Habitable Planet Reality Check: Wolf 1061c Revisited

While stories of exoplanet discoveries made by NASA’s Kepler spacecraft have dominated the media in recent years, there are many other surveys for extrasolar planets taking place some of which were started years (and even decades!) before Kepler was ever launched. One of the better known ongoing exoplanet surveys has been conducted by a European team of astronomers operating the HARPS (High Accuracy Radial velocity Planet Search) spectrograph attached to the European Southern Observatory’s 3.6-meter telescope in La Silla, Chile. Using precision radial velocity measurements, HARPS is able to detect the subtle variations caused by the reflex motion of the parent star as any planets of sufficient size orbit them.

In a recent paper submitted for publication in the peer-reviewed Astronomy & Astrophysics with Nicola Astudillo-Defru (Observatoire de Genève) as the lead author, the latest analysis results of HARP data for five nearby M-dwarf stars are described in detail. Among the new finds is a potentially habitable exoplanet found orbiting the nearby red dwarf GJ 273 or Luyten’s Star located only 12.4 light years away (see “Habitable Planet Reality Check: The Nearby GJ 273 or Luyten’s Star”). Another system described by Astudillo-Defru et al. is GJ 628 better known as Wolf 1061. Back in December of 2015, a team of astronomers led by Duncan Wright (University of New South Wales – Australia) announced the discovery of three exoplanets orbiting this nearby red dwarf they found using publicly available HARPS spectra including one, Wolf 1061c, that has some prospects of being potentially habitable (see “Habitable Planet Reality Check: Wolf 1061”). Because of the new results of Astudillo-Defru et al. along with updated information on the properties of Wolf 1061, it is time to take a fresh look at the potential habitability of Wolf 1061c.

The Star

Wolf 1061 (also known as BD-12° 4523) is a V magnitude 10.1 red dwarf located in the constellation of Ophiuchus. The star first came to the attention of astronomers about a century ago because of its relatively high proper motion of 1.2 arc seconds per year which suggested that it was nearby. As a result, it was included in the catalog of high proper motion stars compiled by German astronomer Max Wolf (1863-1932) of the Heidelberg-Königstuhl State Observatory along with many other nearby red dwarf stars (see “The Real Wolf 359”). The best parallax measurements for this spectral type M3V star places it 14.0 light years from the Sun making this among the closest stars known.

The sky area in the constellation of Ophiuchus near the red dwarf star Wolf 1061. Click on image to enlarge. (CDS/Strasbourg Observatory)

As part of their effort to better characterize the properties of the exoplanets found orbiting Wolf 1061, a team led by Stephen Kane (San Francisco State University) started by refining our knowledge of the properties of the parent star itself. Kane et al. secured photometric measurements of Wolf 1061 in order to search for variations in brightness resulting from a variety of sources including surface activity modulated by the star’s rotation. For these observations, Kane et al. employed the Tennessee State University’s “T11” 0.80-meter APT (Automatic Photoelectric Telescope) located at the Fairborn Observatory in Arizona. Between April 2010 and June 2016, the T11 APT was used to acquire a total of 756 brightness measurements of Wolf 1061 on 464 different nights using a two-channel precision photometer attached to T11. Using a subset of the data from 2011 to 2013 which seem to show the most pronounced rotation induced variation in the brightness of Wolf 1061 (which was typically on the order of 0.02 magnitude), Kane et al. derived a period of rotation of 89.3±1.8 days – similar to the period found by others. This rotation period suggests that Wolf 1061 is in excess of five billion years old.

Tennessee State University’s T11 APT (Automatic Photoelectric Telescope) located at the Fairborn Observatory in Arizona. It was used to gather six seasons f brightness measurements of Wolf 1061. (TSU)

In order to measure the size of this star directly, Kane et al. observed Wolf 1061 using Georgia State University’s CHARA (Center for High Angular Resolution Astronomy) interferometer array located at the Mt. Wilson Observatory on June 30 and August 3-4, 2016. Assuming a limb darkened disk, Kane et al. found that Wolf 1061 had an angular diameter of just 0.695±0.018 milliarc seconds. Using the best available parallax measurement, the actual radius works out to be 0.3207±0.0088 times that of the Sun – about 223,100±6,100 kilometers in conventional units and similar to earlier indirect estimates of this star’s size.

Picture showing the Georgia State University’s CHARA (Center for High Angular Resolution Astronomy) interferometer array located at the Mt. Wilson Observatory. It was used to directly measure the angular size of Wolf 1061. (NOAO)

Kane et al. then used the best published multi-band photometry of Wolf 1061 going back to 1954 in order to calculate the effective temperature of the star which they found to be 3305±46 K. Combined with the radius of Wolf 1061, this yields a luminosity of 0.01102±0.00027 times that of the Sun – somewhat higher than the earlier best values available. Other work estimates the mass of Wolf 1061 to be about 0.294 times that of the Sun. Wolf 1061 is fairly typical of the stars in our neighborhood (and very similar to Luyten’s Star as well) even with the minor adjustments to its measured properties.

The Exoplanets

Because of its small size and relative closeness, Wolf 1061 has been the subject of increasingly sensitive searches for “unseen companions” such as exoplanets for decades. Up until recently, these various surveys had found nothing eliminating the possibility that Wolf 1061 was orbited by companions ranging from Jupiter-sized planets to brown dwarfs. However, recent analysis of Kepler data to determine exoplanet occurrence rates shows that gas giants like Jupiter are rarely found orbiting red dwarfs like Wolf 1061 and that sub-Neptune size worlds are much more common (see “Occurrence of Potentially Habitable Planets around Red Dwarfs”). A more sensitive search was required.

One of the methods that has proven to be sensitive enough to detect small exoplanets around nearby red dwarfs is precision radial velocity measurements. Small variations in the radial velocity of a star could indicate reflex motion resulting from an orbiting exoplanet. And since the mass of red dwarfs is so low and their planetary systems tend to have small orbits, radial velocity measurements can reveal the presence of exoplanets with masses as small as on the order of Earth’s or ~1 M_E. One of the radial velocity surveys that has been monitoring Wolf 1061 and other nearby red dwarfs has been HARPS. An early analysis by the HARPS team of 23 radial velocity measurements presented in a 2013 paper with Xavier Bonfils (Observatoire de Genève) as the lead author found some indications of a variation with a periodicity of about 67 days but the false alarm probability of 3.3% was too high to qualify as a reliable exoplanet detection.

The ESO 3.6m Telescope equipped with HARPS was used to acquire the data used to find the new planets orbiting Wolf 1061. (ESO/H.H.Heyer)

Wright et al. obtained a larger set of 148 publicly available HARPS spectra of Wolf 1061 acquired over 10.3 years for a new analysis whose results were announced in December 2015. Wright et al. had more spectra at their disposal than Bonfils et al. and employed a new data processing technique to extract radial velocity measurements from those spectra with a much improved signal-to-noise. Their analysis of the radial velocity measurements revealed the presence of not only the 67-day signal first hinted in the work by Bonfils et al., but two additional signals with periods of 4.89 and 17.87 days for a total of three exoplanets.

Plots of the HARPS radial velocity data as a function of orbital phase analyzed by Wright et al.: Wolf 1061b (top), c and d (bottom) as a function of orbital phase. The color scale at the top indicates the dates of the data points. Click on image to enlarge. (Wright et al.)

After checking their results for the possible effects of stellar activity or spurious signals from the window function resulting from data acquired irregularly in time, it was determined that Wolf 1061 was orbited by a trio of planets with M_Psini mass values of 1.4, 4.3 and 5.2 times that of the Earth or M_E going from the closest exoplanet outwards. Because the inclination, i, of the orbits to the plane of the sky is unknown, only the minimum masses or M_Psini values are known. The middle exoplanet, designated Wolf 1061c, was even claimed to be a reasonable candidate for being a potentially habitable exoplanet (for a full discussion of this original claim, see “Habitable Planet Reality Check: Wolf 1061”).

A new analysis recently accepted for publication in Astronomy & Astrophysics by Astudillo-Defru et al. has taken a closer look at an expanded set of radial velocity data for Wolf 1061. Astudillo-Defru et al. started with a total of 190 HARPS spectra acquired between June 2, 2004 and September 28, 2015. After rejecting three of these spectra because of possible contamination from the Moon located less than 25° away from the position of Wolf 1061, they also found the inner pair of exoplanets found by Wright et al.. However, a careful analysis by Astudillo-Defru et al. of all the possible Keplerian orbit solutions found that a fairly eccentric orbit with a period of 217 days provided a much better fit of the expanded data set than solutions with a 67-day period

Plots of the expanded HARPS radial velocity data as a function of orbital phase analyzed by Astudillo-Defru et al.: Wolf 1061b (top), c and d (bottom). The color scale at the top indicates the dates of the data points. Click on image to enlarge. (Astudillo-Defru et al.)

The new parameters for the three exoplanets as taken directly from Astudillo-Defru et al. are summarized below in Table 1. Also included are the effective stellar flux or S_eff values given by Astudillo-Defru et al. which provide a measure of the total energy these exoplanets receive from their parent star with the Earth’s value defined as being 1.

Table 1: Properties of the Planets of Wolf 1061 from Astudillo-Defru et al.

Since the inclination, i, of the planets’ orbits with respect to the plane of the sky can not be determined from radial velocity measurements alone, only the minimum mass or M_psini of these exoplanets can be determined at this time. The actual masses will likely be higher than these indicated values.

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 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 sun. 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 Wolf 1061 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. Unfortunately, the only information currently available about these new planets is their M_psini or minimum mass values. Their actual masses and the radii are needed to calculate these exoplanets’ densities and get a handle on their bulk compositions. Given their tight orbits, direct imaging of these new planets will require a ten-meter class, space-based telescope with an advanced starshade – a piece of hardware that will likely not be available for decades.

There is the possibility that one or more of these planets have their orbits aligned by random chance to produce observable transits. Calculations by Astudillo-Defru et al. indicate that there are 3.3%, 1.4% and 0.2% probabilities that Wolf 1061b, c and d produce transits, respectively. Unfortunately, the six seasons of photometric data gathered by Kane et al. using the T11 APT has effectively eliminated the possibility that Wolf 1061b and c produce transits. While no transits of Wolf 1061d have been observed, the existing data are insufficient to definitively exclude the possibility this exoplanet produces them.

This is the brightness of Wolf 1061 (corrected for rotation-related effects) plotted as a function of orbital phase of planet “c”. The lower panel gives a closeup centered on the time Wolf 1061c was expected to transit and shows no evidence of an expected dip in brightness. Click on image to enlarge. (Kane et al.)

In lieu of this vital information on the density of these exoplanets, statistical arguments can be made about the probability they have a rocky composition. An analysis of the mass-radius relationship for extrasolar planets smaller than Neptune performed by Rogers strongly suggests that the population of known exoplanets transitions from being predominantly rocky planets like the Earth to predominantly volatile-rich worlds like Neptune at radii no greater than 1.6 times that of the Earth or R_E (see “Habitable Planet Reality Check: Terrestrial Planet Size Limit”). While rocky planets larger than this are possible, they become more uncommon with increasing radius. A planet with a radius of 1.6 R_E and an Earth-like composition would have a mass of about 6 M_E. More recent work by Chen and Kipping with a larger sample of exoplanets suggests that the gradual transition of the exoplanetary population from predominantly rocky planets to volatile-rich worlds starts at about 2 M_E.

Examining the M_psini values of the exoplanets of Wolf 1061 derived by Astudillo-Defru et al. (and keeping in mind that the actual masses are likely to be larger), they all seem to exceed the 2 M_E mass threshold found by Chen and Kipping indicating that they all have at least some chance of being mini-Neptunes. In the case of Wolf 1061b with an M_psini of 1.9 M_E, there is only about a 5% probability of its actual mass exceeding Rogers’ 6 M_E threshold above which the population of exoplanets is convincingly dominated by volatile-rich mini-Neptunes. This strongly suggests that the odds favor Wolf 1061b being a rocky planet. For Wolf 1061c with an M_psini of 3.4 M_E, there is only a about an 18% probability its actual mass exceeds Rogers’ threshold. While this indicates that there is a fair chance that Wolf 1061c is a mini-Neptune, the odds of it being a rocky planet like the Earth are still improved compared to the M_psini value of 4.3 M_E originally found by Wright et al. in 2015 and the higher 30% probability that its actual mass exceeds Rogers’ threshold. The odds seem to favor Wolf 1061d being a mini-Neptune considering its M_psini of 7.7 M_E.

Another important criterion which can be used to determine if a planet is potentially habitable is the amount of energy it receives from its parent star known as 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 outer limit of the HZ is defined as the point where the addition of any more CO₂ to a planet’s atmosphere no longer raises the surface temperature sufficiently to maintain above-freezing conditions. For a star like Wolf 1061, this happens at an S_eff of 0.24 which, according to Kane et al., corresponds to an orbital distance of 0.21 AU.

The inner limit of the HZ is conservatively defined by the runaway greenhouse limit where a planet’s temperature would soar even with no CO₂ 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 Wolf 1061, this happens at an S_eff value of 0.93 which corresponds to a mean orbital distance of 0.11 AU, according to Kane et al.. For a more massive 5 M_E exoplanet, the S_eff for the inner edge of the HZ is 1.00 due to the compression of the atmospheric column caused by the higher surface gravity.

But since these exoplanets orbit so close to their parent star, their rotation states will be affected by tidal effects and, if the orbital eccentricity is not too high, they will likely become synchronous rotators with one side perpetually facing their sun. While at one time this was thought to be an issue for a planet’s habitability, detailed climate modeling over the last two decades now shows that synchronous rotation is probably not an impediment to global habitability. 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 owing to the formation of a reflective cloud layer on the daylight side. According to the recent work by Yang et al., the inner edge of the HZ for a slow rotator orbiting a star like Wolf 1061 would have an S_eff of 1.60 corresponding to an orbital distance of just 0.083 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 for a synchronous rotator orbiting Wolf 1061.

Diagram of the orbits of the three exoplanet found orbiting Wolf 1061. The habitable zone (HZ) of Wolf 1061 is indicated in gray. Click on image to enlarge. (Kane et al.)

With these conservative limits of the HZ defined, it is immediately evident that Wolf 1061b with an S_eff of 7.34 (almost four times higher than that of Venus) has no prospects of being habitable. Assuming it has a rocky composition, it is likely to be larger and hotter version of Venus. Wolf 1061c with an S_eff of 1.30 seems to orbit comfortably inside the HZ for a slow or synchronous rotator. Kane et al., who were only considering the more conservative definition of the HZ of Kopparapu et al. (2013, 2014) for a faster rotating planet, noted that Wolf 1061c only brushes the HZ at apoapsis by virtue of its apparently nonzero orbital eccentricity. As a result Kane et al. conclude it is unlikely that Wolf 1061c would be able to support liquid on its surface – they may have come to a different conclusion if they included HZ modelling for synchronous rotators in their analysis.

The situation with the highly eccentric orbit of Wolf 1061d allows it to brush the outer limits of the HZ during periapsis. But, as noted by Kane et al. in their analysis, Wolf 1061d spends most of its orbit well outside of the HZ. Combined with the high probability that it is a mini-Neptune with a deep hydrogen-rich atmosphere capping exotic phases of ice that exist only under high temperatures and pressures, it is unlikely that Wolf 1061d is habitable in the conventional sense.

At first blush, it appears that Wolf 1061c has fairly good prospects for being a potentially habitable exoplanet. Comparisons with other exoplanets of similar mass suggest that it has a rocky composition and it seems to orbit fairly comfortably inside of the HZ of a synchronous or slowly rotating planet. But before we invest too much into the prospects of the habitability of this exoplanet, there are some potential issues which could complicate the situation. In addition to the some potential (but so far, untested) concerns about the habitability of any exoplanet orbiting a red dwarf, there is another more subtle potential issue related to orbital eccentricity.

As part of their study of this planetary system, Kane et al. examined the orbital stability and dynamics of these three exoplanets. Assuming that the orbits of the three exoplanets are coplanar and that their minimum masses correspond to their actual masses, Kane et al. found that the resulting system was stable for the 10⁷ year length of their simulations. However, the massive Wolf 1061d in its highly eccentric orbit perturbs the orbits of the inner planets causing their orbital eccentricities to vary regularly over time. In the case of the Wolf 1061c, the eccentricity varies from as low as ~0.03 to as high as ~0.15 over a cycle with a period on the order of 17,000 years. While the current uncertainty in the measured eccentricity is too large to exclude a circular orbit, the dynamics of the system as simulated by Kane et al. dictates that it will have a substantial, nonzero value.

Kane et al. make note of the eccentricity of the orbit of Wolf 1061c in their analysis since it brings the exoplanet into the more conservatively defined HZ during part of its orbit. However, there is a darker side to high orbital eccentricity: tidal heating. The regular flexing of a body in an eccentric orbit can warm the interior of that body as kinetic energy is converted into heat. In small doses, this can help maintain the habitability of a planet for much longer periods than other sources of internal heat like the decay of radioactive elements can. However, excessive tidal heating can cause large amounts of volcanic activity such as that we witness on Jupiter’s moon, Io. In their study of the dynamics of the exoplanets in the GJ 667C system, Makarov and Berghea found that tidal heating of the potentially habitable GJ 667Cc would amount to 1.6X10¹⁶ watts or about a factor of 300 greater than Earth’s current internal heat flow because of its high eccentricity and proximity to its parent star. This would be sufficient to render this exoplanet completely molten inside of 100 million years (see “Habitable Planet Reality Check: GJ 667C”).

Assuming the measured orbital eccentricity of 0.11 for Wolf 1061c (a value which would be regularly exceeded because of interactions with Wolf 1061d, according to Kane et al.) and scaling the results from the similar sized GJ 667Cc, I estimate that the heat flow from tidal heating would be on the order of ~2X10¹⁶ watts. If this rough estimate for tidal heating is confirmed by future detailed calculations of the dynamics of the Wolf 1061 system, it could mean that Wolf 1061c is a sterile ball of molten rock despite orbiting inside of the HZ. Perhaps future measurements of this exoplanet might be able to confirm (or refute!) this hellish scenario for this otherwise promising potentially habitable exoplanet.

Before we totally write off the potential habitability of Wolf 1061c, however, it should be remembered that the actual planetary system of Wolf 1061 may differ significantly from that modelled by Kane et al.. The masses will likely be higher than the minimum values used and it is by no means certain that the orbits are coplanar, especially given the eccentric orbit of Wolf 1061d. Much more needs to be learned before any firm conclusions can be drawn about the orbital dynamics of this system and what role tidal effects might play.

Summary

With the new data about the Wolf 1061 planetary system from Astudillo-Defru et al. and the analysis by Kane et al., it seems that the prospects for the potential habitability of Wolf 1061c have improved in some key ways since the initial assessment made following its discovery by Wright et al. a year earlier. The M_psini of 3.4 M_E for Wolf 1061c is lower than was previously estimated increasing the odds that this exoplanet is rocky like the Earth instead of being a volatile-rich mini-Neptune. While the S_eff has also increased somewhat to 1.30, this value still corresponds to being inside the HZ of a synchronous rotator. This differs from the conclusion of Kane et al. who did not consider HZ models for synchronous rotators in their analysis.

This somewhat rosier assessment of the habitability of Wolf 1061c does come with a caveat in addition to the usual predictions of habitability issues associated with orbiting a red dwarf. Because of the strong gravitational interactions between the inner planets and the outer one with its eccentric orbit, excessive tidal heating might adversely affect the habitability of this exoplanet. More detailed modeling of the dynamics of his system using more accurate data will be needed to investigate this issue. No matter what, the relatively nearby Wolf 1061c and its sister exoplanets will be excellent targets for future study helping scientists probe the limits of planetary habitability.

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Related Reading

“Habitable Planet Reality Check: Wolf 1061”, Drew Ex Machina, December 19, 2015 [Post]

“Habitable Planet Reality Check: The Nearby GJ 273 or Luyten’s Star”, Drew Ex Machina, March 20, 2017 [Post]

General References

N. Astudillo-Defru et al., “The HARPS search for southern extra-solar planets XLI. A dozen planets around the M dwarfs GJ 3138, GJ 3323, GJ 273, GJ 628, and GJ 3293”, arXiv 1703.05386 (accepted by Astronomy & Astrophysics), March 15, 2017 [Preprint]

X. Bonfils et al., “The HARPS search for southern extra-solar planets XXXI. The M-dwarf sample”, Astronomy & Astrophysics, Vol. 549, ID A8, January 2013

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

Stephen R. Kane et al., “Characterization of the Wolf 1061 Planetary System”, The Astrophysical Journal, Vol. 835, No. 2, Article id. 200, February 2017

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

Valeri V. Makarov and Ciprian Berghea, “Dynamical evolution and spin-orbit resonances of potentially habitable exoplanet. The Case of GJ 667C”, The Astrophysical Journal, Vol. 780, No. 2, article id. 124, January 2014

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

D.J. Wright et al., “Three planets orbiting Wolf 1061”, The Astrophysical Journal Letters, Vol. 817, No. 2, Article id. L20, February 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