Interstellar colonization: A new parameter for the Drake equation?

Interstellar colonization: A new parameter for the Drake equation?

|CARUS 41, 193-197 (1980) Interstellar Colonization A New Parameter for the Drake Equation? C L I F F O R D W A L T E R S , R A Y M O N D A. H O O V ...

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|CARUS 41, 193-197 (1980)

Interstellar Colonization A New Parameter for the Drake Equation? C L I F F O R D W A L T E R S , R A Y M O N D A. H O O V E R , AND R. K. K O T R A Chemistry Department, University of Maryland, College Park, Maryland 20742 Received June 1, 1979; revised October 1, 1979 M. H. Hart (1975, Quart. J. Roy. Astron. Soc. 16, 128-135) has argued that the absence of evidence for extraterrestrial visits to Earth indicates that there are no other advanced civilizations in our galaxy capable of interstellar colonization. If so, the possible success of any SETI program must be questioned. The authors propose that limited interstellar colonization may occur and an attempt is made to show the effects of such a journey on the Drake equation.


The search for extraterrestrial intelligence is one of the most exciting and challenging undertakings in all of human history. If this endeavor is successful, it may provide humanity a truer perspective of its destiny. The scientific basis for such a search is related to m o d e m thinking regarding the nature of stars, planets, life, and intelligence. The Drake equation (Shklovskii and Sagan, 1966; Sagan, 1973; Freeman and Lampton, 1975) summarizes the current ideas on the above, and attempts to determine N, the number of communicative civilizations that may be present in our galaxy. The Drake equation is N = R, fgfonefffeL



where mean rate of star formation in the galaxy, f g = fraction of stars suitable for supporting life, L = fraction of stars with planetary systems, r/e = number of planets per planetary system with conditions ecologically suitable for the origin a n d evolution of life, f~ = fraction o f suitable planets where life originates and evolves into more complex forms,


fi = fraction o f planets bearing life with intelligence capable of manipulation, f,. = fraction of planets with intelligence that develops a technological phase during which there is the capability for an interest in interstellar communication, L = mean lifetime of a technological civilization. Of the eight parameters only the first is known to any degree o f certainty. Based on assumptions and calculations that are compatible with their own convictions, several authors have arrived at several values for N (Shklovskii and Sagan, 1966; Kreidfeldt, 1971; Sagan, 1973; P o n n a m p e r u m a and Cameron, 1974; Oliver, 1975). It is the purpose of this paper to introduce a new term, C, into the Drake equation which takes into account the possibility of interstellar colonization. It is necessary to determine the effect of the p h e n o m e n o n on N and, therefore, on any efforts to detect extraterrestrial intelligence. If interstellar colonization is widespread, the profundity of the effect on the value of N is obvious. On the other hand, if the probability is much lower than for any of the other parameters, the equation remains essentially unmodified. The idea of colonization has been discussed primarily in conjunction with explanations for the absence of extraterrestrials on Earth. Hart (1975) has argued that a 193 0019-1035/80/020193-05502.00/0 Copyright © I980by Academic Press, Inc., All rightsof reproduction in any form reserved.



space-faring society could colonize the entire galaxy in 6.5 × l0 ~ years. He concluded that the absence of extraterrestrial contact indicates that no such colonization has occurred; N is thus approximately one. Jones (1976) has supported Hart with additional calculations. Cox (1976) disagrees with Hart and argues that the time restrictions may not permit any extraterrestrials to reach Earth within the galaxy's history. Alternative explanations suggest that extraterrestrials are either within or observing the solar system and are either purposely avoiding contact for the moment (Kuiper and Morris, 1977; Schwartzman, 1977; Papagiannis, 1978) or have isolated the Earth as a preserve or zoo (Ball, 1973). It has been assumed that if colonization occurs N - 1 0 1 1 , and if it does not, N - 1. Both values have negative implications for S E T I programs. Yet if interstellar colonization o c c u r s - - b u t is limited--the probability of success in any SETI program may be significantly improved. In this paper we introduce a new parameter, C, to the Drake equation which takes into account the fraction of civilizations which wish to colonize, the fraction of stars suitable for colonization, and the ability to reach those stars. FORMULATION OF C A space-faring civilization which desires to colonize could do so, provided a star system with a suitable habitat lies within their abilities to reach it. Similarly, established colonies could colonize new systems which lie within their range but are b e y o n d the reach o f the original home planet. Galactic societies could encompass many star systems which were initially excluded by the Drake equation as possessing communicable civilizations. H o w e v e r , if a civilization wishes to colonize, it may not be able if no suitable host system lies within its maximum travel radius. It is possible to construct a simple model to predict the extent of colonization. Equation (2) defines the new factor C, which we propose to add to the Drake equation to

account for the effect of interstellar colonization.

N = R, fgf~neffLLC,


where C = 1 + fx ~ /t=l


fs"mam[(m- 1)a,,,]" ',


fx = fraction o f civilizations which wish to colonize, fs = fraction of stars with suitable envirnoments for colonizations, a,,, = fraction of stars which have rn neighboring stars within a specified radius, n = number o f waves of colonization. If no civilizations wish to colonize (f~ = O, n = O) then C = 1 and the number of communicable societies remains the same as in the original Drake equation. If a fraction o f these civilizations desire to colonize (fx > 0), then the number of initially colonized worlds (n = 1) will be determined by how many suitable host systems are within the maximum travel radius. Only a fraction (al) of civilizations will have only one neighboring star suitable for colonization (m = 1). The number of such civilizations is expressed as Nfx(fsaO. Some fraction (a2) will be able to reach two stars, where a2 < al. The number of these stars is expressed as Nf,,(f~2a2). The total number of all stars available for initial colonization is expressed as a summation of terms, Nf,~ ~, f~mam. After that first wave of colonizaI1~=1

tion, new colonists could be sent forth from established colonies. In this case, there must be at least two compatible star systems within the travel radius; one where the original colonists came from, the other being the host system to which they are going. Hence the term (m - 1)a .... A sum of all stars suitable for colonization from initially colonized stars is given as Nf~ ~ f~[(m ~lt=l

1)a,,,]. This process could then be repeated n number o f times. The total number of all stars which can be colonized can be determined by summing over repeated waves.

INTERSTELLAR COLONIZATION This results in the double s u m m a t i o n t e r m found in Eq. (2). In this model, iff~ ~ (m - 1)a,,, > 1, and ~tl=l

n is a s s u m e d to be limitless, the equation diverges and colonization could proceed to the limits of the galaxy. I f f~ ~] (m ttl=l

Dam < 1, the equation converges indicating that colonization is limited. DISCUSSION

A n E v a l u a t i o n o f f,~

Only a fraction of the stars within a defined travel radius are suitable for colonization. To determine this fraction, fs, m a n y o f the terms utilized in the Drake equation can be applied. It is our opinion that stars which are suitable for colonization are ones which have e n v i r o n m e n t s nearly identical to that o f the h o m e planet and can be immediately exploited by the arriving colonists. It is improbable that e n v i r o n m e n t s which require artificial life-support systems, terra forming, or extensive modifications would be considered. The use of only the transport vessel (Kuiper and Morris, 1977) or asteroid size bodies (Papagiannis, 1978) is also unlikely as little benefit can be gained by leaving the h o m e star and risking the hardships o f interstellar flight. In order for the host s y s t e m to provide a suitable environment, it must already have a planet which has evolved life. One reason is that p r e d e v e l o p e d life can provide the colonists with basic metabolites. Cox (1976) has suggested that incompatibility of the optical isomers used by the native life and the colonists may render the planet as inhospitable. A more important reason for demanding life is that a host planet must have a breathable a t m o s p h e r e . Excluding unknown alien metabolisms, all life utilizes either anaerobic or aerobic pathways. Since only aerobic processes provide the energy d e m a n d e d by higher-ordered life, an oxidizing a t m o s p h e r e is needed for a planet to be considered for colonization. Only


photosynthetic processes can produce such changes in a planetary a t m o s p h e r e , and thus it must be a s s u m e d that the host planet has evolved life. A time factor is needed since only during a portion o f its history is the planet suitable for colonization. The time b e t w e e n formation and d e v e l o p m e n t of an oxidative a t m o s p h e r e must be rem o v e d from consideration. A n o t h e r aspect is that life could evolve to produce a species with a technological culture. During the lifetime of this civilization, colonization by another is unlikely for sociological reasons. The availability of a star for colonization can be e x p r e s s e d by the terms defined in the Drake equation, plus a factor, f~, which is the fraction of planets which are in a period of history suitable for colonization. fs = f g f o n e f f t ,


f = (t, -


to - f f ~ L ) / t , ,

where t a = the average planetary age, to = the time required for the formation of an oxidizing a t m o s p h e r e , f ~ f c L = fraction o f planets with technological societies during the period of desired colonization. A m a x i m u m value for f g f p n , f l is usually set at - 0 . 1 . In evaluating ft, f f ~ L is probably small when c o m p a r e d to the ages of planets. I f to - 2.6 × 10 "~years, which is the time it took on Earth for an oxidative a t m o s p h e r e to form, and ta - 8 × 109 years, f - 0.7. A m a x i m u m value for f~ is thus equal to -0.07. A n E v a l u a t i o n o f a ,,,

Using the region around our sun as a model, it is possible to determine the stellar density, and by using a Poisson distribution, to determine a,, for different travel radii. It is possible to calculate values of C for various f~ and travel radii, a s s u m i n g f x = 1. It can be seen that C is highly dependent on both factors.



The m a x i m u m travel radius is determined by the m a x i m u m velocity and duration of flight. Purcell (1960) and Von H o e r n e r (1962) have shown that relativistic velocities are impossible to obtain using chemical, fission, fusion, or even m a t t e r antimatter drives. Other schemes using ramjets (Bussard, 1960), light sails which are laser pushed (Marx, 1967), and particle acceleration using b e a m e d energy (Jackson and Whitmire, 1978) have been p r o p o s e d to eliminate the need for carrying onboard fuel. Serious problems exist with each method, and it is generally agreed that relativistic travel velocities are not obtainable. Fusion drives are considered the most promising and Projects Orion (Dyson, 1968) and Daedalus have shown how such systems could operate. The m a x i m u m travel velocity, Vf, is dependent on the exhaust velocity, Ve, and the fuel to payload mass ratio, Mf/M,. Vr = V~ln (1 + Mf/Mp).


Realistic values for each have resulted in Vr being equal to 1%c. Travel to even the nearest stars would require hundreds of years. The most reasonable method of such travel is to use an O'Neill-type space colony (O'Neill, 1974, 1976) and modify them into multigeneration space arks by adding a source for interior lighting and heating (Matloff, 1976). It appears reasonable for our evaluation to use 1000 years as the m a x i m u m duration of travel. A m a x i m u m travel radius is therefore set at 10 light-years. With this range and a value of 0.07 for fs, C ~ 1 + fx 10 I.

interstellar colonization. It could be argued that, if possible, a civilization would eventually attempt colonization, fx can be considered as a function of L; such that if L is assumed to be large, f~ - 1. CONCLUSIONS

Our assumptions have led us to believe that C ~ 10. The Drake equation is therefore not strongly effected by interstellar colonization. It also implies that direct contact between extraterrestrials is very rare. We realize that m a n y arguments applicable to colonization may not be valid for exploration particularly for u n m a n n e d probes; yet our evaluation suggests that no " G a l a c tic C l u b s " m a y exist. The prospect of interstellar colonization does not have the devastating impact on S E T I as H a r t and others suggest. Interstellar colonization probably occurs on a small scale. Since c o m m u n i c a t i o n between the h o m e and colonized star systems would be likely, interstellar communication may be c o m m o n yet highly directional. Von H o e r n e r (1961) has suggested that such communication may increase the value of L and hence the introduction of C in the Drake equation may have multiple effects. Most importantly, since the chance of physical contact is so low, an effective S E T I program must rely on electromagnetic communication. The success of such programs can only be i m p r o v e d if interstellar colonization is taken into account.

ACKNOWLEDGMENTS The authors wish to thank Dr. C. P o n n a m p e r u m a , Dr. B. Z u c k e r m a n , Dr. J. P. Harrington, and Ms. J. K e m p e r , all of the University of Maryland, for their helpful c o m m e n t s and assistance.

An Evaluation of f j Since the arguments o f Hart and others need only one civilization to attempt colonization, a value for fx has not been considered. Once it is shown that colonization cannot sweep across the galaxy, it b e c o m e s n e c e s s a r y to investigate the motivations for

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