Dynamics and Habitability in Binary Star Systems
CComplex Planetary SystemsProceedings IAU Symposium No. 310, 2014Z. Knezevic & A. Lemaˆıtre c (cid:13) Dynamics and Habitability in Binary StarSystems
Siegfried Eggl , Nikolaos Georgakarakos and Elke Pilat-Lohinger IMCCE, Observatoire de Paris, 77 Avenue Denfert-Rochereau, F-75014, Paris, Franceemail: [email protected] Higher Technological Educational Institute of Central Macedonia, Terma Magnesias, Serres62124, Greeceemail: [email protected] University of Graz, Institute of Physics, IGAM, Universit¨atsplatz 5, 8010 Graz, Austriaemail: [email protected]
Abstract.
Determining planetary habitability is a complex matter, as the interplay between aplanet’s physical and atmospheric properties with stellar insolation has to be studied in a selfconsistent manner. Standardized atmospheric models for Earth-like planets exist and are com-monly accepted as a reference for estimates of Habitable Zones. In order to define Habitable Zoneboundaries, circular orbital configurations around main sequence stars are generally assumed. Ingravitationally interacting multibody systems, such as double stars, however, planetary orbitsare forcibly becoming non circular with time. Especially in binary star systems even relativelysmall changes in a planet’s orbit can have a large impact on habitability. Hence, we argue that aminimum model for calculating Habitable Zones in binary star systems has to include dynamicalinteractions.
Keywords. habitability, binary stars, exoplanets, celestial mechanics
1. Introduction
One of the most intriguing aspects of exoplanet science is the prospect of finding worldsaround other stars that might be capable of hosting life as we know it. This translates intoa search for terrestrial planets in the so-called Habitable Zones (HZs), i.e. circumstellarregions where an Earth-analog is capable of sustaining liquid water on its surface. Findingplanets in such zones does not automatically mean that they are habitable, though. Thecomplex interplay between insolation, atmosphere, lithosphere and hydrosphere necessi-tates a determination of most planetary, stellar and orbital properties in order to judgepotential habitability. Hence, each newly discovered candidate has to be assessed on anindividual basis. This, of course, raises questions on the purpose and usefulness of the HZconcept. Yet, we believe that providing planet hunters with guidelines on where to lookfor potentially habitable worlds remains important, as long as observational resources arelimited. This implies that predicted HZ borders have to be translatable into detectabilitydomains for the respective exoplanet detection methods. HZ estimates should, therefore,contain reasonably detailed assumptions on the physical processes underlying planetaryhabitability. We argue, for instance, that dynamically induced changes in a planet’s or-bit can substantially change habitability conditions. If quantifiable, they should not beneglected in HZ calculations.
2. Insolation and Orbital Dynamics
So far, considerable efforts have been spent on investigating climatic stability of Earth-like planets leading to largely accepted estimates on the amount and spectral distribution1 a r X i v : . [ a s t r o - ph . E P ] D ec S. Eggl, N. Georgakarakos & E. Pilat-Lohinger
Figure 1. left:
Insolation variability in the two body problem Sun + Earth for mutual orbitswith various eccentricities. mid:
A habitability map (HM) showing different kinds of HabitableZones for an Earth-twin orbiting a Sun-like star on constant orbits with various semi-major axesand eccentricities. The different shades denote: PHZ, EHZ, AHZ and non-habitable regions. Theblack vertical lines correspond to the standard CHZ borders after Kasting et al. (1993) whilethe shaded HZs have been calculated using the values by Kopparapu et al. (2014). One can seethat the PHZ and EHZ decrease rapidly with mounting planetary eccentricities while the AHZremains practically constant up to high e planet values. The difference between Kasting’s andKopparapu’s HZ borders ( e planet = 0) also shows the importance of a classification scheme thatcan adapt to alterations in the climate model. right: A concept of the proposed HZ scheme thatincludes information on the variability of planetary insolation. of insolation that can render a world uninhabitable (Kasting et al. 1993; Selsis et al. 2007;Kopparapu et al. 2013). Recent so-called ”effective insolation” limits can be found, forinstance, in Kopparapu et al. (2014). Naturally, globally averaged climate models suchas used by the previously named authors cannot account for all effects (e.g. Wang et al.2014; Leconte et al. 2013), but they can be considered a reasonable first approximationfor Earth-like planets that are far from the tidal-lock or tidal-heating regime. Alas, HZborders can be calculated by solving the simultaneous equations:
S/I (cid:54)
S/O (cid:62) , leading to r { I,O } = (cid:18) L (cid:63) πS c { I, O } (cid:19) / , (2.1)where S is the insolation at the top of the atmosphere, L (cid:63) is the luminosity of thestar, I = S innereff and O = S outereff denote the effective insolation limits for the innerand outer edge of the HZ, and S c = 1367 [ W/m ] refers to the Solar constant. For theSun and an Earth-like planet Kopparapu et al. (2014) predict I ∼ .
11 and O ∼ . r from the host star: r I ∼ .
95 au and r O ∼ .
67 au. Equation (2.1) describes a spherical shell around the hoststar where planets can populate orbits that respect the insolation limits necessary forhabitability. Yet, what if the planet leaves this shell from time to time? This may happenwhen the planet’s orbit is elliptic. Then, the top of the atmosphere insolation can varyconsiderably with time, see Figure 1. Williams & Pollard (2002) could show that planetswith Earth-like oceans can compensate climatic extremes due to excursion outside theclassical HZs (henceforth CHZ, not to be confused with the Continuous Habitable Zone),as long as the average insolation stays within habitable limits. Later studies indicate,however, that the role of planetary eccentricity and its influence on insolation cannoteasily be discarded (e.g. Spiegel et al. 2010; Dressing et al. 2010). We, thus, propose away to include available information on the variability of planetary insolation directlyinto habitability considerations. ynamics and Habitability circumstellar planet (S-type) circumbinary planet (P-type) Figure 2.
PHZ, EHZ, AHZ, non-habitable and dynamically unstable regions (upper diagonalareas) are shown for a G2V-G2V S-type system with a binary semi major axis of a b = 10 au( left ), and a set of G2V-G2V P-type systems on initially circular orbits with different semi-majoraxes ( right ). The coloring is the same as in Figure 1. The borders of the expected CHZ (to getclassical estimates for P-type systems the radiation of both stars was combined in the binary’sbarycenter) are denoted by vertical lines. The white curves indicate analytical estimates for theextent of the PHZ. Effective insolation values by Kasting et al. (1993) were used. Evidently, theinjected planetary eccentricities grow with the binary’s eccentricity leading to a decrease in thewidth of the PHZs. Even for planets around binaries on circular orbits the harsh restrictions inthe PHZ become evident with growing semi-major axis of the binary star.
3. A Minimum Dynamical Model for HZs
Our aim is to acquire self consistent HZ estimates with a minimum of complexity thatstill retain the relevant physics. To this end we use the effective insolation limits of aglobally averaged atmosphere model, where variations in the planet’s rotation state canbe ignored, as long as its atmospheric properties do not change radically. Alterations inthe activity of the star could be included in theory, but they are difficult to model andshall be neglected for the moment. In such a scenario, changes that are related to theplanet’s orbit can be considered the dominating cause for insolation variability. In orderto include such information into our HZ model, we follow Eggl et al. (2012) and introducethe concepts of the Permanently (PHZ), Extended (EHZ) and the Averaged HabitableZones (AHZ), see Figure 1. The PHZ is the region where a planet always stays within theeffective insolation limits ( I , O ), i.e. S/I (cid:54)
S/O (cid:62)
1. This is the ”classical” defi-nition of a HZ. The EHZ allows parts of the planetary orbit to lie beyond the classicalHZ: (cid:104)
S/I (cid:105) t + σ I (cid:54) (cid:104) S/O (cid:105) t − σ O (cid:62)
1, where (cid:104) S (cid:105) t denotes the time-averaged effec-tive insolation and σ the effective insolation variance. High planetary eccentricity maynot be prohibitive for habitability since the atmosphere can act as a buffer. Consequently,the AHZ encompasses all configurations that support the planet’s time-averaged effec-tive insolation to be within classical limits, e.g. also orbits with very high eccentricities: (cid:104) S/I (cid:105) t (cid:54) (cid:104) S/O (cid:105) t (cid:62)
1. Figure 1 shows a realization of this classification scheme foran Earth-like planet orbiting a Sun-like star.
4. Habitable Zones in Binary Star Systems
The possible existence of terrestrial planets in and around binary star systems (Hatzes2013; Dumusque et al. 2012) has rekindled the scientific community’s interest in deter-mining Habitable Zones (HZ) in and around binary star systems (Forgan 2012, 2014;Kane & Hinkel 2013; Haghighipour & Kaltenegger 2013; Kaltenegger & Haghighipour2013; Eggl et al. 2012, 2013b; Cuntz 2014; Jaime et al. 2014). Given the strong gravi-tational perturbations planets experience in such environments, significant variations in S. Eggl, N. Georgakarakos & E. Pilat-Lohingerplanetary orbits can be expected. Even if planets formed on circular orbits, for instance,the interaction with the binary would force the planet’s orbital eccentricity become non-zero over time. As was shown in e.g. Eggl et al. (2012) the ’momentary’ HZ for binary starsystems are solutions of the two simultaneous planetary insolation equations normalizedwith respect to effective insolation limits. In compact notation that is¯ S I (cid:54) S O (cid:62) , where ¯ S ( t ) { I,O } = N (cid:88) j =1 L j πS c { I j , O j } r − j ( t ) . (4.1)Here I j and O j denote the respective effective insolation limits that serve as spectralweighting factors and L j are the stellar luminosities; ¯ S { I,O } is the normalized total inso-lation at the inner ( ¯ S I ) and outer ( ¯ S O ) border of the combined HZ, and r j ( t ) representthe time dependent planet-to-star distances. For double star systems we have N = 2.M¨uller & Haghighipour (2014) derived a similar expression. Note, however, that two dif-ferent sets of { a, b, c, d } parameters, one for the inner and one for the outer HZ borderare required to simultaneously fulfill the inequalities in their equation (5). MomentaryHZs depend on the current relative positions of the stars and the planet. They tend tofluctuate on orbital and secular timescales. Deriving observational constraints from timedependent HZs can, thus, be difficult (e.g. Eggl et al. 2013a). To include information onthe variability of planetary insolation, we apply the HZ scheme defined in section 2 andpredict planetary insolation and HZ limits analytically using recent results from perturba-tion theory (Georgakarakos 2003, 2005, 2009). This allows us to model the Earth-analog’sorbit and insolation evolution as a function of the system’s initial parameters (Eggl et al.2012). As can be seen in Figure 2, PHZ and EHZ and AHZ behave quite differently forvarious orbital configurations of a terrestrial planet in a binary star system. In all studiedbinary systems a clear decrease in the extent of the PHZ and EHZ can be observed forgrowing eccentricities of the binary’s orbit. Of course, not only the binary’s eccentricity,also its semi-major axis greatly influences the extent of permanently habitable regions.The right panel in Figure 2 shows that the PHZ can be considerably smaller than theCHZ for circumbinary planets (P-type), even if both the binary’s and the planet’s orbitare initially circular. The AHZ are mostly identical with CHZs. Only in regions close tothe system’s stability limits deviations in S-type as well as P-type systems occur. OurHZ estimates have, furthermore, been applied to well characterized S-type binary starsclose to the Solar System (Eggl et al. 2013b). It was found that most systems do notonly allow for habitability in an ’average sense’, they even retain zones of permanenthabitability.
5. Conclusions
The complex interplay between dynamical and radiative influences can turn the deter-mination of Habitable Zones (HZ) in gravitationally interacting systems into a challengingaffair. Flexibility and adaptability should, thus, be considered important properties ofany HZ calculation scheme. We argue that a minimum dynamical model should be in-cluded in HZ calculations to ensure realistic estimates. The proposed classification scheme(PHZ, EHZ and AHZ) retains information on the variability of planetary insolation whileproviding HZ boundaries that remain valid up to stellar evolution timescales. It is flexiblewith respect to changes in atmospheric models as well as the choice of the underlying dy-namical model. An alternative to time consuming numerical insolation calculations, theanalytical estimates presented in Eggl et al. (2012) can help to shed light onto the diversekinds of habitability occurring for terrestrial planets in gravitationally active systems.Their application to nearby S-type binary stars has shown that most of these systems ynamics and Habitability
6. Acknowledgments:
The authors would like to acknowledge the support of the Austrian FWF projectsS11608-N16 (sub-project of the NFN S116) and P22603-N16, the European Union Sev-enth Framework Program (FP7/2007-2013) under grant agreement no. 282703, as wellas the IAU Symposium no. 310 travel grant.