Circumstellar habitable zones of binary-star systems in the solar neighbourhood

Abstract

Binary and multiple systems constitute more than half of the total stellar population in the solar neighbourhood. Their frequent occurrence as well as the fact that more than 70 planets have already been discovered in such configurations – most notably the telluric companion of α Cen B – make them interesting targets in the search for habitable worlds. Recent studies have shown that despite the variations in gravitational and radiative environment, there are indeed circumstellar regions where planets can stay within habitable insolation limits on secular dynamical time-scales. In this paper, we provide habitable zones for 19 near S-type binary systems from the Hipparcos and Washington Double Star catalogue (WDS) catalogues with semimajor axes between 1 and 100 au. Hereby, we accounted for the combined dynamical and radiative influence of the second star on the Earth-like planet. Out of the 19 systems presented, 17 offer dynamically stable habitable zones around at least one component. The 17 potentially habitable systems contain 5 F, 3 G, 7 K and 16 M class stars. As their proximity to the Solar system (d < 31 pc) makes the selected binary stars exquisite targets for observational campaigns, we offer estimates on radial velocity, astrometric and transit signatures produced by habitable Earth-like planets in eccentric circumstellar orbits.

INTRODUCTION

The discovery and confirmation of terrestrial bodies orbiting other stars (e.g. Léger et al. 2009; Borucki 2011; Borucki et al. 2012; Dumusque et al. 2012) have generated enormous public as well as scientific interest. It has shown that after a mere two decades of exoplanetary research finding potentially habitable worlds around other stars seems to be almost within our grasp. Close-by stars and stellar systems are thereby premium targets, as they tend to offer reasonable signal-to-noise ratio (S/N) values for photometry and radial velocity (RV) as well as comparatively large astrometric (AM) amplitudes (Beaugé, Ferraz-Mello & Michtchenko 2007; Guedes et al. 2008; Malbet et al. 2012; Eggl, Haghighipour & Pilat-Lohinger 2012a). As more than half of the stars in the solar neighbourhood are members of binary or multiple systems (Kiseleva-Eggleton & Eggleton 2001), it is not surprising that more than 70 planets in or around binary stars have been discovered (Schneider et al. 2011) despite the current observational focus on single-star systems. Even though NASA’s Kepler mission has been quite successful in finding circumbinary planets (e.g. Doyle et al. 2011; Orosz et al. 2012; Welsh et al. 2012), we will focus on binary-star systems with potential circumstellar habitable zones (HZs) in this study. In fact, most of the planets discovered in double stars are in these so-called S-type configurations (Rabl & Dvorak 1988; Roell et al. 2012), where the planet orbits one star only. The telluric companion of α Cen B is such an example (Dumusque et al. 2012).

An interesting question in this regard is doubtlessly: can S-type binary stars harbour habitable worlds? Already Huang (1960) and Harrington (1977) and more recently Forgan (2012) investigated the effects such configurations have on the insolation hypothetical planets would receive. Eggl et al. (2012b) (in the following referred to as EG12) were able to derive analytic expressions to find HZs in binary-star systems unifying dynamical and radiative balance models for S-type binary star–planet systems. While the exact manner in which planets form in tight binary-star systems is still hotly debated in astrophysical literature – see, for instance, Müller & Kley (2012), Batygin, Morbidelli & Tsiganis (2011), Paardekooper & Leinhardt (2010), Thebault (2011) and references therein, the discovery of α Cen B b has made the existence of terrestrial planets in S-type binary-star systems an observational fact. Opinions still differ on whether it is theoretically possible that planets in α Centauri’s HZs can form on stable orbits. Even though classical N-body simulations with best case accretion scenarios seem to be able to produce terrestrial planets near the HZs of the α Centauri system (Guedes et al. 2008; Quintana & Lissauer 2010), Thébault, Marzari & Scholl (2009) and Thébault, Marzari & Scholl (2008) concluded that even when gas drag is included the encounter velocities between kilometre-sized planetesimals would lead to erosive collisions, thus making constant accretion unlikely. However, in their model they did not include a self-consistent evolution of the gas disc, nor did they consider planetesimal self-gravitation or re-accretion of collisional debris. Paardekooper & Leinhardt (2010) used a self-consistent disc model with planetesimals. They were able produced accretion friendly scenarios when the collision frequency was sufficiently high to prevent orbital dephasing. Other possible solutions to the problem of high encounter velocities range from including planetesimal and embryo migration (Payne, Wyatt & Thébault 2009) over mild inclination of planetesimal discs with respect to the binary’s orbit (Xie, Zhou & Ge 2010) to more realistic radiative modelling of the system’s gaseous disc (Müller & Kley 2012).

Eggl et al. (2012a) show that even if additional Earth-like planets in α Centauri do exist, it is not an easy task to find them given current observational limitations in RV resolution. The RV signal semi-amplitude of α Cen B b was near the current edge of feasibility with δ RV ≃ 50 cm s⁻¹, whereas accuracies lower than 10 cm s⁻¹ would be necessary to discover telluric planets in α Cen B’s HZs. Astrometry is not much more helpful in this case, as the necessary AM amplitudes to detect habitable worlds in α Centauri will only be available near the end of the Gaia mission’s lifetime (Hestroffer et al. 2010).

In this study we tackle the question whether there are S-type systems in the solar neighbourhood that might make for easier targets. For this purpose we select 19 S-type binary systems from ‘The Washington Visual Double Star Catalog’ (WDC) (Mason et al. 2012) with well-determined stellar parameters that lie within a distance of 31 pc from the Solar system, and calculate HZs for each stellar component using the analytic method presented in EG12. We provide estimates on the RV and AM root mean square (rms) signal strengths expected for an Earth-like planet orbiting at the borders of a system’s HZs. Furthermore, we present likely transit depths (TDs) for potentially transiting habitable planets in co-planar S-type double-star systems.

This paper is structured as follows. First, we will discuss the selection criteria for the 19 systems investigated (Section 2). After a brief summary of the main factors that determine habitability for terrestrial planets in binary-star systems (Section 3), the issue of dynamical stability of planets in such configurations is addressed in Section 4. Our results – tables with HZ borders and signal strength estimates – are presented and discussed in Sections 5 and 6. Current problems in modelling tidal-locking of planets in binary systems are mentioned in Section 7. A summary (Section 8) concludes this study.

SELECTION OF BINARY-STAR SYSTEMS

We preselected all detached binaries with semimajor axes 1 < a_b < 100 au using the stellar orbital parameters provided in the WDC, in order to find suitable S-type systems in the solar neighbourhood where Earth-like planets in HZs could be detectable. Hereby, we only considered systems within a distance of d < 31 pc from our Solar system as determined by the Hipparcos mission (van Leeuwen 2007). Together with the prerequisite that the binaries’ orbital elements had to be available, the aforementioned restrictions reduced the number of admissible double-star systems to 313. Furthermore, only double-star configurations with known spectral types of both components were used. Peculiar spectra that might have been classified incorrectly by Hipparcos such as HIP 17544 and 73695 were also excluded, narrowing the set of candidate systems from 313 to 35. The ultimate selection criterion consisted of calculating the binaries’ periods using bolometric luminosity derived masses together with the semimajor axes given in WDS and comparing them to the observed binary periods. The stellar bolometric luminosities and masses required for this purpose were derived as follows: with the distances available through Hipparcos data the systems’ absolute visual magnitudes could be calculated. In order to assess the bolometric luminosities of the binary sample, we performed bolometric corrections (BCs) of the absolute visual magnitudes using the polynomial fits by Flower (1996). The required effective temperatures were estimated via spectral type and luminosity using the ATLAS9 catalogue of stellar model atmospheres (Castelli & Kurucz 2004). We then calculated the binaries’ periods using the masses derived via the mass–luminosity relations given in Salaris & Cassisi (2005). Only those systems whose derived periods did not deviate more than 11 per cent from the observed periods were selected for the final sample. Stellar and orbital parameters for the final set of 19 S-type binary systems are presented in Table 1.

In the next section we will briefly discuss the main points on how to determine HZs for these S-type binary systems.

HABITABILITY OF EARTH-LIKE PLANETS IN S-TYPE BINARY-STAR SYSTEMS

The most pronounced difference between determining classical HZs and HZs for Earth-like planets in binary-star systems lies in the assumption that planetary orbits are basically circular. In fact, the well-known borders defined by Kasting, Whitmire & Reynolds (1993) are built on the premises that planetary insolation will change only on stellar evolutionary time-scales. Thus, the planet is thought to remain more or less at the same distance from its host star on a circular orbit. This assumption is implicitly made in almost all recent works (e.g. Kaltenegger & Sasselov 2011; Pierrehumbert & Gaidos 2011; Kane & Gelino 2012). However, in three-body systems, such as the planet–binary-star configurations we are investigating, gravitational interactions will alter the planetary orbit.

Perturbation theory of hierarchical triples predicts that the orbit of the inner pair – in our case host star and planet – will experience significant alterations in its eccentricity, whereas its semimajor axis remains almost constant (Marchal 1990; Georgakarakos 2002, 2003). For nearly equiplanar systems, the influence of planetary inclination and ascending node to the overall dynamics can be considered small; they will be neglected in what follows. Even though there may be short-periodic variations, some important changes in a planet’s orbit happen also on secular time-scales. Secular periods are usually much larger than the planet’s orbital period. However, they are a lot smaller than stellar evolutionary time-scales for detached binary systems with semimajor axes a_b < 100 au. It is thus necessary to include the effects of changing planetary orbits in our estimates regarding HZs within binary-star environments. In their work, EG12 confirmed that variations in the planet’s orbit are even more important for changes in its insolation than the additional radiation form the second star! The only exceptions to this rule are systems where the second star is much more luminous than the planet’s host-star (L_B/L_A > 4, where binary component A is the planet’s host star in this case). Therefore, a planet’s eccentricity is a dominating factor in determining habitability. Yet, how eccentric can a planetary orbit become, in order to still allow for habitability?

Williams & Pollard (2002) concluded that an Earth-like atmosphere together with surface oceans can buffer the harsh changes between high insolation at periastron and long cold phases near apoastron up to eccentricities of e_p ≈ 0.7, as long as the average insolation is comparable with the current insolation of the Earth. Although planetary eccentricities of such magnitude are usually not reached in close S-type set-ups (EG12), the region where the planet remains within classical insolation boundaries is still strongly impacted. In order to distinguish orbital zones that are only habitable ‘on average’ and zones where the planet will never exceed classical insolation limits, EG12 introduced three types of HZs for binary-star systems.

Permanently habitable zone (PHZ). The PHZ is the region where a planet stays within habitable insolation limits for all times, despite the changes its orbit experiences due to gravitational interactions with the secondary. For this study, we have chosen the classical runaway/maximum greenhouse insolation limits (KHZ) as defined by Kasting et al. (1993) and Underwood, Jones & Sleep (2003).

Extended habitable zone (EHZ). The binary–planet configuration is still considered to be habitable when most of its orbit remains within the HZ boundaries. This is true if the average received insolation plus one standard deviation does not put the planet beyond KHZ insolation limits.

Averaged habitable zone (AHZ). Even an elevated planetary eccentricity (e < 0.7) may not be prohibitive for habitability since the atmosphere acts as a buffer (Williams & Pollard 2002), if the time-averaged insolation stays within habitable limits. The AHZ represents such regions.

For details on the definition and calculation of PHZ, EHZ and AHZ we refer the reader to EG12. We use the interpolation formulae given in Underwood et al. (2003) to calculate effective insolation values for the selected stellar types. After a brief discussion concerning aspects of dynamical stability, the application of the proposed classification scheme to the 19 selected binary-star systems will be presented in the next section.

DYNAMICAL STABILITY OF CIRCUMSTELLAR PLANETS IN BINARY STARS

As was briefly mentioned during the introduction, there are many open questions regarding the formation of planets in double-star environments (Thebault 2011). However, once formed a planet can survive in the dynamically stable region around one of the binary components – a fact proven by observed planets in S-type binary configurations (Dumusque et al. 2012; Giuppone et al. 2012; Roell et al. 2012). If the necessary dynamical prerequisites are fulfilled, even both stars can harbour planets. Generalized dynamical investigations such as Holman & Wiegert (1999), Pilat-Lohinger & Dvorak (2002), semi-analytical (Pichardo, Sparke & Aguilar 2005) or analytical approaches (Szebehely & McKenzie 1977; Eggleton 1983) can be used to determine regions where a test-planet can remain on a stable orbit on secular dynamical time-scales. As the set-up used in this work consists of a planar binary – Earth configuration, the restricted three-body approach used in the articles mentioned above can be considered a reasonable approximation. We will apply the numerical fit by Holman & Wiegert (1999) and results by Pilat-Lohinger & Dvorak (2002) to find critical semimajor axis for circumstellar motion.

RESULTS

The different HZs discussed in Section 3 are presented for a fictitious Earth-like planet in each of the selected double-star systems (Fig. 1). The region of instability (striped) is also marked. The left-hand graph of Fig. 1 represents HZs around the primary (S-type A), and the right-hand graph shows HZs around the secondary (S-type B) (Whitmire et al. 1998). Black (red online) denotes regions which are non-habitable due to excessive or insufficient insolation, dark grey (yellow online), medium grey (green online) and light grey (blue online) represent the AHZ, EHZ and PHZ, respectively. Dashed and full ‘I’ symbols give the inner and outer borders of the classical HZ as defined by Kasting et al. (1993) and Underwood et al. (2003) (KHZ). EG12 found a good correspondence between the KHZ and the AHZ, which is also mirrored in the results at hand. Exceptions are the systems HIP 58001 and 101916 where the more luminous companion shifts the HZs of the less luminous one considerably. Out of the 19 selected systems, 17 permit Earth-like planets in HZs on dynamically stable orbits around at least one stellar component. In total, the 17 habitable systems feature 16 M, 7 K, 3 G and 5 F class stars. Even if the all F and M class stars were to be excluded from the list of hosts for HZ – either because of their comparatively short lifespans (Kasting et al. 1993) or tidal and radiative effects (see Section 7) – more than 26 per cent of the stars in this sample would be capable of sustaining habitable planets on secular dynamical time-scales. If the stars’ mass loss via stellar winds is negligible, and no cataclysmic events occur (Veras & Tout 2012), habitability might be given even for stellar evolutionary time-scales.

A detailed listing of HZ borders as well as expected RV and AM signal strengths produced by a terrestrial planet in the selected systems is presented in Tables 2–4. Maximum and rms¹ signal strengths have been calculated following Eggl et al. (2012a). The corresponding equations are repeated in Appendix A for the reader’s convenience. Comparing AM and RV signal strengths one can see that – current observational equipment assumed – RV seems to stand a better chance to find Earth-like planets in HZs of nearby double stars. With the discovery of α Cen B b the currently feasible RV resolution is approximately 50 cm s⁻¹. For the detection of habitable planets in the α Centauri system, however, semi-amplitudes around 10 cm s⁻¹ would be required (Eggl et al. 2012a). Possible candidate systems such as HIP 14699, 30920, 106972, 114922 or 116132 would offer better conditions for finding habitable Earth analogues via RV than α Centauri does.

As nine out of the 17 potentially habitable systems feature M stars, it is worth mentioning that determining the effective insolation a terrestrial planet receives might not be enough to claim habitability. In fact, Lammer et al. (2011) are convinced that the potentially elevated level of X-ray and extreme ultraviolet (EUV) radiation in M stars might lead to a different atmospheric evolution of an Earth-like planet in an M-star’s HZ, thus preventing the existence of life as we know it. Ultimately, direct observation of the interaction between stellar and planetary atmospheres will be necessary to determine to which degree planets can remain habitable in the vicinity of M-type stars. The proposed transit spectroscopy mission ECHO (Tinetti et al. 2012) can be a step in this direction, although currently only super-Earths down to 1.5 r_⊕ around K–F stars are planned to be observed. With RV signal amplitudes of ≈ 5–12 cm s⁻¹ for potentially habitable planets in systems containing Sun-like G stars (HIP 31711 and 84425), our estimates are comparable to those for α Centauri presented in Eggl et al. (2012a) and Guedes et al. (2008). Detecting planets around Sun-like stars would therefore require a considerable amount of dedicated observation time (Guedes et al. 2008; Dumusque et al. 2012).

The AM amplitudes determined for the 19 systems at hand are well below 1 μas. This will put the systems in consideration even beyond the reach of ESA’s Gaia mission (Hestroffer et al. 2010). However, recently Malbet et al. (2012) proposed the Nearby Earth Astrometric Telescope (NEAT) which would be capable of resolving AM motion down to 0.05 μas at a 1σ accuracy level. This instrument would be able to identify habitable planets in most of the presented binary-star systems. Such a mission would indeed be valuable, since AM does not only favour planet detection in binary configurations with Sun-like components – their HZs are further away from their host stars thus producing larger AM amplitudes – it would more importantly grant observational access to all the planet’s orbital parameters. Especially mutual inclinations are of interest in this case, as they could provide answers to many important problems regarding planet- formation as well as migration in binary-star systems (Wu & Murray 2003; Batygin et al. 2011; Thebault 2011).

POTENTIALLY TRANSITING SYSTEMS

TIDAL LOCKING

The lack of accurate analytical tools to study the influence of tidal interactions in planar S-type configurations as well as the wealth of possible final states depending on the system’s initial conditions put a detailed analysis of the planet–binary system’s tidal evolution beyond the scope of this work.

SUMMARY

Applying the analytic methods presented in Eggl et al. (2012a, EG12), we have shown that 17 out of 19 binary-star systems with well-determined stellar and orbital parameters close to the Solar system allow for dynamically stable Earth-like planets in circumstellar HZs. Four of these habitable systems feature F, three feature G, six feature K and nine feature M class stars. Not surprisingly, M–M binary constellations offer the best chances for detecting planets in HZs via RV observations. However, determining habitability in M star doublets may require additional considerations such as tolerable stellar X-ray and EUV fluxes (Lammer et al. 2011) or the system’s potential for tidally locking the planet to its host star (see Section 7). Habitable planets in systems featuring G-type stars have RV amplitudes comparable to the ones found for α Centauri AB (Guedes et al. 2008; Eggl et al. 2012a). The systems HIP 14699, 30920, 106972, 114922 or 116132 would be promising candidates to search for terrestrial planets in their HZs, as they offer best case RV semi-amplitudes comparable to α Centauri B b (Dumusque et al. 2012). Four of the 17 systems would allow for transiting planets in HZs, which could be detected using current technology. Their mid-TDs were estimated to lie between 44 and 369 ppm with planetary periods ranging from 235 to 476 d. AM signal amplitudes for Earth-like planets in all the investigated systems’ HZs are, in contrast, well below 1 μas. Therefore, dedicated missions such as NEAT (Malbet et al. 2012) will be required in order to detect habitable worlds in binary stars via astrometry. A sample of 19 systems does not offer the possibility to construct a reasonable statistical analysis on the number of potentially habitable binary-star systems in the solar neighbourhood. More precise data on spectral types and orbital elements of nearby double stars are required in this respect. Nevertheless, our findings indicate that including binary-star systems with 1 < a_b < 100 in observational campaigns has the potential to enhance our chances of finding habitable worlds.

The authors would like to acknowledge the support of FWF projects S11608-N16 (EP-L and SE), P20216-N16 (SE, EP-L and BF) and P22603-N16 (EP-L and BF). SE and EP-L would like to thank the Institute for Astronomy and NASA Astrobiology Institute at the University of Hawaii for their hospitality during their visit when some of the ideas for this work were developed. NH acknowledges support from the NASA Astrobiology Institute under Cooperative Agreement NNA09DA77A at the Institute for Astronomy, University of Hawaii, and NASA EXOB grant NNX09AN05G. SE acknowledges the support of University of Vienna’s Forschungsstipendium 2012. This research has made use of the Washington Double Star Catalog maintained at the U.S. Naval Observatory.

REFERENCES

APPENDIX A: MAXIMUM AND rms SIGNAL AMPLITUDES

In a similar manner we can use the formalism applied in Pourbaix (2002) to determine maximum AM signal strengths: