Over the past couple of decades, the pace of exoplanet discoveries has accelerated with literally thousands of extrasolar planets currently known. Today there are numerous databases available where researchers or even interested lay people can scan through the basic properties of all the known exoplanets. One of the underappreciated aspects about these listed properties is how their values are frequently dependent on (and limited by) what we know about the exoplanet’s parent star.

For example, NASA’s highly successful Kepler mission has used the transit method to find its thousands of exoplanets by looking for periodic dips in a star’s brightness as an orbiting exoplanet passes between us. Besides information about the geometry of these transits, the only data about the transiting exoplanet itself that can be directly gleaned from Kepler’s observations are the orbital period (determined from the timing between successive transit events) and the radius of the exoplanet relative to its parent star (determined by how much the brightness of the host star changes during the transit). Other exoplanet properties must be derived from a knowledge of the host star’s properties. By using Kepler’s Third Law, the Kepler-derived orbital period combined with a knowledge of the host star’s mass allows the size of the exoplanet’s orbit to be calculated. The product of the Kepler-derived relative radius of the exoplanet and the actual radius of the host star allows the actual radius of the exoplanet to be calculated. Using the Stefan-Boltzmann Law, the luminosity of the star can be calculated from its effective surface temperature and its radius. The star’s luminosity and the size of the exoplanet’s orbit can then be used to calculate the amount of energy that the exoplanet receives or its effective stellar flux, S eff .

When our knowledge of a star’s properties is inaccurate, then our knowledge of its exoplanet’s properties are also affected. And since a star’s mass, radius, temperature and a host of other properties are all interrelated, a change in our knowledge of one parameter can cascade into sometimes subtle changes of the calculations of its other properties. A perfect example of this are the exoplanets found during Kepler’s extended “K2” mission orbiting a star designated K2-72. When the discovery of these four exoplanets was announced in July 2016, it appeared that they were all smaller than the Earth and two of them might be potentially habitable. Unfortunately, it was already known at the time of this announcement that the assumed properties of the star K2-72 were inaccurate and that its potentially habitable exoplanets might not, in fact, be smaller than Earth or potentially habitable (see “Habitable Planet Reality Check: Kepler’s New Finds at K2-72”). Astronomers have now performed much needed follow up observations of K2-72 and have derived much more accurate properties for this star allowing the exoplanet properties to be updated as well. So does this star still have any potentially habitable planets based on our new and improved knowledge?

Background

The star K2-72 (also known as EPIC 206209135 and 2MASS J22182923-0936444) is a red dwarf star with a V magnitude of 15.3 located in the constellation of Aquarius something like 230 light years away. Kepler observed this star as part of its K2 Campaign 3 which ran from November 14, 2014 to February 3, 2015. The first planet found orbiting this star, K2-72b with a period of 5.58 days, was revealed publicly in November 2015 in a paper with Andrew Vanderburg (Harvard Smithsonian Center for Astrophysics) as the lead author where the Kepler team presented their first-look analysis of the first four K2 observing campaigns. Three more exoplanet candidates with longer periods of 15.19, 7.76 and 24.17 days were confirmed by a new analysis of Kepler’s data as well as follow up observations submitted for publication in July 2016 with Ian Crossfield (Lunar & Planetary Laboratory – University of Arizona) as the lead author.

While all four of these exoplanets appeared to be sub-Earth size and two of them, K2-72c and e, seemed to have some prospects for being potentially habitable, these assessments were based on star properties that Crossfield et al. noted were known to be underestimating the size and brightness of the parent star. In reality, the radii and the amount of energy these exoplanets received from their parent star, the effective stellar flux or S eff , were going to be somewhat larger (see “Habitable Planet Reality Check: Kepler’s New Finds at K2-72”).

The original stellar parameters for K2-72 found in the Ecliptic Plane Input Catalog (EPIC) used by the Kepler team (including Crossfield et al.), summarized below in Table 1, were compiled by a team of astronomers led by Daniel Huber (Sydney Institute for Astronomy/SETI Institute). Huber et al. used the best available multi-band photometry as well as other available data for the stars to be observed during the K2 extended mission as inputs into a model which generated estimates of the radius, mass, luminosity and temperature of the stars. These stellar properties were then used to process Kepler data as well as to calculate the initial estimates of the actual size of the exoplanet’s orbit, its S eff , its actual radii and so on – properties needed to make various types of assessments of these exoplanets including their potential habitability. While the properties derived by Huber et al. represented the best initial estimates of the properties of K2 targets, they did have known shortcomings such as a tendency to underestimate the size and luminosity of red dwarfs.

Because of these limitations in the initial stellar parameters in EPIC, it was known that follow up observations would be required to derive more accurate values as part of the exoplanet candidate validation process. But instead of doing this for hundreds of thousands of stars, astronomers could focus their limited resources on just the tiny subset of those stars that became “objects of interest” as a result of Kepler’s K2 observations. One team of astronomers, whose analysis appears in a paper with Arturo Martinez (San Diego State University/Georgia State University) as the lead author, obtained new spectra of 34 red dwarf stars of interest from the K2 Campaigns 1 through 5 as part of a larger program with Ian Crossfield as the Principle Investigator (who is also one of the paper’s coauthors). Martinez et al. used the SOFI spectrograph on the 3.58-meter European Southern Observatory’s New Technology Telescope (NTT) located in Chile at the La Silla Observatory to obtain infrared spectra in the 0.95 to 2.52 μm wavelength range where red dwarfs are their brightest and display a range of useful spectral features.

A visual inspection of the spectrum by Martinez et al. and a comparison to standard stars in the IRTF Spectral Library confirmed that K2-72 was a red dwarf of spectral type M2.7±0.9. By measuring the widths of key spectral features and comparing them to a set of well-characterized red dwarfs with directly measured radii, the radius, mass, effective temperature and luminosity of K2-72 were determined. These properties, also summarized below in Table 1, confirmed the earlier suspicions of Crossfield et al. that the size and luminosity of K2-72 were underestimated. But while Crossfield et al. speculated that the radius of K2-72 was on the order of 0.4 times that of the Sun, Martinez et al. found a radius of 0.359±0.054 which was somewhat smaller suggesting that the actual radii of the exoplanets orbiting K2-72 were also somewhat smaller than the 1.2 to 1.5 times that of the Earth (or R E ) values Crossfield et al. were expecting.

Martinez et al. were not the only team to be performing follow up observations of K2-72. In a paper with Courtney Dressing (NASA Sagan Fellow at Caltech) as the lead author, the near infrared spectra they had obtained of 144 suspected cool dwarf stars that were identified during K2 Campaigns 1 through 7 were analyzed. Half of these stars turned out to be distant giant stars or much hotter stars whose light had been redden by interstellar dust. Among the 72 actual K and M-type dwarf stars observed as part of this effort was K2-72.

Dressing et al. observed K2-72 on September 24, 2015 using the SpeX instrument on NASA’s 3.0-meter Infrared Telescope Facility (IRTF) located on the summit of Mauna Kea in Hawaii. This spectrum covered wavelengths from 0.7 to 2.55 μm with twice the resolution of the SOFI spectra analyzed by Martinez et al.. Once again, a visual inspection of the spectrum indicated K2-72 is a type M2V star with an estimated ±1 uncertainty in the subclass. A detailed analysis of the spectrum allowed the star’s other properties to be determined as shown below in Table 1. In general, the results of the analysis by Dressing at al. agrees well with the results of Martinez et al. and, because of the superior quality of the spectra used, the former have been adopted in determining the exoplanets’ properties.

Table 1: Stellar Properties of K2-72 from Various Sources

Source Huber et al. Martinez et al. Dressing et al. Spectral Type M2.7±0.9V M2±1V Radius (Sun=1) 0.232±0.056 0.359±0.054 0.331±0.030 Mass (Sun=1) 0.217±0.081 0.361±0.061 0.271 (+0.079/-0.091) Temperature (K) 3497±150 3370±160 3360 (+86/-87) Luminosity (Sun=103) 7.2 14.9±3.2 13.4 (+2.0/-1.7)

All in all, the newly derived properties of K2-72 are very similar to the much closer red dwarfs Luyten’s Star and Wolf 1061 which recently have been found to have potentially habitable exoplanets orbiting them (see “Habitable Planet Reality Check: The Nearby GJ 273 or Luyten’s Star” and “Habitable Planet Reality Check: Wolf 1061c Revisited”).

In a separate paper with Courtney Dressing again as the lead author, the results of various follow up observations of 76 low-mass stars observed during the K2 Campaign 1 through 7, including K2-72, are described. In addition, Dressing et al. reanalyzed the original K2 photometric data and combined these new results with updated host star properties found by them and others to derive improved characterizations of their planetary systems. The updated properties derived by Dressing et al. of the four exoplanets found orbiting K2-72 are summarized below in Table 2. While the radius and effective stellar flux, S eff , values for these exoplanets are higher than the original values derived by Crossfield et al. owing mainly to the improved knowledge of the host star properties, they all still appear to be Earth-size exoplanets suitable for further assessment of their potential habitability.

Table 2: Planet Properties from Dressing et al.

Planet b c d e Radius (Earth=1) 1.08±0.11 1.16±0.13 1.01±0.12 1.29±0.13 Period (days) 5.58 15.19 7.76 24.16 Semi Major Axis (AU) 0.039 0.078 0.049 0.106 S eff (Earth=1) 8.5±1.2 2.2±0.3 5.4±0.8 1.2±0.2

Potential Habitability

A thorough assessment of the habitability of any extrasolar planet would require a lot of detailed data on the properties of that planet, its atmosphere, its spin state, the evolution of its volatile content and so on. Unfortunately, at this very early stage, the only information typically available to scientists about extrasolar planets are basic orbit parameters, a rough measure of its size and/or mass and some important properties of its parent star. Combined with theoretical extrapolations of the factors that have kept the Earth habitable over billions of years (not to mention why our neighbors are not habitable), the best we can hope to do at this time is to compare the known properties of extrasolar planets to our current understanding of planetary habitability to determine if an extrasolar planet is “potentially habitable”. And by “habitable”, I mean in an Earth-like sense where the surface conditions allow for the existence of liquid water on the planet’s surface – one of the presumed prerequisites for the development of life as we know it. While there may be other worlds that might possess environments that could support life, these would not be Earth-like habitable worlds of the sort being considered here.

The first step in assessing the potential habitability of the planets orbiting K2-72 is to determine what sort of worlds they are: are they rocky planets like the Earth or are they volatile-rich mini-Neptunes with little prospects of being habitable in an Earth-like sense. If we know the radius and mass of an exoplanet, its mean density can be readily calculated which in turn can be used to constrain its bulk composition. While the radii of the exoplanet orbiting K2-72 have been derived from Kepler measurements, unfortunately there are no mass measurements currently available. One method used today that could provide the mass of an exoplanet is the analysis of precision radial velocity measurements. The reflex motion of K2-72 as a result of its quartet of orbiting exoplanets is expected to have amplitudes of 0.8 to 1.4 meters per second – a level of accuracy frequently reached when observing nearby red dwarfs. Unfortunately, the apparent brightness of K2-72 is probably too low for current radial velocity surveys to measure with the required accuracy but future instruments operating in the infrared may have better luck.

Without radial velocity measurements to help estimate the mass of these exoplanets, another method is needed. Since the orbits of K2-72c and d seem to be in a 2:1 mean motion resonance while K2-72b and c are close to a 5:7 resonance, it is expected that the orbits of these exoplanets will vary noticeably over time due to strong mutual gravitational interactions. This opens the possibility that the masses could be derived indirectly by analyzing transit timing variations (TTV). But once again, the dimness of K2-72 will complicate this task. K2-72, with a V magnitude of 15.1, is too dim to be observed by either NASA’s TESS (Transiting Exoplanet Survey Satellite) or ESA’s CHEOPS (CHaracterising ExOPlanets Satellite) which will be targeting brighter stars. Observing time on a more sensitive telescope will be required such as NASA’s Spitzer Space Telescope which was recently used to make photometric measurements of the transiting exoplanet orbiting TRAPPIST-1 (see “Habitable Planet Reality Check: The Seven Planets of TRAPPIST-1”).

Without any information on the masses of the transiting planets of K2-72 immediately forthcoming, we are forced to rely on statistical arguments based on the observed mass-radius relationship of other exoplanets. A series of analyses of Kepler data and follow-up observations published over the last several years have shown that there are limits on how large a rocky planet can become before it starts to possess increasingly large amounts of water, hydrogen and helium as well as other volatiles making the planet a Neptune-like world. Rogers has shown that planets with radii greater than no more than 1.6 R E (and more likely 1.5 R E ) have a higher probability of being mini-Neptunes than smaller worlds (see “Habitable Planet Reality Check: Terrestrial Planet Size Limits”). A more recent analysis of the mass-radius relationship with a much larger collection of exoplanetary data by Chen and Kipping suggests that that the gradual transition from rocky to volatile-rich exoplanets starts at about 1.2 R E again with the probability that a planet is rocky decreasing with increasing radius or mass.

Looking at the four exoplanets of K2-72, it is apparent that K2-72b and d with radii of 1.08 R E and 1.01 R E , respectively, are clearly below the 1.2 R E threshold seen by Chen and Kipping even when the uncertainties in their radius values are taken into account. These two exoplanets are most likely rocky worlds like the terrestrial planets of our solar system. K2-72c, with a radius of 1.16±0.13 R E , seems to be right on this threshold suggesting that while it is most likely to be rocky, the possibility that it is a mini-Neptune can not be entirely excluded. Finally, K2-72e with a radius of 1.29±0.13 R E likely exceeds this the 1.2 R E threshold of Chen and Kipping but is still clearly below that found by Rogers. While K2-72e is more likely to be a mini-Neptune than K2-72c, it seems that overall it is more probable to be a rocky planet like the Earth.

With the odds favoring the quartet of exoplanets orbiting K2-72 being rocky, we can consider another criterion for assessing their potential habitability: the effective stellar flux or S eff . According to the work by Kopparapu et al. (2013, 2014) on the limits of the habitable zone (HZ) based on detailed climate and geophysical modeling, the inner limit of the HZ is conservatively defined by the runaway greenhouse limit where a planet’s temperature would soar even with no CO 2 present in its atmosphere resulting in the loss of all of its water in a geologically brief time in the process. For an Earth-size planet orbiting K2-72, this happens at an S eff value of 0.93 which corresponds to a mean orbital distance of 0.120 AU.

Since all four of these exoplanets orbit their parent star so closely, they would be expected to be synchronous rotators with the same side perpetually facing their sun. Detailed climate modeling over the last two decades now shows that synchronous rotation is probably not the impediment to global habitability as it was once thought. In fact, it has been shown that slow or synchronous rotation can actually result in an increase of the S eff for the inner edge of the HZ because of the formation of a substantial reflective cloud layer over the daylit side. According to the recent work by Yang et al., the inner edge of the HZ for a slow rotator orbiting a star like K2-72 would have an S eff of 1.62 corresponding to an orbital distance of just 0.091 AU. A more recent paper by Kopparapu et al. (2016) which takes into account the effects of short orbital periods on atmospheric circulation also suggests a similar S eff value for the inner edge of the HZ.

Looking at the four exoplanets in this system, K2-72b and d with S eff values of 8.5 and 5.4, respectively, clearly orbit well outside of the HZ and are likely to be hotter and slightly larger versions of Venus. While K2-72c appeared to have some chance of being potentially habitable based on the properties originally given by Crossfield et al., the updated S eff with a Venus-like value of 2.2 now makes this look unlikely. Only K2-72e with an S eff value of 1.2±0.2 seems to clearly orbit inside of the HZ of a slow or synchronous rotator. Combined with its high likelihood of being a rocky planet, K2-72e can still be counted as a good candidate for being a potentially habitable exoplanet despite the changes to its key properties.

Summary

As expected, the significant update of the stellar properties of K2-72 by Dressing et al. has resulted in a noticeable change in the derived properties of the quartet of exoplanets found orbiting K2-72 by Crossfield et al.. While the planet radii and S eff values have increased, K2-72e still appears to have good prospects for being potentially habitable. Although its mass has yet to be measured, it appears likely that it is a rocky planet and it seems to orbit comfortably inside of the HZ for a slow or synchronously rotating exoplanet. In terms of size, K2-72e has better prospects for being habitable than well known Kepler finds like Kepler 62e or Kepler 452b but not quite as good as the slightly smaller Kepler 186f (see “Top Five Known Potentially Habitable Planets”).

This generally good assessment comes with the usual caveats about the potential habitability of any exoplanet orbiting a red dwarf. There have been a fair number of predictions made over the decades about various proposed mechanisms that could desiccate such exoplanets, strip them of their atmospheres, irradiate their surfaces from flares and so on. There have been yet other predictions published in the peer-reviewed literature which suggest these might not be major impediments to potential habitability especially for more massive red dwarfs whose potentially habitable planets have larger orbits. Only more observations of this class of exoplanets to characterize them and their atmospheres will provide the data needed to confirm or refute these sometimes contradictory predictions being made. The four similar-sized exoplanets of the K2-72 system could provide yet another ideal natural laboratory to probe the limits of planetary habitability.

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Related Reading

“Habitable Planet Reality Check: Kepler’s New Finds at K2-72”, Drew Ex Machina, July 22, 2016 [Post]

“The First Year of Kepler’s K2 Mission”, Drew Ex Machina, November 29, 2015 [Post]

General References

Jingjing Chen and David Kipping, “Probabilistic Forecasting of the Masses and Radii of Other Worlds”, The Astrophysical Journal, Vol. 834, No. 1, Article id. 17, January 2017

Ian J.M. Crossfield et al., “197 Candidates and 104 Validated Planets in K2’s First Five Fields”, The Astrophysical Journal Supplement Series, Vol. 226, No. 1, Article id. 7, September 2016

Courtney D. Dressing et al., “Characterizing K2 Candidate Planetary Systems Orbiting Low-mass Stars I. Classifying Low-mass Host Stars Observed during Campaigns 1–7”, The Astrophysical Journal, Vol. 836, No. 2, Article id. 167, February 2017

Courtney D. Dressing et al., “Characterizing K2 Candidate Planetary Systems Orbiting Low-Mass Stars II: Planetary Systems Observed During Campaigns 1-7”, arXiv 1703.07416 (submitted for publication March 21, 2017), [Preprint]

Daniel Huber et al., “The K2 Ecliptic Plane Input Catalog (EPIC) and Stellar Classifications of 138,600 Targets in Campaigns 1-8”, The Astrophysical Journal Supplement Series, Vol. 224, No. 1, Article ID. 2, May 2016

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

Ravi Kumar Kopparapu et al., “The Inner Edge of the Habitable Zone for Synchronously Rotating Planets around Low-mass Stars Using General Circulation Models”, The Astrophysical Journal, Vol. 819, No. 1, Article ID. 84, March 2016

Arturo O. Martinez et al., “Stellar and Planetary Parameters for K2’s Late-type Dwarf Systems from C1 to C5”, The Astrophysical Journal, Vol. 837, No. 1, Article id. 72, March 2017

Leslie A. Rogers, “Most 1.6 Earth-Radius Planets are not Rocky”, The Astrophysical Journal, Vol. 801, No. 1, Article id. 41, March 2015

Andrew Vanderburg et al., “Planetary Candidates from the First Year of the K2 Mission”, The Astrophysical Journal Supplement Series, Vol. 222, No. 1, Article ID. 14, January 2016

Jun Yang et al., “Strong Dependence of the Inner Edge of the Habitable Zone on Planetary Rotation Rate”, The Astrophysical Journal Letters, Vol. 787, No. 1, Article id. L2, May 2014