Constraining the Radiation and Plasma Environment of the Kepler Circumbinary Habitable Zone Planets

9.3 MB·English

by  Jorge I. Zuluaga

Draftversion February2,2016
PreprinttypesetusingLATEXstyleemulateapjv.01/23/15
CONSTRAINING THE RADIATION AND PLASMA ENVIRONMENT OF THE KEPLER CIRCUMBINARY
HABITABLE-ZONE PLANETS
Jorge I. Zuluaga1,2, Paul A. Mason3, Pablo A. Cuartas-Restrepo2
Draft versionFebruary 2, 2016
ABSTRACT
The discovery of many planets using the Kepler telescope includes ten planets orbiting eight binary
6
stars. Three binaries, Kepler-16, Kepler-47, and Kepler-453, have at least one planet in the cir-
1
cumbinary habitable-zone (BHZ). We constrain the level of high-energy radiation and the plasma
0
environment in the BHZ of these systems. With this aim, BHZ limits in these Kepler binaries are
2
calculated as a function of time, and the habitability lifetimes are estimated for hypothetical ter-
n restrial planets and/or moons within the BHZ. With the time-dependent BHZ limits established, a
a
self-consistent model is developed describing the evolution of stellar activity and radiation proper-
J
ties as proxies for stellar aggressiontowards planetary atmospheres. Modeling binary stellar rotation
0 evolution, including the effect of tidal interaction between stars in binaries is key to establishing the
3
environment around these systems. We find that Kepler-16 and its binary analogs provide a plasma

environment favorable for the survival of atmospheres of putative Mars-sized planets and exomoons.
]
P Tides have modified the rotation of the stars in Kepler-47 making its radiation environment less
E harsh in comparison to the solar system. This is a good example of the mechanism first proposed
by Mason et al. Kepler-453 has an environment similar to that of the solar system with slightly
.
h better thanEarthradiationconditionsattheinner edgeofthe BHZ.Theseresultscanbe reproduced
p and even reparametrized as stellar evolution and binary tidal models progress, using our online tool
- http://bhmcalc.net.
o
r Keywords: binaries: general–planet-starinteractions–planetsandsatellites: individual(Kepler-16b,
t Kepler-47c,Kepler-453b)– stars: activity
s
a
[
1. INTRODUCTION arebeingmadetoconstrainthemagneticandplasmaen-
2 vironmentofcircumbinaryplanets(Mason&Clark2012;
The outstanding work of the Kepler Observatory cir-
v
Masonetal.2013;Sanz-Forcadaetal.2014),findingthat
6 cumbinary team has resulted in the discovery of 10 con-
binaries could potentially pose severe restrictions on the
9 firmed planets around eight moderately separated bina-
habitabilityofEarth-likeplanetsandexomoons. Wenow
2 ries (all have binary periods in the range of 8-60 days).
know that stellar aggression, in the form of high-energy
0 These are Kepler-16 (Doyle et al. 2011), Kepler-34 and
radiation and coronal-activity-related mass-loss, would
0 Kepler-35 (Welsh et al. 2012), Kepler-38 (Orosz et al.
haveaneffectontheevolutionofplanetaryatmospheres,
. 2012b), Kepler-47 (Orosz et al. 2012a), Kepler-64 (Kos-
1 especially their capacity to retain water (see, e.g. Lam-
tovetal.2013;Schwambetal.2013),Kepler-413(Kostov
0 et al. 2014), Kepler-47 (?) and Kepler-453 (Welsh et al. mer 2013).
5 In Mason et al. (2013) we proposed a mechanism for
2015). Interesting, three out of eight of these systems
1 which some BHZ planets experience Earth-like or lower
(38%), namely, Kepler-16, Kepler-47, and Kepler-453,
:
v host giant planets in the circumbinary habitable-zone levelsofstellaraggressionandtherebyhavethepotential
i (BHZ)4. to retain water. Tidal torquing of stellar rotation, espe-
X
ciallyforcertainbinaryperiodsandinitialeccentricities,
Thestudyofconditionsthatplanetsfacewhileorbiting
r aids in the reduction of stellar activity. The reduction
a binary system has attracted the attention of the exo-
a
in intensity of rotationally driven dynamo action results
planetary community. Several authors have studied the
in a decrease in stellar coronal activity, potentially pro-
stabilityoftheirorbits(Dvorak1986;Holman&Wiegert
moting life on planets. We refer to the sum of these and
1999)andthekindandlevelofinsolationexperiencedby
otherbeneficialeffects forlife onplanetsaroundbinaries
planetswhileilluminatedbytwostars(Harrington1977;
as the Binary Habitability Mechanism (BHM).
Haghighipour & Kaltenegger 2013). The conditions for
Recent observations lend support to the tidal astro-
the formation and migration of these planets have been
physics of BHM. For example, Wasp-18, a 0.63 Gyr old
studied by Pierens & Nelson (2008), Kley & Haghigh-
F6 star, is orbited by a nearby giant planet, with a 0.94
ipour (2014), and Kley & Haghighipour (2015). Efforts
day orbital period. The star shows a low level of activ-
1Harvard-Smithsonian Center for Astrophysics, Cambridge, ity, normally expected for a much older star (Pillitteri
MA02138, USA et al. 2014). This effect has been described as “prema-
2FACom-InstitutodeF´ısica-FCEN,UniversidaddeAntio- ture aging.” In another example, the interaction of HD
quia,Calle70No. 52-21,Medell´ın,Colombia
189733 with a close-in planet, has resulted in the oppo-
3New Mexico State University - DACC, Las Cruces, NM,
site effect ona muchlargertimescale (Wolk et al.2011).
88003, USA
4Recently,thediscoveryofathirdplanetaroundKepler-47. The HD 189733, a relatively old star, displays anomalously
discoveryofthisplanetmayimplyamodificationoftheproperties high activity levels, lending support to our prediction
ofKepler-47casconsideredhere.
2
thatearlytidalrotationaltorquingcouldresultinahigh Inordertoprovidethereaderanopportunitytorepro-
levelofactivity. Wecallthelatterphenomenonthe“for- ducetheseresultsandtofurtherexplorethevastparam-
ever young” effect, in reference to the fact that tidal in- eter space of circumbinary planets, a Web-based BHM
teractionofa star witha stellaror substellarcompanion Calculator, BHMcalc , is made available using the link
could make the star very active (to appear young) for http://bhmcalc.net. In Mason et al. (2015) we intro-
a longer time than expected from single-star evolution duced the first version of the tool. Here we present a
(Mason et al. 2013; Sanz-Forcada et al. 2014). comprehensiveversionofthe calculator,detailing allthe
Although the specific physical mechanisms operating new physical effects described in this paper, and provid-
in the case of Wasp-18 and HD 189733 may be differ- ing an improved and user-friendly interface.
ent from those predicted in stellar binary systems, these Other online tools have recently been made available
discoveriesconfirm the necessity of including tidal inter- (Cuntz & Bruntz 2015; Mu¨ller & Haghighipour 2014).
action in order to assess stellar activity levels of stars Like these, the BHMcalc provides renditions of the in-
with companions and its effect on their planets. stantaneous and continuous BHZ. In addition, BHMcalc
Inpreviouswork,weusedfirstorderestimationoftidal calculates time-dependent stellar and planetary proper-
synchronizationtimes(Masonetal.2013). Morerecently ties and utilizes them to study HZ environments. Most
(Masonetal.2015),weexploredhabitablenichesaround critically, the rotational evolution of the stellar compo-
hypothetical circumbinary environments, using a basic nents is derived, allowing for estimates of the resulting
modelforstellarrotationevolutionincludingstellartides stellar mass loss and magnetic activity. Stellar emis-
but applied only to the early phases of main-sequence sion is used to evaluate effects experienced by planets.
evolution. Specifically, we select the integratedX-ray and extreme-
Here our models are refined by (1) extending the time ultravioletradiation(XUV)andstellarwind(SW)fluxes
frame to the critical pre-main-sequence phase where ro- as derived for planets, located over a range of distances
tational and activity evolution is much richer; (2) ap- fromthebinarycenterofmass,asproxiesforhabitability.
plying a more physically motivated model for stellar ro- Forthispurposeweestimatethe XUV-andSW-induced
tational evolution, including but not restricted to angu- planetary atmospheric mass loss. In all cases, the evolu-
lar momentum (AM) transport inside the star; and (3) tion of each star is calculated independently and orbital
estimating mass loss and X-ray emission using the lat- averagesare used to calculate the combined effect of the
est solar-inspired models, relating basic stellar proper- binary on the planet.
ties and rotation to chromospheric and coronal activity This paper is organized as follows: In Section 2, the
(Cranmer et al. 2013). sample of three Kepler binaries possessing BHZ planets
For these three critical refinements, we are applying isdescribed. Section3presentsanefficientmodeltocal-
modelsthathavebeendevelopedandtestedinthecaseof culateBHZsandtheirevolutionintime. InSection4,we
single-stars. Weareassumingherethatthesamemodels revisitthe argumentfor the need to access the radiation
can be applied to describe low-mass stars in moderately andplasmaenvironmentofplanetsaspotentialdriversof
separatedbinaries(orbitalperiodslargerthan8daysand atmosphericevolution. High-energyradiationandwinds
separations larger than several tens of stellar radii). We are key to constraining habitability. The comprehensive
willjustifyandtestthisassumptionlateroninthepaper. model used to calculate the evolution of rotation and
We apply our improved and extended model to the activity is described in detail in Section 5. The model
interesting and well-characterized Kepler binaries with is applied to constrain the radiation and plasma envi-
BHZ planets. The planets currently knownin those sys- ronments of the solar system as a reference in Section
tems are Neptune to Saturn sized, so no surface habit- 6. The binary rotational evolution affects potential cir-
ability is expected. However, it is reasonable to suspect cumbinary worlds and so is presented in Section 7, and
that Earth-like planets may exist in the BHZ of similar the radiation and plasma environments are investigated
binaries (Egglet al. 2013). Additionally, since circumbi- in Section 8. Finally, in Section 9, a summary and the
nary giant planets appear to be common, some of them conclusions of this investigation are presented.
mayharborpotentiallyhabitableexomoons(Helleretal.
2014). These planets and putative moons are expected 2. KEPLERCIRCUMBINARYHABITABLE-ZONEPLANETS
to experience harsh environments from aggressive host Itisinterestingtonotethatwhilenoneofthecurrently
stars. Thus, understanding the radiation and plasma known transiting circumbinary planets are Earth-like or
environment experienced by these bodies is a key effort even super-Earths, this may be due purely to three se-
to accessing their potential habitability (Zuluaga et al. lection effects. The Kepler telescope is most sensitive to
2012; Heller & Zuluaga 2013). the detection of large planets, orbiting small stars, on
The present aim is to constrain the radiation and short-period orbits. However, the fact that on average
plasma environment of these HZs and to investigate the circumbinaryplanetshavelongerperiodsthanthoseKe-
effectthattheseconditionshaveontheatmosphericevo- plerplanetswithsingle-starhostsisnotaselectioneffect.
lution of hypothetical terrestrial planets and exomoons. Short-periodcircumbinaryplanetsarelimitedbydynam-
This model can readily be applied to other Kepler bi- ical stability (Harrington 1977; Dvorak 1986; Holman &
naries or any other system with well-determined param- Wiegert 1999) and probably also because of formation
eters. Future telescopes like PLATO (Rauer et al. 2013) (Pierens & Nelson 2008; Kley & Haghighipour 2014).
willlikelydiscovercircumbinaryplanets exhibiting some Remarkably, the BHZ extends well beyond the orbital
potentialforhabitability. Ouraimhereistoinformsuch stability limit in many cases (see Mason et al. 2015). In
searches by showing how a more comprehensive theory addition, residence of planets in the BHZ appears to be
of planetary habitability can be applied to circumbinary common, as 3 of the 10 known transiting planets are lo-
planets especially in the presence of interacting stars. cated in the BHZ and three binaries out of eight harbor
3
a BHZ planet. The limits of the HZ, around either single-stars or a
InTable1,propertiesofthethreetransitingBHZplan- binary, are calculated by finding the radius of a circle
ets and their host stars are listed. Hereafter, we will centered in the barycenter of the system, where the av-
refer to this as the KBHZ sample. The binaries in the erage flux S received from the star or the binary is
h i
KBHZ sample areamongthe best-characterizedbinaries equal to the critical flux calculated with Eq. (1).
known, mainly owing to the extraordinaryobservational In the case of a single-star, S is equal to the nearly
h i
constraintsprovidedby transiting circumbinaryplanets. constantflux S =L/d2 measuredatdistance d. Here
sing
To study the binaries in the KBHZ sample, we focus L is the bolometric luminosity of the star measured in
on three different scenarios, selected to answer the fol- solar units and d is in astronomical units (AU). More
lowing questions: (1) If the actual circumbinary plan- precisely and as we will explain later, L is a corrected
ets wereEarth-likeplanets insteadofgiantplanets, then luminosity that takes into account the response of the
wouldthose planets be habitable?5. Fromnecessity, this atmosphere to the incident stellar radiation (see Eq. 4).
must be based on current understanding of Earth-like The radius of the ith HZ edge l will then be given
sing,i
habitability. (2) Assuming that the actual circumbinary by:
planets,whichhavemasseslargerthanoraroundthatof
Saturn, would be able to harbor a Mars-sized exomoon, L
S = (2)
then would these moons be able to retain a dense and eff,i l2
sing,i
moist atmosphere in order to sustain life? And maybe
mostimportantly,binariesliketheseareverycommon,so Around binaries, planetary atmospheres, even if plan-
(3) what are the constraints on habitability of currently ets are in a circular orbit, will be subject to a variable
unseen planets within the BHZ of similar binaries? In- flux andspectrum of radiation. The instantaneous bolo-
sightintotheseandotherquestionsisgainedbystudying metric flux on a circumbinary planet is calculated as
well-observedcases, where the environmental conditions
L L
experiencedbyplanetsunderthereignofthebinarymay 1 2
S (d,θ)= + (3)
be investigated. bin R2(d,θ) R2(d,θ)
1 2
It is important to stress that the current investiga-
where R and R are the distances from the stars to
tion is not restricted by dynamical or formation con- 1 2
a point in a circle of radius d. θ is the angle between
straints, which may or may not limit the likelihood of
the line joining the stars and a fixed point on the circle.
these scenarios (Chavez et al. 2013, 2015; Andrade-Ines
Thisangleisafunctionoftime,anditwilldependonthe
& Michtchenko 2014; Forgan et al. 2015; Pilat-Lohinger
relativeangularvelocityofthe binaryandatestparticle
et al. 2014). The basic dynamical constraint imposed
on the circle.
planets have stable orbits is included as it extends into
R and R are given by
the BHZ in some cases (see Section 3). We assume that 1 2
exomoons and multiple planets could lie in stable orbits
withintheBHZofthesebinaries,basedonourownbasic R2(d,θ)=(d r sinθ)2+r2cos2θ
tests using numerical orbital integrations. 1 − 2 2
R2(d,θ)=(d+r sinθ)2+r2cos2θ
2 1 1
3. THECIRCUMBINARYHABITABLE-ZONE
wherer =qr/(1+q)andr =qr aretheinstantaneous
1 2 1
EstimatesofBHZboundariesquicklyfollowedthe Ke- distances of the stars to the barycenter and q =M /M
2 1
plerdiscoveries(Mason&Clark2012;Quarlesetal.2012; isthebinarymassratio. Therelativedistancer between
Haghighipour& Kaltenegger2013;Kane& Hinkel 2013; the starsisalsoafunction oftime forthe generalcaseof
Masonetal.2013). Ourapproach,asthatofothers,isto an eccentric binary orbit.
usethemodelsofKastingetal.(1993),updatedbyKop- Since the two stars have different effective tempera-
parapuetal.(2013b)derivedforsinglestarstoalsoesti- tures, S and S cannot be directly compared as in
bin eff,i
matethemorecomplexBHZlimits. Animprovedversion the case of single-stars. However, in the case of stellar
ofthefirst-ordermethodpresentedinMasonetal.(2013) twins, the two sources will have the same effective tem-
is developed and applied here. perature and their fluxes can be summed directly. On
HZlimitsaredeterminedbythecriticalfluxesatwhich theotherhand,indisparatebinariestheratiooftheflux
planetary surface temperatures are compatible with the of the secondary to that of the primary scales with the
existence of liquid water. Using one-dimensional atmo- fourth power of the ratio of their effective temperatures.
sphericmodels,Kopparapuetal.(2013b)calculatedcrit- Asaresultthecombinedspectrum,tofirstorder,maybe
ical fluxes assuming that the planet is exposed to black- assumedtohaveaneffectivetemperatureequaltothatof
body radiation with an effective temperature Teff: the primary and the total flux equals Sbin (Mason et al.
2013). A verification of this approximation is discussed
Seff,i ≡Seff,i,⊙+aiT∗+biT∗2+ciT∗3+diT∗4 (1) below.
A more consistent method to take into account the
Here T = T 5780K, and S and a,b,c,d are
∗ eff eff,i i i i i
− differences in effective temperatures of the stellar com-
the effective critical flux for a solar-mass star and the
ponents is to replace bolometric luminosities L and L
interpolationcoefficientsfortheithboundary(seeTable 1 2
in Eq. (3) by weighted luminosities (Haghighipour &
3 in Kopparapu et al. 2013a).
Kaltenegger 2013; Cuntz & Bruntz 2015):
5 It isimportantto stresshere that this isanhypothetical sce-
nario. Wearenot under any circumstance assumingthat the dis- L′ =L (1+[S (T ) S ]l2 ) (4)
covered giants planets can behabitable orthat terrestrialplanets 1,2 1,2 eff,i 1,2 − eff,i,⊙ i,⊙
alsoexistintheBHZofallofthem. The weights in parenthesis account for the different
4
Parameter Kepler-16b Kepler-47c Kepler-453b
Stellar Properties
M1 (M⊙) 0.6897±0.0034 1.043±0.055 0.944±0.010
R1 (R⊙) 0.6489±0.0013 0.964±0.017 0.833±0.011
Teff1 (K) 4450±150 5636±100 5527±100
Prot,1 (d) 35.1±1.0 7.775±0.022 20.31±0.47
M2 (M⊙) 0.20255±0.00066 0.362±0.013 0.1951±0.0020
R2 (R⊙) 0.22623±0.00059 0.350±0.006 0.2150±0.0014
Teff2 (K) ... 3357±100 3226±100
Prot,2 (d) ... ... ...
[Fe/H] (dex) -0.20 -0.25 -0.34
Closest Evolutionary Track
M1∗ (M⊙) 0.70 1.05 0.90
M2∗ (M⊙) 0.20 0.35 0.20
Z1∗ (M⊙) 0.010 0.010 0.008
∆τ∗ (Gyr) > 13 5.53 10.1
MS,1
Binary Properties
Tage (Gyr) 2.0–3.0 1.0–5.0 1.5–2.5
Pbin (d) 41.07922±0.00007 7.44837695±0.00000021 27.322037±0.000017
abin (AU) 0.22431±0.00035 0.0836±0.0014 0.18539±0.00066
ebin 0.15944±0.00062 0.0234±0.0010 0.0510±0.0037
Planetary Orbit
Pp (d) 228.776±0.029 303.158±0.072 240.503±0.053
ap (AU) 0.7048±0,0011 0.989±0.016 0.7903±0.0028
ep 0.0069±0.0012 < 0.411 0.0359±0.0088
References
Doyle et al. 2011; Winn et al. 2011 Orosz et al. 2012b Welsh et al. 2015
Table 1
The KBHZ sample, Kepler binary systems harboring planets in theBHZ. Note. Quantities marked with an “*” are model
parameters.
spectral distribution of each source and the response of formula. No numerical integrations or calculations over
planetary atmosphere to these spectra. a grid of points around the system are required. This
ToobtainthelimitsoftheBHZ,S givenbyEq. (3), feature greatly improves the speed of calculation, which
bin
theequationshouldbeaveragedoveratimelongenough is especially important for the exploration of the vast
compared to the periods of the system. If the binary parameter space of circumbinary habitability.
eccentricity is not too large, an analytical expression for We have compared the BHZ limits for all the Kepler
S may be used: binarieswith knowncircumbinaryplanets calculatedus-
h i
ing our method and those used in three different inves-
tigations. The results are presented in Figure 1. We
hSbini(d)= n6=m√A2mL′n−Bm2 "1−π1arctan √AB2mm−Bm2 !# (5) htwaveeenfotuhnedBthHaZttlhimeiatsveurasignegotfhtehenreewlatmiveethdoiffderaenndcethbaet-
P
with n,m=1,2, A d2+r2 and B 2dr . of Haghighipour & Kaltenegger (2013) is less than 4%
Finally, the BHZmli≡mits aremcalculatemd≡by solvming the 6 The difference found by comparing our method with
equation that of Mason et al. (2013) is less than 1%. The limits
calculated by Cuntz & Bruntz (2015) are systematically
S = S (l ) (6) more conservative than all of the other methods, with
eff,i bin bin,i
h i
the inner limits 10% farther out and the outer limits
Although other authors have developed alternative ∼
10% closer in than the other methods.
methods to estimate the limits of the BHZ (Haghigh- ∼
ipour & Kaltenegger 2013; Kane & Hinkel 2013; Mason
3.1. Evolution of Insolation and BHZ
etal.2013;Cuntz&Bruntz2015;Mu¨ller&Haghighipour
2014), all of them share the most important character- Generally, it is possible to assume that moderately
istics of the method presented here. In particular, our separated stars in binary are formed at the same time.
method is an improvedversionof the first order method Moreover, stellar evolution shows that stars with differ-
used in Mason et al. (2013) by incorporating some key entmassesevolveatdifferentratesandindifferentways.
elements of the methods presented by Haghighipour &
Kaltenegger (2013) and Cuntz & Bruntz (2015). An in- 6 Themethoddevisedbytheseauthorsproducesdynamicaland
asymmetric BHZ. Comparison with our method depends on the
terestingadvantageofourmethodwithrespecttoothers
assumptionsmadeabouthowtoconverttheirasymmetricallimits
is the fact that for low eccentricities, the calculation of intooursymmetricones. Partofthediscrepancymayinvolvethis
theBHZlimitsrequiresfindingtherootsofananalytical ambiguity.
5
Figure 2. Kepler-47 is shown as an example of the evolution
of the BHZ (green area). BHZ limits are shown as a function of
age (solid blue and red lines). The HZ for a single-star with a
Figure 1. Comparison of BHZ limits for all the Kepler binaries massequal tothe primaryisalsoshown(dashed lines). Since the
having circumbinary planets, calculated with four different meth- system iscomposed of asolar-likestar andanM dwarfthe limits
ods: Haghighipour & Kaltenegger (2013); Mason et al. (2013); for the single primary and the binary are almost the same. The
Cuntz & Bruntz (2015) and the current paper. The limits calcu- CBHZishighlighted(shadedgrayregion;seetextforexplanation).
latedwiththemethodpresentedhereareusedasreferencevalues The semimajor axis of Kepler-47c, is shown as a horizontal line.
(abcsisavaluesandsolidblacklinesinupperpanel). Dashedlines Neglectingeccentricityeffects,thehabitabilitylifetimeofthisorbit
correspondtoadifferenceof0.1AU(∼10%). isroughly3.5Gyr.
Thus, in order to investigate habitability around a bi-
Wehavetestedthatthistimeisclosetothetimeofzero-
nary,stellarevolutionmodels for eachstarmust be used
agemain-sequence(ZAMS)oftheprimarystar,whichby
to determine the time dependence of the BHZ.
definition is the more massive component of the system.
Itisimportanttoaskwhetherthefundamentalproper-
Planets in the CBHZ remain inside the BHZ during the
ties of low-mass stars, such as effective temperature and
entiremain-sequencestageoftheprimaryasitisthestar
luminosity used to calculate the BHZ, evolve in binaries
with the shortest lifetime. The definition of the CBHZ
exactly as they do in single-stars. For moderately sep-
inner edge is trickier. We define it as the position of the
arated binaries, (periods larger than 8 days, stellar sep-
inneredgeoftheinstantaneousBHZcalculatedwhenthe
arations larger than tens of stellar radii), such as those
primary star abandons the main-sequence (close to the
studied in our sample, the Roche lobes of the stars are
end of the nuclear hydrogen-burning phase).
oneorderofmagnitudelargerthanthestellardiameters.
In order to assess the present insolation conditions in
For instance, in the case of the tightest binary in our
theKBHZsampleweplot,inFigure3,theinstantaneous
sample (Kepler-47), the filling factor of the primary (ra-
BHZ calculated in the middle of the range of estimated
tio of stellar radius to Roche lobe size) is 0.2 during
∼ age (See Table 1 for ages and references). Along with
PMS (when the star is largest) and 0.1 during main-
∼ BHZ limits, the insolation and photosynthetic photon
sequence (Eggleton 1983). At those filling factors the
fluxdensity(PPFD)areshownasafunctionofplanetary
shape of the star is only slightly modified by the com-
orbital phase. See Mason et al. (2015) for details on
panion and its interior and atmospheric properties are
PPFD calculations.
practically the same as for a single-star.
In the BHZ diagrams of Figure 3, the planetary or-
HZ evolution is also a natural outcome of the evolu-
bit has been placedamong different landmarkdistances:
tionofsingle-stars. Inthe samewaythatthe continuous
BHZ and CBHZ edges, binary orbit, equivalent Earth
HZ is defined for single-stars (Kasting et al. 1993), it
insolation distance, and last but not least, the critical
is generalizedto binaries and a continuous circumbinary
stability distance a , defined as the minimum distance
habitable zone (CBHZ) is defined. crit
wheretestparticleshavestable circumbinaryorbits. We
InFigure2,theevolutionoftheBHZforKepler-47and
computethiscriticaldistancewiththesemi-empiricalre-
its associated CBHZ is shown. We use stellar evolution-
lationship of Holman & Wiegert (1999):
ary models, at each age, to calculate the instantaneous
properties of both stars. Then the limits of the HZ at
thattimearedetermined. ShownherearethetheRecent a (1.60+5.10e 2.22e2 + (7)
Venus andEarlyMarscriteria. The outerCBHZ limitis crit≈ bin− bin
4.12µ 4.27e µ 5.09µ2+
defined by the instantaneous outer edge of the BHZ as − bin −
calculatedatthe time whenthe binaryflux isminimum. 4.61e2 µ2)a .
bin bin
6
Figure 3. BHZs, insolation and PPFD (see Mason et al. (2015) for an explanation) for the KBHZ sample. Left: Along with the BHZ
instantaneouslimits,thebinaryorbit,thecriticaldistance(dashedblackline),theplanetorbit(solidblackline),thelimitsofthecontinuous
BHZ(orangesolidlines),anddistancesofbinaryorbitresonances(concentricgraycircles)areshown. Thedistanceatwhichtheequivalent
Earthinsolationisreceivedismarkedwithadottedblackline. Right: InsolationandPPFDarecalculatedinunitsofpresentEarthlevels
notonlyatthedistanceoftheplanet(blueandredsolidlines,respectively)butalsoatalllocationswithintheBHZ(shaded areas).
7
Here µ = M /(M +M ), and a and e are the So far we have calculated insolationas a way to assess
2 1 2 bin bin
binary semimajor axis and eccentricity,respectively. Al- habitability conditions in circumbinary planets. But in-
though dynamical instability likely occurs outside the solationisnottheonlyfactorconstrainingthecapability
critical limit as well, as also discussed by Holman & of a planet to sustain life (for a review of many other
Wiegert (1999), all the planets in our sample are safely factorsseeKasting2009andreferencestherein). Among
beyondthiscriticaldistance. However,inKepler-16,a other endogenous and probably exogenous factors, the
crit
lies inside the BHZ, restricting the instantaneous exten- presence of a properly dense atmosphere with the right
sion of the BHZ as well as the CBHZ; see top left panel amount of water is mandatory.
of of Figure 3. When a is larger than the inner edge Thesolarsystemisagoodexampleofaplanetarysys-
crit
ofthe continuousBHZ we useits value asthe inner edge tem where among three planets (and a sizeable moon),
distance. located close or inside the HZ, two of them, Venus and
In the instantaneous BHZ diagrams of Figure 3, dis- Mars (plus the Moon), are un-inhabitable mainly due
tances at which orbital resonances with the binary oc- to factors related to the composition and mass of their
cur are also shown. It is very interesting to notice, and atmospheres.
likely not coincidental, that in both cases, Kepler-16b The evolution of a planetary atmosphere is driven by
and Kepler-453b,the planet remains entirely in between the influx of high-energy radiation and plasma from the
two resonances throughout its orbit. This supports the host star. This has been a matter of researchin the last
idea that orbital binary resonances may play a role in two decades (Kasting 1996; Lammer et al. 2007, p. 127;
theformationandfinalarchitectureofcircumbinarysys- Lammer et al. 2009, p. 399; Lammer et al. 2010; Lam-
tems. Notice also that Kepler-47c crosses many tightly mer2013;Tianetal.2013,p.567). Althoughitisnotyet
spaced resonances, not plotted in its BHZ diagram in clear which factors determine the survival of Earth-like
Figure 3 for clarity. atmospheresordrivetheircompositiontofavorhabitable
The planet Kepler-16b has a nearly circular orbit just conditions, multiple lines of evidence show that the in-
inside the maximum greenhouse limit. Kepler-47c has teraction of a planet with its young host star is a strong
a highly eccentric orbit and leaves the BHZ for part of factor in determining the fate of potentially habitable
its orbit. It does, however, currently spend most of its planet atmospheres (Lammer et al. 2007, p. 127; Lam-
time within the HZ, especially given the slower velocity mer et al. 2009,p. 399; Tian 2009; Zendejas et al. 2010;
at apastron (see insolation diagram in the middle right Zuluaga et al. 2013).
panelofFigure3). TheplanetKepler-453bhasaslightly Two key factors are involved in this interaction. The
eccentricorbitandalwaysremainsinthe HZ,just inside firstisthelevelofX-raysandextreme-ultraviolet(EUV)
the runaway greenhouse limit. radiation, collectively called XUV radiation, incident on
According to our calculations, of all the circumbinary theplanet. Thesephotonsheatuptheupperatmosphere
Kepler planets, only Kepler-16b is in the CBHZ, i.e. it andundercertainconditionscouldleadtomassivelossof
will lie inside the BHZ during the whole lifetime of the volatiles (Tian 2009; Tian et al. 2013, p. 567). The flux
primary star, which is in turn larger than the age of the ofchargedparticles,mainlyprotons,andtheirassociated
universe. This condition would seem at first very fa- magnetic fields (SW) is the other factor. The direct in-
vorable for the emergence and evolution of complex life. teraction between this continuous flow of particles and
However other factors could limit the long-term habit- fields and planetary atmospheres strongly impacts un-
ability within environments surrounding Kepler-16 and magnetized planets and moons (e.g., Venus, Mars and
similar binaries (see Section 8). the moon). Resulting nonthermal processes may remove
Kepler-47c and Kepler-453b do not remain inside the large fractions of planetary atmospheres, or in extreme
BHZ for the main-sequence lifetime of the primaries. cases they can strip them almost completely (Zendejas
However, both remain inside (although very close to et al. 2010). Mars is the best known example of the ef-
the inner edge of) the BHZ for astrobiologicallyrelevant fect of this kind of aggression eliminating habitability.
times (3.5 Gyr and 4 Gyr respectively). If we believe Recent data from the MAVEN Mission (Rahmati et al.
stellar evolution models, Kepler-47c is about to leave or 2014;Jakoskyetal.2015)areshowingtheincreasedlevel
hasjustleft the mostoptimistic BHZ,beingcurrentlyin of importance that SW interaction with the atmosphere
a Venus-like state in terms of stellar insolation. hasinshapingthe evolutionofMars’scapabilityto have
In order to calculate BHZ evolution and other key liquid water on its surface (habitability).
quantities for models, the stellar properties available in Modeling the interaction between the radiation and
the PARSEC v1.2 evolutionary tracks are used (Bressan plasma fields of the star and, in this case, the binary
et al. 2012, 2013) 7. In addition to providing good cov- system is key in assessing the habitability of all plan-
erage in metallicity and mass, the PARSEC tracks sample ets. However,since binaries are relatively novelenviron-
the PMS stages of stellar evolution well (and of course ments, at least for planetary systems, we need to under-
also the main sequence), a key feature when attempting standandlearntomodelaspectsofstellarevolutionthat
to study the early evolution of stellar rotation. More- havebeenappliedforyearstosingle-stars. Inthefollow-
over, these models reflect improvements for low-mass ingsectionswedevelopatheoreticalframeworktomodel
stars (Chen et al. 2014). In the BHMcalc tool we pro- the evolutionofstellaractivityandits roleinthe chang-
vide access to other evolutionary model results. ingconditionsfacedbytheatmosphereofacircumbinary
habitable planet.
4. THEEVOLUTIONOFATMOSPHERESASAKEY
5. STELLARROTATIONANDMAGNETICACTIVITYIN
FACTORFORASSESSINGHABITABILITY
BINARIES
7 http://people.sissa.it/bressan/parsec.html 5.1. Evolution of Stellar Rotation
8
The evolution of stellar rotation has been a matter of n f (e2) (1 e2)3/2f (e2)Ω .
intense research over the last several decades, not only ×(1 e2)6 (cid:20) 2 − − 5 n(cid:21)
−
in single but also in binary stars (for a recent review see
Bouvier 2013 and references there in; for the evolution Here k2 is the apsidal motion constant that quantifies
of rotation in binaries see Claret et al. 2005). the response of the star to tidal distortion, and it de-
The largediversityofstellarrotationperiods observed pends in generalon the internalmass distribution of the
in stars of all ages (especially PMS stars)has driven the star; t = f (M R2 /L )1/3 is the timescale
diss diss targ targ targ
developmentofadiversearrayofsemi-empiricalandphe- for dissipation of tidal energy inside the target star, and
nomenological models describing the evolution of stellar
κ I/(M R2 ) is the gyration radius. Eccentric-
AM (Kawaler 1988; Chaboyer et al. 1995; Matt et al. ≡ q targ targ
2012). Thesemodelshavebeenextensivelytestedagainst ity functions f (e2) and f (e2) are defined by Eqs. (2)
2 5
samples of stars (both single and binary) in young stel- and (3) in Hut (1981).
larclustersandmorerecentlyinlow-massfieldstars(Ir- We assume that while tides are raised over the whole
win et al. 2011). The details of these models depend on star,only tides within the convective layer contribute to
weakly constrained parameters; however, a general con- AM dissipation (Zahn 2008). As a result, the torque in
sensus has been reached about the general forces and Eq. 10 only affects the envelope of the star. Alterna-
timescales driving stellar rotation evolution. tively, we can assume that tides raised in the radiative
Here we apply and extend some of these models for core are dissipated on timescales much larger than that
starsinmoderatelyseparatedbinaries(i.e. binarieswith in the convective zone, rendering the resulting torque
similar masses and orbits to those of the KBHZ bina- comparatively small.
ries). For details concerning the physical motivations, The parameter f quantifies the efficiency of tidal
diss
history of development, and success of these models at energy dissipation. Although a fundamental theory of
reproducing observations, please refer to Bouvier (2013) this process capable of correctly explaining observations
and references therein. of close binaries is still lacking (see Claret 2011 for a
Although the applicability of these models to stars in discussion) we assume for simplicity that f 1, as is
diss
≈
binary systems has not been systematically tested, we used,forexample,inClaret(2012). Alternativetheories,
assumethatsome ofthe underlyingmechanisms willop- predict values of f within one order of magnitude.
diss
erate in the stellar components of these binaries as if Thus, for instance, the turbulent dissipation theory of
they wereisolatedstars. A detailedtestofthis hypothe- Zahn (2008) predicts a value f 3.5.
diss
≈
sis shouldbe pursuedin future researchefforts. Still, for For nonnegligible eccentricities, tidal braking could
the range of orbital separations and stellar masses con- drive stars to a pseudosynchronous final state where ro-
sidered here, the evolution in insolation hypothesis re- tational angular velocity is related to, but not exactly,
main as a goodone for the same arguments givenbefore the averageorbital angular velocity (Hut 1981),
to support the applicability of single-star evolutionary
models.
Ω 1+ 15e2+ 45e4+ 5 e6
In general, the AM of the ith layer of a star evolves n sync = 2 8 16 (10)
while obeying Newton’s angular second law: sync ≡ ω (1 e2)23(1+3e2+ 3e4)
− 8
For binary eccentricities e in the range 0 0.5, 1 <
dJi = . (8) nsync <2.8, implying that provided enough ti−me, stellar
dt Ti components of a binary will be locked in a rotational
X
state where their periods are close to that of the binary
Here J = I Ω is the instantaneous AM of the layer, period. This result will not depend on the mass loss
i i i
I its moment of inertia, Ω its instantaneous angular history of each star. Once locked, the magnetic activity
i i
velocity, and is the net torque over the layer. of the stars becomes frozen at a given value, which in
i
In the case ofTlow-mass stars (M <1.3M ), it is cus- some cases could mimic the behavior of a star that is
P ⋆ ⊙
tomary to assume that the star has two distinct interior much younger or older (Mason et al. 2013).
layers: a radiativeinner core(i=core) anda convective ThesecondexogeniceffectremovingAMfromthecon-
envelope (i= conv). It is also assumed that both layers vective layer is mass loss via magnetized SWs. Not only
rotate independently as rigid bodies (i.e. no differential does the mass leaving the surface of the star carry AM,
rotation). but in magnetically active stars the flow of chargedpar-
The convective envelope is subject to two different ex- ticles is also coupled with the corotating magnetic field,
ogeniceffects: (1)tidalbreaking, ,and(2)lossofAM up to few to several tens of stellar radii. This leads to a
tid
via a magnetized SW . T lossofAMthatisseveralordersofmagnitudelargerthan
SW
To calculate , weTuse the formalism developed by that in stars without a convective envelope (Schatzman
tid
Hut(1981). AccTordingly,atargetstarofmassM and 1962).
targ
radius R , rotating at an instantaneous rate Ω and Although a successful, comprehensive, and self-
targ
affected by a secondary star of mass M in an orbit consistentmodelof magnetizedSW AM loss has notyet
field
with semimajor axis a, eccentricity e, and mean angular been developed, a semi-empirical formula, developed by
velocity n, feels an effective tidal torque given by Kawaler (1988) and modified by Chaboyer et al. (1995),
succeeds at producing results consistent with observa-
tionsforalargerangeofstellarmassesandages. Accord-
3k I M 2 R 6 ingly, the torque exerted by the magnetized SW scales
2 field targ
= (9) withangularvelocityΩ,stellarmassM ,andradiusR ,
Ttid −κ2t (cid:18)M (cid:19) (cid:18) a (cid:19) × ⋆ ⋆
diss targ
9
following this earlycontractionisto integratethe angularvelocity
instead of the AM using
1/2 −1/2
TSW =KCΩmin(Ω,Ωsat)2 (cid:18)RR⊙⋆(cid:19) (cid:18)MM⊙⋆(cid:19) ddΩti = I1iddJti −ΩiddIti (16)
(11)
wheretheterm Ω (dI /dt)accountsforthecontraction
KC and Ωsat are two free parameters that can be (expansion) of t−heirespiective layer. It is important to
adjusted to reproduce the scale of observed rotational
stressthatalthoughthelargerchangesinI happendur-
rates and their distribution, respectively. In order to re- i
ingthePMS,wearealsointegratingEq. (16)duringthe
ducethenumberoffreeparametersinourcomprehensive
main sequence.
model, Ω is calculated following the scaling relation-
sat From a purely dynamical point of view this contrac-
ship
tiontermisassociatedwithtwodiscrepancies. Therapid
contraction of the star during the first stages of stellar
τ
conv,⊙
Ω =Ω (12) evolutioniscompoundedwiththegainofspecificAMby
sat ⊙
(cid:18) τ (cid:19)
conv accreting gas. Angular accelerationof the star may con-
tinue even to near breakup velocities (P 0.1 days).
where τ is the convective overturn time (see Section rot
conv ∼
Observations, however, show that the rotation rates of
5.2.2). This scaling relationship has proven to be useful
PMS stars are orders of magnitude slower (with periods
in reproducing the distribution of rotation periods for
of 2 10 days). Although still debated, the solution to
low-mass field stars (Irwin et al. 2011).
−
this discrepancy may rest on the assumption that stars
More recently, success in modeling the rotational rate
transferthisAMexcesstotheiraccretiondisk. Thisdisk
distributionofstarsinyoungclusterswasachieved(Matt
lockingpersists fora timescale τ 2 5Myr,ending
etal.2012;Gallet&Bouvier2013)usingasemianalytical disk
∼ −
with disk dissipation.
fit of MHD simulations to the originalmodel of Kawaler
The second discrepancy arises when considering the
(1988) along with a recent model for stellar mass loss
value and sign of the contraction term for the radiative
(Cranmer & Saar 2011). However, its application is still
core. In stellar evolution simulations, the core suddenly
restrictedto starswith mass nearlyidentical to the Sun.
forms at around 10 100Myr and grows to its final size
Ourinteresthereisinstarsrangingfrom0.2to1.05M ;
⊙ −
over a time an order of magnitude smaller. As a result,
see Table 1. A comparison between the results obtained
the moment of inertia of the core increases rapidly, po-
with the semi-empirical formula used here (Eq. 11) and
tentially producing a sudden rotational breaking of this
those obtained with the formula by Matt et al. (2012)is
layer. EvenafterconsideringtheexchangeofAMduring
left for a future work, but it is not expected to alter the
the growth of the core, as is done in Allain (1998), this
major conclusions of the current work.
sudden braking still occurs. Although unobservable, a
As the convective envelope loses AM, a difference in
sudden deceleration of the radiative core would produce
angular velocity between the envelope and the radia-
a signature in the evolution of the envelope and would
tive core is established. A variety of physical processes,
create a discrepancy with observations.
such as magnetic fields, hydrodynamical instabilities,
Tobe consistentwithpreviousresults,weassumethat
andgravitywaves,mayredistributeAMinthestellarin-
thecontractiontermforthecoreinEq. 16isthesameas
terior, reducing this difference with time. To model AM
that of the convectiveenvelope. An investigationof how
redistribution we follow, as is customary, the prescrip-
this apparent deceleration in the radiative core seems
tion by MacGregor& Brenner (1991), by estimating the
to be prevented is a critical matter in need of further
mutual torque due to the difference in rotation rates as
research.
given by
For each system studied here, numerical integrations
∆J of Eqs. (16) were performed for both stars in the bi-
∆J = (13) nary including their mutual tidal interaction. For that
|T | τ
ce purposewe takeasinputs the valuesofkeystellar struc-
The AM exchanged is ∆J = (I J turepropertiesasafunctionoftime(e.g. apsidalmotion
conv core
−
I J )/I , and τ is a free parameter called the constants,momentsofinertia,andconvectivezonethick-
core conv tot ce
core-envelope coupling timescale. ness), from stellar evolutionary models (Bressan et al.
Insummary,theAMoftheconvectiveenvelopeandthe 2012, 2013) as well as from interior structure models
radiative core of each star in the binary evolve following (Baraffe, 2014, personal communication).
the equations
5.2. Magnetic Activity
dJ Theultimatepurposeofcalculatinginstantaneousstel-
conv
= + + (14)
tid SW ∆J lar rotational periods is to calculate the magnetic activ-
dt T T T
ity as a function of time. Magnetic phenomena in the
dJ
rad
= . (15) atmospheres of cool stars are driven by the action of a
∆J
dt −T
dynamo in their convective zones that in turn is respon-
Themomentofinertiaofboththe convectiveenvelope sibleforproducingSWsandhigh-energyradiation(XUV
and the radiative core evolves in time and affects the emission).
rotational history of the whole star. PMS evolution is Progress in understanding and characterizing these
especially important in this respect. During PMS, stars processes in the Sun, allowed S. Cranmer and S. Saar
contractthe most. A pragmaticapproachto accountfor to develop a self-consistent model of SW acceleration
10
applicable to other cool stars (Cranmer & Saar 2011). a valid constraint for stars in the moderately separated
Their model accurately predicts stellar activity observ- binaries under consideration.
ables such as the average photospheric magnetic field At distances large enough from the binary or in very
strengthandmasslossratesasafunctionofseveralbasic disparate binaries (q 1), it is reasonable to assume
≪
stellar properties such as mass, radius, luminosity, and that the SW flux and dynamic pressure are simply the
rotational period. sum of the quantities produced by each star, i.e.
TheirpubliclyavailableroutineBOREASis appliedhere
in order to calculate the instantaneous mass loss rate of F F +F (21)
SW,bin SW,1 SW,2
each star in the binary system. For details on the input ≈
physics, assumptions, and free parameters used by the
models of Cranmer and Saar, refer to Cranmer & Saar PSW,bin PSW,1+PSW,2. (22)
≈
(2011).
For close orbiting planets, these simple assumptions
are expected to break down under realistic conditions in
5.2.1. SW
some binaries. Recently, the conditions under which the
Armed with the mass loss rate M˙ , the properties of interaction between the winds of binaries could strongly
the SW are calculated in a straightforwardmanner. We interact, rendering this approximation imprecise, have
assume that the wind reaches its terminal velocity vSW been studied using MHD simulations. The results of
at a distance rt from the stellar center, being equal to these simulations suggest that even in an extreme case
the local escape velocity: of solar-mass twins, the SW flow is only strongly mod-
ified at close circumbinary distances. Within the BHZ
2GM⋆ the simple approximationgivenin Eq. (21)is applicable
v = (17)
SW r r for the purposes of studying the plasma environment of
t
potentially habitable planets.
Adistancer =2.5R isassumedinordertoreproduce
t ⋆
the current average solar wind condition as observed at 5.2.2. XUV Emission
Earth distance.
One of the most detrimental effects that planets face
By mass conservation, the particle mean density as
is earlystellar activity. During the earlyhistory ofplan-
measured at a distance r from the star is given by
ets,thehigh-energyradiationfluxfarexceedsthatwhich
M˙ theyreceivelateron. InthecaseofEarthforexample,it
n = (18) hasbeen estimated (Guinan & Engle2009)that 4.5Gyr
SW µmp4πr2vSW agothe X-raysflux was10-100times largerthan present
Earthlevel(hereafterPEL)owingtosolarcoronalactiv-
where µ is the mean molecular weight of the wind parti-
ity.
cles and m is the proton mass. For a fully magnetized
p The effect that such flux has over time on planetary
SW µ=0.6 (Cranmer 2008; Cranmer & Saar 2011).
atmospheres ranges from simply a modification of the
This stream of charged particles continuously impacts
upper atmospheric chemistry (Tian et al. 2008; Segura
the atmosphere of planets, at a rate given by
et al. 2010; Hu et al. 2012, 2013; Hu & Seager 2014) to
rapid photoevaporation via induced heating of the exo-
F =n v . (19)
SW SW SW sphere(Lammeretal.2003;Lammeretal.2009,p. 399;
At the distance of the HZ, the wind is supersonic and Lammer et al. 2010; Zendejas et al. 2010). Both phe-
has a negligible thermal pressure. As a result, it exerts nomenacouldhaveverydetrimentaleffectsonplanetary
adynamicpressureoverplanetarymagnetospheresgiven habitability. Estimatingthefluxofhigh-energyradiation
by is thus an essential element in the assessment of habit-
ability of any planetary environment.
P =µm n (v2 +v2 ) (20) TheemissionofX-RayandEUVradiation(1-91.2nm)
SW p SW SW orb andtheirdependenceonstellarageandrotationalperiod
where v is the orbital velocity of the planet. have been extensively studied in the case of single-stars.
orb
The Cranmer & Saar model has been developed in or- Astronganticorrelationbetween ageandXUV luminos-
der to describe activity in single-stars. The previous ity has been observed (Ribas et al. 2005; Penz & Micela
assumptions concerning how to convert mass-loss rates 2008; Penz et al. 2008).
into SW properties, may work well in describing SWs Binary stars follow a different set of rules. First, ro-
for moderately spaced binaries, as well as isolated stars, tation and age are not necessarily correlated, especially
but the applicability of these models to binaries has not when the binary period is short (of the order of days)
beentested. Additionally,othereffectscouldarise,mod- orif the binary eccentricity is largerthanabout 0.1,ow-
ifying the underlying assumptions on which this model ing to tidal torques. Second, and as explained before,
is built. For example, a star could illuminate the atmo- strong magnetic interaction between the stellar compo-
sphere of the companion, thereby modifying the vertical nentsinthefirsttensofMyrcoulddriverotationalevolu-
atmospheric structure. Coronal X-ray heating may play tionandhenceactivitytowardvaluesthatareuncommon
a critical role in some cases. The acceleration due to in single-stars.
gravity is also modified by the presence of a close com- In spite of the most common recipes used to estimate
panion. Stellar wind shocks could also arise, modifying XUVlevelsasafunctionofstellarage(see,e.g.,Zuluaga
the simple model described herein. We assume that the et al. 2012), which will not be applicable in the case
acceleration mechanism working in single stars provides of binaries for the reasons given above, we use here an