GJ 832c: A Super-Earth in the Habitable Zone

Abstract

We report the detection of GJ 832c, a super-Earth orbiting near the inner
edge of the habitable zone of GJ 832, an M dwarf previously known to host a
Jupiter analog in a nearly-circular 9.4-year orbit. The combination of precise
radial-velocity measurements from three telescopes reveals the presence of a
planet with a period of 35.68+/-0.03 days and minimum mass (m sin i) of
5.4+/-1.0 Earth masses. GJ 832c moves on a low-eccentricity orbit
(e=0.18+/-0.13) towards the inner edge of the habitable zone. However, given
the large mass of the planet, it seems likely that it would possess a massive
atmosphere, which may well render the planet inhospitable. Indeed, it is
perhaps more likely that GJ 832c is a "super-Venus," featuring significant
greenhouse forcing. With an outer giant planet and an interior, potentially
rocky planet, the GJ 832 planetary system can be thought of as a miniature
version of our own Solar system.

Full text

arXiv:1406.5587v1 [astro-ph.EP] 21 Jun 2014
GJ 832c: A super-earth in the habitable zone1
Robert A. Wittenmyer1,2,7, Mikko Tuomi3,4, R.P. Butler5, H.R.A. Jones3, Guillem
Anglada-Escud´e6, Jonathan Horner7,1,2, C.G. Tinney1,2, J.P. Marshall1,2, B.D. Carter7,
J. Bailey1,2, G.S. Salter1,2, S.J. O’Toole8, D. Wright1,2, J.D. Crane9, S.A. Schectman9,
P. Arriagada5, I. Thompson9, D. Minniti10,11, J.S. Jenkins12 & M. Diaz12
rob@phys.unsw.edu.au
ABSTRACT
We report the detection of GJ 832c, a super-Earth orbiting near the inner edge
of the habitable zone of GJ 832, an M dwarf previously known to host a Jupiter
analog in a nearly-circular 9.4-year orbit. The combination of precise radial-
velocity measurements from three telescopes reveals the presence of a planet
with a period of 35.68±0.03 days and minimum mass (m sin i) of 5.4±1.0 Earth
masses. GJ 832c moves on a low-eccentricity orbit (e= 0.18±0.13) towards the
1School of Physics, UNSW Australia, Sydney 2052, Australia
2Australian Centre for Astrobiology, UNSW Australia, Sydney 2052, Australia
3University of Hertfordshire, Centre for Astrophysics Research, Science and Technology Research Insti-
tute, College Lane, AL10 9AB, Hatfield, UK
4University of Turku, Tuorla Observatory, Department of Physics and Astronomy, V¨ais¨al¨antie 20, FI-
21500, Piikki¨o, Finland
5Department of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 Broad Branch Road,
NW, Washington, DC 20015-1305, USA
6Astronomy Unit, School of Mathematical Sciences, Queen Mary, University of London. UK
7Computational Engineering and Science Research Centre, University of Southern Queensland,
Toowoomba, Queensland 4350, Australia
8Australian Astronomical Observatory, PO Box 915, North Ryde, NSW 1670, Australia
9The Observatories of the Carnegie Institution of Washington, 813 Santa Barbara Street, Pasadena, CA
91101, USA
10Institute of Astrophysics, Pontificia Universidad Catolica de Chile, Casilla 306, Santiago 22, Chile
11Vatican Observatory, V00120 Vatican City State, Italy
12Departamento de Astronom´ıa, Universidad de Chile, Camino el Observatorio 1515, Las Condes, Santiago,
Chile, Casilla 36-D

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inner edge of the habitable zone. However, given the large mass of the planet, it
seems likely that it would possess a massive atmosphere, which may well render
the planet inhospitable. Indeed, it is perhaps more likely that GJ 832c is a “super-
Venus,” featuring significant greenhouse forcing. With an outer giant planet and
an interior, potentially rocky planet, the GJ 832 planetary system can be thought
of as a miniature version of our own Solar system.
Subject headings: planetary systems: individual (GJ 832) – techniques: radial
velocities – astrobiology
1. Introduction
For hundreds of years, it was assumed that if planetary systems existed around other
stars, they would look substantially like our own Solar system (Kant 1755; Laplace & Young
1832). That is, they would feature giant outer planets and rocky inner planets, moving
on nearly-circular orbits. The discovery of hundreds of extrasolar planetary systems2over
the last 20 years have instead revealed a picture of planetary system diversity “far stranger
than we can imagine” (Haldane 1927). We now know that planetary systems containing
a “Jupiter analog” (a gas giant planet which has remained in a low-eccentricity orbit be-
yond the ice line after planetary migration) are relatively uncommon (Gould et al. 2010;
Wittenmyer et al. 2011a, 2014b), while results from the Kepler spacecraft (Borucki et al.
2010) have shown us that super-Earths in compact multiple systems are very common
(Howard et al. 2012; Batalha et al. 2013; Petigura et al. 2013). While Kepler has revo-
lutionized exoplanetary science and provided a first estimate of the frequency of Earth-
size planets in Earth-like orbits, long-term radial-velocity surveys (Wittenmyer et al. 2006;
Robertson et al. 2012a,b; Zechmeister et al. 2013) complement these data with measure-
ments of the frequency of Jupiter-like planets in Jupiter-like orbits. This in turn will reveal
how common Solar-system-like architectures are.
In addition to the finding that small, close-in planets are far more common than long-
period gas giants (Howard 2013), planet-search efforts are now expanding into new realms
of parameter space, seeking to understand how the detailed properties of planetary systems
1This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas
Observatory, Chile.
2The Exoplanet Orbit Database at http://exoplanets.org

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depend on the properties of their host stars. In the early days of exoplanet observations, host
stars significantly more massive than our Sun were neglected, due to the difficulties in deter-
mining precise radial velocities. In recent years, however, several radial velocity surveys have
begun to take advantage of stellar evolution by observing such higher-mass stars once they
have evolved off the main sequence to become subgiants and giants. This approach has been
successfully used by several teams (e.g. Setiawan et al. 2003; Hatzes et al. 2005; Sato et al.
2005; Johnson et al. 2006; D¨ollinger et al. 2007; Niedzielski et al. 2009; Wittenmyer et al.
2011b).
Meanwhile, at the low-mass end, M dwarfs are being targeted by a number of near-
infrared radial-velocity surveys searching for rocky and potentially habitable planets (e.g.
Quirrenbach et al. 2010; Bean et al. 2010; Mahadevan et al. 2012; Barnes et al. 2012; Bonfils et al.
2013a). Notable results from these M dwarf surveys are that small, rocky planets are com-
mon (Bonfils et al. 2013a), and close-in giant planets are rare (Endl et al. 2006); as yet there
are no robust statistics on the population of longer-period giant planets.
One example of an M dwarf known to host a long-period giant planet is GJ 832.
Bailey et al. (2009) reported the discovery by the Anglo-Australian Planet Search (AAPS) of
a 0.64MJup planet in a near-circular orbit with period 9.4±0.4 yr. The AAPS has been in op-
eration for 15 years, and has achieved a long-term radial-velocity precision of 3 m s−1or better
since its inception, which is enabling the detection of long-period giant planets (Jones et al.
2010; Wittenmyer et al. 2012b, 2014b). GJ 832b is one of only a handful of such giant
planets known to orbit M dwarfs. The others are GJ 179b (Howard et al. 2010), GJ 849b
(Butler et al. 2006; Bonfils et al. 2013a), GJ 328b (Robertson et al. 2013), and OGLE-2006-
BLG-109Lb (Gaudi et al. 2008; Bennett et al. 2010). Of the long-period giant planets known
to orbit M dwarfs, GJ 328b is the one with the largest separation (a= 4.5±0.2 AU). GJ 832b,
which lies at a= 3.4±0.4 AU (Bailey et al. 2009), is clearly a Jupiter analog, and may well
play a similar dynamical role in the GJ 832 system to that played by Jupiter in our Solar
system (e.g. Horner & Jones 2008, 2009; Horner et al. 2010).
We report here a second, super-Earth mass planet in the GJ 832 system – with a semi-
major axis of a∼0.16 AU, the GJ 832 system can be considered a miniature Solar system
analog, with an interior potentially rocky and habitable planet, and a distant gas giant.
This paper is organized as follows: Section 2 briefly describes the three data sets and gives
the stellar parameters. Section 3 details the traditional and Bayesian orbit fitting proce-
dures, and gives the parameters of GJ 832c. In Section 4, we give a discussion on potential
habitability before drawing our final conclusions.

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2. Observational Data
We have combined three high-precision radial-velocity data sets that span a variety of
baselines. The data covering the longest baseline (39 epochs over 15 years) were taken by
the Anglo-Australian Planet Search (AAPS) team, using the UCLES echelle spectrograph
(Diego et al. 1991). An iodine absorption cell provides wavelength calibration from 5000 to
6200 ˚
A. The spectrograph point-spread function (PSF) and wavelength calibration are de-
rived from the absorption lines embedded on the spectrum by the iodine cell (Valenti et al.
1995; Butler et al. 1996). The result is a precise Doppler velocity estimate for each epoch,
along with an internal uncertainty estimate, which includes the effects of photon-counting
uncertainties, residual errors in the spectrograph PSF model, and variation in the underlying
spectrum between the iodine-free template and epoch spectra observed through the iodine
cell. All velocities are measured relative to the zero-point defined by the template observa-
tion. GJ 832 has been observed on 39 epochs since (Table 1), with a total data span of 5465
d (15 yr). The mean internal velocity uncertainty for these data is 2.6 m s−1.
GJ 832 has also been observed with the Planet Finder Spectrograph (PFS) (Crane et al.
2006, 2008, 2010) on the 6.5m Magellan II (Clay) telescope. The PFS is a high-resolution
(R∼80,000) echelle spectrograph optimised for high-precision radial-velocity measurements
(e.g. Albrecht et al. 2011, 2012; Anglada-Escud´e et al. 2012; Arriagada et al. 2013). The
PFS also uses the iodine cell method as descibed above. The 16 measurements of GJ 832 are
given in Table 3. The data span 818 days and have a mean internal uncertainty of 0.9 m s−1.
A further 54 velocities were obtained from a HARPS-TERRA (Anglada-Escud´e & Butler
2012) reduction of the publicly available spectra and and are given in Table 2. The AAPS
data are critical for constraining the long-period outer planet, and the extremely precise
HARPS and PFS data are necessary for characterizing the inner planet.
To account for possible intrinsic correlations in the radial velocities, we used the same
statistical model as Tuomi (2014) that assumes that the deviation of the ith measurement of a
given instrument from the mean depends also on the deviation of the previous measurement.
In other words, these deviations are correlated with a correlation coefficient of φexp { −
(ti−ti−1)/τ}that decreases exponentially as the gap between the two measurements (the
difference ti−ti−1) increases. We set the correlation time-scale such that τ= 4 days
(Baluev 2013; Tuomi et al. 2014). Parameter φ∈[−1,1] is a free parameter in the model of
Tuomi et al. (2014). The maximum a posteriori estimates of these “nuisance parameters”
are given in Table 4. Only for the HARPS-TERRA data does the correlation coefficient
φdiffer significantly from zero. We thus consider an additional data set in our analysis,
“HARPS-CR,” which has been corrected for these intrinsic correlations. Those data are also
shown in Table 2.

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3. Orbit Fitting and Planetary Parameters
GJ 832 (HD 204961, HIP 106440, LHS 3685) is a very nearby M1.5 dwarf, lying at 4.95
pc (van Leeuwen 2007). The parameters of the host star are summarized in Table 5. While
the original discovery paper for the giant planet (Bailey et al. 2009) did not note any residual
signals of interest, Bonfils et al. (2013a) combined AAT (N= 32) and HARPS (N= 54)
data to refine the planet’s orbital parameters and mentioned a potential 35-day residual
periodicity. They concluded that the data in hand did not yet warrant a secure detection
as the false-alarm probability (FAP) exceeded 1%. The AAT data published in Bailey et al.
(2009) contained 32 epochs spanning 3519 d (9.6 yr). Combining all available data, we
now have 109 epochs covering a 15-year baseline, enabling us to better characterize the
long-period planet, and increasing our sensitivity to any residual signals of interest.
3.1. Bayesian approach
We analysed the combined HARPS, PFS, and UCLES radial velocities in several stages.
First, we drew a sample from the posterior density of a model without Keplerian signals,
i.e. a model with k= 0, by using the adaptive Metropolis algorithm (Haario et al. 2001).
This is a generalization of the Metropolis-Hastings Markov chain Monte Carlo technique
(Metropolis et al. 1953; Hastings 1970) that adapts the proposal density to the informa-
tion gathered from the posterior. This baseline model enabled us to determine whether the
models with k= 1,2, ...n Keplerian signals were, statistically, significantly better descrip-
tions of the data by estimating the Bayesian evidence ratios of the different models (e.g.
Kass & Raftery 1995; Tuomi 2014; Tuomi et al. 2014). For this purpose, we used the simple
estimate described in Newton & Raftery (1994).
The search for periodic signals in the data was performed by using tempered sam-
plings (Tuomi & Anglada-Escud´e 2013; Tuomi 2014; Tuomi et al. 2014) such that a scaled
likelihood l(m|θ)βand a scaled prior density π(θ)β, where mis the measurements and θ
the parameter vector, instead of the common likelihood l(m|θ) and prior πθ. We choose
β∈(0,1) low enough such that the posterior probability density is scaled sufficiently to
enable the Markov chains to visit repeatedly all relevant areas in the parameter space, the
period space in particular. In this way, we can estimate the general shape of the posterior
density as a function of the period parameter to see which periods correspond to the highest
probability maxima. This is not necessarily possible with “normal” samplings (i.e. when
β= 1) because one or some of the maxima in the period space could be so high and sig-
nificant that the Markov chains fail to visit the whole period space efficiently due to the
samplings getting “stuck” in one of the corresponding maxima. This could happen because

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the parameter space around some maximum is in practice so much less probable that any
proposed values outside the maximum are rejected in the MCMC sampling. The application
of such tempered samplings thus enables an efficient search for periodicities in the data.
We maximised parameter β∈(0,1) such that the period parameter visited all areas in
the period space between one day and the data baseline during these tempered samplings.
The results from this period search reveal the shape of the posterior probability density
as a function of period (see Figure 1). This enabled us to identify all relevant maxima in
the period space because such transformation artificially decreases the significances of the
maxima, while leaving their locations unchanged. To ensure that the Markov chains visited
all areas of high posterior probability in the parameter space, and especially through the
period space, we applied the delayed-rejection adaptive-Metropolis algorithm (Haario et al.
2006), where another proposed parameter vector from a narrower proposal density is tested
if the first proposed vector is rejected. This enables an efficient periodicity search because
the chains visit the narrow probability maxima in the period space. One such sampling is
shown in the middle panel of Figure 1 when searching for a second periodicity in the data.
The chain clearly identifies a global maximum at a period of 35.7 days.
After such tempered samplings, we started several “cold chains,” i.e. normal chains such
that β= 1, in the vicinity of the highest maxima to determine which of them were significant
according to the detection criteria discussed in Tuomi (2014) and Tuomi et al. (2014). The
statistical significance of a signal is quantified by the Bayesian evidence ratio B(k, k −1). We
required that the Bayesian evidence ratio be at least 104times greater for a model with k+ 1
than for a model with ksignals to state that there are k+ 1 signals present in the data. That
is, the model with the signal must be 10000 times more probable than the model without.
For the combination of the three data sets considered here, we obtain B(1,0) = 4.5×1060
(in favor of a one-planet model over zero planets). The 35-day signal is also significant with
respect to our detection threshold as it is detected with B(2,1) = 6.6×105. The maximum
a posteriori estimates of the model parameters, together with the corresponding Bayesian
99% credibility intervals, are listed in Table 6. The data and best-fit models are shown in
Figure 3 (GJ 832b) and Figure 4 (GJ 832c).
In addition to the velocities, various activity indices are also available for the epochs of
the GJ 832 HARPS observations (Bonfils et al. 2013a). Those metrics, derived from the
cross-correlation function (CCF) are the bisector inverse slope (BIS), described fully in
Queloz et al. (2001), and the CCF full width at half maximum (FWHM). We modelled
correlations of the HARPS-TERRA velocities with BIS, FWHM, and S-index by assuming
these correlations were linear that represents the first-order approximation for such depen-
dence. However, accounting for these correlations did not improve the model, which indicates

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that such linear correlations were insignificant. Furthermore, when we computed the best-fit
estimates for such linear correlation parameters, they were all consistent with zero, as shown
in Table 7.
3.2. Traditional approach
The combination of three data sets with high precision and long observational baseline
yields evidence for a second, low-mass planet orbiting GJ 832. Given that we have used data
from every telescope which is able to achieve sufficient velocity precision for this Southern
M dwarf (δ=−49.0o), independent confirmation of GJ 832c is problematic. It is prudent,
then, to employ an independent analysis to test the plausibility of the 35-day signal.
For this analysis, we use the HARPS data set which has been corrected for intrinsic
correlations as described above – labeled here as “HARPS-CR.” An instrumental noise term
was derived from the excess white noise parameter given in Table 4– HARPS-CR: 1.33m s−1,
PFS: 1.45m s−1, AAT: 4.66m s−1. Before orbit fitting, that noise was added in quadrature to
the uncertainties of each data point. We repeated our analysis using the unaltered HARPS-
TERRA velocities, and found throughout that the HARPS-CR and HARPS-TERRA data
sets gave the same results.
First, we fit a single-planet model to the three data sets using the nonlinear least-
squares minimization routine GaussFit (Jefferys et al. 1988). The velocity offsets between
the three data sets were included as free parameters. The rms scatter about the three
data sets are as follows – AAT: 5.72 m s−1, HARPS-CR: 1.88 m s−1, PFS: 1.74 m s−1. We
performed a periodogram search on the residuals to the one-planet fit, using the generalized
Lomb-Scargle formalism of Zechmeister & K¨urster (2009). Unlike the classical Lomb-Scargle
periodogram (Lomb 1976; Scargle 1982), this technique accounts for the uncertainties on the
individual data points, which is critically important for the case of GJ 832 where we have
combined data sets with significantly different precisions. The periodogram of the 1-planet
fit is shown in Figure 2; the highest peak is at 35.67 days. The FAP was estimated using a
bootstrap randomization method (K¨urster et al. 1997). From 10,000 bootstrap realizations,
the 35.67-day peak is shown to be highly significant, with FAP=0.0004 (0.04%).
We then used a genetic algorithm to search a wide parameter space for two-planet
models, and to check that any candidate secondary signal is indeed the global best-fit.
Our group has used this approach extensively (e.g. Tinney et al. 2011; Wittenmyer et al.
2012a, 2014a) when the orbital parameters of a planet candidate are highly uncertain. We
allowed the genetic algorithm to fit 2-Keplerian models to the three data sets simultaneously,

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searching secondary periods from 10 to 3000 days. It ran for 50,000 iterations, testing a total
of about 107possible 2-Keplerian configurations. The genetic algorithm converged on P2∼35
days, giving confidence that this is the most likely period for a candidate second planet.
We then obtained a final 2-planet fit using GaussFit. Again, we performed the fit twice,
using the two versions of the HARPS velocities. The details of each fit are summarized in
Table 9. Both fits gave the same results, though the HARPS-CR set (“Fit 2”) gave a slightly
better rms and smaller uncertainties on the planetary parameters - hence, we adopt those
results in Table 8. These fits reveal a second planet, GJ832c, with P= 35.68±0.03 d and
m sin i= 5.40±0.95M⊕on a nearly-circular orbit. A periodogram of the residuals to the
2-planet fit is shown in Figure 5; the highest peak at 40.2 days has a bootstrap FAP of 0.0456
(4.6%).
4. Discussion and Conclusions
4.1. Testing the planet hypothesis
If the 35-day signal is real, adding data should result in a higher significance level, i.e.
a lower FAP determined by the bootstrap method described above (K¨urster et al. 1997).
We test this by performing one-planet fits on various combinations of the three data sets
considered here. In these fits, the parameters of the outer planet are started at the best-
fit values in Table 10, but are allowed to vary. For data combinations with insufficient
time baseline to adequately fit the outer planet, its parameters are instead fixed at their
best-fit values. After each fit, we removed the signal of the outer planet, examined the
periodogram (Zechmeister & K¨urster 2009) of the residuals, and computed the FAP of the
highest remaining peak using 10,000 bootstrap randomizations. The results are summarized
in Table 10. The AAT data alone are not sufficiently precise to detect the K<
∼2m s−1signal
of the candidate planet, nor did the addition of only 16 epochs from PFS enable the detection
of any significant residual signals. Nevertheless, we see in Table 10 that the addition of data
indeed strengthens the significance of the 35.6-day signal, adding confidence that the signal
is real and not an artifact of one particular instrument. Table 10 also indicates that the
HARPS data are necessary to pull out the signal of GJ 832c, and the AAT data, while noisy,
are necessary for constraining the outer planet.
The next obvious question to ask is whether the detected signal is intrinsic to the star.
As noted in Bonfils et al. (2013a) and in Section 3.1, the HARPS planet-search programs
use the additional diagnostics BIS and CCF-FWHM to check for star-induced variability.
Being contemporaneous with the velocity measurements, both of these measures can be

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directly compared with the velocity derived from a given spectrum. If BIS or FWHM show
correlations with the velocities, a candidate radial-velocity signal can be considered suspect.
Figure 6 plots the HARPS velocities (after removing the outer planet) against the BIS (left
panel) and the CCF FWHM (right panel). No correlations are evident, and the highest
BIS periodogram peak at 179.6 days has a bootstrap FAP of 17%. For FWHM, the highest
periodogram peak at 6322 days has a bootstrap FAP<0.01%. For comparison, the outer
planet has a period of 3660 days, and the HARPS FWHM data only span 1719 days; for
these reasons, we maintain the conclusion of Bailey et al. (2009) that the long-period velocity
signal is due to an orbiting body. As shown in Table 7, none of these activity indicators
had correlations significantly different from zero. These results are further evidence that the
35.6-day signal is not intrinsic to the star.
4.2. GJ 832c: a habitable-zone super-Earth
In recent years, a growing number of super-Earths have been discovered that orbit their
host stars at a distance that may be compatible with the existence of liquid water somewhere
on the planet were it to have a surface (i.e. within the classical habitable zone). A list of these
planets is given in Table 11. Of those planets, perhaps the most interesting are those orbiting
GJ 581. In that system, a total of six planets have been claimed, although at least two of
these are still the subject of significant debate (e.g. Mayor et al. 2009, Vogt et al. 2010,
Tuomi 2011, von Braun et al. 2011, Tadeu dos Santos et al. 2012, Vogt et al. 2012, Baluev
2013). The proposed planetary system around GJ 581 displays an orbital architecture that is
strikingly similar to a miniature version of our own Solar system. The similarity to our own
Solar system has recently been enhanced by the results of the DEBRIS survey (Matthews et
al. 2010), which recently discovered and spatially resolved a disk of debris orbiting GJ 581
(Lestrade et al. 2012), analogous to the Solar system’s Edgeworth-Kuiper belt.
We can estimate the location of the classical habitable zone following the prescriptions
given in Selsis et al. (2007) and Kopparapu et al. (2014), using the stellar parameters
detailed in Table 5. In both cases, we find that GJ 832c lies just inside the inner edge of the
potentially habitable region - with the Selsis et al. prescription yielding a habitable zone that
stretches between 0.13 and 0.28 au, and the Kopparapu et al. prescription suggesting that
the conservative habitable zone for a 5M⊕planet lies between 0.130 and 0.237 au, compared
to the measured a= 0.163±0.006 au for GJ 832c.
Although GJ 832c is sufficiently far from its host star that there is the potential for
liquid water to exist on its surface, this does not necessarily make that planet truly habitable.
Indeed, there is a vast number of factors that can contribute to the habitability of a given

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exoplanet beyond the distance at which it orbits its host star (e.g. Horner & Jones 2010,
Horner 2014). Given the planet’s proximity to its host star, it seems likely that GJ 832 c
will be trapped in a spin-orbit resonance, though moderate orbital eccentricity may mean it
is not necessarily trapped in a resonance that causes one side of the planet to perpetually
face towards the Sun. In our own Solar system, the planet Mercury is trapped in such a
resonance: rotating three times on its axis in the time it takes to complete two full orbits of
the Sun. Mercury’s capture to that particular resonance is almost certainly the result of its
relatively eccentric orbit (e.g. Correia & Laskar 2009) - and so it is certainly feasible that
GJ 832 c, whilst tidally locked, is not trapped in 1:1 spin-orbit resonance. Even if the planet
is trapped in such a resonance, however, that might not be deleterious to the prospects for its
being habitable. For example, recent work by Yang et al. (2014), employing a 3-dimensional
general circulation model, suggests that planets with slower rotation rates would be able to
remain habitable at higher flux levels than for comparable, rapidly rotating planets.
Given the planet’s large mass, however, it is likely to be shrouded in a dense atmosphere
- which might in turn render it uninhabitable. In that scenario, the dense atmosphere would
provide a strong greenhouse effect, raising the surface temperature enough to cause any
oceans to boil away, as is thought to have happened to Venus early in the lifetime of the
Solar system, e.g. Kasting (1988). Kasting et al. (1993) proposed that tidally locked planets
around late-type stars might be rendered uninhabitable by atmospheric freeze-out if they
were locked in a 1:1 spin-orbit resonance. However, such a massive atmosphere would also
be able to prevent the freeze out of the planet’s atmosphere if it were trapped in a 1:1
spin-orbit resonance (Heath et al. 1999). A detailed review of the potential habitability of
planets around M dwarfs by Tarter et al. (2007) re-opened the possibility of habitability for
such planets. More recently, Kopparapu et al. (2014) have argued that the inner edge of the
habitable zone moves inward for more massive planets – a scenario which would operate in
favor of GJ 832c’s habitability.
Given the large mass of GJ 832c, and the high probability of it having a thick, dense
atmosphere, it is reasonable to assume that it is unlikely to be a habitable planet. However,
it is natural to ask whether it could host a giant satellite, which might itself be habitable.
Speculation about habitable exomoons is not a new thing, and in recent years, a number
of papers have been published discussing the prospects for such satellites orbiting a variety
of newly discovered planets – e.g. the gas giants HD 38283b (Tinney et al. 2011), and
HD 23079b (Cuntz et al. 2013), and the super-Earth Kepler-22b (Kipping et al. 2013), or
discussing the viability of such satellites as potential locations for life in a more general sense
(e.g. Heller 2012, Forgan & Kipping 2013, Heller & Barnes 2013). As such, it is interesting
to consider whether GJ 832c could host such a potentially-habitable satellite, although we
acknowledge that the detection of such a satellite is currently well beyond our means.

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Within our Solar system, one planet (the Earth) and several of the minor bodies (such
as Pluto) are known to have giant satellites that are thought to have formed as a result of
giant impacts on their host object toward the end of planet formation (e.g. Benz et al. 1986,
Canup 2004, Canup 2005). In the case of the Pluto-Charon binary, the mass of Charon is
approximately 1/9th that of Pluto - were that extrapolated to the case of GJ 832c, it would
result in a moon somewhat greater than half of the mass of the Earth3. But could GJ 832c
retain such a satellite whilst orbiting so close to its host star?
The Hill sphere of an object is the region in which its gravitational pull on a satellite (or
passing object) would dominate over that from any other object. Typically, within our Solar
system, the regular satellites of the planets orbit their hosts well within their Hill sphere.
Our Moon, for example, orbits at approximately one-quarter of the Hill radius. For GJ 832c,
assuming a mass of 5.406 times that of the Earth, and a host-star mass of 0.45M⊙, the Hill
radius would be just 0.00306 au - or 460,000 km. In and of itself, this result does not seem to
preclude the existence of a habitable exomoon orbiting GJ 832c. However, Cuntz et al.(2013)
found that, for the case of the gas giant planet HD 23079b, satellites on prograde orbits were
only stable out to a distance of approximately 0.3 Hill radii - a result that compares relatively
well to the orbital distance of the Moon, which currently orbits Earth at a distance of ∼0.25
Hill radii. Were the same true for the case of GJ 832c, this would reduce the region of
stability, requiring that a satellite orbiting that planet must remain within an orbital radius
of ∼138,000 km in order to remain bound on astronomically long timescales.
Heller & Barnes (2013) consider the possibility of habitable exomoons orbiting the super-
Earth Kepler-22b and the gas giant planet candidate KOI211.01. By considering the influence
of tidal heating on the potential satellites of these planets, they reach the conclusion that “If
either planet hosted a satellite at a distance greater than 10 planetary radii, then this could
indicate the presence of a habitable moon.” If we assume that GJ 832c is a predominantly
rocky/metallic object, then we can obtain a rough estimate of its radius by following Seager
et al. (2007). For a silicaceous composition, given a mass of approximately 5M⊕, it seems
likely that GJ 832c would have a radius approximately fifty percent greater than that of the
Earth, or approximately 10,000 km. We can therefore determine a rough inner-edge to the
circum-planetary habitable zone for GJ 832c, at approximately 10 times this value. In other
words, for GJ 832c to host a habitable exomoon, potentially formed by means of a giant
collision during the latter stages of planet formation, such a satellite would most likely have
to orbit between ∼100,000 and ∼138,000 km - a very narrow range. Although the idea of
3We note that the m sin idetermined from radial velocity measurements would actually be the total mass
of the exoplanet in question, plus any moons it hosts. For example, if GJ 832c hosts a moon with 20% of its
own mass, then the planet mass would actually be only 0.8 times the m sin igiven in Table 8.

– 12 –
a habitable exomoon companion to GJ 832c is certainly interesting, the odds seem stacked
against the existence of such an object.
4.3. Conclusions
We have combined high-precision radial-velocity data from three telescopes to detect a
super-Earth (5.4±1.0 M⊕) orbiting GJ 832 near the inner edge of the habitable zone. We
attribute this detection to two key differences from the Bonfils et al. (2013a) analysis. The
first is that our Bayesian techniques are better at picking out weak signals; this was powerfully
demonstrated by Tuomi & Anglada-Escud´e (2013), who used this approach for the GJ 163
system and obtained results consistent with Bonfils et al. (2013a) with only 35% of the
HARPS data used in the discovery work. The second is that the HARPS-TERRA velocities
are more sensitive to planet c than the velocities derived by the HARPS team in Bonfils et al.
(2013a); Anglada-Escud´e & Butler (2012) showed that HARPS-TERRA produces better
velocities for M dwarfs.
Given GJ 832’s close proximity it is bright enough for high contrast imaging (Salter et al.
2014), even though it is an M-dwarf. However, due to its likely old, though uncertain, age
even GJ 832b (0.63MJup ) would not be bright enough to be detected by the current state of
the art instruments such as the Gemini Planet Imager on Gemini South (Macintosh et al.
2008). With a rare Jupiter analog and a potentially rocky inner planet, the GJ 832 system
can be considered a scaled-down version of our Solar system. With this in mind, it would be
interesting to see if that analogy continues beyond the planetary members of the system to
the debris. There is a growing body of work, based on Spitzer and Herschel observations,
revealing correlations between the presence of debris disks and planets (Wyatt et al. 2012;
Maldonado et al. 2012; Bryden et al. 2013, e.g. ). As GJ 832 is very nearby (4.95 pc),
it is an ideal candidate for future imaging efforts to search for debris disks akin to our
own Edgeworth-Kuiper belt and main asteroid belt. Recent work by Marshall et al. (2014)
showed a correlation between low (sub-Solar) metallicity, low mass planets and an elevated
incidence of debris from Herchel data and radial-velocity results. As GJ 832 is quite metal-
poor ([F e/H ] = −0.3), it would thus appear to be a promising target for debris detection.
Future observations of GJ832 hold the promise to yield up further secrets from this intriguing
system.
Circumstellar debris discs around mature stars are the byproduct of a planetesimal
formation process, composed of icy and rocky bodies ranging from micron sized grains to
kilometre sized asteroids (see reviews by e.g. Wyatt 2008, Krivov 2010 and Moro-Martin
2013). The dust we actually observe is continually replenished in the disc through the colli-

– 13 –
sional grinding of planetesimals as the grains are much shorter lived than the age of the host
star, being removed by radiative processes and collisional destruction (Backman & Paresce
1993). Since planets are believed to be produced through the hierarchical growth of planetes-
imals from smaller bodies and dust grains are produced through their collisional destruction,
we expect the two phenomena to be linked. The solar system represents one outcome of the
planet formation process, comprising four telluric planets, four giant planets and two de-
bris belts - the inner, warm Asteroid belt at 3 AU (Backman et al. 1995) and the outer,
cold Edgeworth-Kuiper belt at 30 AU (Vitense et al. 2012). We detect thermal emission
from warm dust around 2±2% of sun-like stars (Trilling et al. 2008) and cold dust around
20±2% of sun-like stars (Eiroa et al. 2013); such measurements are limited by sensitivity
particularly for the warm dust. By comparison, the solar system’s debris disc is atypically
faint, expected to lie in the bottom few percent of disc systems (Greaves & Wyatt 2010) and
currently beyond the reach of direct detection by ground or satellite observatories. Around
other stars, many host infrared excesses with two characteristic temperatures, typically at
∼150 K and ∼50 K (Morales et al. 2011). Drawing an analogy to the solar system, discs
with two temperature components are interpreted as being the product of physically distinct
debris belts at different orbital radii. Due to the tendency of dust to migrate away from the
debris belt where it was created (Krivov et al. 2008), the presence of more or less narrow de-
bris rings around a star has been attributed to the existence of unseen planet(s) shepherding
the dust and confining its radial location through dynamical interaction, creating observable
warps, clumps, gaps and asymmetries in the disc (Moro-Martin et al. 2007, Morales et al.
2009). Several such cases of planets interacting with a debris disc have now been proposed,
with candidate planets identified through direct imaging searches around several of the stars
(e.g. Vega, Wyatt 2003; Beta Pic, Lagrange et al. 2010; HD 95086, Rameau et al. 2013).
Indeed, planet-disc interaction has been vital in the formation and evolution of life on Earth,
with minor body collisions providing both a late veneer of volatile material to the Earth’s
surface (O’Brien et al. 2006), the migration of Jupiter thought to be responsible for the late
heavy bombardment at ∼800 Myr (Gomes et al. 2005) and subsequent infrequent catas-
trophic bombardment drastically altering the climate during the history of the solar system
(Covey 1994; Toon et al. 1997; Feulner 2009). Therefore, any discussion of the potential
habitability of an exoplanet should consider the possibility of volatile material delivery to a
planet located in the habitable zone from remnant material located elsewhere in the system.
This research is supported by Australian Research Council grants DP0774000 and
DP130102695. Australian access to the Magellan Telescopes was supported through the
National Collaborative Research Infrastructure Strategy of the Australian Federal Govern-
ment. This research has made use of NASA’s Astrophysics Data System (ADS), and the

– 14 –
SIMBAD database, operated at CDS, Strasbourg, France. This research has also made
use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org
(Wright et al. 2011).
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This preprint was prepared with the AAS L
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– 21 –
Table 1. AAT/UCLES Radial Velocities for GJ 832
JD-2400000 Velocity (m s−1) Uncertainty (m s−1)
51034.08733 7.5 2.2
51119.01595 14.6 6.0
51411.12220 11.4 3.3
51683.26276 18.0 2.8
51743.14564 19.0 2.7
51767.08125 25.0 2.3
52062.24434 19.8 2.2
52092.16771 9.0 2.5
52128.12730 2.2 4.0
52455.23394 0.5 1.6
52477.14549 10.0 2.6
52859.08771 -4.1 2.1
52943.03605 -5.4 2.7
52946.97093 0.5 1.9
53214.20683 -9.5 2.5
53217.21195 -13.9 2.4
53243.05806 -2.1 2.4
53245.15092 -15.4 2.5
53281.04691 -17.3 2.0
53485.30090 -13.1 2.0
53523.30055 -4.9 1.6
53576.14194 -11.5 1.6
53628.06985 -0.4 5.2
53629.05458 -15.2 2.1
53943.10723 -6.3 1.3
54009.03770 -10.4 1.6
54036.95562 -7.2 1.5
54254.19997 3.2 1.8
54371.06683 0.2 1.6
54375.04476 2.5 1.7
54552.29135 8.7 4.0
54553.30430 17.0 2.8
55102.99894 6.4 2.6
55376.26506 9.2 2.5
55430.16511 15.4 2.5
56087.23879 16.1 2.4
56139.24349 14.5 4.6
56467.24320 1.6 3.0
56499.09217 -6.3 4.0

– 22 –
Table 2. HARPS Radial Velocities for GJ 832
JD-2400000 HARPS-TERRA HARPS-CR
Velocity (m s−1) Velocity (m s−1) Uncertainty (m s−1)
52985.51975 -5.1 -8.4 0.5
53158.90619 -3.1 -6.6 0.6
53205.74533 -5.4 -9.0 0.7
53217.74390 -8.7 -12.4 0.4
53218.70745 -9.3 -12.8 0.2
53229.72411 -6.7 -10.2 0.4
53342.54349 -9.6 -13.3 0.6
53490.92722 -12.1 -16.0 0.8
53491.91352 -7.7 -11.3 1.3
53492.92944 -8.4 -15.1 1.0
53551.85358 -7.8 -11.7 0.3
53573.80021 -11.2 -15.1 0.3
53574.73313 -12.1 -16.9 0.3
53575.73634 -10.4 -14.5 0.3
53576.78382 -11.1 -16.0 0.3
53577.79171 -11.0 -15.1 0.3
53578.74684 -11.9 -15.9 0.3
53579.72975 -11.3 -14.5 0.3
53580.76546 -10.4 -13.8 0.3
53950.81187 -8.6 -12.9 0.4
53974.63508 -6.6 -11.0 0.4
54055.52259 -4.0 -8.4 0.4
54227.91203 -1.2 -5.7 0.4
54228.91277 -1.2 -3.9 0.4
54230.88177 -0.3 -3.4 0.4
54233.92916 -0.1 -3.9 0.7
54234.92383 0.0 -4.0 0.4
54255.84319 1.7 -2.9 0.4
54257.88296 1.7 -3.4 0.4
54258.91849 0.8 -3.9 0.4
54291.81785 2.6 -2.0 0.5
54293.78153 3.4 -1.6 0.3
54295.82951 4.4 -0.5 0.4
54299.83521 6.9 2.0 0.7
54314.77282 2.4 -2.4 0.4
54316.60452 1.0 -4.5 0.2
54319.80379 0.7 -4.2 0.4
54339.64829 5.2 0.5 0.2
54341.76270 5.9 1.1 0.3
54342.67095 3.0 -2.7 0.1
54347.71453 0.0 -4.4 0.3
54349.72920 0.8 -2.6 0.4
54387.61499 4.0 -0.7 0.1
54393.60450 3.6 -1.3 0.4
54420.51798 2.4 -2.4 0.3

– 23 –
Table 2—Continued
JD-2400000 HARPS-TERRA HARPS-CR
Velocity (m s−1) Velocity (m s−1) Uncertainty (m s−1)
54426.51760 3.4 -1.0 0.3
54446.53786 9.5 4.7 0.5
54451.53099 9.5 4.5 0.5
54453.53428 7.1 1.1 0.2
54464.53844 6.2 1.3 0.5
54639.91552 10.7 5.7 0.3
54658.87484 15.7 10.7 0.6
54662.86973 14.5 9.3 0.2
54704.70377 11.6 6.5 0.5
Table 3. Magellan/PFS Radial Velocities for GJ 832
JD-2400000 Velocity (m s−1) Uncertainty (m s−1)
55785.64157 0.0 0.9
55787.61821 0.0 0.8
55790.61508 0.3 0.8
55793.63258 0.8 0.9
55795.70095 1.2 0.8
55796.71462 2.5 0.9
55804.66221 0.2 0.9
55844.60440 3.1 0.9
55851.62322 -0.5 0.9
56085.87962 -1.4 0.9
56141.67188 -7.3 0.8
56504.79755 -12.1 1.1
56506.76826 -13.7 1.0
56550.60574 -14.8 0.9
56556.65127 -18.3 1.0
56603.55010 -18.7 0.9
Table 4. Maximum a posteriori estimates and 99% credibility intervals for the nuisance
parameters: reference velocities with respect to the data mean (γ), excess white noise (σ),
and intrinsic correlation (φ).
Parameter HARPS PFS UCLES
γ4.56 [-1.83, 11.63] -6.64 [-17.20, 3.91] 1.14 [-5.52, 7.80]
σ1.33 [0.90, 1.91] 1.45 [0.44, 2.99] 4.66 [3.13, 6.15]
φ0.90 [0.25, 1] 0.77 [-1,1] 0.11 [-0.30, 0.57]

– 24 –
Table 5. Stellar Parameters for GJ 832
Parameter Value Reference
Spec. Type M1.5 Gray et al. (2006)
M1V Jenkins et al. (2006)
Mass (M⊙) 0.45 Bonfils et al. (2013a)
0.45±0.05 Bailey et al. (2009)
Distance (pc) 4.95±0.03 van Leeuwen (2007)
logR′
HK -5.10 Jenkins et al. (2006)
[F e/H] -0.3±0.2 Bonfils et al. (2013a)
-0.7 Schiavon et al. (1997)
Teff (K) 3472 Casagrande et al. (2008)
Luminosity (L⊙) 0.020 Boyajian et al. (2012)
0.026 Bonfils et al. (2013a)
log g4.7 Schiavon et al. (1997)

– 25 –
Fig. 1.— Estimated posterior density of the period of the Keplerian signals based on MCMC
sampling. The red arrow indicates the global maximum identified by the chain and the hor-
izontal lines denote the 10% (dotted), 1% (dashed), and 0.1% (solid) probability thresholds
with respect to the maximum. Top panel: GJ 832b. Middle panel: GJ 832c. Bottom panel:
Residuals to two-planet fit; this periodicity did not meet our criteria for a significant detec-
tion.

– 26 –
Table 6. Maximum a posteriori estimates and 99% credibility intervals of the Keplerian
parameters and the linear trend ˙γ.
Parameter GJ 832b GJ 832c
P[days] 3660 [3400, 3970] 35.67 [35.55, 35.82]
K[ms−1] 15.51 [13.47, 17.36] 1.62 [0.70, 2.56]
e0.08 [0, 0.17] 0.03 [0, 0.25]
ω[deg] 246 [149, 304] 80 [0, 360]
Mean anomalya[deg] 40 [315, 109] 246 [0, 360]
a[AU] 3.60 [3.18, 3.96] 0.162 [0.145, 0.179]
msin i[M⊕] 219 [168, 270] 5.0 [1.9, 8.1]
˙γ[ms−1year−1] 0.18 [-0.46, 0.69]
γHARP S 4.56 [-1.83, 11.63]
γP F S -6.64 [-17.20, 3.91]
γAAT 1.14 [-5.52, 7.80]
aComputed for epoch JD=2450000.0
Table 7. Correlations of GJ 832 velocities with activity indicators
Indicator MAP estimate 99% confidence interval
BIS -0.21 [-0.66,0.14]
FWHM -0.04 [-0.10,0.04]
S-index (m/s/dex) 1.5 [-8.2,11.0]
Table 8. Least-squares Keplerian orbital solutions for the GJ 832 planetary system.
Uncertainties are given as a ±1σrange.
Parameter GJ 832b GJ 832c
P[days] 3657 [3553, 3761] 35.68 [35.65, 35.71]
K[ms−1] 15.4 [14.7, 16.1] 1.79 [1.52, 2.06]
e0.08 [0.02, 0.10] 0.18 [0.05, 0.31]
ω[deg] 246 [224, 268] 10 [323, 57]
Mean anomalya[deg] 307 [285,330] 165 [112,218]
a[AU] 3.56 [3.28, 3.84] 0.163 [0.157, 0.169]
msin i[M⊕] 216 [188, 245] 5.40 [4.45, 6.35]
˙γ[ms−1year−1] 0.0 (fixed)
γHARP S 1.05 [0.27, 1.83]
γP F S -9.35 [-11.07, -7.63]
γAAT 3.08 [2.19, 3.96]
aComputed for epoch JD=2450000.0

– 27 –
Fig. 2.— Generalized Lomb-Scargle periodogram of the residuals to a single-planet fit for
GJ 832. A strong peak at 35.67 days is present, with a bootstrap FAP of 0.04%.

– 28 –
Table 9. Characteristics of 2-planet fits for GJ 832
AAT rms HARPS-TERRA rms HARPS-CR rms PFS rms Total rms χ2
ν
m s−1m s−1m s−1m s−1m s−1
Fit 1 5.66 1.53 · · · 1.60 3.57 1.206
Fit 2 5.63 · · · 1.40 1.55 3.53 1.080
Fig. 3.— Radial velocities and fit for GJ 832b; the signal of the second planet has been
removed. AAT – green, HARPS – red, PFS – blue.
Table 10. FAP of residual signal after removing GJ 832b
Data Used NPeriod FAP Data Used NPeriod FAP
(days) (days)
AAT 39 2.77 0.1481
AAT + PFS 55 15.38 0.7279
HARPS-TERRAa54 40.5 0.0066 HARPS-CRa54 35.6 0.0017
HARPS-TERRA + PFSa70 35.66 0.0331 HARPS-CR + PFSa70 35.66 <0.0001
AAT + HARPS-TERRA 93 35.6 0.0461 AAT + HARPS-CR 93 35.7 0.0014
AAT + HARPS-TERRA + PFS 109 35.7 0.0164 AAT + HARPS-CR + PFS 109 35.7 0.0004
aParameters of GJ 832b held fixed at best-fit values in Table 8

– 29 –
Fig. 4.— Top: Radial velocities and fit for GJ 832c; the signal of the outer planet has been
removed. AAT – green, HARPS – red, PFS – blue. Bottom: Same, but the AAT data have
been omitted from the plot to more clearly show the low-amplitude signal.

– 30 –
Fig. 5.— Generalized Lomb-Scargle periodogram of the residuals to the two-planet fit for
GJ 832. All three datasets are included. The peak at 40 days has a bootstrap FAP of 4.56%,
100 times less significant than the peak due to the inner planet (Figure 2).

– 31 –
Fig. 6.— HARPS radial velocities (after removing the signal of GJ 832b) versus the bisector
inverse slope (BIS: left panel) and the FWHM of the cross-correlation function (CCF FWHM:
right panel). No correlations are evident, supporting the hypothesis that the 35.6-day signal
is due to an orbiting planet.

– 32 –
Table 11. Candidate habitable-zone exoplanets
PlanetaMassb(M⊕) Semimajor axis (AU) HZ rangec(AU) Eccentricity Referencesd
GJ 163c 6.8±0.9 0.1254±0.0001 0.134-0.237 0.099±0.086 1,2
GJ 581ge2.242±0.644 0.13386±0.00173 0.095-0.168 0.0 3,4,5,6,7,8,9
GJ 581d 5.94±1.05 0.21778±0.00198 0.095-0.168 0.0 8
GJ 667Cc 3.8 [2.6,6.3] 0.125 [0.112,0.137] 0.118-0.231 0.02 [0,0.17] 10,11,12,13
GJ 667Cf 2.7 [1.5,4.1] 0.156 [0.139,0.170] 0.118-0.231 0.03 [0,0.19]
GJ 667Ce 2.7 [1.3,4.3] 0.213 [0.191,0.232] 0.118-0.231 0.02 [0,0.24]
GJ 832c 5.406±0.954 0.163±0.006 0.130-0.237 0.18±0.13 This work
HD 40307g 7.1 [4.5,9.7] 0.600 [0.567,0.634] 0.476-0.863 0.29 [0,0.60] 14
Kepler-22b <36 (1σ) 0.849+0.018
−0.017 0.858-1.524 ··· 15,16
Kepler-61b ··· 0.2575±0.005 0.295-0.561 0.0+0.25
−0.017,18
Kepler-62e <36 (95%) 0.427±0.004 0.457-0.833 0.13±0.112 17,19
Kepler-62f <35 (95%) 0.718±0.007 0.457-0.833 0.0944±0.021
Kepler-174d ··· 0.677 · · · 0.431-0.786 20
Kepler-296f ··· 0.263 · · · 0.143-0.277 20
Kepler-298d ··· 0.305 · · · 0.351-0.65 20
Kepler-309c ··· 0.401 · · · 0.228-0.434 20
aPlanet data from the Habitable Exoplanets Catalog at http://phl.upr.edu/hec.
bUncertainties given in square brackets refer to the 99% credibility intervals on the value in question,
whilst those given as ±refer to the 1σuncertainty.
cConservative habitable-zone limits computed after Kopparapu et al. (2014) and
http://www3.geosc.psu.edu/∼ruk15/planets/
dReferences in the table are as follows: [1] Bonfils et al. 2013, [2] Tuomi & Anglada-Escud´e 2014, [3]
Mayor et al. 2009; [4] Vogt et al. 2010; [5] Tuomi 2011; [6] von Braun et al. 2011; [7] Tadeu dos Santos et
al. 2012; [8] Vogt et al. 2012, [9] Lestrade et al. 2012; [10] Anglada-Escud´e et al. 2012; [11] Anglada-Escud´e
et al. 2013; [12] Delfosse et al. 2013; [13] Makarov & Berghea 2014; [14] Tuomi et al. 2013a; [15] Borucki
et al. 2012; [16] Neubauer et al. 2012; [17] Borucki et al. 2011; [18] Ballard et al. 2013; [19] Borucki et al.
2013; [20] Rowe et al. 2014; [21] Tuomi et al. 2013b.
eFor the purposes of this table, we list the cirular 5-planet model for GJ 581 given in Vogt et al. (2012).