arXiv:1703.00878v3 [astro-ph.EP] 28 Jun 2017 ik-a,mn fwihobtMdaf [ M-dwarfs orbit which of many Milky-Way, oeta ehns o rnpriglf o rfo,the from, or [ to, a Earth life as transporting system Solar for own mechanism our (pansper- potential in Panspermia investigated another widely material? to been rocky consequences: has planet of transfer one the profound through from mia) with spread raises life this question could planets, TRAPPIST-1 immediate the of an one on exist sis) ehp,ee isgaue [ and, biosignatures atmospheres even de- possess perhaps, planets to ra- these observations whether further and termine out unique mass [ carrying a Earth a for represents the opportunity system of has that transiting them to TRAPPIST-1 equal of the nearly each reside is planets that and dius seven HZ, the the of ultra- within three since the [ remarkable transiting TRAPPIST-1 more planets star seven dwarf of cool discovery the (ii) to easier [ comparatively analyze are and been have they detect M-dwarfs ca- as of theoretically studied, - region water extensively the liquid - supporting of (HZ) pable zone habitable the in [ life exist habit- there supporting planet that of a known capable make that i.e. factors able, the of understanding ubro icvrdeolnt o ubrn nthe in numbering [ now thousands exoplanets total discovered the of with decades, number two past the in advances markable ytmaesprtdol by only separated are system ,tenaeteolntt h oa ytm[ system Solar the to exoplanet Centauri Proxima nearest the of the discovery over the advances b, (i) remarkable namely two year, past witnessed has stars ∗ † [email protected] [email protected] fcniin aorbefrteoii flf (abiogene- life of origin the for favourable conditions If h edo xpaeayrsac a inse re- witnessed has research exoplanetary of field The h erhfreolnt rudnab low-mass nearby around exoplanets for search The 9 – 13 .Tepaesi h Zo h TRAPPIST-1 the of HZ the in planets The ]. 1 lnt nteTAPS- ytm hs eut r loapp also are systems. results planetary These other in system. exomoons TRAPPIST-1 life because the whether s higher, in evaluating be of planets for to number metrics likely observational the also propose that is show planets we life-bearing compared ecology, consequence of planets theoretical a TRAPPIST-1 from As the models on case. more enhanced Earth-to-Mars magnitude is the ul of abiogenesis to orders the potentially compared orbiting is system planets panspermia seven that of find system discovered recently .Ti a enacmaidb better a by accompanied been has This ]. nacditrlntr asemai h RPIT1syst TRAPPIST-1 the in panspermia interplanetary Enhanced epeetasml oe o siaigtepoaiiyo i of probability the estimating for model simple a present We 2 avr-mtsna etrfrAtohsc,6 adnSt Garden 60 Astrophysics, for Center Harvard-Smithsonian .INTRODUCTION I. 4 ]. ∼ 10 avr nvriy 9Ofr t abig,M 23,USA 02138, MA Cambridge, St, Oxford 29 University, Harvard 1 8 10 onA alo colo niern n ple Sciences, Applied and Engineering of School Paulson A. John ]. ∼ 6 aial lnt nthe in planets habitable .Telte salthe all is latter The ]. 0 . 01 aav Lingam Manasvi 2 U eso times of tens AU, .I snwwell- now is It ]. 3 .Planets ]. 7 .Hence, ]. 5 ,and ], ,2, 1, ∗ n baa Loeb Abraham and alwti t rvttoa peeo nune[ influence they of that sphere provided wherein gravitational Y model its Planet simple by within a captured fall use are we rocks value Instead, actual the the cases. than most smaller in magnitude of orders many lntY and Y, Planet where lnt(lntY ta vrg itneof distance average an target at the Y) impact successfully (Planet that planet rocks of number The rmtehs lnt(lntX uigasnl vn is event single a during X) (Planet N planet host the from plan- other to analysis sup- our to systems. extend Weetary ecology and theoretical findings, abiogenesis. from our port models of upon probability draw the also higher sig- in much correspondingly increase a the the to nificant that leads within panspermia show of We panspermia probability for system. TRAPPIST-1 model quantitative simple panspermia system. that this Thus, hypothesize in to enhanced Mars. be inclined and would be Earth between would distance one the than less hsmodel, this et h rcino ok atrdprevent. per repre- captured (RHS) rocks right-hand-side of fraction the the on sents factor second The where hc ssrcl ai nyfor only valid strictly is which R lntXis, X Planet I IHPNPRI IPEMODEL SIMPLE A - LITHOPANSPERMIA II. y x e sspoeta h oa ubro ok ejected rocks of number total the that suppose us Let a proposing by possibility this explore we Here, avl paig emyexpect may we speaking, Naively n sueta h ok r mte isotropically. emitted are rocks the that assume and , sterdu fPae .Hwvr hsestimate, this However, Y. Planet of radius the is fteicesdrtso mirto.We immigration. of rates increased the of a ntae ypnpri nmultiple on panspermia by initiated was σ a y rco wr trTAPS-,and TRAPPIST-1, star dwarf tracool y steeetv rs-etoa rao lntY. Planet of area cross-sectional effective the is and ieyt cu nteTRAPPIST-1 the in occur to likely ial ohbtbeeolnt and exoplanets habitable to licable eistaserdadtenumber the and transferred pecies eageta h rbblt of probability the that argue we , oteSlrsse.B adopting By system. Solar the to abig,M 23,USA 02138, MA Cambridge, , trlntr asemai the in panspermia nterplanetary M M σ y y ⋆ 2, = stems ftehs star; host the of mass the is r h eimjrai n asof mass and axis semi-major the are N † y η xy = πa N x y 2 ·  4 2 πD M M σ ietimpact direct y y ⋆ xy 2  , 2 σ / em 3 y , = πR ol be would , D η y 2 xy where , xy 14 .In ]. san is from (2) (1) 2 amplification factor introduced to account for the effects the planetary system’s lifetime is required, which cannot of gravitational focusing, secular resonances, etc. Com- be quantified at this stage. bining Eqns. 1 and 2, we arrive at, Moreover, panspermia does not merely depend on the fraction of rocks transferred, but also on other factors. 2 2/3 Ny ay My Many of them have to do with the survival of microorgan- Pxy = =0.16 ηxy , (3) Nx Dxy   M⋆  isms during the processes of ejection from X, transit from X toY, andreentryonY [20]. Since the biological charac- as the cumulative fraction of rocks ejected from Planet X teristics of the organisms in question, one cannot quantify that will impact Planet Y. We also introduce the average these probabilities; even for Earth-based microbes, there transit time τxy that is given by, exist uncertainties [21]. But, if we assume that hvi is the same for Earth and most of the TRAPPIST-1 plan- Dxy ets, we see that the transit time, from Eq. 4, amongst τxy = , (4) hvi the TRAPPIST-1 habitable planets is about 100 times shorter than that of Earth-to-Mars. A higher value of where hvi is the average velocity of the ejected rocks. hvi, albeit one much lower that the escape velocity, could We can now attempt to calibrate this model in the reduce the transit time even further, for e.g. becoming Solar system, by choosing X and Y to be Earth and 4-5 orders of magnitude lower than the Earth-to-Mars Mars respectively. Substituting the appropriate values, value. Hence, if the probability of surviving the transit −5 we obtain PEM ∼ 0.75 ηEM × 10 . Upon comparison is inversely proportional to τxy, the survival probabilities with the older simulations carried out by Gladman et al. of microbes on the TRAPPIST-1 system could be several [10], Mileikowsky et al. [15], Gladman et al. [16], we find orders of magnitude higher. that ηEM ∼ 20−200. Similarly, if we use the recent value We emphasize that the above model does not explic- for PEM from Table 4 of Worth et al. [13], we obtain itly take into account the architecture of a given plane- ηEM ≈ 270. Next, we consider the TRAPPIST-1 system tary system, thereby neglecting effects arising from grav- with X and Y being TRAPPIST-1e and TRAPPIST-1f itational focusing, resonances, eccentricity and mutual respectively. Upon substituting the appropriate parame- inclination, to name a few [1]. We have also implicitly ters [7], we find, assumed that the planets settled into their present orbits quickly, and that there exist a sufficiently high number of ηef Pef ≈ 0.04 , (5) meteorites to cause spallation [12]. Many of these aspects ηEM  can only be studied through detailed numerical models, which fall outside the scope of this work. Despite these which implies that a non-trivial percent of the rocks simplifications, our conclusions are in agreement with re- ejected from TRAPPIST-1e during each impact event cent numerical simulations [17] which had incorporated will land on TRAPPIST-1f. As a result, the fraction most of the aforementioned factors. of rocks that are transferred between planets would be comparable to (although smaller than) the fraction of rocks that fall back on the surface of the originating planet.1 This conclusion is fully consistent with the pre- III. CONSEQUENCES FOR ABIOGENESIS vious numerical simulations undertaken by Steffen and Li [17]. Thus, the TRAPPIST-1 system is expected to be We now turn our attention to quantifying the implica- more efficient than the Earth-to-Mars case in facilitating tions of panspermia in promoting abiogenesis by draw- panspermia. ing upon an equation similar to that developed by Frank It should be noted that Pxy only quantifies the fraction Drake in the context of the Search for Extraterrestrial of rocks that impact the target planet, and not the total Intelligence (SETI). The primary parameter of interest number. The latter is dependent on Nx, which is gov- is the probability λ of life arising per unit time [22, 23]. erned by the frequency and magnitude of impacts [10, 18]; According to the Drake-type equation proposed in Scharf the crater impact rate itself is regulated by the prop- and Cronin [24], λ is computed as follows: erties of the planetary system under consideration [19]. Hence, we shall not attempt to quantify Nx (or Ny) for Nb λ = · fc · Pa, (6) the TRAPPIST-1 system as there are too many unknown hn0i factors involved. We reiterate that Pxy is the fraction of rocks transferred per event, and to obtain the total esti- where Nb is number of potential building blocks, hn0i is mate, a knowledge of the total number of impacts over the mean number of building blocks per organism, fc is the fractional availability of these building blocks during a given timespan, and Pa is the probability of abiogene- sis per unit time and per a suitable set of these building 1 Gravitational perturbations by the densely packed planets could blocks. All of the factors, apart from Pa, are depen- also disperse the ‘cloud’ of rocks out of the planetary system (due dent on complex biological and planetary factors which to unstable orbits). we shall not address here. 3

Instead, we mirror the approach outlined in Scharf smaller scales) on the Earth, namely islands. If we look and Cronin [24], where Pa can typically be enhanced via upon the habitable planets of the TRAPPIST-1 sys- panspermia by a factor, tem as ‘islands’, the similarities are readily apparent: although these ‘islands’ are isolated to a degree, they n Pa = P0 E , (7) are also subject to ‘immigration’ from the ‘mainland’. In planetary terms, this ‘immigration’ would essentially where n is the number of panspermia events, P0 is the amount to transfer of lifeforms (or genetic material) via probability in the absence of panspermia (i.e. with n =0) panspermia. The only difference is that islands occupy and E is the enhancement arising from each event. A few a 2D surface and planets a 3D volume, but most of the clarifications are in order: by “enhancement”, we refer to relevant orbits in the latter case share a common plane. molecular the fractional increase in the number of build- This analogy enables us to draw upon the rich and ing blocks (not biological species) transferred per event. versatile field of island biogeography [27, 28], which pri- This is a less stringent requirement, possibly extant even marily arose from the seminal paper by MacArthur and in our own Solar system [25], implying that this mecha- Wilson [29]. In Cockell [30], the theory of island biogeog- nism of ‘pseudo-panspermia’ has a higher chance of being raphy was employed to qualitatively explore the possibil- effective. ity that photosynthesis could be transferred via inter- At this stage, it is equally important to highlight the planetary panspermia. The basic insight of MacArthur limitations of the above ansatz. The exponential gain and Wilson [27, 29] was that there exists a dynamic equi- most pos- represents an idealized scenario, namely, the librium between the immigration (I) and extinction (E) itive outcome possible. In reality, the scaling with n rates on the island, which determines the equilibrium would be much weaker, possibly being algebraic (or even number of species. MacArthur and Wilson [29] had hy- logarithmic). In addition, the introduction of these new pothesized that, molecular ‘species’ does not necessarily enhance the prob- ability of abiogenesis, since they could have landed in a exp(−ΓDxy) habitat on the planet that is inimical for their survival I ∝ AxRy , (9) Dxy and growth. Moreover, the reaction networks (proto- metabolic or otherwise) contributing to abiogenesis and where Ax is the area of the ‘source’ from which immi- subsequent evolution could have been primarily engen- gration occurs, Ry is the diameter of the island, Dxy dered by the multitude of environmental factors on the is the distance between the source and the island, and planet [26], as opposed to external contributions through Γ represents a characteristic inverse scale length. If we panspermia. consider the Earth-Mars and TRAPPIST-1 systems, it is The value of n varies widely from study to study apparent that I will be much higher for the latter case [15, 20] since it depends on the minimum size of the because of the smaller value of Dxy. The expression for E ejecta that is capable of sustaining life (or molecular ma- is more ambiguous, but it suffices to say that it increases terial), and on many other biological and dynamical con- as the area of the island decreases. Thus, as compared siderations. However, even for the conservative choice to Mars, the extinction rate is likely to be lower for the 3 4 of E = 1.01 and n ∼ 10 , it follows that Pa/P0 ∼ 10 . TRAPPIST-1 system. If we compare the relative probabilities for any of the The species diversity S is expressible as, TRAPPIST-1 habitable planets and the Earth, assum- dS ing E to be the same in both instances, we find, = I (S − S) − ES, (10) dt P P (T ) a n(T )−n(E) n(T ) and the equilibrium species diversity S is thus given by, (E) = E ≈ E , (8) ⋆ Pa I S = S , (11) where the last equality follows from our argument that ⋆ P I + E panspermia events are likely to be much more common on TRAPPIST-1. Although we cannot hope to estimate where SP is the total number of species capable of migrat- E or n(T ), a robust qualitative conclusion can be drawn: ing from the source [31]. Thus, we see that S⋆ increases the presence of an exponential scaling on the RHS of Eq. with respect to SP and I, and decreases with respect 8 ensures that the probability of abiogenesis via pansper- to E. Since I is much higher and E is slightly lower for mia can be orders of magnitude higher than on Earth in the TRAPPIST-1 system, it follows that the species di- the optimal limit. versity will be much higher than the Earth-Mars case, provided that the values of SP are similar. Hence, the TRAPPIST-1 planets seeded by panspermia are charac- IV. ANALOGIES WITH ECOLOGICAL terized by a greater number of species thus transferred, MODELS compared to the Solar system. The similarities between the TRAPPIST-1 system and The close proximity of the TRAPPIST-1 planets is ecological models extend beyond island biogeography. reminiscent of an analogous environment (albeit at much Another important paradigm in theoretical ecology is the 4 concept of a metapopulation, which is commonly referred Other statistical metrics proposed for distinguishing be- to as a “population of populations” [32]. Further details tween the cases of null and finite panspermia [40, 41] are concerning the central tenets of metapopulation ecology also useful in this context. can be found in Hanski [33, 34]. Let us proceed to couch Another means of detecting lifeforms is through the the TRAPPIST-1 system in terms of metapopulation dy- “red edge” of vegetation, which corresponds to a sharp in- namics. crease in the reflectance at around 0.7 µm on the Earth The central premise is that the metapopulation (plan- [42]. Thus, if the red edge is detected through photo- etary system) comprises of different ‘patches’ (planets). metric observations on two (or more) different planets, We suppose that the total number of distinct populations at the same wavelength, it would strengthen the case for (life-bearing planets) is N , whose governing equation is, panspermia. Since TRAPPIST-1 is an ultracool dwarf star, its peak blackbody brightness is at 1.1 µm. Hence, dN N = IN 1 − − EN , (12) any searches for the “red edge” must be cognizant of the dt  NT  possibility that it may be shifted to longer wavelengths than on Earth [43]. Due care must also be taken to iden- where NT is the total number of sites available (num- tify false positives such as minerals and other ‘artificial’ ber of habitable zone planets), while I and E are the spectral edges. immigration and extinction rates respectively. For the Life-as-we-know-it is characterized by homochirality, equilibrium number N⋆, we find i.e. living organisms are comprised of left-handed amino acids and right-handed sugars. Homochirality has been E posited to be a universal attribute of biochemical life, N⋆ = NT 1 − . (13)  I  and can be detected in principle via remote sensing us- ing circular polarization spectroscopy [44]. Hence, the This result implies that N⋆ increases monotonically with discovery of homochirality on multiple planets orbiting NT and I, and decreases monotonically with E. Using the same star may serve as an alternative route for dif- the information presented earlier, we conclude that the ferentiating between panspermia and independent abio- TRAPPIST-1 system is consistent with a greater number genesis. of life-bearing planets because of the higher immigration To summarize, the transfer of life via panspermia can rates and total number of available planets (in the hab- be tested by determining whether the same biosignatures itable zone) compared to the Solar system. are detected on multiple planets. Consequently, this can The aforementioned mathematical models are very also be used to study the sensitivity of life to initial con- useful in deducing qualitative or semi-quantitative fea- ditions, such as the illumination, surface gravity, atmo- tures of the TRAPPIST-1 system. Apart from the two spheric pressure, and other factors. analogies explored here, a promising and diverse ar- ray of formalisms and concepts introduced in theoreti- cal ecology [35–39] ought to be capable of furthering our understanding of panspermia and abiogenesis in multi- B. Looking beyond TRAPPIST-1 planetary systems. Although most of our discussion was centered around TRAPPIST-1, many of the conclusions discussed herein V. IMPLICATIONS OF PANSPERMIA have a broader scope.

Finally, we explore some of the major consequences M-dwarfs: Consider a generic multi-planet system arising from our analysis. around an M-dwarf, where multiple planets lie within the habitable zone. From Figure 7 of Kopparapu et al. [45], we infer that the width of the habitable zone is around A. Detecting the existence of panspermia 0.03-0.05 AU for a star of 0.1-0.2 M⊙. If there exists more than one planet in this region, we conclude that D ∼ a ∼ O 10−2 AU. We can then estimate the We have stated earlier that the probability of abiogen- xy y relative fraction of rocks that are transferred compared esis increases from a value of P without panspermia to
0 to the Earth-to-Mars scenario using Eq. 3, thereby ob- Eq. 7 if panspermia is present. Suppose that we de- taining, tect k planets in the TRAPPIST-1 system with signs of life, typically via molecular biosignatures in the plan- 2/3 −2/3 ets’ atmospheres [8]. The probability of abiogenesis oc- Pxy ηxy My M⋆ k ≈ 20 , (14) curring independently on them would be P0 , whereas it PEM ηEM  M⊕  0.1 M⊙  k could equal Pa if all planets exchange material with each k −3 other. As the ratio (Pa/P0) is plausibly much greater where PEM = 2 × 10 [13]. Thus, for most M-dwarf than unity for k ≥ 1, detecting life on two (or more) plan- systems, the fraction of rocks impacting the target planet ets strengthens the case for abiogenesis via panspermia. is conceivably around an order of magnitude higher than 5 the Earth-to-Mars value. Using Eq. 4, we conclude that, We explored the implications of panspermia for the ori- gin of life in the TRAPPIST-1 system by drawing upon τ D hv i xy ≈ 0.007 xy EM , (15) the quantitative approach proposed recently by Scharf τEM 0.01 AU  hvi  and Cronin [24]. If panspermia (or pseudo-panspermia) is an effective mechanism, it leads to a significant boost with τEM =4.7 Myr [13], implying that the transit time is two (or more) orders of magnitude lower as compared in the probability of abiogenesis because each pansper- to the Earth-to-Mars value. Collectively, Eqns. 14 and mia event can transfer a modest number of molecular 15 would result in higher immigration rates, which imply ‘species’, and the cumulative probability scales exponen- that our previous ecology-based results are likely to be tially in the best-case scenario. Thus, it seems reasonable applicable. to conclude that the chances for abiogenesis are higher in the TRAPPIST-1 system compared to the Solar system. Exomoons: A second analogous setup involves a We also benefited from the exhaustive field of theoret- planet with multiple exomoons in the circumplanetary ical ecology in substantiating our findings. By drawing habitable zone. Habitable exomoons cannot exist over upon the analogy with the theory of island biogeography, we argued that a large number of species could have ‘im- long timescales when the star’s mass is < 0.5 M⊙ since their orbits are rendered dynamically unstable [46]. migrated’ from one planet to another, thereby increasing Nonetheless, this case should be evaluated on the same the latter’s biodiversity. As known from studies on Earth, footing as M-dwarf planetary systems, since habitable ex- a higher biodiversity is correlated with greater stability omoons may even outnumber habitable exoplanets [47], [50], which bodes well for the multiple members of the and will soon be detectable by forthcoming observations TRAPPIST-1 system. We also utilized metapopulation [48]. Most of our analysis will still be applicable, except ecology to conclude that the possibility of multiple plan- for the fact that the exoplanets and star must be replaced ets being ‘occupied’ (i.e. bearing life) is higher than in by exomoons and exoplanet respectively. the Solar system, given the considerably higher immigra- To gain an estimate of the relative increase in tion rates. probability with respect to the Earth-to-Mars case, In order to observationally test the presence of life let us make use of Eqns. 14 and 15. Suppose that seeded by panspermia, we proposed a couple of general −2 tests that can be undertaken in the future. We reasoned My ∼ 0.1 M⊕, M⋆ ∼ 10 M⊙ and Dxy ∼ 0.01 AU using parameters consistent with Heller et al. [47]; we also as- that a ‘smoking gun’ signature for panspermia may re- quire the following criteria to be valid: the detection sume ηxy ∼ ηEM and hvi ∼ hvEM i. With these choices, of (i) identical biosignature gases, (ii) the spectral “red we find Pxy/PEM ≈ 20 and τxy/τEM ≈ 0.007, which equal the characteristic values obtained for low-mass edge” of vegetation occurring at the same wavelength, M-dwarf planetary systems. Thus, exomoon systems and (iii) distinctive homochirality. However, we predict in the circumplanetary habitable zone are conducive that some of these observations may only fall within the capabilities of future telescopes, such as the Large to panspermia, all other things held equal. This also 2 implies a greater degree of biodiversity, and a higher UV/Optical/Infrared Surveyor (LUVOIR). number of moons seeded by panspermia, as per our Lastly, we extended our discussion beyond that of earlier arguments. the TRAPPIST-1 system and presented other scenarios where panspermia, and hence abiogenesis, are more likely Brown dwarfs: As seen from Eq. 3, the capture than in the Solar system. We identified exoplanetary sys- −2/3 tems orbiting lower-mass M-dwarfs (and perhaps brown probability has an M dependence. If we assume that ⋆ dwarfs), and exomoons around Jovian-sized planets as there exist multiple habitable planets around a brown potential candidates that favor panspermia. dwarf, the low value of M relative to the Sun could, the- ⋆ It seems likely that exoplanetary systems akin to oretically speaking, enhance the probability of pansper- TRAPPIST-1, with multiple exoplanets closely clustered mia. However, the habitable zone around brown dwarfs in the habitable zone, will be discovered in the future. migrates inwards over time [49], thereby diminishing the We anticipate that our work will be applicable to these chances for abiogenesis and panspermia to occur. exotic worlds, vis-à-vis the greater relative probability of panspermia and abiogenesis on them. VI. DISCUSSION AND CONCLUSIONS ACKNOWLEDGMENTS In this paper, we addressed the important question of whether life can be transferred via rocks (lithopansper- We thank James Benford, Sebastiaan Krijt, Amaury mia) in the TRAPPIST-1 system. By formulating a sim- Triaud and Ed Turner for their helpful comments regard- ple model for lithopanspermia, we demonstrated that its ing the manuscript. This work was partially supported likelihood is orders of magnitude higher than the Earth- to-Mars value because of the higher capture probability per impact event and the much shorter transit timescales 2 involved. https://asd.gsfc.nasa.gov/luvoir/ 6 by a grant from the Breakthrough Prize Foundation for the Starshot Initiative.

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