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The Stability of Exomoons in the Habitable Zone

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The Stability of Exomoons in the Habitable Zone The Stability of Exomoons in the Habitable Zone Henrik Nordanger Lund Observatory Lund University 2014-EXA85 Degree project of 15 higher education credits May 2014 Supervisor: Melvyn B. Davies Lund Observatory Box 43 SE-221 00 Lund Sweden Abstract This is an analysis of all the planets at exoplanets.org, with the goal of finding out how many of these that could possibly have moons supporting life. I have first calculated the ranges of the habitable zones (HZ:s) for the stars in the archive, using the Runaway Greenhouse model for the inner limit, and the Maximum Greenhouse model for the outer limit, as presented by Kopparapu et al. (2013A). Then I investigate the stability of moons in systems with multiple planets, by inspecting the separation between the planets in terms of their the mutual Hill radii. I calculate how many habitable moons (0:3MC) individual planets can have, by first placing one at the edge of the planet's Roche lobe, and then another a variable number of mutual Hill radii further in, and then repeating until I reach the point where the moon or the planet fills its own Roche lobe. Finally, I attempt to fit hypothetical planets in the systems with 'gaps' in the habitable zone between discovered planets. A total of 19 confirmed planets were found in habitable zones, out of which 8 are in multiplanetary systems. Out of all 19, all except one were seemingly able to have at least one habitable moon, and a majority even able to have more than 10. Out of all confirmed planets, over 90% seemed to be able to have moons of habitable size, with almost 40% being able to have 10 or more. These numbers can be considered as upper limits, but even as such are quite optimistic as they rely on perfectly circular orbits, and are arrived at while ignoring destabilising phenomena such as mean-motion resonances. Popul¨arvetenskaplig Sammanfattning Detta arbete handlar om m¨ojligheternaatt finna beboeliga m˚anarsom kretsar kring plan- eter runt andra stj¨arnor¨anv˚aregen sol - s˚akallade exom˚anar. Sj¨alva unders¨okningen¨ar en analys av ¨over 5000 planeter fr˚anonlinearkivet exoplanets.org, f¨oratt se hur m˚angaav dessa som skulle kunna ha m˚anarsom st¨odjerliv. Aven¨ om majoriteten av fokuset i s¨okandet efter utomjordiskt liv har legat p˚aexoplan- eter ¨ans˚al¨ange,s˚afinns det ingen uppenbar anledning till varf¨orliv inte skulle kunna finnas p˚aen mindre kropp, som kretsar kring en s˚adanplanet. Dagens observationsme- toder ¨arinte tillr¨ackligt precisa f¨oratt uppt¨acka exom˚anari de flesta fall, men de villkor som m˚asteuppfyllas f¨oratt liv skulle kunna finnas ¨ari princip identiska med vad som skulle kr¨avas p˚aen exoplanet. De f¨orstaav dessa villkor ¨aratt planeten eller m˚aneninte kan ligga f¨orn¨araeller f¨or l˚angtifr˚ansin stj¨arna,d˚atemperaturen m˚astevara lagom h¨ogf¨oratt vatten ska kunna finnas i flytande form. Aven¨ om det inte ¨arabsolut s¨akert att vatten ¨arett krav f¨or liv, s˚avar denna unders¨okningfokuserad p˚aendast detta scenario. Detta krav ¨arn¨ara sammankopplat till begreppet beboelig zon, vilket helt enkelt ¨ardet omr˚aderunt en stj¨arna d¨artemperaturen kan vara lagom h¨ogf¨oreventuellt liv. Zonens utstr¨ackning beror p˚a stj¨arnansljusstyrka, och i mindre utstr¨ackning p˚adess f¨arg. Ju ljusare och r¨odareen stj¨arna¨ar,desto l¨angreifr˚anden m˚asteen kropp befinna sig f¨oratt kunna vara beboelig. En andra faktor att ta i beaktning ¨aratt m˚anen eller planeten beh¨over en atmosf¨ar. Utan en s˚adanskulle kroppens yta vara mycket og¨astv¨anlig,fr¨amstp˚agrund av str˚alning, och det faktum att temperaturskillnader mellan dag och natt skulle kunna vara mycket stora. F¨oratt bibeh˚allaen atmosf¨arm˚astekroppen vara tillr¨ackligt massiv f¨oratt gravita- tionellt h˚allakvar den, vilket i praktiken inneb¨aratt den m˚astevara betydligt st¨orre¨analla m˚anarnai solsystemet. N˚agonl¨agstamassa kr¨avsocks˚af¨oratt planeten eller m˚anenska vara geologiskt aktiv, vilket tros vara n¨odv¨andigtf¨orliv d˚adet bidrar med att ˚atervinna material p˚akroppens yta. Slutligen m˚astede ovan n¨amndavillkoren varit uppfyllda under en l¨angretid, s˚aatt eventuellt liv ska kunna ha f˚atten chans att uppst˚a.F¨oratt h˚allasig stabil tillr¨ackligt l¨ange,f˚arinte kroppens omloppsbana st¨orasf¨ormycket av andra objekt. Detta kan vara fallet om planeter eller m˚anarligger f¨orn¨aravarandra, vilket s¨attergr¨anserf¨orhur t¨att packat ett planetsystem kan vara, och f¨orhur m˚angam˚anarindividuella planeter kan ha. Genom att ta dessa faktorer i beaktning, visade det sig att totalt 19 planeter fr˚an exoplanets.org verkar ligga i beboeliga zoner, varav 18 verkade kunna ha minst en beboelig m˚anevar. 14 av dem verkade till och med kunna ha s˚amycket som 5 m˚anar var. Dock g¨allerdessa siffror endast i det ideala fallet d˚aalla m˚anarsomloppsbanor valts specifikt f¨oratt maximera stabiliteten i systemen, vilket s¨agerv¨aldigtlite om hur vanliga exom˚anar verkligen ¨ar. Till exempel visade unders¨okningenatt planeterna i solsystemet skulle kunna ha m˚angafler m˚anar¨ande faktiskt har. Contents 1 Introduction 6 1.1 Habitable Zones . .7 1.2 Mass Limits for Habitable Bodies . 10 1.3 Multiplanetary Systems . 11 1.3.1 Separations in Terms of Roche-, and Mutual Hill Radii . 11 1.3.2 Stability Timescales . 13 1.3.3 Adding Hypothetical 'Gap' Planets . 14 1.4 Systems With Moons . 16 1.4.1 Inner and Outer Limits for Moon Orbits . 16 1.4.2 The Procedure of Placing Moons . 17 2 Analysis 18 2.1 Results . 18 2.1.1 Planets in Habitable Zones . 19 2.1.2 Gap Planets . 22 2.1.3 Multiple Moons . 23 2.1.4 Applying the Approach to the Solar System . 25 2.2 Discussion . 26 2.2.1 Underestimations of Required Separations . 27 2.2.2 Capacities of Planets to have Massive Moons . 28 2.2.3 Comparison of Results for Confirmed and Unconfirmed Planets . 28 2.2.4 Accuracy of Habitable Zone Ranges, and Comparison with The Hab- itable Zone Gallery . 29 2.2.5 Missing Data . 30 2.2.6 Lower Mass Limit for Habitable Bodies . 30 2.2.7 Moons in very Small or Large Orbits . 31 3 Conclusions 32 A Luminosities and Radii of Zero-age-, and Terminal Main-Sequence Stars 36 B Analytic Solution for the Optimal Semi-Major Axis of Hypothetical 'Gap' Planets 39 2 CONTENTS CONTENTS C Methods for Discovering Exoplanets 40 3 List of Figures 1.1 Habitable Stellar Flux as a Function of Effective Stellar Temperature . .8 1.2 Habitable Zone Ranges as a Function of Stellar Mass . .9 1.3 Roche Lobes in a two-body System . 11 1.4 ∆-Factors for an Earth-Mass Planet Between Earth and Mars. 15 2.1 Illustratuion of All Results, in Numbers . 19 2.2 Confirmed Planets in Habitable Zones, by Stellar Mass . 20 2.3 Multiplanetary Systems with Discovered Planets in the Habitable Zone . 21 2.4 Multiplanetary Systems with Possible Gap Planets in the Habitable Zone . 22 2.5 Number of Possible Gap Planets as a Function of Required Planet Separation 23 2.6 Fraction of Planets that can have 0.0123MC-Moons . 24 2.7 Fraction of Planets that can have 0.3MC-Moons . 24 2.8 Fraction of Planets that can have 1MC-Moons . 25 A.1 Luminosity and Radius of Stars, as Functions of Stellar Mass . 37 A.2 Effective Temperature of Stars, as a Function of Stellar Mass . 38 4 List of Tables 1.1 Coefficients for the Runaway and Maximum Greenhouse Models . .8 1.2 Coefficients for Calculations of Time Before First Close Encounter . 13 2.1 Confirmed Planets in the Habitable Zone . 20 2.2 Results for the Solar system . 26 A.1 Coefficients for Calculations of Radii and Luminosities of Stars . 37 5 Chapter 1 Introduction In the investigation into the habitability of extrasolar objects, the main focus has long been on exoplanets, while exomoons have only been considered properly during the last few years. A reason for this is the obvious difficulty in detecting objects that do not primarily orbit a star, but rather a secondary object, while also being generally smaller than planets. At present time, the number of confirmed exoplanets are over 1000 (exoplanets.org), while only a few exomoon candidates exist (see, e.g., Bennet et al. 2014). Still, detection of extrasolar moons in the near future seems feasible, using current methods, and the transit method in particular (Hinkel & Kane 2011, Kipping et al. 2009). The conditions necessary to sustain life are in essence the same regardless of whether it is a planet or moon that is being considered. Assuming liquid water to be a requirement, an atmosphere must be present, and limits are set for what ranges of temperature and pressure that are of interest. The constraints on the temperature in turn mean that the body must lie within a certain range of distances from the star, in the so-called Habitable Zone (HZ). The body must also be massive enough to gravitationally keep the gas of its atmosphere from escaping, and for it to have plate tectonics. The latter is believed to be a required mechanism for life, as it recycles materials on the surface of the body. These conditions must then be upheld for quite some time to allow potential life to arise, meaning the orbit of the body must be fairly stable.
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