Finding the Drake Equation for Tidally Heated Exomoons P.W. Overgaauw Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Leiden, The Netherlands [email protected] October 2014 ABSTRACT In the past ten years several exoplanets have been directly imaged. However, none of these objects have rocky surfaces and the search for a rocky exoplanet that could potentially harbour life is still ongoing. Recent results indicate that it may be possible to directly image Tidally Heated Exomoons (THEMs) with existing and planned imaging facilities, potentially making THEMs the first ob- jects with rocky surfaces outside our own Solar System to be directly imaged. We present a search for observable THEMs in the Hipparcos Main Catalogue and in orbit around known RV (radial velocity) selected exoplanets. Using an analogue to the Drake Equation we propose an equation to estimate the number +2:2 of THEMs in a population of stars and find that there may be 10:7−2:0 THEMs around the 782 closest AFGKM Hipparcos stars. Furthermore, we investigate the requirements for directly imaging possible THEMs around 354 RV selected planets. We find that GJ 832 b, Epsilon Eri b and Beta Gem b are the most likely candidates. Unfortunately they would require considerable eccentricities and a large planet-moon mass fraction. We estimate lifetimes on Myr timescales for potential THEMs, reducing chances for direct imaging. 1. Introduction For thousands of years, since the first time men looked up at the stars in awe, we have wondered whether or not we are alone in the universe. Many have tried to answer this question through philosophy, religion and, more recently, through science. Many even claim they have a definitive answer. However, no tangible evidence has ever come to light. This lack of evidence made Enrico Fermi pose the question "Where is everybody?" in 1950, a question which was addressed in more detail by Hart(1975), and is now known as Fermi's Paradox. Fermi stated that given the large amount of planetary systems in the Milky Way { 2 { galaxy, assuming that over the course of billions of years technological civilizations could have evolved and that even at a slow pace of interstellar travel the galaxy can be completely colonized in tens of millions of years, we should have encountered some form of physical contact with other civilizations. However, this is not the case. To add to the discussion, Frank Drake (Drake 2013) formulated an equation in 1961 to estimate the number of active, communicative extraterrestrial civilizations in our galaxy. This equation is given by N = R∗ fp ne fl fi fc L, (1) · · · · · · where N is the number of civilizations in our galaxy with which radio-communication might be possible, R∗ is the average rate of star formation in our galaxy, fp the fraction of those stars that have planets, ne the average number of planets that can potentially sup- port life per star that has planets, fl the fraction of planets that could support life that actually develop life at some point, fi the fraction of planets with life that go on to develop intelligent life (civilizations), fc the fraction of civilizations that develop a technology that releases detectable signs of their existence into space and L the length of time for which such civilizations release detectable signals into space. This equation was mainly intended to stimulate scientific dialogue at the first SETI (Search for Extraterrestrial Intelligence) meeting, in which it succeeded. In the following decades, scientists have relentlessly searched for a glimpse of extraterres- trial life (e.g. Project Ozma; Drake 1961) and tried to define the parameters needed for a world to be able to sustain it. This led to the formulation of the Habitable (or Goldilocks) Zone (e.g. Kasting et al. 1993), the zone around a star where liquid water is possible on a planet's surface. The formulation of the HZ (Habitable Zone) led to several searches for Earth-size and larger planets in this zone (e.g. the Kepler Mission; Borucki et al. 2009), in the hope of finding a planet that may be able to sustain life. So far the Kepler Mission has confirmed close to a thousand exoplanets in more than 400 stellar systems1. The next step towards finding possible intelligent life would be to directly image a rocky planet. However, in order to directly image an exoplanet they need to be both young and at a large projected separation (at least tens of AU) from their primary. Rocky planets tend to be in close-in orbits around their parent star and so far only gaseous planet candidates have been directly imaged. Examples include the HR8799 system (Marois et al. 2008), β Pictoris b (Lagrange et al. 2010), HD 95086 b (Rameau et al. 2013) and HD 106906 b (Bailey et al. 2014). In recent years the possibility of and interest in the detection of exomoons have increased, 1http://kepler.nasa.gov/Mission/discoveries/ { 3 { especially in Tidally Heated Exomoons (THEMs). Peters & Turner(2013) argue that it is possible to directly image THEMs and that this may be easier to do than with giant exoplan- ets, THEMs do not suffer from the above mentioned limitations. Peters & Turner showed that moons can be heated to hundreds of degrees, giving them a large enough luminosity so they might be able to be detected in infrared. In addition, since THEMs may be hot even if they receive negligible stellar irradiation, they may be luminous in mid-infrared at large separations from the system primary, this reduces or even eliminates the requirement of high contrast imaging capabilities. Furthermore, Barnes & O'Brien(2002) found that Earth-like satellites of Jovian planets are plausibly stable for 5 Gyr around most stars with masses greater than 0.15 M and planet mass greater than 0.3 MJ . This means that THEMs may remain hot and luminous for periods of the order of a stellar main sequence lifetime and so could be visible around old stars as well as young ones. The main goal of this research is to estimate the number of THEMs around Hipparcos stars and then find THEM-candidates for direct imaging around nearby stars. In Section 2 we will discuss the parameters needed for an equation that can estimate the number of THEMs. In Section 3 we will search for the values of these parameters. In Section 4 we will try to find direct imaging candidates around nearby stars. We will end this report with a short discussion and conclusion. 2. Finding an equation for THEMs We propose the following equation for the number of THEMs in a collection of stars D = N fM ff fs fT . (2) · · · · Several parameters are important to take into account when formulating this equation. First and foremost is the number of stars, N, in the sample. The second term in our equation is the fraction of stars that have a massive planetary companion, fM . According to Peters & Turner(2013), if Io were as massive as Earth, it would be bright enough for the James Webb Space Telescope (JWST ) to detect at a distance of five parsec. This means that we need massive moons if we want to detect them at large distances. Moon systems of gaseous planets contain a similar fraction (1:1 10−4 × to 2:5 10−4) of their respective planets mass (Canup & Ward 2006). In order for a planet × to have a massive satellite, the planet itself needs to be massive. This second term also accounts for planets with stable orbits. Without the presence of a moon, a THEM is impossible. The third parameter in our equation { 4 { is, therefore, the fraction of massive planets that form moons, ff . For an exomoon to be able to be detected and confirmed, it needs to be in a stable orbit for a long time. Without this stability the moon might be removed from its orbit around its host. This removal can happen through several processes. Satellites induce a tidal bulge on their parent planet. This bulge perturbs the orbit of the satellite (e.g., Burns & Matthews 1986), causing migrations in the semi-major axis of the orbit. These migrations can lead to the loss of the satellite. For an isolated planet, the satellite's orbital semi-major axis can increase until it escapes or it can decrease, making the satellite spiral inward until it impacts the planet's surface (Counselman 1973). For planets that are not isolated, which are close enough to their parent star, stellar-induced tidal friction slows the planet's rotation. The resulting planet-satellite tides cause the satellite to spiral inward toward the planet (Ward & Reid 1973; Burns 1973). The fourth parameter in our equation, fs, is the fraction of exomoons that can remain in a stable orbit on a Gyr timescale. The final parameter in our equation is the fraction of moons that are heated through tidal interaction, fT . This is the most uncertain quantity in our equation and we will spend most of this paper on investigating it. 3. Values 3.1. N The stars in our sample are drawn from the Hipparcos Main Catalogue. This sample comprises 782 AFGKM stars with a distance of up to 20 parsec, giving our value for N. A distance of 20 parsec would potentially make the JWST able to detect planets with semi- major axis down to 7 AU in the M (4:7µm) band, which is close to the limit of current ∼ RV selected planets. Using their spectral types we estimate masses using Cox(2000). The stars have masses in the range 0:15 < M∗=M < 2:9.