Habitable zones about main sequence stars

Habitable zones about main sequence stars

ICARUS37, 351--357 (1979) Habitable Zones about Main Sequence Stars MICHAEL H. H A R T 1 Systems and Applied Sciences Corporation, 6811 Kenilworth ...

475KB Sizes 36 Downloads 161 Views

ICARUS37, 351--357 (1979)

Habitable Zones about Main Sequence Stars MICHAEL

H. H A R T 1

Systems and Applied Sciences Corporation, 6811 Kenilworth Avenue, Suite 606, Riverdale, Maryland 20840 Received November 16, 1977; revised July 10, 1978 Calculations show that a main sequence star which is less massive than the Sun has a continuously habitable zone about it which is not only closer in than the corresponding zone about the Sun, but is also relatively narrower. Let L (t) represent the luminosity after t billion years of a main sequence star of mass M, and let rinnerand routerrepresent the boundaries of the continuously habitable zone about such a star--that is, the zone in which an Earthlike planet will undergo neither a runaway greenhouse effect in the early stages of its history nor runaway glaciation after it develops an oxidizing atmosphere. Then our computer results indicate that rout~J ri . . . . is roughly proportional to [L(3.5)/L(1.O)] 11~. This ratio is smaller for stars less massive than the Sun (because they evolve more slowly), and the width of the continuously habitable zone about a main sequence star is therefore a strong function of the initial stellar mass. Our calculations show that rl .... = routerfor M ~ 0.83M® (i.e., K1 stars), and it therefore appears that there is no continuously habitable zone about most K stars, nor any about M stars. 1. INTRODUCTION I n a n earlier p a p e r ( H a r t , 1978), herea f t e r referred to as P a p e r I, t h e a u t h o r has discussed t h e c o n s t r u c t i o n of a c o m p u t e r s i m u l a t i o n which follows the e v o l u t i o n of the a t m o s p h e r e of t h e E a r t h over t h e course of geologic time. T h a t m o d e l a t t e m p t s to explicitly t a k e i n t o a c c o u n t all the m a j o r processes w h i c h h a v e affected the b u l k c o m p o s i t i o n of t h e a t m o s p h e r e a n d the m e a n surface t e m p e r a t u r e of the Earth. 2 T h e results of those c a l c u l a t i o n s i n d i c a t e d t h a t h a d the E a r t h b e e n s i t u a t e d o n l y 5 % closer to the S u n a r u n a w a y 1Present address: Physics Department, Trinity University, San Antonio, Texas 78284. 2 The possibility exists, of course, that there are other processes, not taken into account in the model, which had a major effect on the Earth's surface temperature or atmospheric composition. Similarly, even the processes included in the model might have been approximated inadequately.

g r e e n h o u s e effect w o u l d h a v e o c c u r r e d a b o u t 4 b y (billion years) ago. O n the o t h e r h a n d , if the E a r t h h a d b e e n s i t u a t e d o n l y 1 % f u r t h e r from t h e Sun, r u n a w a y glaciation would have occurred a b o u t 2 by ago, w h e n free 02 a p p e a r e d in the E a r t h ' s a t m o s p h e r e a n d all b u t t r a c e a m o u n t s of r e d u c i n g gases were e l i m i n a t e d ( t h e r e b y s h a r p l y r e d u c i n g the g r e e n h o u s e effect). T h o s e results i n d i c a t e d t h a t the continuously h a b i t a b l e zone a b o u t the S u n (i.e., the region w i t h i n which a p l a n e t m i g h t e n j o y m o d e r a t e surface t e m p e r a t u r e s cont i n u o u s l y t h r o u g h o u t t h e 3 or 4 b y n e e d e d for a d v a n c e d life forms as we k n o w t h e m to evolve) is s u r p r i s i n g l y n a r r o w . I t is n a t u r a l , therefore, to i n q u i r e how wide the C H Z ( c o n t i n u o u s l y h a b i t a b l e zone) is a b o u t o t h e r m a i n s e q u e n c e stars. I t is to t h a t q u e s t i o n t h a t this p a p e r is addressed. I n the course of this p r o j e c t a long series of c o m p u t e r r u n s were m a d e , each one

351

0019-1035[79/010351-07502.00/0 Copyright O 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.

352

MICHAEL H. HART

following the evolution of the a t m o s p h e r e of an Earthlike planet orbiting a b o u t a main sequence star. The only inputs varied from run to run were: (a) the mass, and therefore the luminosity, L(t), of the central s t a r ; and (b) the radius of the planet's orbit. I t was assumed t h a t life would spontaneously arise and continue to evolve on a n y such planet provided t h a t the surface t e m p e r a t u r e was m o d e r a t e enough for there to be liquid w a t e r at some location on the planet's surface, a n d t h a t evolution to the stage of photosynthetic organism would only require ~ 8 X 108 years. N o t surprisingly, the results show t h a t the C H Z (continuously habitable zones) a b o u t smaller, less luminous stars are closer in t h a n the C H Z a b o u t the Sun. More importantly, those results (which are presented in Section 3 of this paper) indicate t h a t the C H Z a b o u t small stars are relatively narrower t h a n the C H Z a b o u t the Sun. T h a t is, if router and ri . . . . . represent the outer and inner radius of the CHZ, the ratio router/ri . . . . is smaller for less massive stars. E v e n a b o u t the Sun, the ratio r o u t e r / ri . . . . is only a b o u t 1.05. For a star of mass 0 . 8 3 M o - - a typical K1 s t a r - - w e find t h a t router/ri . . . . ---- 1.0. In other words, there is no continuously habitable zone a b o u t most K or M stars. This perhaps surprising conclusion depends, of course, not only on the model used for the E a r t h ' s atmosphere, but also on the form of the mass-luminosity law for main-sequence stars, and on the evolution rates of main-sequence stars. The derivation of t h a t input data is described in Section 2 of this paper. Such data, however, no m a t t e r how carefully derived, m a y be in error. The sensitivity of our results to the input d a t a on luminosities is discussed in Section 4. The sensitivity of our results to some of the possible errors in the underlying c o m p u t e r simulation

(the one described in P a p e r I) is discussed in Section 5. 2. MASS-LUMINOSITY RELATIONSHIPS The luminosity of a main-sequence star (of a given age) depends on its mass, and can be a p p r o x i m a t e d - - f o r stars whose mass is not too different from the S u n ' s - - b y L = K ( M / M o ) p . The a p p r o p r i a t e value to be used for p depends, however, on the age of the stars involved. Let us denote b y m the a p p r o p r i a t e value of p for the zero-age m a i n sequence, a n d let us denote b y n the value a p p r o p r i a t e for a set of main-sequence stars of age 4.5 by. Since low mass stars evolve more slowly t h a n heavier stars, it is plain t h a t n ~ m. A star's rate of evolution, of course, depends on its initial composition. Since those few stars whose masses are well known are of varying compositions, it is impractical to estimate m and n from astronomical observations. A more practical w a y of estimating m is to use the theoretical stellar models of D e m a r q u e and Larsen (1964). T h e y constructed models of zero-age main-sequence stars having various masses, but all having the composition X = 0.67; Y - - 0.30; and Z = 0.03. The best fit to their results, for stars in the range 0.80 < M / M o < 1.03, is obtained b y using m = 5.139. On the other hand, the best fit to the zero-age models of I b e n (1967)--who used the composition X = 0.708; Y = 0.272; Z = 0.020--is obtained b y using m = 5.021. Copeland (1970) used X = 0.70 ; Y = 0.27 ; and Z = 0.03, and the best fit to his results is m = 4.902. Maeder (1976) used the same composition as Copeland, but his results are best m a t c h e d b y using m = 5.015. All these figures are close to each other, which indicates t h a t minor differences in composition (or in the c o m p u t a t i o n s of stellar structure) do not greatly affect the value of m. We should therefore not be too far off b y using their average, m = 5.02. (Of course, it is logically possible t h a t the

HABITABLE ZONES theories of all those a u t h o r s are off systematically.) If we e s t i m a t e n f r o m t h e e v o l u t i o n a r y m o d e l s of D e m a r q u e a n d L a r s o n (1964) we get n = 6.037. If, i n s t e a d , t h e m o d e l s of M a e d e r (1976) are e m p l o y e d , t h e r e s u l t is n - - 5 . 8 5 0 . T h e a v e r a g e of those t w o figures is n = 5.94. T a b l e I, w h i c h f o r m e d the basis of o u r m a i n c o m p u t e r r u n s , was c o n s t r u c t e d b y u s i n g the v a l u e s m = 5.02; n = 5.94 a n d b y a s s u m i n g t h a t L(O.O)/L(4.5 by) = 0.75 for t h e S u n (Ulrich, 1975). I t is p l a i n t h a t if m a n d n are each increased b y t h e s a m e a m o u n t , t h e figures i n c o l u m n 4 of T a b l e I will n o t be altered. B u t c h a n g i n g ( n - m) will affect t h a t ratio, a n d will therefore affect t h e r e l a t i v e w i d t h (i.e., rout~r/ri. . . . ) of t h e C H Z a b o u t a m a i n s e q u e n c e star. 3.

RESULTS FOR (n - m) = 0.92

T h e p r i n c i p a l series of c o m p u t e r r u n s w h i c h were m a d e e m p l o y e d as L(t) l i n e a r interpolations from the data given in c o l u m n s 2 a n d 3 of T a b l e I. T h e results of those r u n s are e x h i b i t e d i n T a b l e I I . 3 I t c a n be seen t h a t t h e C H Z a b o u t a G8 s t a r is v e r y n a r r o w , a n d t h a t t h e r e is no C H Z a b o u t m a i n s e q u e n c e stars l a t e r t h a n KO. The computer simulations indicate that o n p l a n e t s w h i c h are much closer to the c e n t r a l s t a r t h a n rin,~ it is a l w a y s too h o t for oceans to condense. O n p l a n e t s h a v i n g a n o r b i t a l r a d i u s o n l y s l i g h t l y less t h a n the critical distance, oceans will exist i n t h e e a r l y stages of t h e p l a n e t ' s h i s t o r y ; b u t t h e b u i l d u p of a t m o s p h e r i c gases, c o m b i n e d w i t h t h e increase i n l u m i n o s i t y of t h e c e n t r a l star, causes a r u n a w a y g r e e n h o u s e 3 Since the input data fed into the computer simulation is not reliable to three decimal places, it is plain that the results in this table cannot have three-figure accuracy either. The extra decimal places in this table were retained only to enable the reader to clearly see the trend of the results, since the trend itself is physically meaningful. Similar comments apply to the figures in Tables III-V.

353 TABLE I

MAss-LuMINOSITY RELATION FOR MAIN-SEQUENCE STARS

M/M®

LzAMs/L®

L4.~by/L® L4.~by/ SpT LZAMS

1.20 1.15 1.10 1.05 1.00 0.95 0.90 0.85 0.80

1.873 1.513 1.210 0.958 0.750 0.580 0.442 0.332 0.245

2.953 2.294 1.761 1.336 1.000 0.737 0.535 0.381 0.266

1.577 1.516 1.456 1.395 1.333 1.271 1.210 1.148 1.086

F7 F8 F9 GO G2 G5 G8 K0 K2

to Occur a f t e r a b o u t 109 years. I t is t h e r e fore t h e stellar l u m i n o s i t y a f t e r a b o u t 109 years w h i c h is crucial i n d e t e r m i n i n g t h e i n n e r b o u n d a r y of the C H Z . Since ri . . . . is r o u g h l y p r o p o r t i o n a l to l-L(1.0 by)-] 1/~, a n d s i n c e L ( 1 . 0 by) ¢¢ MI,n+2/9(n-m)l = M5.22, we w o u l d expect t h a t ri . . . . o~ M2.01. I n d e e d , the formula ri . . . .

:

0 . 9 5 8 ( i / M o ) 2.6~ A U

(1)

t u r n s o u t to be a close a p p r o x i m a t i o n to t h e results listed i n c o l u m n 3 of T a b l e II. I n our c o m p u t e r s i m u l a t i o n s , E a r t h l i k e p l a n e t s which are s i t u a t e d considerably f u r t h e r from t h e i r S u n t h a n router u n d e r g o r u n a w a y g l a c i a t i o n as soon as m o s t of the TABLE II HABITABLE ZONES ABOUTMAIN-SEQUENCI!~ STARS LIGHTERTHANTHE SUNa Stellar mass

(M / M 0)

1.00 0.95 0.90 0.85 0. 835

Approximate spectral type

G2 G5 G8 K0 K1

Continuously habitable zone r~..... (AU)

r o u t ~ width (AU) (AU)

0. 958 0. 837 0. 728 0.628 0. 598

1. 004 0. 867 0. 743 0.629 0. 598

0. 046 0. 030 0. 015 0.001 --

Calculated using (n - m) = 0.92 (=best estimate).

354

MICHAEL H. HART

r e d u c i n g gases are eliminated f r o m their atmospheres, which generally occurs a b o u t 2.5 b y after the planet is formed. But, for planets s i t u a t e d just b e y o n d router, r u n a w a y glaciation does not occur until a b o u t t = 3.5 by. I t is therefore the stellar l u m i n o s i t y after a b o u t 3.5 b y which determines the o u t e r b o u n d a r y of the CHZ. Since L(3.5 by) o: M~,~+7/9(,,-,~)~ = M 5.74, we would expect t h a t router cc ~l~r2.sT. Indeed, the f o r m u l a routor = 1 . 0 0 4 ( M / M o )

2"87 A U

(2)

is an excellent fit to the c o m p u t e r results given in c o l u m n 4 of Table I I . For planets s i t u a t e d a b o u t stars heavier t h a n the S u n (see Table I I I ) r u n a w a y glaciation occurs s o m e w h a t earlier, a n d the relationship w e a k e n s to routor ~ M 2'~8I t m i g h t be expected t h a t the C H Z is wider a b o u t stars which are slightly more massive t h a n the Sun. Such is indeed the case (see T a b l e I I I ) , a n d the C H Z is quite wide a b o u t G O a n d F8 stars. But, b y the time t h e y are 4 b y old, stars of mass >__ 1 . 1 0 M o are emitting considerable a m o u n t s of uv r a d i a t i o n - - s o much, in fact, t h a t on planets orbiting a b o u t t h e m at a m o d e r a t e distance t h e u v flux is so great as to severely inhibit the spread of life to d r y land. (See discussion in P a p e r I a n d in TABLE III HABITABLE ZONES ABOUT MAIN-SEQUENCE STARS: STARS HEAVIER THAN THE SUN a

Stellar mass ( M / M ®)

1.00 1.05 1.10 1.15 1.20

Approximate spectral type G2 GO F9 F8 F7

Continuously habitable zone rlnner (AU)

router width (AU) (AU)

0. 958 1. 086 1.240 1.420 1. 616

1. 004 1.150 1.310 1. 481 1. 668

0. 046 0. 064 0.069 0. 061 0.054

a Calculated using (n - m) = 0.92 (= best estimate).

B e r k n e r a n d 5~Iarshall, 1964). For such stars, (1) u n d e r e s t i m a t e s ri ..... a n d a b e t t e r fit to the inner b o u n d a r y of the C H Z is given b y ruv = 0 . 9 2 7 ( M / M o )

TM

AU.

(3)

I n a n y event, m a i n - s e q u e n c e stars heavier t h a n a b o u t 1 . 2 M o evolve so quickly t h a t planets which are near e n o u g h to a v o i d r u n a w a y glaciation at t = 3.5 b y i n v a r i a b l y b e c o m e far too h o t b y t = 0.4 by. If intelligent life takes ~ 4 . 5 b y to develop, we c a n n o t expect it to develop a b o u t such stars. (The formulas used to c o n s t r u c t Table I c a n n o t be used for such stars, since such formulas only a p p r o x i m a t e mainsequence evolution, a n d do not approxim a t e evolution into the red-giant stage). 4. SENSITIVITY OF RESULTS TO VALUE ADOPTED FOR ( n - m) F r o m the foregoing, it is obvious t h a t the w i d t h of the C H Z a b o u t a star d e p e n d s on how r a p i d l y t h a t star evolves. T h e c o m p a r a t i v e rates of evolution of a g r o u p of stars depends, in turn, on the value of the q u a n t i t y ( n - m). Since, even for a specified initial composition, we do not k n o w (n - m) exactly, it is necessary to see how sensitive our results are to the value of (n -

m).

First, let us suppose t h a n (n -- m) = 0.5, r a t h e r t h a n 0.92. Using, for simplicity, the values m = 5.0, n = 5.5, we can c o n s t r u c t a table (not shown) c o r r e s p o n d i n g to T a b l e I. A set of c o m p u t e r runs were m a d e using luminosities i n t e r p o l a t e d f r o m such a table. T h e results of those runs are s h o w n in Table IV. We see t h a t even using this v e r y low estimate of ( n - m) the c o m p u t e d C H Z is v e r y n a r r o w a b o u t stars with M < 0 . 8 5 M o (roughly K O stars), a n d there is no C H Z at all a b o u t stars h a v i n g m _< 0 . 7 1 5 M o (KS stars). Alternatively, we can suppose t h a t ( n - m) = 1.25. Using m = 5.0, a n d n --6.25, we can c o n s t r u c t still a n o t h e r table (not shown) c o r r e s p o n d i n g to T a b l e I. A

HABITABLE ZONES TABLE IV HABITABLE ZONES ABOUTMAIN-SEQUENCE STARSa Stellar mass ( M / M ®)

1.20 1.15 l . 10 1.05 1.00 0.95 0.90 0.85 0.80 0.75 0.715

Approximate spectral type F7 F8 F9 GO G2 G5 G8 K0 K2 K4 K5

Continuously habitable zone ri .... (AU)

router width (AU) (AU)

1. 543 1. 370 1.221 1. 083 0. 958 0. 840 0. 732 0. 634 0.542 0. 460 0.407

1. 630 1. 454 1.292 1. 143 1. 004 0. 874 0. 755 0. 649 0.551 0.463 0.407

0. 087 0. 084 0.071 0. 060 0. 046 0. 034 0. 023 0. 015 0.009 0. 003 --

Calculated using (n - m) = 0.5 (=low estimate). set of c o m p u t e r r u n s were m a d e u s i n g l u m i n o s i t i e s i n t e r p o l a t e d from t h a t t a b l e too, a n d t h e i r r e s u l t s are p r e s e n t e d in T a b l e V. T h o s e r e s u l t s i n d i c a t e t h a t if (n - m) is as high as 1.25, t h e n t h e C H Z is v e r y n a r r o w e v e n a b o u t G8 stars, a n d does n o t exist a t all for K stars. W e c o n c l u d e t h a t the r e s u l t s are n o t e x t r e m e l y sensitive to t h e exact v a l u e used for ( n - rn). F o r a n y p l a u s i b l e v a l u e of ( n - m) t h e r e is no C H Z a b o u t M s t a r s a n d t h e C H Z a b o u t K s t a r s is e i t h e r v e r y n a r r o w or n o n e x i s t e n t . T h e C H Z is p r o b a b l y q u i t e n a r r o w a b o u t late G stars also, w i t h the exact w i d t h d e p e n d i n g o n t h e details of the a s s u m p t i o n s m a d e . 5. SENSITIVITY OF RESULTS TO ASSUMPTIONS IN COMPUTER SIMULATION All of the foregoing r e s u l t s h a v e b e e n o b t a i n e d b y m a k i n g use of t h e c o m p u t e r s i m u l a t i o n d e s c r i b e d i n P a p e r I. T h e r e are, of course, a p p r o x i m a t i o n s a n d u n c e r t a i n t i e s i n a n y such c o m p u t e r s i m u l a t i o n . I t is therefore r e a s o n a b l e to ask to w h a t degree defects i n t h a t c o m p u t e r p r o g r a m will affect the r e s u l t s of this a n a l y s i s .

355

T h a t p r o g r a m , for example, c o m p u t e s t h e i n n e r r a d i u s of the C H Z a b o u t t h e S u n to be 0.958 AU. S u p p o s e t h a t , b y n o t u s i n g a sufficiently s o p h i s t i c a t e d m e t h o d of c a l c u l a t i n g the g r e e n h o u s e effect, t h e p r o g r a m has o v e r e s t i m a t e d t h a t distance, a n d t h a t a m o r e a c c u r a t e figure w o u l d be 0.93 AU. [-That was t h e lowest v a l u e s u g g e s t e d b y Rasool a n d de B e r g h (1970)3. H o w s h o u l d this affect o u r e s t i m a t e s of rl . . . . a b o u t o t h e r m a i n s e q u e n c e s t a r s ? Since t h e r e is some t h e o r e t i c a l j u s t i f i c a t i o n for t h e v a l u e of t h e e x p o n e n t i n (1), we m i g h t r e a s o n a b l y replace t h a t e q u a t i o n b y ri . . . .

=

0 . 9 3 ( M / M o ) 2"~1 AU.

(la)

If we t h e n c o m b i n e ( l a ) a n d (2), we find t h a t ri . . . . = router for M = 0 . 7 4 5 M o . T h a t w o u l d m e a n t h a t there is some C H Z (albeit a n a r r o w one) a b o u t m a i n s e q u e n c e stars as late as K4. If ri . . . . a b o u t the S u n s h o u l d r e a l l y be 0.912 A U (which w o u l d m e a n t h a t t h e c o m p u t e r s i m u l a t i o n of P a p e r I h a s u n d e r e s t i m a t e d the w i d t h of t h e C H Z , b y a factor of 2) t h e n we m i g h t p l a u s i b l y replace (1) b y rl . . . . The

=

0 . 9 1 2 ( M / M o ) 2.6I AU.

c o m b i n a t i o n of

(lb)

and

(lb)

(2) gives

TABLE V HABITABLE

ZONES

Stellar mass ( M / M 6))

Approximate spectral type

1.20 1.15 1.10 1.05 1.00 0.95 0.90 0. 871

F7 F8 F9 GO G2 G5 G8 K0

ABOUT MAIN-SEQUENCE

STARS a

Continuously habitable zone rinner (AU)

router width (AU) (AU)

1. 668 1. 456 1. 262 1.089 0. 958 0. 836 0. 726 0. 664

1. 692 1.499 1. 321 1.155 1. 004 0. 861 0. 732 0. 664

0. 024 0. 043 0. 059 0.066 0. 046 0. 025 0. 006 --

Calculated using (n - m) = 1.25 (=high estimate).

356

MICHAEL H. HART

Merit--0.691Mo, which is about a K6 star. Since even larger errors in the computation of ri .... cannot be definitely excluded, the possibility exists that there are CHZ about all main sequence K stars, although much narrower than those about G stars. Defects in the algorithms for estimating r,,ut,r are much less likely to affect the conclusions of this paper. In the first place, the calculations for r u n a w a y glaciation are somewhat simpler than those for the r u n a w a y greenhouse effect. In the second place, the range of possible values of routo~ about the sun is severely limited. Most climate models of the E a r t h indicate that even t o d a y a reduction of more than 4% in the solar constant (possibly much less) would cause r u n a w a y glaciation (Budyko, 1969; Sellers, 1969; Schneider and GalChen, 1975). 4 It follows that router is probably no greater than 1.020. Replacing (2) by

routor = 1 . 0 2 0 ( M / M o ) 2s7 AU

(2b)

g i v e s - - w h e n combined with (1)--Merit = 0.786Mo. T h a t would allow a narrow CHZ about K2 stars, but none about stars later than K3. This would be only a slight modification of the conclusions stated in Section 3. Another important assumption is that the planet in question has the same mass and radius as the Earth. Since m a n y of the processes involved depend on the size of the planet (for example, a larger planet might well have a thicker atmosphere and therefore a larger greenhouse effect) it would be useful to know how sensitive the results are to the planet size assumed. Research now in progress by the author indicates that the numbers in Tables I I - V are surprisingly sensitive to planet size, although the trends illustrated in columns 4 Of course, those climate models may not be correct. Currently available climate models still have feedback problems associated with them which cause their results to be uncertain.

3-5 still hold for planets somewhat larger or smaller than the Earth. 6. SUMMARY AND DISCUSSION Our calculations indicate that the continuously habitable zone is fairly narrow, even about G2 stars, and is even narrower about later G stars. There is probably no CHZ about most K and M stars. These results are fairly insensitive to the initial composition assumed for the central stars, unless it is so extreme as to make (n - m) significantly less t h a n 0.5. T h a t might possibly be the case for very metalrich stars, having Z > 0.04 (see Tinsley, 1976). The results of the analysis do not seem to be very sensitive to the minor details of the computer simulation. The results do, however, depend on the overall picture which that computer simulation gives of the evolution of our atmosphere, to wit: (a) The early atmosphere of the earth contained large quantities of reducing gases such as H~, CO, or CH4. (b) Oxygen released by photosynthesis converted that atmosphere into an oxidizing one. (c) The crossover occurred about 2 billion years ago. Such a sequence of events seems quite plausible. Of course, the habitable zone is wider about GO and late F stars. But stars earlier than F7 become red giants in less than 4 by, so it is unlikely that an advanced civilization could originate about such stars. I t appears, therefore, that there are probably fewer planets in our galaxy suitable for the evolution of advanced civilizations than has previously been thought. ACKNOWLEDGMENT Much of this research was conducted while the author held an NRC Resident Research Associateship at the Laboratory for Planetary Atmospheres in NASA's Goddard Space Flight Center.

H A B I T A B L E ZONES REFERENCES BERKNER, L. V., AND MARSHALL,L. C. (1964). The history of the growth of oxygen in the earth's atmosphere. In The Origin and Evolution of Atmospheres and Oceans (P. M. Brancazio and A. G. W. Cameron, Eds.), pp. 102-126. Wiley, New York. BUDYKO, M. I. (1969). The effect of solar radiation variations on the climate of the Earth. TeUus 21, 611-619. COPELAND,H., JENSEN, J. O., ANDJORGENSEN,U. U. (1970). Homogeneous models for population I and population II compositions. Astron. and Astrophys. 5, 12-34. DEMARQUE, P. R., AND LARSON, R. B. (1964). The age of galactic cluster NGC 188. Astrophys. J. 140, 544-551. FAEGRE, A. (1972). An intransitive model of the Earth-atmosphere-ocean system. J. A ppl. Meteorol. 11, 4-6. HART, M. H. (1978). The evolution of the atmosphere of the Earth. Icarus 33, 23-39.

357

IBEN, I. (1967). Stellar evolution. VI. Evolution from the main sequence to the red-giant branch for stars of mass 1M®, 1.25Mo, and 1.5 M®. Aslrophys. J. 147, 624-649. MAEDER, A. (1976). Stellar evolution. V. Evolutionary models of population I stars with or without overshooting from convective cores. Astron. and Astrophys. 47, 389-400. RASOOL, S. I., AND DE BERGI-I, C. (1970). The runaway greenhouse and the accumulation of CO2 in the Venus atmosphere. Nature 226, 1037-1039. SCHNEIDER, S. H., AND GAL-CHEN, T. (1973). Numerical experiments in climate stability. J. Geophys. Res. 78, 6182-6194. S~:LLERS, W. D. (1969). A global climate model based on the energy balance of the Earth-atmosphere system. J. Appl. Meteorol. 8, 392-400. TINSLEY, B. (1970). Effect of main-sequence brightening on the luminosity evolution of elliptical galaxies. Astrophys. J. 203, 63-65. ULRICrr, R. K. (1975). Solar neutrinos and variations in the solar luminosity. Science 190, 619-624.