Advanced Aspects of the Galactic Habitability
AAstronomy & Astrophysics manuscript no. Djosovic_ms_production_version c (cid:13)
ESO 2019April 16, 2019
Advanced aspects of Galactic habitability
Vladimir Ðošovi´c , Branislav Vukoti´c (cid:63) , and Milan M. ´Cirkovi´c Department of Astronomy, Faculty of Mathematics, University of Belgrade, Studentski Trg 16, 11000 Belgrade, Serbia, e-mail: [email protected] Astronomical Observatory, Volgina 7, P.O.Box 74 11060 Belgrade, Serbia, e-mail: [email protected] , e-mail: [email protected]
Received April 16, 2019 / Accepted
ABSTRACT
Context.
Astrobiological evolution of the Milky Way (or the shape of its ‘astrobiological landscape’) has emerged as a key researchtopic in recent years. In order to build precise, quantitative models of the Galactic habitability, we need to account for two opposingtendencies of life and intelligence in the most general context: the tendency to spread to all available ecological niches (conventionallydubbed ‘colonization’) and the tendency to succumb to various types of existential catastrophes (‘catastrophism’). These evolutionarytendencies have become objects of study in fields such as ecology, macroevolution, risk analysis, and futures studies, though a seriousastrobiological treatment has so far been lacking.
Aims.
Our aim is to numerically investigate the dynamics of opposed processes of expansion (panspermia, colonization) and extinction(catastrophic mechanisms) of life in the Galaxy.
Methods.
We employed a new type of numerical simulation based on 1D probabilistic cellular automaton with very high temporalresolution, in order to study astrobiological dynamics.
Results.
While the largest part of the examined parameter space shows very low habitability values, as expected, the remaining parthas some observationally appealing features that imply, among other things, a reduction in the amount of fine-tuning necessary forresolving the Fermi paradox.
Conclusions.
Advanced aspects of Galactic habitability are amenable to precision studies using massive parallel computer simu-lations. There are regions of the parameter space that correspond to a quasi-stationary state satisfying observable constraints andpossessing viable SETI targets.
Key words. methods: numerical - Galaxy: evolution - extraterrestrial intelligence - astrobiology
1. Introduction: Habitability and colonization
Studies of habitability – circumstellar, galactic, and cosmologi-cal – have rapidly become the main topic of astrobiological re-search in recent years (e.g. Chyba & Hand 2005; Javaux & De-hant 2010; Horner & Jones 2010; Lineweaver & Chopra 2012;Dayal et al. 2015). Both important theoretical insights and novelnumerical models have been developed and deployed in thecourse of the last decade in order to obtain a better quantita-tive handle on the hitherto mostly intuitive concept of habit-ability. In particular, cosmological structure formation simula-tions (Vukoti´c et al. 2016; Forgan et al. 2017) and semi-analyticmerger trees (Stanway et al. 2018) have been used successfullyto that e ff ect. Clearly, there is much work to be done in this area,with refinement of both computing resolution and empirical con-straints on habitability.There is, however, another aspect of habitability that has notyet been quantitatively studied. This is the interplay between (of-ten intuitively assumed, but rarely explored in detail) two gener-alized ecological tendencies that characterize life irrespective ofits exact definition: the tendency to spread to all available nichesand the tendency to become extinct as a consequence of catas-trophic changes in its physical environment. While intuitivelygeneralized from our observations of terrestrial life, there is noreason whatsoever to assume that extraterrestrial life, if it ex-ists, will be exempt from either of these two grand trends. The (cid:63) Corresponding author spread of life over various cosmic distances has been usually op-erationalized as either panspermia or intentional colonization byintelligent life. Since the classical study of Newman & Sagan(1981), there have been several specific studies of the modesof spreading of intelligent life through the Galaxy (e.g. Bjørk2007; Cotta & Morales 2009; Starling & Forgan 2014). On theother hand, most of the contemporary studies of habitability takeinto account at least some of the astrophysical catastrophic risks,such as those from supernovae and gamma-ray bursts (e.g. El-lis & Schramm 1995; Scalo & Wheeler 2002; Galante & Hor-vath 2007; ´Cirkovi´c & Vukoti´c 2008; Gowanlock 2016; Stan-way et al. 2018). In fact, one could even state that the ‘catas-trophic’ aspects of the overall astrobiological evolution havebeen overemphasized in recent years. The very concept of hab-itable zones, bounded in space and time, which has emerged asthe ‘bread and butter’ of astrobiology (e.g. Gonzalez 2005), tes-tifies to the resurgence of catastrophism as a key ingredient inany viable astrobiological theory.In contrast, the aspect of astrobiological evolution that dealswith spreading of life has thus far been largely neglected ordownplayed in quantitative models (even though the philosoph-ical justification of life’s tendency to spread and consequent im-plications for astrobiology is well-studied under the title of thecontinuity thesis; cf. Fry 2000; ´Cirkovi´c 2012). Often a lip ser-vice is paid to the tendency of life to spread and fill all avail-able ecological niches (e.g. Hanson 1998; Sagan 2000), but itis seldom analysed and modelled in detail. There are essentially
Article number, page 1 of 8 a r X i v : . [ phy s i c s . pop - ph ] A p r & A proofs: manuscript no. Djosovic_ms_production_version two modes of spreading of life which might be co-present inthe overall astrobiological landscape: panspermia (simple life)and colonization (complex life, specifically technological civi-lizations). The two are not entirely disjunctive, since the emer-gence of spacefaring civilization is accompanied by possibilityof directed panspermia (Crick & Orgel 1973; Sleator & Smith2017). Actual concerns about planetary contamination and plan-etary protection (e.g. Rummel 2001) testify how even a primi-tive technological civilization, like the present-day human one,faces this problem quite early in its spacefaring attempts. There-fore, it makes sense to discuss both these aspects of the same‘spreading of life’ tendency in a unified way, as we are doingin the present model; we refer to this dual tendency as ‘colo-nization’, while keeping in mind that the model parameters areactually adaptable enough to include all kinds of panspermia. (Asimilar dual construal is applicable on the catastrophism side ofthe story, where we can subsume both naturally occurring andtechnogenic events, such as the nuclear winter, which is capa-ble of causing widespread ecological devastation and extinction,under the same controlling parameter.)Therefore, trying to achieve a more complete picture ishighly justified. Cellular automata approach, a grid of cells (eachdescribed with some variable called state) that evolve in dis-crete time steps (see Ilachinski 2001) has been shown to be apromising modelling platform for such phenomena (Vukoti´c &´Cirkovi´c 2012a,b). However, since life-friendly matter condi-tions are usually found on planetary bodies, and in particularthe habitability of systems of such bodies is greatly influencedwith galactic parameters, the required spatio-temporal dynami-cal range for such models is huge. Consequently, vast computa-tional resources are required. Clearly, a practical di ffi culty in in-corporating these two opposing tendencies in a single syntheticmodel is the discrepancy between relevant timescales in the gen-eral case. The present study seeks to address at least some ofthese issues, by concurrent simplification of the spatial structureand drastic increase in temporal resolution of the simulation. Ourpilot study has shown that even a very simple, 1D (temporal) toymodel of such phenomena is a fruitful approach (Ðošovi´c et al.2018), and has the upper hand over the similar approach realizedwith 2D cellular automata (Vukoti´c & ´Cirkovi´c 2010; Bezsud-nov & Snarskii 2010; Galera et al. 2019), since the spatial as-pect of the model is greatly simplified. This enables much bettertemporal resolution of the simulation that can model phenom-ena with ∼ yr characteristic timescale during the lifespanof the Galactic disk. This is comparable to the historical spanof human civilization on Earth. On the other hand, the temporalaspects of evolution of life can be studied against our empiri-cal knowledge of the Earth’s fossil record, while even the highlysuccessful contemporary exo-planet studies have yet to figureout the empirical signatures of life on other planets. Even withmultiple modern panspermia studies (e.g. Wallis & Wickramas-inghe 2004; Lingam 2016), it is still highly contentious how e ffi -cient naturally occurring panspermia is in the Galaxy (Gordon &Hoover 2007; Mcnichol & Gordon 2012). On the other hand, thee ffi ciency of directed panspermia is not in doubt, in contrast tothe frequency of the technological civilizations capable of under-taking it, which remains unknown. Therefore, it makes sense totry to model both jointly. Also, the model presented is rather con-servative in that it employs the conventional notion of habitableplanets and fairly gradual evolutionary processes (even if punc-tuated by occasional catastrophes), and it does not include a typeof more radical transformative processes, in particular postbio-logical evolution of extraterrestrial intelligence (e.g. Dick 2003). This paper is organized as follows. The description of code,its structure, and phenomenology included is given in Section 2.Section 3 contains the description of simulations, with the com-puting resources employed. The main results are presented inSection 4, while the discussion and prospects for further workare given in the concluding section.
2. Method
Unlike standard cellular automata approach, where spatial influ-ence is implemented through the interaction of the cell with itsneighbours, our model is simplified so that probability of col-onizing (or possible panspermia seeding) of a particular spatialsite is dependent on the total number of colonization capableentities (sites that have su ffi ciently evolved to be able to colo-nize other sites) in a given time step of the simulation. From thetechnical point of view, this can be regarded as a cellular au-tomaton where each cell has a neighbourhood comprised of allother cells in the simulation. While this approach limits the in-ference on for example, modes of spatial spreading, such as sim-ple spherical expansion vs. resource-driven percolation schemes(e.g. Galera et al. 2019), the benefits from higher resolution oftemporal scales are evident. The main features of our model areas follows: – The habitable sites in the Galaxy are represented as entitiesthat have a particular state which evolves over time. – Each site can evolve through four discrete states designatedas: 0 – no life, 1 – simple life, 2 – complex life, 3 – techno-logical civilization. – Each site evolves according to probabilistic evolution ruleswith fiducial timescales representing the Earth’s fossil recordand planetary formation rate. During the course of the sim-ulation, the sites are gradually activated to state 0 as perdistribution of the Earth-like planets’ formation rate fromLineweaver (2001). – Each cell in state 3 can colonize only one cell in state 1 or 2per time-step, according to a Poisson-like probability distri-bution.We do not enter into complex and partially philosophical issuessuch as what exactly constitutes a technological civilization. In-stead, we have adopted pragmatic approach of classic studiessuch as Newman & Sagan (1981) that technological civilizationis an entity capable - unless destroyed by an existential catastro-phe - of colonizing nearby habitable planetary systems, sooneror later. We also used the terrestrial values in the present proof-of-concept model as the starting point, since the Copernican as-sumption has served us well in both science in general and as-trobiology in particular (for an extended discussion of the lattersee ´Cirkovi´c, 2012).
At the beginning of the simulation there are no active sites. Asthe simulation run progresses, the 1000 simulated sites are ac-tivated to state ‘0’ according to probability density distributionrepresentative of cosmic Earth-like planet formation rate fromLineweaver (2001) (for other works see also Zackrisson et al.2016). We used only the most recent 10 Gyr of this distribu-tion and normalized it in such a way as to activate all sites (ina probabilistic manner) during our simulation time span of 10Gyr. The frequency of site activation peaks at ∼ . ff with a shallower slope Article number, page 2 of 8ošovi´c et al.: Advanced aspects of Galactic habitability towards the end of the simulation. Also, once activated, each siteis assigned the main sequence lifetime of 10 m − . , where m is the stellar mass selected randomly with uniform probabilityfrom [0 . − .
3] M (cid:12) mass interval. If the time from the site activa-tion exceeds the assigned main sequence time the site is removedfrom the simulation.The modelled transitions are presented in Figure 1. Each sitemight preserve its state to the next time step, sites in 0-2 statescan evolve to + ff erenceis that this work uses Epanechnikov instead of a Gauss kernel tocalculate transition probabilities from the parameters of the rele-vant transition timescales (Table 1). The active site in state i canevolve to state j according to Epanechnikov kernel (Epanech-nikov 1967), E ( u ) = . − u ), where | u | ≤
1. Epanechnikovkernel is much less computation intensive than widely used Nor-mal distribution kernel. As explicated in our recent pilot studyconcerning the topic of this work (Ðošovi´c et al. 2018), at thebeginning of each run, each of the simulated sites is assigned aset (one for each possible transition) of random variates from auniform probability distribution in (0 −
1) interval ( f ). The stateof the site is changed if the resulting cumulative density functionat a time t has higher value than this pseudo-random number(we used a pseudo-random number generator SFMT, see Saito& Matsumoto 2008): E cd f (cid:18) t − τσ (cid:19) > f , (1)where t is time that a site have spent in state i since activation orthe last transition, if applicable, τ is a characteristic time (meanvalue of kernel) for transition i → j where j is the next stateand σ is standard deviation, that is, width of the kernel. Whenthe transition occurs for the particular object, a random variatefor that particular transition is reinitialized. The above model isused for evolution-type transitions, where site evolution is not tobe influenced by spatial spreading agents, such as colonizationor panspermia. A similar equation is adopted for the calculationof probability for colonization-induced transitions: E cd f (cid:32) t − τ col σ (cid:33) > f , (2)where t is time that object have spent in state 3 (up to the currenttime step), τ col is the characteristic time of colonization while it’sstandard deviation is σ . When the state 3 object reaches a timestep where the above condition is fulfilled it makes a coloniza-tion attempt and it’s t gets reset to zero regardless of coloniza-tion success. The colonization attempt is considered a failure ifthere are no objects in state 1 or 2 (at a particular time step),which is highly improbable. If there are objects in state 1 or 2then the following conditions are tested: N N a < f , (3) N N a < f . (4)The total number of objects in state 1 and 2 are represented with N and N , respectively, while N a is the total number of activated Table 1.
Parameters of the transitions in our model. From left to right:transition designation, type, characteristic time, standard deviation. i → j Type τ σ [yr] [yr]0 → × × → × × → × × → , ] 0 . ∗ τ → , ] 0 . ∗ τ → , ] 0 . ∗ τ objects from the beginning of the simulation run. The above con-ditions are tested for each colonizing (state 3) object at a giventime step. Two separate random variates f and f are generatedeach time the conditions are tested. If the first condition is true,then the randomly selected object in state 1 is colonized. Other-wise, if the first condition is false, then the second condition istested. If the second condition is true, the randomly selected state2 object is colonized. In the case when the second condition isfalse (i.e. both conditions are false), then the corresponding colo-nization attempt is considered a failure. When the object in state1 or 2 gets colonized, the random variate of the correspondingevolutionary 1 → → → t res τ cat < f cat , (5)where t res is a simulation time step, τ cat is a characteristic timescale for catastrophic events and f cat a uniform random variategenerated each time the condition is tested. Otherwise, the objectis degraded to state 2. Table 1 summarizes transitions and theirparameters.For the characteristic times from Table 1, for the emergenceof life and its evolution to complex forms are according to Doddet al. (2017) and Maloof et al. (2010), respectively. Finally, weused a figure of 600 million years for the development of intelli-gent life and civilization, roughly following the Copernican as-sumption about typicality of evolution of complex life and intel-ligence on Earth. The catastrophic timescale that represent highrisk events such as close gamma-ray burst, supernovae, and as-teroid impacts is variable in the interval indicated in Table 1. In-dependent of catastrophic transition, the two timescales for thecolonization transitions are varied together (have equal values ineach simulation). We have neglected colonization rates to sites instate 0, in order to avoid seeding of planets incapable of support-ing life at given time. This makes the model more conservativeand more in line with the conventional scenarios of colonizingplanets possessing at least some biotic resources. The simulations were run on PARADOX III super-computer atThe Institute of Physics Belgrade. PARADOX III consists of106 computing nodes. Each node has 16 CPU cores (2x8) SandyBridge Xeon 2.6GHz, with 32 GB RAM memory. All nodes areinterconnected by the QDR InfiniBand network. A great deal ofthe required computation was also carried out at the Bibliotheca
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Fig. 1.
Modelled transitions with a symbolic scheme of states (we assume that a Mars-like planet could have been habitable for simple life in atleast some epochs of its history).
Alexandrina High-Performance Computing machine, BA-HPCC2. BA-HPC C2 consists of 98 servers (each with 128 GB ofRAM memory), with a total of 1968 CPU cores and 288 TB ofstorage.Each simulation covers the time span of 10 Gyr in steps of10 kyr. The input timescales for colonization and catastrophismwere di ff erent for each simulation. They were selected from aninterval of 10 to 10 yr on exponential scales in increments of0.05. This gives a total of 14641 combinations of input param-eters which is also the total number of simulations performed(and the total number of the output files). We ran one simulationper core. A pseudo random number generator is seeded with thenumber of the simulation, that is, from (0 , s of wall-clocktime, while some of the fastest were completed in a matter of7 × s. The downside of the sequential output is that it is notfeasible to perform ‘atemporal’ analysis of the model (e.g. tocalculate the number of sites at a fixed state over all snapshots).
3. Results
We present the results of our simulations in Figures 2-4. Figure2 shows the colour coded plot of the average total number ofsites in state 3 at the end of the simulation (at 10 Gyr) for eachset of varied characteristic timescales. For the greater part, theplot surface shows the number of objects to be below the middlepoint of the colour scale (the indicated mean value is below 450).This apparent dominance of catastrophism is also evident in theprominent diagonal feature lying below the τ cat = τ col line. Themiddle value of the colour bar settles at ≈ = τ cat = τ col .The light blue to orange region in the upper right corner of theplot with τ cat = τ col > is not dominated by catastrophicevents. There, even if τ cat < τ col , it is possible for the number ofobjects in state 3 to be above the average. The gradient of colourcoded values in this part is also smaller than in the catastrophismdominated region. The area with τ col < and τ cat < showssome fluctuations.In Figure 3 we plot how the average number of sites in eachstate changes with time for a selected set of variable input param-eters. The standard deviation of curves from Figure 3 is given inFigure 4. While Figure 2 is useful for discussion of the emerg-ing ‘habitability regimes’, Figures 3 and 4 are more suitable for Article number, page 4 of 8ošovi´c et al.: Advanced aspects of Galactic habitability grasping the underlying mechanics of the evolution timescalesand their relation to di ff erent evolution scenarios.Each data point in Figures 2 and 3 is the mean value of 100runs of the simulation. The first row of panels in Figures 2 and 3shows that catastrophism overwhelms the colonization and thereare almost none of the objects in state 3 throughout the wholesimulated time span. The standard deviation for all emergentcurves is at a level of approximately ten which implies no suddenchanges and a steady evolution.This is very similar to the third row of panels with coloniza-tion as a dominant agent. The main di ff erence however is a re-gion of instability between 3 and 4 Gyr (left most and middlepanel). Once the colonization starts it takes about 0 . − τ col = up to τ col = , respectively) to colonize mostof the objects in states 1 and 2. Once the equilibrium with catas-trophism is evident in the middle panel of this row and the num-ber of objects in state 2 is approximately ten until the end of thesimulation. The panel on the right hand side shows no such be-haviour and is very similar to the panels in the first row, exceptfor existence of a significant number of state 3 objects, mostlyat the expense of the population in state 2. Similar curve shapes,but with lesser number of objects in state 3 are emergent in themiddle row in central and the right hand side panel, while theleft most panel in this row shows a typical signature of dominantcolonization.A somewhat larger fluctuations, both in the numbers of state3 objects and in their standard deviation is evident in the mid-dle row (when compared to the third row). The larger values forcatastrophic timescales give a smooth appearance of the curvewhile smaller values suppress the appearance of state 3 sites.The small number of state 3 sites in the right-hand side and inthe middle panel of the middle row in Figure 3, approximatelyten, shows a slightly larger relative spread and a non-stable be-haviour (Figure 4). Apart from being of little value for makingthe quantitative conclusions from the statistical point of view italso lacks credit from a methodical view point. ´Cirkovi´c (2018),argues that even the discovery of a single to a few advanced civ-ilizations would have a little power in resolving Fermi’s paradoxin its stronger forms. The similar standard deviation curve forstates 1 and 3 in colonization dominated cases (at 3 − ff erences. This di-rectly imprints on the state 1 curve since it is subjected to colo-nization at a pace dictated by the state 3 curve. A similar processshould hold for state 2 curves, but this is not obvious from thepresented plots as state 2 does not have enough time to build upin numbers as state 1 does.
4. Discussion
The larger part of the plot surface in Fig. 2 is grey or dark-blue-coloured, indicating that catastrophic events might play a dom-inant role in shaping the parameter space for the evolution oflife. Even only in a mild catastrophic regime, with no 3 → → ff ect on evolution asa whole (through evo-devo mechanisms, adaptive radiations sim-ilar to the Cambrian explosion, etc.), as has been speculated, forinstance, by the ‘rare Earth’ theorists (Ward & Brownlee 2000),following an early idea of the physicist John Cramer 1986. Withthat interpretation, we would rather expect a U-shaped depen-dence, even if skewed, of the frequency of complex life on therate of occurrence of catastrophic events.Our model of transitions is very conservative as far as col-onization is concerned, at least when compared with catas-trophism. From Figure 1, state 3 can be pumped with evolu-tion from state 2 and colonization from states 1 and 2. At thesame time it is drained only by catastrophism to state 2. Theoverall compendium of empirical evidence from astrophysics,biology, geology, sociology, philosophy, and even anthropology)implies that life-hazardous events have occurred in the past andare a probable threat in the future. Even our present existenceon Earth, in the light of the probabilistic anthropic selection ef-fect ( ´Cirkovi´c et al. 2010), is consistent with a significant under-estimate of hazardous event frequency. On the other hand, wehave no such empirical background in estimating relevant colo-nization timescales; at least without significant extrapolation tofuture technologies. Enforcing a certain level of handicap to in-terstellar colonization over naturally- or technologically-inducedcatastrophes should give more restrictive but reliable results asfar as outlining the parameter space regions with a large num-ber of state 3 sites is concerned. For this purpose, state 3 objectswere restricted to make a colonization attempt towards only onepossible target during the τ col . In addition, the success of col-onization depends also on the relative number of the availabletargets. It is evident from Figure 2 that at the onset of coloniza-tion the rate of making the state 3 objects has a rapid increaseand then gradually decreasing as the number of state 3 objectsbecomes larger.Even with such restrictions the τ cat = τ col > region isdominated by a high number of state 3 objects. It appears thatthis is the consequence of setting the 2 → × yr. This implies that the shape of distinctionpattern between colonization- and catastrophism- dominated re-gions is primarily determined by the ability of the habitable sitesto recover from the catastrophic events. With the recovery pacebeing larger than the frequency of hazards, the state 3 objectsclearly dominate the scene. Also, the steeper slope of this pat-tern in the τ cat = τ col > region indicates that there is lessdependence on the colonization time scale, even for points in ex-cess of 500 state 3 objects at the end of the simulation. Here, thesignificant number of state 3 objects should not be contributedto colonization but rather to evolution and increased life timebecause of the larger τ cat .The panels on the main diagonal in Figure 3, τ cat = τ col showa very interesting behaviour of state 1 curve. With respect to theresults presented in Figure 2, the catastrophism-dominated part(with both timescales at 10 or 10 yr) shows a convex shape ofstate 1 curve at epochs later than ∼ τ cat = τ col = yr, objects in state 3 do appearduring the simulation run. The shape of the state 1 curve might Article number, page 5 of 8 & A proofs: manuscript no. Djosovic_ms_production_version
Fig. 2.
Dependence of the number of sites in state 3 as a function of timescale for catastrophism and colonization at the end of the simulated timespan (10 Gyr). Axes are designated with decadic logarithm of time in years. The grey colour represents pixels with exactly zero number of sites instate 3, while the numbers values higher than zero are colour-coded as displayed. The mean value of the plotted matrix is 391 .
90 and is indicatedwith the black dash on the colour bar. be explained by the colonization action of state 3 upon state 1.Some of the state 3 objects manage to colonize state 1 objectsbefore they are catastrophically degraded to state 2. This e ff ectreduces towards later epochs since the number of available state1 targets gets smaller. Since the state 2 curve does not show sim-ilar features, likely because of also being catastrophically pop-ulated back from state 3, the shape of the state 1 curve mightbe indicative of the colonization action even in the absence ofdetecting (or existence) of colonizing objects themselves at thepresent epoch. The quantification of this e ff ect requires furtherexamination and fine-tuning of the colonization model.With regard to our current ignorance of exo-civilizations, thered-coloured part of the parameter space in Figure 2 is not of par-ticular interest for better understanding of the Fermi’s paradox,while the yellow and light-blue regions might be very signifi-cant. In other words, all the regions of the parameter space witha very small number of state 3 objects, especially the sub-partswith smaller colonization timescales (i.e. τ col < yr). Thecolour bar in Fig. 2 indicates that a number of colonized sites canreach up to a 20% of the total number of sites with a very steepgradient. This implies that the conventional (and perhaps naive)view of gradual, melioristic evolution towards increasing com-plexity – which is incompatible with our observations – shouldbe reconsidered. Clearly, the higher resolution sampling of the parameter space is of particular importance for measuring thisgradient and relating it to the adopted evolutionary timescales.In addition to an earlier study by Schulze-Makuch et al.(2011), a recent surge of works (Kashyap Jagadeesh et al. 2018;Saha et al. 2018; Kulkarni & Desai 2018; Rodríguez-Mozos &Moya 2017; Kashyap Jagadeesh et al. 2017; Barnes et al. 2015)demonstrate the classification possibility of the discovered pop-ulation of exoplanets according to their habitability. The primarymotivation for these works is the advance in the field of exo-lifesearch. However, these works also o ff er a prospect for advanc-ing our understanding of Fermi’s paradox. A detailed compari-son of the relative abundance of objects in di ff erent states (suchas the curves in Figure 3) and habitability classification of exo-planets might introduce an abundant source of empirical data tofurther constrain the parameter space of possible evolutionarytimescales.
5. Summary
We have presented the results of our study that used a simpli-fied version of the spatial spreading of life in the Galaxy in or-der to achieve higher computational e ffi ciency for the purpose ofmapping the colonization vs. catastrophic timescales parameterspace. The other relevant timescales for the life evolution (bi-ological) are tentatively taken to be adequately represented by Article number, page 6 of 8ošovi´c et al.: Advanced aspects of Galactic habitability
Fig. 3.
Number of cells in each state (colour-coded as listed in bottom right panel) as a function of time. Di ff erent plots means di ff erent initialconditions for colonization timescale ( τ col ) and catastrophism ( τ cat ). The number of sites in each state after 10 Gyr is indicated at the top of eachpanel. the Earth’s fossil record, as per the Copernican principle. Theemerging shape of the number of highly evolved sites showslower than average values for the greater part of the examinedparameter space, indicating the dominance of catastrophism overcolonization. This fits well into our current perception of exolifeand as our results have demonstrated, indicates a possibility of afine-tuning solution to Fermi’s paradox. However, further under-standing and improvements of the present model are required.Among possibilities to be considered in the course of the fu-ture work, there are both ‘conservative’ (better theoretical mod-els of the habitable planets’ ages, and di ff erent averaging pro-cedures) and ‘radical’ ones (more di ff erent discrete sites, and awider Poissonian distribution of the transition timescales, takinginto account correlated artificial disasters like large-scale warsor pandemics). In any case, the present proof-of-concept studyclearly shows that discrete models of this kind are capable ofcapturing some of the complexity of astrobiological evolution. Acknowledgements.
We thank an anonymous referee for an extensive and in-sightful review that has greatly improved the overall content of the paper. Fruitfuldiscussions with Sr ¯da Jankovi´c, Milan Stojanovi´c, Anders Sandberg, and JohnSmart have enormously contributed to the ideas presented in this paper. The au-thors acknowledge financial support from the Ministry of Education, Scienceand Technological Development of the Republic of Serbia – VÐ through theproject
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Fig. 4.
Similar plot as in Figure 3, except that it shows the standard deviation of the number of cells in each state.
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