One of the objectives of NASA’s Kepler mission, as well as one of the important drivers of its design, was to detect Earth-size planets in Earth-like orbits around Sun-like stars. While there has yet to be a confirmed discovery of such a world, extrapolations of Kepler’s results to date suggest that several can be expected to be detected during the on going analysis of this mission’s data (see “Abundance of Earth Analogs”). In fact, there have already been some candidates of such worlds detected whose planetary status is currently being confirmed by follow-up observations and analysis (see “Earth Twins on the Horizon?”).

While scientists are continuing their work to find an Earth twin, they have been able to make better progress in the study of the planetary systems of smaller and much more numerous M-dwarf stars. Studies of Kepler data to date have already shown that about half of M-dwarf planetary systems are, on average, composed of about a half dozen planets in tight orbits with low mutual inclinations (see “Architecture of M-Dwarf Planetary Systems”). Planets in systems like these orbiting M-dwarf stars are easier to detect owing to their shorter orbital periods (which produces more frequent transits), their smaller orbits (which increases the probability of producing a transit) and their larger size relative to the star they orbit (which produces deeper transit events) compared to their counterparts orbiting more Sun-like stars. Some of these M-dwarf planets even orbit inside the habitable zone (HZ) of their systems (see “Habitable Planet Reality Check: 8 New Habitable Zone Planets” and “Habitable Planet Reality Check: Kepler 186f Revisted”). As a result, there has been more work published to date about these easier-to-find potentially habitable planets orbiting M-dwarfs than hotter G-type stars like the Sun.

A New Study

Courtney Dressing and David Charbonneau (Harvard-Smithsonian Center for Astrophysics) have recently submitted for publication in The Astrophysical Journal the most in depth analysis of the Kepler data set to estimate the occurrence rate of planets orbiting inside the HZ of M-dwarf stars. Dressing and Charbonneau reviewed the complete 18-quarter Kepler database to identify 157 planets and planet candidates orbiting M-dwarf stars including two new objects that had not been previously identified. They checked all of the openly available follow-up observations and analyses for these systems to estimate the “false positive” probability of the finds. They also analyzed the detection thresholds of the data processing pipeline for the 4,915 M-dwarfs observed by Kepler by injecting 2,000 simulated transit signals with known properties into each stars’ light curves. They then performed a statistical analysis to estimate the number of planets in various size ranges M-dwarfs have in various types of orbits.

Dressing and Charbonneau found that planets with radii greater than 2.5 times that of the Earth (or R E ) are rare in M-dwarf planetary systems out to orbital periods of 200 days confirming the results of earlier published analyses. For planets with orbital periods less than 50 days, Dressing and Charbonneau found that the occurrence rate decreases as the planet radii increases from 1.0 R E to 3.5 R E (corresponding roughly to Earth-size to Neptune-size planets). For planets with orbital periods less than 50 days, they found an occurrence rate of 57% (+6%/-5%) for Earth-size planets with radii between 1.0 and 1.5 R E and 51% (+7%/-6%) for super-Earths with radii between 1.5 and 2.0 R E . Previous analyses of Kepler finds over the past year have shown that these “super-Earths” (a term invented before the true nature of these worlds was known) are actually more likely to be mini-Neptunes with smaller planets having a much higher probability of having rocky compositions (see “Habitable Planet Reality Check: Terrestrial Planet Size Limit”). Smaller sub-Earth-size planets with radii between 0.5 to 1.0 R E (corresponding roughly to Mars to Earth-size worlds) were tougher to detect but have estimated occurrence rate of 71% (+9%/-6%). Looking at planets with periods out to a maximum of 100 days, Dressing and Charbonneau find slightly higher occurrence rates of 73% (+9%/6%), 68% (+7%/-5%), 61% (+8%/-6%) for sub-Earth-size, Earth-size and super-Earth-size planets, respectively.

Dressing and Charbonneau then analyzed the occurrence rates of various size planets as a function of insolation or effective stellar flux, S eff (i.e. the amount of energy the planets receive from their sun with Earth’s S eff defined as 1). This allowed them to estimate the occurrence rate of planets of various size ranges as a function of the S eff limits for a wide variety of definitions of the HZ. One of the more conservative limits for the HZ (which I tend to favor as do many others) is based on the work of Kopparapu et al. with the inner edge of the HZ defined by the runaway greenhouse limit and the outer edge defined by the maximum greenhouse limit for a CO 2 dominated greenhouse. These correspond to S eff values of roughly 0.88 and 0.25, respectively, for a typical M-dwarf star.

Using the conservative limits for the HZ, Dressing and Charbonneau found an occurrence rate of 18% (+18%/-7%) for Earth-size planets with radii of 1.0 to 1.5 R E (which are likely to be rocky planets like the Earth) and 11% (+10%/-5%) for super-Earths with radii of 1.5 to 2.0 R E (which are likely to be mini-Neptunes with little real prospect for being habitable except for any large moons they might have). The statistics for smaller planets with radii in the 0.5 to 1.0 R E range (the lower end of which corresponds roughly to the smallest likely size of a habitable world) are much poorer since such worlds can only be detected orbiting an estimated 13% of the M-dwarf stars in the Kepler sample. Nonetheless, Dressing and Charbonneau estimate that the occurrence rate of these smaller worlds in the conservatively defined HZ is about 14% (+32%/-6%) with the large uncertainty reflecting the poorer statistics of the smaller sample. Looking at all planets orbiting M-dwarf stars with radii between 0.5 to 1.4 R E (which encompasses the full size range of planets expected to have rocky compositions with any real prospects of actually being habitable), Dressing and Charbonneau find an occurrence rate of 29% (+25%/-12%). Naturally, less conservative definitions that result in much wider HZs have higher occurrence rates for the various classes of planets.

Conclusions

This first statistical analysis of the full Kepler data set by Dressing and Charbonneau has allowed them to produce the best estimates to date for the occurrence rates of planets of various sizes orbiting M-dwarf stars in general as well as in the HZs of these dim stars in particular. Their results indicate that potentially habitable planets (i.e. planets in the HZ that are large enough to be habitable but not so large as to be mini-Neptunes) can be expected to be relatively common. Dressing and Charbonneau suggest that the nearest potentially habitable planet orbiting an M-dwarf star could be just 8 light years away, assuming the conservative limits of the HZ defined by Kopparapu et al.. Factoring in the probability that such worlds would have their orbits aligned to produce an observable transit, the nearest potentially habitable planet orbiting an M-dwarf producing transits could be only 36 light years away – close enough and orbiting a star bright enough to be detected and studied by any number of current or future extrasolar planet survey projects. Assuming that about three-quarters of the estimated 200 to 400 billion stars in our galaxy are M-dwarfs, we can expect on the order of 65 billion, give or take, potentially habitable planets orbiting M-dwarfs in our galaxy alone.

Although not discussed by Dressing and Charbonneau in their paper, the occurrence rates of various size planets orbiting M-dwarf stars neatly explains the lack of planet detections by various surveys looking at well known, nearby M-dwarf stars like Proxima Centauri and Barnard’s Star (see “The Search for Planets Around Proxima Centauri” and “The Search for Planets Around Barnard’s Star“) . To date, no planets have been detected orbiting either of these closest M-dwarfs down to Neptune-size objects and smaller, depending on the orbital period. The results of Dressing and Charbonneau suggest that planets of this size and larger are relatively uncommon or even rare in M-dwarf planetary systems. Factoring in various observational limitations, the lack of any planet detections is not unusual at this stage in the search for planets.

As impressive as this work by Dressing and Charbonneau is, there are still large uncertainties associated with their results with more data required to refine them. The ongoing analysis of the data set from Kepler’s primary mission as well as the data from the extended “K2” mission should provide some new finds. NASA’s Transiting Exoplanet Survey Satellite (TESS) mission, which will observe 1,000 nearby red dwarfs among its half million relatively bright targets, should provide many finds to improve occurrence rate estimates especially in the star fields near the ecliptic poles that will be observed for longer periods of time. These planets offer the potential of detailed follow-up study that will help scientists begin to probe the potential habitability of planets orbiting M-dwarfs which are the most common star type in the galaxy.

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Related Reading

“Architecture of M-Dwarf Planetary Systems”, Drew Ex Machina, October 24, 2014 [Post]

“Habitable Planet Reality Check: 8 New Habitable Zone Planets”, Drew Ex Machina, January 8, 2015 [Post]

“Habitable Planet Reality Check: Terrestrial Planet Size Limit”, Drew Ex Machina, July 24, 2014 [Post]

“Habitable Planet Reality Check: Kepler 186f Revisted”, Drew Ex Machina, April 17, 2016 [Post]

General References

Courtney D. Dressing and David Charbonneau, “The Occurrence of Potentially Habitable Planets Orbiting M Dwarfs Estimated from the Full Kepler Dataset and an Empirical Measurement of the Detection Sensitivity”, arVix 1501.01623 (submitted to The Astrophysical Journal), January 7, 2015 [Preprint]

R. K. Kopparapu et al., “Habitable zones around main-sequence stars: new estimates”, The Astrophysical Journal, Vol. 765, No. 2, Article ID. 131, March 10, 2013

Ravi Kumar Kopparapu et al., “Habitable zones around main-sequence stars: dependence on planetary mass”, The Astrophysical Journal Letters, Vol. 787, No. 2, Article ID. L29, June 1, 2014