. The solid, black diamond shows the “pivot point” of the planet distribution model. The pivot point was chosen within the microlensing regions because the majority of their data was from microlensing, leading to a more accurate solution. Image credit: Clanton and Gaudi (2015).
A few key things are still missing from this type of analysis. First off is the issue of planet migration. We know from hot Jupiters that Jupiter-like planets can change their orbital distance over time, so there is no guarantee that the orbital distances we are observing now are the same as when the planet formed. The inferred planet population needs work as well, since the exact values depend on how these Jupiter-like planets formed. While the two preferred theories of giant planet formation both indicate a single population of planets, the planet populations indicated by each model are somewhat different.
The development of this type of model population is a crucial step forward in recognizing that our disparate detection methods and telescopes are all detecting a single same population of Jupiter-like planets. The fact that a model population represents the observed planets so well tells astronomers that all of the various exoplanet surveys are looking at different sections of the same puzzle rather than different puzzles altogether.
Future versions of this analysis would hopefully include the most recently detected planets from the Gemini Planet Imager, OGLE, and MOA. Follow-up observations on some Kepler planet candidates might add transiting large-orbit Jupiters, and the Transiting Exoplanet Survey Satellite (TESS) could also contribute transiting planets to the analysis. If we find more Earth-sized or Neptune-sized planets with multiple methods this type of analysis could be applied to smaller planets, as well.
Knowing the actual distribution of Jupiter-like planets will inform our designs of future telescopes and our interpretation of future results. If we know how how many planets of a certain mass and orbital separation are supposed to be there, we can design our future telescopes to find as many as possible, or to look for planets with specific properties. And afterwards, we can compare the number and types of planets found to the number expected and know if our existing model makes sense, or if we are still missing a large piece of the puzzle.