In search of other planetary systems

I N S E A R C H O F O T H E R P L A N E T A R Y S Y S T E M S

DAVID C. BLACK

Space Science Division, NASA-Ames Research Center, Moffett Field, Calif. 94035, U.S.A.

(Received 11 January, 1979)

Abstract. Numerous recent developments have led to an increasing awareness of and interest in the detection of other planetary systems. A brief review of the modern history of this subject is presented with emphasis on the status of data concerning Barnard's star. A discussion is given of'plausible observable effects of other planetary systems with numerical examples to indicate the nature of the detection problem. Possible types of information (in addition to discovery) that observations of these effects might yield (e.g., planetary mass and temperature) are outlined. Also discussed are various candidate detection techniques (e.g., astrometric observations) which might be employed to conduct a search, the current state-of-the-art of these techniques in terms of measurement accuracy, and the capability of existing or planned facilities (e.g., space telescope) to perform a search. Finally, consideration is given to possible search strategies and the scope of a comprehensive search program.

1. Introduction

1.1. HISTORICAL PERSPECTIVE

A c o m p r e h e n s i v e rev iew of the h is tory of this sub jec t would begin at the dawn of

r e c o r d e d h is tory and ex t end to the presen t . I n d e e d the p lane t s of our, own p l a n e t a r y

system, a l though not r ecogn ized as p lane t s by ear ly man , p l a y e d cent ra l ro les in much

of his fo rma l i zed re l ig ious and my tho log i ca l thought , and the obse rva t i ona l s tudies of

these p lane t s f o r m e d in large m e a s u r e the beg inn ings of a s t ronomy. H o w e v e r , in

view of l imi ted space , we shall on ly be c o n c e r n e d here with the ' m o d e r n ' h is tory of

this subjec t .

I t has long been rea l i zed that a s t rome t r i c s tudies of s tars might r evea l the p re sence

of so-ca l led d a r k c o m p a n i o n s to those stars. A classic e x a m p l e of this type of s tudy

concerns the b ina ry s tar sys tem Sirius A and Sirius B. B a s e d on obse rva t ions of Sirius

A, which showed that Sirius A ' w o b b l e d ' as it m o v e d across the sky, F. W. Bessel

ca l cu la t ed tha t the w o b b l e was due to an unseen c o m p a n i o n of cons ide rab l e mass.

A l t h o u g h Besse l was ab le to p red ic t the pos i t ion of the c ompa n ion , it r e m a i n e d

und i s cove red unti l 1864. The c o m p a n i o n , Sirius B, is now k n o w n to be a whi te dwarf

whose mass is c o m p a r a b l e to the mass of the Sun.

T h e p e r t u r b a t i o n in Sirius A ' s m o t i o n as seen f rom the E a r t h is a b o u t four arc sec.

If the c o m p a n i o n had the mass of Jup i te r , r a the r than tha t of the Sun, the

p e r t u r b a t i o n would have been p r o p o r t i o n a t e l y smal ler . Such a smal l p e r t u r b a t i o n is

at the l imit of the m e a s u r e m e n t capab i l i ty of p r e se n t te lescopes . H o w e v e r , t he re are

a n u m b e r of s tars less mass ive than Sirius A , a few of which are also c loser to the so lar

system. Pe t e r van de K a m p at Sprou l O b s e r v a t o r y , rea l iz ing that p e r t u r b a t i o n s in the

m o t i o n of these nearby , less mass ive stars might be de tec t ab le , in i t ia ted the first

sys temat ic search for o t h e r p l a n e t a r y sys tems and ushe red in the ' m o d e r n ' e ra of ou r

subject .

Space Science Reviews 25 (1980) 35-81. 0038-6308/80/0251-0035 $07.05. Copyright 0 1980 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston U.S.A.

36 D A V I D C. B L A C K

The first results with the Sproul Observatory 's 24-inch telescope were presented in

1943 by K. A. Strand. The results indicated that one of the two small stars in the binary star system known as 61 Cygni had a dark, or unseen, companion. The 61

Cygni study was soon followed by other tentative discoveries of dark companions to

small stars with such strange sounding names as BD + 43 ~ 4305, Epsilon Eridani, Lalande 21185 and Barnard 's star (see Table I). One object among those listed in

Table I has received far more attention, caused more excitement and controversy than all of the others listed; that object is Barnard 's star. We will discuss this

interesting subject in Section 1.4.

TABLE I

Suspected planetary systems

Name of system Distance Planet masses Periods (light yr) (Jupiters) (yr)

Barnard's S 5.9 1.1, 0.8 26, 12 Lalande 21185 8.2 20 8.0 Epsilon Eridani 10.8 6-50 25 61 Cygni 11.0 8 4.8 BD + 42 ~ 4305 16.9 10-30 28.5

Although modern activity in the area of detecting extrasolar planetary systems has been ongoing for several decades, the subject has languished in the relatively quiet

backwaters of astronomy, as technology opened other new and exciting vistas for

astronomical study. Three separate studies which have been carried out during the past four years have both led to and exemplified a renewed interest in searching for other planetary systems. The watershed for current intensified interest was a series of

six N A S A - A m e s Research Center sponsored scientific workshops, during the interval 1974-1976, chaired by Philip Morrison. These workshops were directed at

an indepth evaluation of the scientific basis of, and strategy for, the undertaking of a

Search for Extraterrestrial Intelligence (SETI). A document (NASA SP-419) sum- marizing the findings of the SETI Workshops is now available f rom the Government

Printing Office. As the only form of intelligent life we know of originated and developed on a planet, it was natural for the SETI Workshops to consider the status of evidence for the existence of other planetary systems. As a consequence of the SETI Workshops, a separate workshop on planetary detection was convened in 1976

under the direction of Jesse L. Greenstein and David C. Black. (Detailed minutes from the two Planetary Detect ion Workshops are available upon request.) The Greenste in-Black Workshops concentrated on determining which techniques might be employed in a search for extrasolar planets, as well as potential difficulties at tendant to those techniques. One of the major conclusions of the Greens te in- Black Workshops is that the technical problems associated with the various potential

IN S E A R C H O F O T H E R P L A N E T A R Y S Y S T E M S 37

planetary detection techniques could be solved with relatively modest effort. The third recent study related to detection of extrasolar planets was a summer faculty systems design study (NASA SP-436) at NASA's Ames Research Center. The

study, dubbed Project Orion, was sponsored jointly by Stanford University and Ames Research Center and was directed by the author. The principal thrust of Project Orion was to develop a system design for an improved ground-based astrometric telescope. The rather novel telescope concept which emerged from that study has a theoretical accuracy which is some 30-50 times the accuracy that is attainable with existing instrumentation. In addition to developing a systems concept for a ground-based astrometric telescope, the Project Orion study considered system aspects of two space-based planetary detection techniques which were first discussed in the Greenstein-Black Workshops. The Project Orion study corroborated in part the aforementioned conclusion of the Greenstein-Black Workshops, namely that proper application of existing or near-term, state-of-the-art technology would produce significant results. A fourth NASA Ames sponsored workshop chaired by the author, is currently underway and will examine in more detail the physical and technological limitations to the accuracy of ground-based techniques, as well as what one could learn from such techniques if they were operating at their accuracy limit. The results of this fourth study should be available by June of 1979.

1.2. A SCIENTIFIC PERSPECTIVE

A concerted effort to search for other planetary systems could be envisioned as the logical extension of the current exploration of the solar system. However, such an effort involves more than exploration; it also would permit new and important measurements in many other areas.

One of the major goals of the NASA, as well as the research careers of some of the most distinguished thinkers in history is to understand the origin of the solar system. This goal will be forever unattainable if we do not obtain quantitative information regarding characteristics (e.g., frequency of occurrence, dependence on stellar type, architecture) of planetary systems as a general phenomena. Unless we have the type of information against which we can compare theoretical constructs, we will be relegated to a posture of speculation regarding the origin of the solar system. The situation is analogous to trying to understand the evolution of the Sun in the absence of data concerning other stars. Our current rather complete understanding of the general features of stellar evolution is on a firm basis only becuase we have amassed observational data pertaining to a large number of stars. A program to search for other planetary systems could provide a break-through in understanding of such systems comparable in scope to that afforded by the HR diagram in understanding stellar evolution.

At present we have no firm quantitative, and only suggestive qualitative, evidence regarding the formation and evolution of planetary systems. Currently accepted hypotheses suggest that the conditions necessary, if not sufficient, to form planets arise around newly formed (or forming) stars as a natural consequence of the star

38 DAVID C. BLACK

formation process. Observations to affirm or deny this prediction or to provide the foundations for alternative hypotheses, would come directly from a program designed to search for extrasolar planetary systems.

In addition to the direct results of a search for other planetary systems, there is a long list of valuable observations which could be carried out with the instrumentation which would be developed in order to conduct a search. For example, second order tests of general relativity could be performed using astrometric observations which are accurate at the 10 -6 a r c sec level. Radial velocity studies with systems which operate at the 10 m s -1 accuracy level would yield significant advances in knowledge concerning the frequency and nature of binary systems (high mass ratio single line spectroscopic systems which are undetectable at present would be easily detected). Other applications, depending on the type of instrument(s) developed for a search could be listed, and the reader can probably imagine many which the author would overlook.

1 .3 . W H A T IS A P L A N E T A R Y SYSTEM?

It is appropriate at this point to define a few concepts, particularly that of 'planetary system'. To the more pragmatic readers, this section may seem unnecessary; they will simply try to detect the smallest astronomical objects that available instrumentation allows, and not be concerned with what these objects might be called. However, from an interpretive aspect, the question posed in this section is, I believe, relevant.

The reader no doubt has his own idea as to what constitutes a planetary system. Generally, the definition of planetary system involves a gravitationally bound system consisting of a star and at least one planet. For example, Huang (1973) states 'A planetary system must be stable in a timescale comparable to that of the central star in the main-sequence stage, and have one or more planets revolving around the star in nearly coplanar and circular orbits in the same sense'. This and similar definitions of a planetary system (hereafter referred to as PS) require a definition of the term 'planet'. Most efforts in this regard define a planet as an object whose mass falls within certain limits (we will not be concerned here with a lower mass limit as none of the foreseeable detection techniques would detect such a small object).

What is the upper mass limit for a planet? Any self-gravitating object which at some phase of its evolution derives a major fraction of its total luminosity from nuclear fusion of hydrogen is defined to be a star. Theoretical studies (e.g., Graboske and Grossman, 1971) indicate that the lower mass limit for hydrogen burning is

0.06-0.08M| Grossman and Grabosky (1973) have shown that if an object has a sufficient abundance of deuterium (fraction by mass - 2 x 10-4), nuclear burning of deuterium via the reaction 2D(p, v) 3 He can produce sufficient internal luminosity to give rise to a deuterium main-sequence. The relatively low ignition temperatures required for deuterium burning can be reached by objects with mass > 0.01MG. If the primordial deuterium abundance in stars is lower than 2 x 10 -4, burning will still occur, but significant energy will only be produced for higher masses. There is at least one other mass limit at which there occurs a qualitative change in the structure of an

IN S E A R C H OF O T H E R P L A N E T A R Y S Y S T E M S 39

object. A low mass, low temperature, solid body must rely on interatomic elec- trostatic forces to counterbalance gravity. In this case, the relation between the mass

M and radius R of the body is R w . M 1/3. However, as the mass increases there is a

continuing increase in internal pressure. Ultimately, the pressure becomes great enough to ionize the material. Once a sufficient number of free electrons are produced, their degeneracy pressure exceeds the interatomic forces and becomes the major agent counteracting gravity. When electron degeneracy pressure is important, the mass-radius relation becomes R o c M -~/3. Thus R increases with mass as M ~/3

until a maximum radius Rc is reached and degeneracy effects become important, whereupon R decreases with increasing mass as M 1/3. Zapolsky and Salpeter (1969) have at tempted to determine Rc and the associated critical mass Mc for bodies of various compositions. Their results indicate that Mc ranges from 0.001 12M| for a pure helium body to 0.003 16Mo for a pure hydrogen body and to 0.005 89Mo for a pure iron body.

In his review article, Huang (1973) suggests that the upper mass limit for a planet should be one at which only a small ( ~< 10 -3) fraction of an object 's luminosity is ever derived from thermonuclear processes. However, there were no studies available to him, such as that by Grossman and Graboske, which calculated that limit. Thus, Huang adopted the upper mass limit for a planet of -0 .06 -0 .08M| Utilizing Grossman and Graboske's results in conjunction with Huang's luminosity criterion, one would set the upper mass limit for a planet at - 0 . 0 1 M| Huang further recognized that there may be field objects of planetary mass, referring to such objects as 'planet-like', and added the requirement that a planet must be gravitationally bound to a star as well as have the correct mass.

It would appear that there are at least two mass limits which might be used to define what is meant by 'planet' and hence what constitutes a planetary system. It further appears that there is no a priori fundamental justification for choosing one of these limits over the others as a defining criterion; we can only say with'confidence what is not a planet. One is led to the conclusion that although we have knowledge in varying degrees about nine 'planets', the collective knowledge is not yet sufficient to specify the defining characteristic of a planet in a rigorous, scientifically meaningful manner.

If we cannot define 'planet', can we meaningfully define 'planetary system'? If one is concerned with improving our understanding of the processes which governed the origin of the solar system, our definition of 'planetary system' must contain implicity some discrimination with regard to processes. A recent study (Abt and Levy, 1976) has shown that the mass function for the secondary members of long period ( > 1 0 0 y r ) binaries is consistent with the van Rhijn function (Figure 1) which characterizes field stars in general, whereas the mass function for short period (< 100 yr) binaries (Figure 1) is markedly different. These authors note that their data for short period systems can be represented approximately by the relation

N ( M ) ~ M ~ , (1)

40 D A V I D C. BLACK

1.0

I I I I P < 10 2 years

Z

0 "J .5

; / 2 ~ 0

1 / 3 ~ ' / - ~ Q ~ 1 / 3 0 ~ ~ 1/2

I I I I I 1.1 .6 .3 .15 .0"/5

M (SOLAR MASSES)

I I Ivan Rhijn~_ P > 102 y e a r s ~

Z _ /)r 103"105

I I 1,1 .6 .3

Fig. 1. The logarithm of the number of secondary bodies of a given mass is plotted against secondary mass. The left panel pertains to binaries with orbitals periods < 10 2 yr; the right hand panel to binaries with periods > 10 2 yr. Dashed curve in right hand panel is the distribution due to van Rhign. Dashed curves in the left hand panel are theoretical curves of the form N ( M ) e c M t~ for/~ = 0, �89 and 3.1 Figure' is'

from Branch (1976).

where N ( M ) is the number of secondary objects of mass M and/3 is a positive exponent. Abt and Levy obtain/3 = �89 from their study. Branch (1976) reexamined their data after applying corrections for a bias in the data which favored inclusion of short period binaries in the data sample (the Abt-Levy survey was a magnitude limited survey), and came to the same qualitative conclusion as had Abt and Levy. However, Branch stressed that the uncertainties in the data precluded establishing with certainty that the mass function of the secondaries is a power law, and they certainly preclude establishing that/3 = �89 If one assumes that the mass function for secondaries is given by equation (1) and integrates over the mass range 0.07 < M < < 1.2M| (the average mass of the primary star in the Abt -Levy survey is - 1.2Me), one finds that ~ 55% of stars have short period stellar companions for/3 -�89 If the integration is carried over the mass range 0 . 0 ' 1 < M < 0.07M| it indicates that

15% of the stars have short period, deuterium burning companions. Finally, one finds that - 1 2 % of the stars have short period companions in the mass range M < 0.01Mo. These percentages are highly uncertain owing to a strong sensitivity to the value of/3 and, more importantly, on the extrapolation of Equation (1) to a mass regime well beyond the data set. A measure of the sensitivity to/3 can be had by noting that if/3 = 1, the number of companions with M < 0 .07Me is reduced by a factor of two over the corresponding number for/3 = �89 If/3 = 0, the distribution is singular in the sense of predicting an infinite number of companions with M < 0.07Mo. In spite of these uncertainties, the Abt-Levy study raises the possibility that a significant number of stars have short period, low mass (~<0.001M| companions.


To date, all of the available evidence concerning the architecture of multiple star systems shows that when three or more objects are involved, the orbits involve a hierarchy of binary systems (e.g., co-revolving binary system and a single star for a triple system, or co-revolving binary systems for a quadruple system). If low mass

( - 0 . 0 0 1 M e ) companions are formed in binary systems, and if the orbital architecture observed for wholly stellar multiple systems also obtains for multiple systems involving a star plus two or more non-stellar companions, then these systems would have a markedly different orbital structure than does the solar system. In the solar system, the loss mass companions principally revolve about the star; there is no binary type hierarchy. This suggests that the formation mechanisms operative in the formation of the solar system differed from those operative in the formation of binary and multiple systems.

The point of view adopted here is that a PS is any bound system consisting of a star and at least two sub-stellar mass companions, and with a nonhierarchial orbital architecture. Thus, a system comprised of a star and a companion with a mass equal to that of Jupiter is not a PS. This definition of PS avoids the pitfalls of defining in an independent (and as we have seen, ad hoc) way what one means by 'planet'. In fact, strict application of this definition of PS to observed systems may operationally define the physical characteristics of a 'planet'. Throughout the remainder of this article the term planet will be used, but it should be stressed that the term as used here is operationally defined through the above definition of a PS.

1.4. HAVE ANY OTHER PLANETARY SYSTEMS BEEN DISCOVERED.9

As noted earlier, one object among those listed in Table I has received far more attention and caused more controversy than all of the others combined; namely Barnard's star. In view of the relative notoriety of the Barnard's star story, the somewhat scattered literature on the subject, and the relevance of this story to the subject of this review, we attempt to summarize and place in perspective the various studies of this M-dwarf star.

The attention given this otherwise average star stems directly from Sproul Observatory data (Figure 2) which, if correct, indicate that Barnard's star has a very low-mass, dark companion (or companions). Two early analyses of the Sproul data have been given by van de Kamp (1963, 1969). The former showing that a single companion of mass comparable to the mass of Jupiter revolves about Barnard's star in an eccentric orbit (e = 0.6) with an orbital period of 24 yr. Van de Kamp's (1969)

analysis showed that the Sproul data were equally consistent with the interpretation that the wobble in the motion of Barnard's star is due to two Jovian mass dark companions with orbits that are circular and coplanar, and with orbital periods of 12 yr and 24 yr. Two points should be made regarding the Sproul data shown in Figure 2. First, they reveal very little perturbation in the y-coordinate (Decl.); the perturbation occurs primarily in the x-coordinate (RA). Second the x-coordinate data reveal rather pronounced displacements around the 1949 and 1957 epochs. We will return to these two points later. The conditions of circular and coplanar orbits


Fig. 2.

PLANE A S T R O M E T R Y

RA "~Eo A �9 0. , I0 �9 ~ , t , , , ~ o ~ o - - 0

_ - " ' � 9 " ~'-~ I I i I I i

1940 45 1950 55 1960 65 I 0"01 I I I I I I

- - O O - - - - O0 0 . - - + 1 # - ~ tre'~- " �9 J " " " - 6 ~ o ~ ~ o uecl. �9 �9 ~""0 ~ ~ , O -

- - �9 �9 �9 " - - - 1 / z

Perturbations in RA(x) and Decl.(y) of Barnard's star. Figure is from van de Kamp (1969).

cited in van de Kamp's (1969) analysis were no t derived from the data, but rather were input assumptions to the data analysis.

Two of the key papers involving the controversial aspects of the Barnard's star story appeared in 1973, the first authored by Hershey and the second by Gatewood and Eichhorn. Hershey, working at Sproul, found from a detailed astrometric analysis of Sproul plates taken of the field of AC+65 ~ 6955 that this plate field revealed small, 'sudden' changes in the x-coordinate. These discontinuities appear to be related to adjustments and/or alterations to the Sproul 24-inch refractor (Hershey, 1973) and occur noticeably at the 1949 and 1957 epochs - coincident with the epochs of abrupt x-coordinate perturbation in the apparent position of Barnard's star. Gatewood and Eichhorn (1973) studied a total of 241 plates taken of Barnard's star using the 20-inch visual refractor at Van Vleck Observatory and the 30-inch photographic refractor at Allegheny Observatory. Their findings of the x-coordinate behavior of Barnard's star are shown in Figure 3. (The size of the plotted data represents statistical weights, larger points representing more accurate data.) The Gatewood-Eichhorn study clearly does not confirm the Sproul data, and if correct would vitiate previous interpretations concerning the nature and perhaps existence of any dark companion(s) to Barnard's star. In an attempt to address the documented discontinuities in the Sproul data, van de Kamp (1975) re-examined the Sproul data

4-wtO ~

, l ~ . . e

02 I

0 .1

== A A V "",,o �9 ~ s -

/ ~'qL. J

I I I I I I I I I I .2 .3 .4 .5 .6 .7 .8 .9 1.0 1.1

PHASE

Fig. 3. Perturbations in RA(x) of Barnard's star. Figure is from Gatewood and Eichhorn (1973).

IN SEARCH OF OTHER PLANETARY SYSTEMS 43

from the years 1950-1974. These data were also reduced using an improved plate measuring machine. The yearly mean data from this revised study are shown in Figure 4 (compare Figures 2 and 4). Van de Kamp retained the assumption of circular orbits in his analysis of the data and found that the long-period perturbation that was prominent in his earlier data was much weaker, but still present in the new analysis, and that the short-period perturbation was 'confirmed'. He estimated that the masses of the long-period and short-period companions were respectively one Jovian mass and 0.4 Jovian masses. Unlike his earlier work, he did not constrain his modeling of the companion system to coplanar orbits, and found that the best fit to the data obtained when the companion orbits were inclined relative to each other by 20 ~ .

RIGHT ASCENSION O / X I 1 ~ ' I j I ~ 0 . '701 I

1950 X / 55 1.960 65 1970 75 - - 1980 I ' I ' I ' I

u O 0 O0 O O

O O O

DECLINATION D O

Fig. 4. Perturbat ions in RA(x) and Decl.(y) of Barnard ' s star. Figure is from van de Kamp (1975).

The most recent examination of all astrometric data on Barnard's star since 1950 is that by Gatewood (1976). Gatewood attempted to incorporate the Sproul data, after applying corrections to that data which he discusses in his paper, with similar data from the Allegheny and Van Vleck telescopes. His intent was not so much to provide higher accuracy by means of an expanded data set, but rather to ascertain whether there exists any evidence from the three independent sets of data which is at least consistent with a wobble in the motion of Barnard's star. Gatewood concluded that the combined data are 'suggestive' of a perturbation, although in light of the strong possibility of unremoved systematic errors, one might better say that the data are 'not inconsistent with' a perturbation.

What then can be said about Barnard's star, or more specifically, the elusive dark companions to B arnard's star? There are still questions as to whether simply ignoring pre-1950 Sproul data avoids systematic effects in the Sproul data. Certainly van de Kamp's use of a rather small number of reference stars (4 compared to 19 in the Gatewood-Eichhorn analysis) makes his analysis more susceptible to systematic effects, although it is difficult to quantify the effect of including additional reference stars in the analysis. It would seem that we can make two statements concerning the available data concerning planetary companions to Barnard's star. First, this data is at best ambiguous, and second, any perturbations to the motion of Barnard's star are at or below the level of present astrometric observational accuracy. The practical implications of these two statements are respectively that:


(1) there is at present no firm observational evidence for the existence of other planetary systems; and

(2) significantly improved instrumentation will be required if we are to obtain firm observational evidence on the existence of other planetary systems.

The remainder of this review is divided into four sections. In Section 2, we discuss possible observable manifestations of the planetary systems, while Section 3 deals with potential techniques by which these observable effects might be detected. Section 4 contains a summary of the major points in this review, as well as some specific suggestions regarding future activity in this important research area.

2. Observable Manifestations ot Extrasolar Planetary Systems

Having defined what we mean by 'planetary system', we consider some of the possible observable manifestations of a PS.

2.1. GENERAL CONSIDERATIONS

The task of detecting other PS is essentially that of detecting the planetary members of such systems. There are two general categories of effects by which these planets might be detected. One category involves radiation from a planet, while the other category involves effects that a planet has upon its central star. We shall refer to detection based on effects in the former category as direct detection (DD), whereas detection based on effects in the latter category will be termed indirect detection (ID).

Planets can be sources of both thermal and non-thermal radiation. The temperature characterizing the thermal component of a planet's radiation is determined by a balance between energy input (e.g., internal radioactivity and external stellar radiation) and radiative loss from the planet. The non-thermal radiation component

can arise from processes which are intrinsic to a planet, as well as from reflected radiation from the central star of a PS. Two potentially relevant examples of non-thermal planetary radiation are the Jovian decametric bursts (e.g., Carr and Desch, 1976) and the recently discovered CO2 emission feature at I = 10.6 ~m in the

spectrum of Venus (Townes, 1976). Under the rubric of ID, one can identify at least three potentially observable

effects, viz., perturbations in the proper motion of a star as it moves with respect to a reference frame defined by other stars, variations in the apparent wavelength of spectral features in a stellar spectrum, and dimming in the apparent luminosity of a star. If a star has a planetary companion, the star will revolve about the barycenter of the planet-star system with an orbital period equal to the orbital period of the planet. The projection of that orbital motion on the plane of the sky gives rise to the first effect mentioned above, whereas the projection of the orbital motion along the line-of-sight to the star gives rise to the second effect. The third effect derives not from dynamics but rather from a transit of the star as a planet moves between the

star and an observer.

IN S E A R C H OF O T H E R P L A N E T A R Y SYSTEMS 45

2.2. CHARACTERIZING THE OBSERVABLES

Although the list of observable manifestations of a PS given above is almost certainly not complete, it does provide a basis for a more detailed analysis and characterization of possible detection schemes. The following material outlines the functional rela- tions governing these observables, thereby permitting a quantification of the detection problem, as well as considering the possible additional information content (beyond detection) from observations of these effects.

2.2.1. Governing Equations

Imagine a simple PS consisting of a star and two planetary companions (Figure 5). The mass, diameter and temperature of the star are denoted respectively by M, , d, , and T,, and the corresponding parameters for the ith planet are denoted by M~, d~, and T~. The barycenter (center of mass) of this hypothetical PS is located at distances IR,I and IRel from the centers of mass of the star and planets respectively. For simplicity, it is assumed that the planetary orbits, and hence the reflex orbit of the star, are coplanar. Also, the planetary orbits about the barycenter are taken to be circular and characterized by an orbital period P~.

Fig. 5.

M1 _

M 2

Schematic diagram of an imaginary simple planetary system. Planetary orbits are assumed to be coplanar and circular.

A representation of the instantaneous positions of the planets is shown in Figure 6. The x-axis corresponds to RA, the negative y-axis to Decl., and the z-axis to the line-of-sight (LOS) of a distant observer. The position angles (Ai) of each planet in the orbital plane vary in time according to Ai -- 2~rt/Pi. The instantaneous position of

46 DAVID C. BLACK

the star in the orbital plane of the star with respect to the barycenter is given by the conditions:

M,R, cos A, =MIR1 cos A1 +M2R2 cos A2,

M,R, sin A, = M1R1 sin itl +M2R2 sin A2. (2.1)

The instantaneous position of the star in terms of its projection on the plane of the sky is

x = R , [cos A,(cos 4' cos & - s i n 4' sin q~ cos i ) -

- s i n A,(sin 4' cos ~b +cos 4' sin cb sin cos i)],

y = R, [cos 4' sin ~ +sin 4' cos ~b cos i)+

+sin A,(sin 4' sin ~b - c o s ~ cos & cos i)]. (2.2)

This variant of Euler's angles is frequently used in astrometry, and the coefficients in parentheses are related to the Thiele-Innes constants (cf. van de Kamp, 1967) (convention varies in defining the angles; frequently the angle q~ which here defines the line of nodes, that is the intersection of the true orbital plane with the plane of the sky, is measured relative to the negative y-axis (Decl.). However the longitude of periastron, 4', and the inclination i of the true orbit to the plane of the sky are

generally defined as shown in Figure 6.) For circular orbits, 4' = 0 ~ and Equation

(2.2) becomes

x = R, [cos A, cos ~b - s i n i t , sin ~b cos i ] ,

y = R, [cos it , sin ~b - s i n i t , cos 4~ cos i] . (2.3)

\ / -

|

PLANE OF THE SKY

Fig. 6. Definition of the geometry used in deriving the equations used in Section 2. The various quantities are defined in the text.


One other equation which will be of interest is the component of the stars velocity along the LOS, viz.,

V,(LOS) = - V. sin (A, +X) sin i , (2.4)

where it is assumed that & defines the ascending node and X is the angle between the star's radius and velocity vectors (X = 7r/2 for circular motion). Note that the orbital constraint on the definition of a PS can be formally stated as

IR,I<[Rll for all time. The convention in numbering planets is that planet I is the nearest to the barycenter.

The total radiation flux ~i(v) from one of the planets depicted in Figure 5 will consist of a sum of three components, thermal, reflected and non-thermal (reflected radiation is non-thermal, but from this point on in the discussion we shall take non-thermal to apply to planet-specific radiation),

~ i ( P ) = (~TH(,b') + ~ R E F ( / 2 ) -~- (/)NT(b') . ( 2 . 5 )

The various @(v) terms represent the flux per unit frequency interval. A general characterization of q~NT(V) is not possible owing to the wide range of physical mechanisms which could give rise to non-thermal emission. We will however consider some specific examples in Section 2.3. If one assumes that the intrinsic thermal flux from a planet is that of a black body at temperature Ti, then

2~2d 2 h~ 3

qbTr~(v) = c2 [exp (hu /kT~) - 1] ' (2.6)

where c, h, and k are respectively the speed of light in vacuum, Planck's constant, and Boltzmann's constant, the reflected component of planetary radiation may be expressed as

qOREV(~ ) = rffqb, (V), (2.7)

where f denotes the fraction of the stellar radiation flux ~ . ( v ) that is incident upon the planet, and the parameter rt denotes the fraction of the incident radiation which is reflected. In the context of Figure 5, one may write

( d i ~ 2 f = \ 4 R J " (2.8)

The parameter r/is generally a complex function of frequency and composition of the reflecting media, and also depends on the relative alignment of an observer with respect to the star-planet pair. Typical albedo values for atmosphereless planets in the solar system (e.g., Mercury, Moon) are - 0.1, whereas corresponding values for terrestrial and gas giant planets range from - 0.3 to ~ 0.7, with detailed frequency dependence (particularly due to absorption in the planetary atmosphere) varying markedly from planet to planet. In the spirit of this review, we shall not attempt to


model 7/based on details of solar system planetary r/values, rather we shall take *7 to be roughly constant, the value of that constant being a free parameter.

We may rewrite Equation (2.5), excluding ~NT(V), using Equations (2.6)-(2.8) as follows:

4~(~,)--c~d~L r3+ c2(v, r,) 3 (2.9)

where ca = 2~'2h/c 2 is a constant, and

c2(v, T) = [exp (hv /kT) - 1] -1 .

In deriving Equation (2.9) it has been assumed that 4),@) is given by Equation (2.6) with stellar variables replacing the appropriate planetary variables (i.e. Ti ~ T, , di ~ d,). Equation (2.9) indicates the energy per unit frequency interval leaving the planet. A quantity which is of greater relevance from the detection standpoint is the fraction of that energy which would fall upon a detector located on or near the Earth. Ignoring effects such as limb darkening and energy losses in the interstellar medium,

we have

l a B ( v ) ] .~ , , EDET(V) = [ ' ~ - ~ - J '~'i~V), (2.10)

where A and B(v) are respectively the area and the frequency bandwidth of the detector and D is the distance from the planet to the Earth. The number of photons NDET(V) arriving at the detector is

NDZT(V) EDrST(V), (2.11) hv

provided that B (v) << v. One other parameter of interest is the ratio H(v) of planetary radiation to stellar radiation, viz.,

H(v) = ~ i ( v ) /O , ( v )

T,) + ] \ d , ] Lc-~, T,) 1 6 R f J ' (2.10)

where we have ignored any q)~T(V) contributions to q)i(v). At high frequencies,

d 2 H ( v > k T , / h ) ~ 16R~ "

At this limit, H(v) is independent of stellar properties and of v. At low fequencies,

T, df H ( v < kTdh) - T , d2, ,

again independent of v, but dependent on both stellar and planetary properties. Equations (2.3)-(2.10) provide an admittedly simplistic but useful characterization of the key aspects of observables accessible to DD techniques.


As noted earlier, we will consider here three observables which are in principle amenable to study by ID techniques.

(A) The amplitude of the reflex orbital motion of the star depicted in Figure 5 about the barycenter of the PS is R, . However, the observed quantity is not R, , but rather the apparent orbit size suitably scaled to allow for the distance D between the observer and the PS. (We have assumed that the necessary first steps in defining the position of the photocenter of the star, viz., correction for proper and parallactic motion, have been done.) The apparent instantaneous angular position of the photocenter with respect to the barycenter is given by

0x ~- arctan (x/D),

Oy ~ arctan (y/D). (2.11)

In general, x/D and y/D are small so that Ox(Oy)-x/D (y/D) for 0 expressed in radians. Combining Equations (2.1), (2.3), and (2.11),

Ox(t)=9.8xlO-4KiMlfr /2rrt ) /[cos cos -

(2rrt+ ~:1) sin d~ cos i] + -sin \ P1

+aft[ c~ '21 ] c ~ . /2rrt ~ i]}, (2.12) 6 - s i n ~-p-~--2 + ,2 / s in ~b cos

where K1 = RI/M., a = M2/MI,/3 = Re~R1, M, and Mi are expressed respectively in units of solar and Jovian masses, Ri are expressed in AU, and D is expressed in parsecs. In deriving Equation (2.12) we have used Ai = (27rt/PO+,i where ,~ is a phase angle corresponding to the value of X,. at t = 0. A similar relation may be written for G- Equation (2.12) gives 0x in arc sec.

(B) Motion of the star about the barycenter could also give rise to Doppler shifts in spectral lines associated with the star. The instantaneous orbital speed of the star about the barycenter is given by

V . = 2~-K1M1[~-~ + (~2~)2 +p21~ cos 0] 1/2 , (2.13)

where the parameters K, a, and/3 are as defined above, and

(P2-PI~ 0 = 2rr\~lP2J +,1 +'2.

The only observable Doppler shift will arise from the component of the orbital motion which is directed along the LOS. Using Equation (2.4) in conjunction with Equation (2.13), we have

[ 1 /afl\: 2a/3 ]1/2 V,(LOS) = -2r ) + p---~2 cos Oj sin (A,+x)s in i.

(2.14)


The fractional change in wavelength for stellar spectral features due to this orbital motion is

a2t V,(LOS)

2to c (2.15)

where 2t 0 is the rest wavelength of a spectral line and c is the speed of light. Comparing Equations (2.12) and (2.15), one notes that amplitude of the radial

velocity observable is independent of the distance D, whereas the amplitude of the astrometric observable varies inversely with D. (There is however an implicit distance dependent effect related to the radial velocity observable that arises because the accuracy with which one can measure AA depends in part upon the apparent brightness of the source.)

(C) If the planet-star orbital plane depicted in Figure 5 is oriented such that the planet will pass between a distant observer and the star, the apparent magnitude of the star will decrease during the transit of the planet "across the stellar disk. The magnitude of the brightness change, Ami, due to such a transit by planet i is given by

Ami = --2.5 log [1 -- (di/d.)2]. (2.16)

The Am value given by Equation (2.16) is the maximum possible, these would be a correspondingly smaller effect if the transit were partial. Equation (2.16) describes an average luminosity dimming. However, as pointed out in an extensive paper by Rosenblatt (1971), a potentially more sensitive indicator of this type of transit would be to photometrically monitor stars at different wavelengths. The essential point is that stellar limb darkening varies as a function of wavelength; being stronger at shorter wavelengths than at longer wavelengths. This wavelength dependent feature leads to a colorimetric transit signature, namely a blue enhancement at the onset and termination of the transit and a red enhancement during the middle of transit. This two-color discrimination of a transit event is clearly strongest when the body transits the stellar disk along a chord through the center of the disk, and is less pronounced if the transit is along shorter chords. Also, the enhanced blue appearance of the star at onset (termination) of transit occurs over only a fraction (-0.2) of the total transit, making it a transient condition. As with the radial velocity effect, the amplitude of this observable is not explicitly dependent upon the distance D. One other similarity with the radial velocity observable is the dependence of the observable on the orientation of an observer to the orbital plane of the planet(s) about the star under observation. However, whereas the radial velocity effect varies slowly with the angle i (sin i dependence), transit is observable only over a very limited range of orientations. We will examine the probability of detecting such a transit in Section 2.3. Equations (2.11)-(2.17) provide a characterization of observables which are accessible to ID techniques. We turn now to a discussion of the potential information content inherent in observations of the various observables.


2.2.2. Information Content

The generally employed modus operandi for scientific study of solar system objects involves a progression of activity from discovery to preliminary reconnaissance (either remote or in situ) to scientific exploration. In the context of most spacecraft missions, discovery has already occurred and missions generally center on the more advanced programmatic phases of reconnaissance or exploration. However, in the context of the topic of this review, the discovery phase is the first objective. An important question is the extent to which these observations that lead to discovery can also provide reconnaissance type information regarding planets/planetary systems which are discovered.

The essential aspects of information content for DD techniques are contained in Equations (2.7) and (2.10). The net energy flux on a detector, EDET(U), is effectively a measured quantity. The frequency u, detector area and bandpass B(u) are also known quantities. If we assume that the distance D to the star under observation is also known, then

where

M(A) = d/2 [c2(A, Ti) + ~fc2(A, T,)] , (2.17)

so that

M(A) -~ d~c2(A, Ti).

If observations are made of two or more infrared wavelengths, the temperature T~ can be determined provided that the thermal spectrum is that of a black body. Knowing the temperature, one can estimate the size of the planet, di from the measured parameter M(A ). The orbital period can also be determined from observations. Given the orbital period and an independent estimate of the mass of the star (from stellar evolution theory and the location of the star on the main-sequence), one can determine Ri from Kepler's Third Law. One possible use of knowledge concerning Ri involves a comparison of the temperature T~ with the temperature, Tss, of a perfectly conducting black sphere (Tss = 0.5T,(d,/Ri)l/2). If T/ is significantly greater than TBs, it could be indicative of important atmospheric effects on the planet or of significant internal heat sources in the planet.

In the visual portion of the spectrum, the inequality given in (2.19) is reversed so that

2 2 did, M(A) ~ r l l - ~ i 2 c2(A, T , ) .

4 2 5 [ ~DA ] M(A) = [ c Z -(x )JJ~DET(A ). (2.18)

Equation (2.17) relates measured parameters, M(A ), to the intrinsic properties of an observed PS. In the infrared portion of the spectrum,

c2(Z, T,) >> ~( d* ~2c2(A, T,) (2.19) \4Ri ]

52 DAVID C. BLACK

Values for T, and d , can be estimated from spectral observations of stars and stellar evolution theory, and a value for Ri can be estimated as discused above. However, in contrast to observations made at infrared wavelengths, observations made at visual wavelengths only provide a measure of the product ~d~; there is no way to independently determine either r /or di. In principle, multicolor observations of the planet could provide useful clues regarding the nature of the reflecting medium. For example, the reflected component of the Earth's radiation appears blue relative to solar light owing to the selective reflection of shorter wavelengths by the Earth's atmosphere.

The basic equation for astrometric observables is Equation (2.12) with the measured quantity being directly related to 0x and 0y. The mass of the star under study, M, , can be estimated as described above, and the distance D to the star can be measured. Thus, astrometric observations will yield data relating to the products M~R~. The orbital periods of the perturbing bodies provide an independent measure of Ri, thereby making it possible to obtain a measure of Mi. Although it is not obvious from the simplified exposition on astrometry given here, astrometric studies would also reveal much concerning the architecture of the PS.

The measurable parameters involved in radial velocity studies can be directly related to the product Mi sin i (see Equations (2.14) and (2.15)). Radial velocity studies do not provide any way of independently obtaining either Mi or sin i, so that one cannot be sure if a small measured value of AA is due to a low-mass companion or to a low value of i. This contrasts with astrometric studies where M~ is, in principle, obtainable from the data. Although radial velocity observations would not unam- biguously show that a given star has a planetary companion, they would provide statistical evidence for the existence of planetary companions. This evidence would rely on the assumption that the distribution for the relative orientation of extrasolar planetary orbits to an observer's LOS is not sparse, that is, the angle i has a reasonable probability of falling anywhere in the range 0 ~< i ~< ~-/2. Such an assumption is a fairly good one (the available evidence on the orientation of the rotation axes of stars and of the orbital angular momentum vectors for binary systems is in fact consistent with i being randomly distributed (e.g., Kraft, 1965)).

The information content inherent in photometric detection of other planetary systems is essentially contained in Equation (2.16). The measured or derivable parameters in that equation are Amg and d, , making it possible in principle to determine d~. As with the other ID observables, knowledge of the planet's orbital period will also result from the observations.

2.3. Q U A N T I F Y I N G T H E O B S E R V A B L E S : S O M E N U M E R I C A L E X A M P L E S

The equations presented earlier in this section indicate the relationship between the observable parameters associated with certain effects and the intrinsic parameters of the PS. In this section we consider specific star-planet parameter values in order to quantify the various observables and thereby gain insight into the magnitude/difficulty of a search. In view of the tack of a priori knowledge concerning


the 'probable' values for the parameters M,, d,, T, , Ri, Mi, di, and T~, we will consider a range in values for these parameters. An alternative approach would be to define a standard PS and determine the detectability of that standard system.

2.3.1. Direct Detection Observables

The principal equation concerning DD observables is Equation (2.7), and the relevant input parameters are d, , T,, Ri, d~, and T~. One of the unknowns which is particularily important for infrared searches for other planetary systems is T~. The highest equilibrium temperature that a solid black or grey body can attain as a result of stellar radiation is x/2 TBs. Generally speaking, the temperatures of solar system planets, as inferred primarily from infrared observations, is lower than this theoretical maximum, they are, however, in rough agreement with TBS. The run of Tas as a function of Ri for main sequence stars of spectral type 05 to M5 are presented in Figure 7. In the absence of any significant internal heat source, one would expect that the run of TBs indicated in Figure 7 would be representative of the run of T~. Planets whose mass is comparable to that of Jupiter can be expected to have non-negligible internal energy. Estimates of the relative energy balance in the case of present day Jupiter indicate that roughly �89 of Jupiter's luminosity is due to primordial heat left

g arises from solar radiant over from the formation of the planet, and the remaining 2 �9 input (Erickson et al., 1978). This level of primordial luminosity is equivalent to an effective temperature of - 9 7 K; which is shown as the vertical line in Figure 7. As pointed out by Black (1979), a 4.5 • 109 yr old Jupiter-like planetary companion to the majority of stars (i.e., those later than spectral type K0), would be much warmer than expected on the basis of stellar radiation input for R~-values greater than

M0 KK;\G0/G5 A5 M5 ~ / / / F 5 / A0 B5 B0 05

20

15

,~-

4 LOG TBS (k)

Fig. 7. Run of TBs as a function of Ri for various types of central star. Curves are calculated according to TBs = 0.5 T , (d,/Ri) 1/2. The horizontal line of TBs = 97 K corresponds to the effective temperature of

Jupiter due only to its intrinsic luminosity."

54 DAVID C. BLACK

1-5 AU. Thus, Jovian-like planets located at several A U from the intrinsically dim,

but numerous, late spectral type main-sequence stars would be much more luminous

than expected from radiation balance considerations alone. If we ignore for the moment this perhaps significant gain in infrared luminosity and

simply set Ti = TBs, we can calculate q0i(~,) vs 7, for hypothetical planets revolving

around a specified spectral type star. Figures 8a-12a show the variation of ~bi(u) vs ~,

for various assumed values of Ri and for five types of main-sequence stars (spectral

1014

1012

1010

s 108

106

10 4

10 2 10 0 10 9

10-2 7 b 1011~ C

;o? H 1 0 - 7 ~ 0.5

Q 103

I0-8 [--10-9~ - 101W l l i ~

1010 1011 1012 1013 1014 1015 108 109 1010 1011 1012 1013 10 TM 1015 108 105 1010 1011 1012 1013 10 TM 1015

v, Hz u, Hz v, Hz

Fig. 8. (a) The flux ~i (ergs Hz -1) is plotted against frequency ~. The central star is assumed to be an M0, main-sequence object. The run of ~i is shown for values of Ri = 0.5, 1, 2, 5, 10, and 20 AU. (b) The ratio Hi is plotted against frequency ~, with Ri varied as in (a). (c) The parameter Ol = H, ffPi is plotted as a

function of frequency, with Ri varies as in (a).

1014 V-

1

8,

#

100 109 1010 1011 1012 1013 1014 1015

Fig. 9.

10-2 b 1011

10-3 109

10-4

10_ 5 107

10 6 105 --

H 10-7 Q 103

10-8

10_ 9 101

10 -10 10 1

10-11 _ [ 10 -3

C

10-12 __ 2x 10-13 I I I t l i I 10-5 I L I I I I I

108 109 1010 1011 1012 1013 1014 1015 108 109 1010 1011 1012 1013 10 TM 1015

v, Hz v, Hz v, Hz

(a) Same as Figure 8a, but for a K0 spectral type star. (b) Same as Figure 8b, but for a K0 spectral type star. (c) Same as Figure 8c, but for a K0 spectral type star.


type A0, F0, GO, K0, and M0). If we consider a PS located at a distance D = 10

par sec, one can calculate the number of photons s -1 arriving on a detector with a

specified area and bandwidth. The infrared flux for a planet with a diameter of

1.5 x 101~ cm (somewhat larger than the diameter of Jupiter and close to the largest

diameter possible for a low temperature object) and a temperature equal to that of a

perfectly conducting black sphere located at distances of 0.5 and 20 A U from its

primary star is shown in Table II. These figures were calculated assuming that

1014 F

1

1

a

108 109

Fig, 10.

1018 1011 1012 1013 1014 1015 v, HZ

10-2

10-3

10-4

10-5 ;

10-6

10-7 H

10-8 --

10-9 --

10-10 --

10-11 --

10-12 _

2 • 10 -13 108

I 109

b lO11~ C

1 0 0 _

10 7 - -

105 0.~

Q 103

101

10-3 ~- i

I I I 1 I ~ l o - s L I I I I I I 1010 1011 1012 1013 1014 1015 108 109 1010 1011 1012 10 t3 1014

~, Hz v, Hz

(a) Same as Figure 8a, but for a GO speetral type star. (b) Same as Figure 8b, but for a GO spec~tral type star. (c) Same as Figure 8c, but for a GO spectral type star.

1014

1012

1810

10 6

104

10 z 108 109 1010 1011 1013 1013 1014 1015

10-2

10-3 J

10-4

10-5

10-6

H 10-7

10-0

10- 9

10-10

10-11

10-12

2 X 10 -13 108

Fig. 11.

b 1011 C

70; k //////

1o1 s///// III lO-, _r 10-3

I I I i I I I io ~5 ~ _ J i I i 109 1010 1011 1012 1013 1014 1015 108 109 1010 1011 1012 1013 10 TM 1

~,, Hz ~, Hz u, Hz

(a) Same as Figure 8a, but for a F0 spectral type star. (b) Same as Figure 8b, but for a F0 spectral type star. (c) Same as Figure 8c, but for a F0 spectral type star.

56 DAVID C. BLACK

101'1- a ~ AU 10-27

L-. 1o-? / '~ ~ 10 -4L.-

1 1012 ~ 2

5 10_ 5 101(; ~ ' ~ 1 0

/ ~ 2 0 10 -6

H 10-7 108

+'- I io-~ 106 10 -0

10-1c

1 0 4 ~ 2 ~ 10-11 --

10-12 10 z 2 x 10 -13

io I~ C

10 9

10 7

0,5 10~ 1

lO_ 1 ~ ~ " ' - 2o

I I I I I

10-3

10-5 I I i I I I 108 109 1010 1011 1012 1013 t014 1015

p, Hz 108 109 1010 1011 1012 1013 1014 1015

~, Hz

i 10s 100 1010 1011 1012 1013 1014 1015

~, Hz

Fig. 12. (a) Same as Figure 8a, but for a A0 spectral type star. (b) Same as Figure 8b, but for a A0spectral type star. (c) Same as Figure 8c, but for a A0 spectra/type star,

T A B L E II

IR photon flux (D = 10 pc)

Spectral type NDET(Ri = 0.5 AU) N~ET (Ri = 20 AU)

A0 840 30 F0 270 2 GO 174 9.3 K0 94 0.02 M0 31 - 10 -5 (10)

* Parenthetical value for M0 pertains to a planet with Ti = 100 K.

A -- 1 m z and B(v) = 0.1u (u = 1013 Hz; h = 30 txm). Clearly, planets close to early

spectral type stars provide a reasonable photon flux, whereas even planets close to late spectral type stars yield a relatively small photon flux. A related problem is that the spatial resolution of a telescope (at h = 30 ixm) with a clear aperture ~ 1 m is - 7 arc sec, which corresponds to roughly 70 AU at a distance of 10 parsec. In order to obtain spatial resolution corresponding to a few A U at a distance of 10 parsec would require an aperture of ~ 35-40 m[

However, spatial resolution is not the entire story. The values of H/ (v)= = ~ i ( u ) / ~ . ( ~ , ) for the star-planet parameters represented in Figures 8a-12a are

plotted in Figures 8b-12b. Two general characteristics of H(p) are of interest. First, the contrast ratio at longer wavelengths is more favorable for later spectral type stars than for earlier spectral types (the contrast ratio at short wavelengths is independent of stellar type). Second, the variation of contrast ratio with Ri at a fixed frequetacy is


most pronounced for frequencies in the transition region between the low and high

frequency, constant H(z,) regions. In particular, if we consider the variation of H (u ) with Ri for v = 1013 Hz, the variation is very severe ( ~ 107) around an M0 star, while

it is moderate ( - a factor of 30) around an A0 star for R/vary ing from 0.5 A U to 20 AU. The rather strong variation in H(v) with R~ for M0 stars obtains if the planet's temperature is that of a perfectly conducting black sphere. If, as noted earlier, a Jovian mass planet of modest age ( ~< a few billion years) is revolving about an M0 star, its intrinsic luminosity will be such as to keep if at an effective temperature - 1 0 0 K independent of its distance from the central star (for Ri ~> 1.5 AU).

Based on energy flux alone (i.e., ~ ( v ) ) one would argue that the infrared region of the spectrum is to be preferred over the visual portion in a search for planetary companions to late spectral type stars, whereas for early spectral type stars the choice of frequency regime is less obvious. However, consideration must be given to both energy flux and star-planet contrast ratio. The parameter O~(v)=t-L(u)cPi(v) is plotted in Figures 8c-12c for the same set of parameter values used in connection with Figures 8a-12a. Based on the parameter O(~,), one concludes that the infrared portion of the spectrum is more favorable than the visual for all spectral types. This preference for the infrared is made stronger if one is concerned with the number of

photons (a given energy flux corresponds to a factor of sixty fewer visual photons than infrared photons for h = 0.5 txm and h = 30 txm respectively).

As noted earlier in this section, there are a variety of non-thermal planetary radiation mechanisms. Several solar system planets (e.g., Earth, Saturn, and Jupiter) show evidence for non-thermal radiation arising from the interaction of charged particles with planetary magnetic fields. This radiation often occurs in bursts and typically occurs at frequencies which correspond to the gyrofrequency of a charged particle in the planetary field. Jupiter's strongest decametric bursts yield fluxes

10 9 Jy (1 Jy = 1 0 - 2 6 W m - 2 Hz-1). The flux from Jupiter as viewed from a distance

D is then

0.625 ~NT(JUpiter) ~ ----D-i-- Jy ,

where D is expressed in parsec. Current sensitivities for meter wavelength telescopes are - 1 Jy, so that one might hope to detect a Jovian strength burst arising from a planet revolving around stars within a few parsec of the Sun. It is possible that super-Jupiters exist in that they may have more energetic bursts and could thus be detected at corresponding greater distances. However, the very energetic bursts are short in duration (so-called L bursts last from 1-10 s, and the S bursts from 0.001-0.050 s; Carr and Desch (1976)) and tend to occur in a random fashion. The recently discovered CO2 emission line at A = 10.6 txm in the atmosphere of Venus is another example of non-thermal planetary radiation. Although this feature is too weak to be detected over interstellar distances, the possibility exists that maser amplification of certain molecular lines could be much stronger on other planets.


The magnitude of those effects which are amenable to study by ID techniques may be estimated from Equations (2.12) and (2.16). Consider the effect due to a planet with mass equal to that of Jupiter (i.e., M1 = M)s). The maximum angular perturbation in the position of the central star 0max = 9.8 X IO-4(K1M1/D), is shown in Figure 13a as a function of distance D and for various values of the parameter K1. Also shown (horizontal dashed line) in Figure 13a is the present level of accuracy obtained by the highest quality astrometric observation. Clearly there is a limited range of K1 and D values for which a Jupiter mass planet would give rise to a perturbation which could be measured with current astrometric facilities. The effect

P

E

103

102

101

1

10-1

10-2

10-3

10 -4

I a ii Ri/M.-- K 1 = 100 M1 = M 21

CURRENFoRAsTTRACCURyACYLIMIT --~

10 100 D (pc)

I ~ _ M 1 = M~ b

lO-1

~ 1 ~ -

~ io-4-

1o-S

10-6

lO-7 I 10 100

D (pc)

Fig. 13, (a) The max imum angular deflection 0max of a star, due to a planet with a mass equal to the mass of Jupiter, is plotted as a function of distance D between the Ear th and the star. The run of 0m,x is shown for a range of K1 = R1/M, values. The horizontal line indicates the accuracy of current ground-based astrometry observations. (b) Same as Figure 13a, with the mass of the companion planet set equal to the

mass of the Earth.


due to a planet with a mass equal to that of the Earth is shown in Figure 13b for the

same range of K1 values represented in Figure 13a. There is no range of parameter values in this latter case which lead to a perturbation that could be detected with current astrometric facilities.

Figures 13a and b show the maximum perturbation to be expected from a single planetary companion, however, we have defined a PS as having at least two planetary companions. What types of complication enter as one considers multi-planet

systems? Shown in Figure 14a is the one component of the photocenter motion as a function of time for a star with four planetary companions. Both 0y and time are in arbitrary units; the orbital periods of the four planetary companions are shown as

vertical lines. The parameters for this system are: a2 = 0.30, a3 = 0.046, a4 = 0.054, f12 = 1.84, f13 = 3.69, and f14 = 4.78. Similar plots for a three planet and two planet system are shown in Figures 14b and c respectively. The parameters for Figure 14b

are: a2=0 .153 , a3=0 .180 , f l2=2.01, f l3=3.15, while for Figure 14c the parameters are a2 = 1.18 and fl = 1.57. Two points can be made regarding Figure 14a. The first is that one would need measurements with errors much smaller than the peak amplitude of the perturbation in order to be able to accurately determine the fine structure of the perturbation. The second point is that although the reality of a perturbation could be established from a reasonably dense data set taken over a time base of 1-2P1, a detailed characterization of the perturbing system requires data over a time base > P4. Essentially similar conclusions follow from Figure 14b. A third point can be made from Figure 14c, namely that certain ai, fli combinations can give rise to photocenter displacements which are nearly constant over a reasonably long (compared to P~) interval of time. If an astrometrist were unfortunate enough to observe this PS during that time when there was essentially no change in 0y (there is also very little change in 0x during this interval of time; Figure 15), he would erroneously conclude that there are no companions to the star under study. If P1 and P2 are small ( ~ 5 - 1 0 yr), a typical long-term astrometry program would extend beyond this interval where dO/dt - 0. If, however, P I ~ several decades, this interval could persist for - 20-30 yr. Some readers might be thinking that these example PS are ad hoc and unlikely to exist in Nature. They are admittedly ad hoc, but at least one of them does exist. Figure 14a is the perturbation in the Sun's motion due to the combined gravitational influence of Jupiter, Saturn, Uranus, and Neptune. Figure 14b is the motion if Jupiter is removed and Figure 14c is the motion if only Uranus and Neptune were present. The final point to be made with regard to Figures 14a, b, and c is that if the orbital periods are all relatively short (i.e., ~> 1-2 yr), it becomes imperative that one have as much accuracy as possible in a few observations. The accuracy limit ( ~ 0.003 arc sec) cited in connection with Figure 13a pertains to a yearly normal point; the accuracy of a single night's observation is much poorer ( - 0.02 arc sec).

Equation (2.14) describes the LOS velocity of the star in our planetary system. Considering the effect of a single planet, for example that of Jupiter on the Sun, one finds that the star's orbital velocity about t he barycenter is a simple oscillatory

60 DAVID C. BLACK

~,~ 0

P1 P2 P3 P4

fiig, lv,t,, , i

time -,

i

b

P1 P2 P3

J j v v ~ " V V V V " v v v v ~ -

time -~-

0 v

P1 P2

C

TIME-*

Fig. 14. (a) The variation in 0y as a function of t ime for a four planet system. Both #y and time are in orbitrary units; the orbital periods of the four planets are shown as vertical lines. (b) Same as Figure 14a,

but with only three planets. (c) Same as Figure 14a, but with only two planets.

IN SEARCH OF OTHER PLANETARY SYSTEMS

17 �9 O16

�9

61

O14

O13

0.0024 AU 10 =~ �9 12 7 " O0 �9

BARYCENTER 11 �9 8

07

01 0 6

0 2 0 5

0 4 03

Fig. 15. A polar plot of the mot ion of a star with two planetary companions (the same system as shown in Figure 14c). At t ime zero (point 0), the planets are assumed to lie on the same radius vector. Subsequent points are indicated in units of a tenth of the orbital period of planet 1 (i.e., point 12 corresponds to 1.2 revolutions about the barycenter by planet 1). Note that points 9 - I 1 correspond to virtually no deflection

in y, and very little in x.

function with a peak to peak amplitude of - 26 sin i m s .-1. Shown in Figure 16 is the run of reflex speeds as a function of planet mass expected for various values Of the product, M.RI (Mi, M,, and Ri are in units of Jovian mass, solar masses and A U respectively). These speeds are for single planet perturbations only. However, as is

evident from Equation (2.14), the inclusion of a second planet introduces compli- cations. Specifically, the LOS component varies in time not only due to projection effects (sin (h . +X)), but also due to time variations in the magnitude of the star's velocity. For example, using the parameters of the system depicted in Figure 14c, one finds that the amplitude of the star's reflex velocity at the times of minimal astrometric motion (point 9, 10, and 11 in Figure 15) is respectively 0.18, 0.06, and

0.14 of its maximum value. This amplitude time variation occurs with an effective period PEFF = P1P2/(P2 - P1) =/3 3/2p I / (/3 3/2 -- 1). The convolution of this amplitude variation with the time variation of the projection of the velocity vector along the LOS could be a significant problem in terms of data interpretation.

Equation (2.16) describes the effect related to the third ID technique considered here. Using values of d~ and d , appropriate for Jupiter and the Sun, we find that Arni -- - 0.01 mag., whereas using d~ = de, we find that Arni -- - 9 x 10 -5 mag. Care- ful ground-based photometric studies can detect Am-values as small as 0.001 mag.,


10+2 [

10 -1

10-2

, d i i ill ~ i 10-3 10-2

. . . . I ' i ~ l ,

,S ......

10 -1 1 M i (M~.)

i r i ~ l l l ~ i i i i L , l i

10 10 2

Fig. 16. The maximum orbital speed of a star, due to perturbat ions by a planet of mass Mi.

so that one might expect to be able to detect a transit by a large planet, but detection

of a transit due to a terrestrial size planet is out of the question with current

ground-based instrumentation. For a given planet, the magnitude of the effect is greater the later the spectral type of the central star (because d , decreases). An

important consideration with regard to this effect is the probabili ty that a given

observer will be properly oriented so as to observe a transit of a distant star. The probabili ty PEcL that an observer will be located relative to an arbitrary PS in such a way as to see transit of the stellar member of that PS by one of its planetary

companions is PECL = D,/2Ri, where D , and Ri have their usual meaning. Ex- pressing D , and Ri in units of the solar diameter and A U respectively,

PEaL = 2.3 x 10 -3 D,/Ri. As PEeL << 1, the probability POBS that an arbitrary obser-

ver will be located so as to observe at least one transit in a sample of N stars is

POBS = 1 - (1 - PECL) N = ] -- e--NPEcL .

In order to have a 63 % chance of success, one must observe N - P E ~ L stars, whereas

one must observe N--3PE~L in order to have a 95% chance of success. Thus, continuous observation of - 2000 M 0 - G 0 stars over one year would provide a 95% chance of detecting a transit caused by a planet with a one year orbital period provided that (1) each of the stars has such a companion and (2) the orbital planes are

randomly distributed. The continuous nature of such an observing program (continuous here means that the time between successive observations of a given star must be ~< the duration of the transit event, which is slightly less than a day for this

specific example) should be stressed. The probability, QECL, that any given observation will occur during a transit is smaller than PECL by the factor D,/2rrRi, or QECL-- 1.7 X 10 6D2R2. In order to have a 95% chance of success of detecting a


transit arising from a planet with R; = 5 AU, assuming again one year of continuous observation, one must search - 2000 • 6 0 - 105 stars. Clearly, this ID technique is best suited for a search for large planets (a planet the size of Uranus or Neptune would give rise to a A m i ~ 0.003 mag. for an M0 star). One obvious problem with this technique involves verification that the observed variation in apparent brightness of a given star is due to transit by a planetary companion. Unfortunately, the best type of stars from the standpoint of maximizing the probability of detection (i.e., late spectral type) undergo intrinsic luminosity variations that are comparable to or greater than those expected from a transit event. This is a significant problem in terms of interpreting the data. The variant on the transit technique due to Rosenblatt is both less sensitive to intrinsic luminosity variations and more sensitive to intrinsic luminosity variations and more sensitive to transits by smaller planets.

Having discussed the observable effects of PS, the information content of observations of a given effect, and the order of magnitude for these effects in example PS, we turn now to a discussion of possible methods/instrumentation for observing these effects.

3. Potential Search Techniques

The discussion in the previous section was concerned with identifying some of the likely observable manifestations of other planetary systems and the order of magnitude of these observable effects for a range of specific star-planet parameters (i.e., a range of values for d,, T,, Ri, di and T~). In this section, we briefly consider some potential observational approaches which might be employed to detect these effects.

3.1. GENERAL COMMENTS

As we have seen, DD of extrasolar planetary systems at visual wavelengths involves detection of a relatively dim object (planet) which is close (in terms of angular separation) to a relatively bright object (star). The close angular proximity of planet and star is, of itself, no particular problem. There have been significant advances in recent years in the areas of speckle interferometry and active optics which permit ground-based telescopes to circumvent to a large extent the resolution limitations posed by the Earth's atmosphere. However, the aspect of the detection problem which these new methods do not address is the large brightness contrast between the planet and star. This brightness contrast problem makes it necessary to carry out DD above the Earth's atmosphere. Although the brightness contrast between planet and star at infrared wavelengths is more favorable from the detection standpoint, the effects of the Earth's atmosphere are again very deleterious to detection with ground-based telescopes. It appears that DD of other planetary systems must be done from space (a possible exception to this statement is discussed in Section 3.2.3).

Concerning ID of other planetary systems, the effects of the Earth's atmosphere range from inconsequential to significant, depending on the specific observable under study. The Earth's atmosphere does not present any particular difficulty for

64 DAVID C. BLACK

radial velocity observations, and it presents relatively minor problems for photometric observations. However, it appears that the Earth's atmosphere; specifically turbulent motion in the atmosphere, is the factor which will set the ultimate limit on the precision with which ground-based relative astrometry observations can be made (cf., Project Orion, 1979; Connes, 1976).

3 .2 . D I R E C T DETECTION TECHNIQUES

3.2.1. Detection of Reflected Visual Radiation

One expression of the resolving power ~ of a clear aperture telescope is

~(A, do)= 1.22~o ~ , (3.1)

where A is the wavelength of the radiation and do is the aperture size. Equation (3.1) is generally attributed to Rayleigh and hence is known as the Rayleigh criterion. Using Equation (3.1), one finds that a very modest aperture telescope (do - 25 cm) in space would have sufficient angular resolution at A = 0.5 txm to resolve two light sources separated from each other by a distance of 5 AU, and separated from an observer by a distance of 10 parsec (i.e., ~ -- 0.5 arc sec). However, the Rayleigh criterion is strictly applicable to resolving two light sources of equal intensity, (i.e. H = 1) it is not applicable to resolving two light sources where H << 1.

The transmission of light in a clear aperture is constant over the aperture and zero outside the aperture. This abrupt change in transmission at the aperture edge produces an intensity pattern in the image plane of the telescope of the form.

r-o 2, z ( 0 ) = t 2 o "

where the aperture is taken to be circular, 0 is the angle measured from the optical axis of the system, and I1 is the first order Bessel function. It is assumed in writing Equation (3.2) that O in radians is small so that sin 0 - 0. The intensity I(0) at 0 = 0 is

simply

1r2d~ I ( 0 ) = (3.3)

16

If the light is monochromatic, all of the higher order maxima in I(0) would be present. However, in astronomical studies, a number of wavelengths are simultaneously observed causing all but the first several maxima to be smeared into a generally smooth background by the superposition of the J1 patterns for the various A-values. For values of 0 such that I(0)<< I(0) and for typical bandwidths, an asymptotic expansion of j2 may be used to obtain the ratio I(0)/(I(0)), viz.,

I(0) - 3 x 10-1srd~ 3, (3.4) (I(O)) LAJ


where (1(0)) is the mean intensity at angle 0. Equation (3.4) may be used to obtain a

generalization of the Rayleigh criterion which is valid in the limit of small contrast ratios between two light sources (i.e., H << 1),

do0 = 7 . 1 1 • 104 h H1/3, (3.5)

where H = ~ i / ~ , - (1(0))/1(0) is the brightness contrast ratio at angle 0 (expressed

in arc sec). Using the Sun-Jupiter example discussed in Section 2.4 (0 = 0.5 arc sec, H = 2 x 1 0 -9 ) and A = 0.5 Ixm, Equation (3.5) indicates that the required clear aperture to resolve such a system must have d o - 5 6 m! An instructive alternative formulation of Equation (3.5) is

O.86 D d o - ~ T X [ R ~ / ~ / 3 ] h , (3.6)

where the parameters Ri, di, and D are as defined in Section 2. This formulation shows that the clear aperture size required to resolve (i.e., signal/noise ~ 1) a planet from its central star in visible light is independent of the spectral type of the star, and depends only weakly (minus one-third power) on the size of the planet's orbit. It should be noted that although the aperture size required for resolution is independent of stellar type, there is a dependence on stellar type which enters through a requirement on photon flux from the planet; the flux is greater the brighter the central star.

Clearly, these requirements on clear aperture size, even for a telescope in space, are prohibitive. Several ingenious schemes have been suggested to alleviate the need for such a large aperture. Huang (1973) discusses a scheme, attributed by Spitzer (1962) to Danielson, which involves placing an occulting disk in front of a telescope in order to reduce the observed amount of light from the central star. If the disk is considered as a semi-infinite plane, located a distance z from the telescope, then the intensity I of the stellar signal varies with distance, x, from the edge of the geometric shadow according to

hz I (z, x) ~ 4,rr2x 2 (3.7)

for x2/z ~> 4h and I normalized to unity outside of the shadow. The optimal location of the occulting edge, as seen from the telescope is about half-way between the star and planet. If we consider a PS where a planet is separated from its central star by 1 arc see, then x/z ~ 2.4 x 10 -6. Thus,

105h 5 x 10 -3 I(z, x) ~---5 (3.8)

"h" X X

for x expressed in meters and h = 0.5 ~m. As noted in Section 2, contrast ratios at this wavelength vary from - 10 -7 to - 5 x 10 -11 as Ri varies from 0.5 A U to 20 AU. It is not unreasonable to expect that a reduction in starlight ~ 10 -5 can be obtained in


the telescope, so the reduction needed from the occulting disk would range from 10 -2 to - 10 -5. For / - 10 -2, one only needs x - 1 m (z = 400 km). For I - 10 -5, one

needs x ~ 500 m (z ~ 2 • 105 km). A major problem associated with this technique is

the problem of station keeping, that is, controlling the relative positions of the occulting disk, the telescope, and the star being occulted. This is a formidable problem and is one which is exacerbated by the fact that one must observe any suspected PS several times in order to verify that the dim companion is not a background object. This requirement for repeated observation (to observe orbital motion of the dim companion) with essentially identical relative alignment for all observations presents a challenge which may be too severe for existing or planned technology.

An interesting variation on the occulting disk concept has recently been advanced by Elliot (1978). He proposes using the black-limb of the Moon as the occulting edge. As most of the considerations discussed above also pertain to his scheme, they will not be repeated here. Elliot does present a rather detailed discussion of the station keeping and orbital problems associated with this technique. One problem which is alluded to in Elliot's paper, but which is not considered in detail, is that with the z-values (see Equation (3.7)) he envisions ( - 4 x 105 km), linear irregularities in the

lunar limb on a scale of a few hundred meters (a modest lunar hill) correspond to angular irregularities comparable to the angular separation between star and planet in his model PS. The presence of these irregularities, which do not enter in the man-made occulting disk approach, pose severe problems for data interpretation.

An alternative approach to direct visual imaging, that of apodization, has been considered by KenKnight (1977) and Oliver (1976). As noted earlier in this section, the difffraction pattern produced by a clear aperture has a rather large amount of light contained in the rings of the diffraction pattern. Formally, the source of this light derives from the abrupt change in transmission of light at the edge of the aperture. If the transmission could be made to approach zero more slowly at the aperture edge, particularly if gradients in transmission near the edge can be made small, the reduction in light intensity in the rings can, in principle, be significant. Following Oliver (1976), consider an apodizing mask which gives rise to a transmission function

of the form

T~(r)=(1-r2/r~)~; r<~ro I (3.9)

= 0 ; r>~ro j

where/~ >I 0 is not necessarily an integer. Functions of the form in Equation (3.9) are often referred to as Sonine functions. Note that/~ = 0 corresponds to an unapodized clear aperture. A transmission function such as T, (r) gives rise to the condition

Odo ~ [(1 ~ . , j , (3.10)

which is the analog of Equation (3.5) that was derived for the case /z = 0. (The


mathematics involved in obtaining Equat ion (3.10) from Equat ion (3.9) is straight-

forward. Interested readers are referred to Oliver 's paper for details.) Values of Odo (assuming A = 0.5 txm) in units of meter x arc sec are given in Table III . As can be

seen from Table III , apodization with/z - 3 leads to a significant reduction in Odo over the value that obtains for /x = 0. Also, the reduction in Odo becomes relatively insensitive to ~ for/x -> 3, depending on the value of H. (There is very little gain from

apodization in the infrared because, as we have seen, H-va lues typically are large

compared to those at visual wavelengths and the reduction in Odo with increasing/x is less the greater the H-value) . If we consider the Sun-Jupi ter example cited in connection with Equation (3.5), that is H = 2 x 10 -9 and 0 = 0.5 arc sec we find that

do = 1.74 m is sufficient to resolve the planetary signal from that of the star. This is a

reduction by a factor - 3 3 in the required aperture size!

TABLE III

Odo values at/~ = 0.5 ixm

tz H = 10 -s H = 1 0 - 9 H = 10 lo

0 16.5 35.6 76.7 1 2.4 3.8 6.0 2 1.2 1.6 2.3 3 .8 1.1 1.4 5 .7 .8 .9

In theory then a suitably apodized, modest size (1-2 m) optical telescope could

directly image large planets in other PS. However , no one has yet demonstra ted that a telescope can be fabricated which is able to operate in the fashion calculated here. Some of the problems are; fabrication of an apodizing mask, reduction of scattered

light, and optical surface figure accuracy. Studies sponsored by N A S A - A m e s are currently underway on the subject of mask fabrication, and preliminary results

appear promising. The pr imary technique under study is that of fabricating a mask by means of thin-film metal deposition. The problem of scattered light involves both

telescope optics and microscopic dust particles. No detailed studies of these prob-

lems has been undertaken. Estimates (KenKnight, 1977; Oliver, 1976) on the required surface accuracy for H - 1 0 - 9 indicate that the optical surfaces in the telescope must be figured to an accuracy ~< 10 -2 A over a scale - A / 0 - 10 cm for

,~ = 0.5 txm and 0 = 0.5 arc sec.

Another concept for direct visual imaging of other planetary systems was discussed

in Project Orion. The Orion approach was to combine an apodizing system with an interferometer , in this application the interferometer considered is a modified Mach-Zender interferometer . The function of the interferometer is to take advantage of the fact that the light from a planet would be incoherent with respect to light from its central star. Thus, proper manipulat ion of the received light (i.e., reversing and folding of wavefronts) could lead to a high degree of cancellation of light from

68 DAVID C. BLACK

the central star without cancellation of light from the planet (in fact a double image of the planet would be produced). Assuming 99% cancellation by such an interferometer (a reasonable assumption), the required reduction by the apodizer is made less severe by two orders of magnitude. It should be noted that the above discussion on visual DD of other planetary systems is perhaps overly pessimistic in that the quantitative requirements on light reduction are such as to reduce the background stellar light signal to the same level as the planetary signal. If the intensity pattern produced by the optical system can be determined with sufficient accuracy, data reduction techniques and integration time could be used to detect a planetary signal which is - 10 -2 of the background. That is, one is really concerned with comparing the planetary signal with fluctuations in the stellar background signal.

3.2.2. Detection of Intrinsic Thermal Radiation

As discussed in Section 2, the most favorable region of the spectrum from the standpoint of DD of other planetary systems is the infrared. Typical H-values in the infrared (see Figures 8b-12b) range from - 10 -4 to - 10 -3 at h = 50 txm. Utilizing

Equation (3.10), one finds the values for the product Odo listed in Table IV. The clear aperture required to resolve an object with 0 = 0.5 arc sec is - 113 m for H = 10 -3.

TABLE IV Odo values at h = 50 ixm

/x H=0.1 H=0.01 H=0.001 H= 0.0001

0 12.2 26.2 56.5 121.6 1 13.5 24.0 42.7 175.9 2 37.9 60.1 3 36.2 53.1

Values of Odo are also tabulated for H = 0.1 and H = 0.01. These are calculated to show the effect of requiring not that the stellar signal equal the planetary signal, but that the planetary signal be - 1 0 -2 of the similar signal. Note that the relative

decrease in aperture size is considerably less in the infrared ( - x2) than it is at visual wavelengths ( - x33). One other important difference between the infrared and the visible concerns the variation of H with R~. In the visual, HocR7 2, whereas H oc R 71/2 in the infrared. Using Equation (3.10), we find that for a specified central star, the required aperture at infrared wavelengths varies as

Dh doOC - (3.11)

R ~ I R '

where aiR = (5 + 2/Z )/(6 + 2/X). In the visual,

Dh d o ~ - - (3.12) R~,o'


where o~ = (1 +/z) / (3 +/~). As a~ < a i r for reasonable values of /z ; we see that the

aperture size required to 'resolve' a system decreases with increasing 0 (Ri at fixed D) more rapidly at infrared wavelengths than at visual wavelengths. Note also that for late spectral type stars, the self-luminous effect for large planetary bodies dominates the intrinsic radiation so that do oc R ~-1 (H independent of Ri).

Based on the results given in Table IV, it would appear that for H ~ 0.1, a clear aperture with do - 10 m would be adequate to resolve Jupiter-like planets revolving about M0 stars provided that R~(AU)/> D (pc). The surface figure requirements on such a telescope are not likely to be too severe, indicating that some form of shuttle-borne deployable facility m a y b e adequate.

An alternative to a single aperture is an interferometer. One such interferometer scheme is developed in the Project Orion report, and has been further refined by Bracewell and MacPhie (1979). Details of the interferometer scheme are given by Bracewell and MacPhie; we shall only discuss the essential aspects of this method.

The angular resolution R (S, A) of an interferometer of baseline S is given by

A R(S, A) = 2-- ~ . (3.13)

Equation (3.13) describes the situation where radiation from a given source (a star) travels slightly further, a distance of A/2 to reach one of the two apertures separated by a distance S. The light amplitudes received at the detector must be added vectorially, giving rise to a null signal as the radiation at one aperture is 180 ~ out of phase with radiation at the other aperture. Requiring that R (S, A ) - 0.5 arc sec at

= 40 txm gives S - 8 m, a reasonable size. An interferometer has the added advantage of simultaneously providing angular

and intensity resolution. If the star under study were a true point source, and if a space-based interferometer could be pointed with infinite precision, the stellar signal could be nulled out as well as the power from the two apertures can be balanced. However, stars within ten parsecs of the Sun are not point sources. For example, the angular extent of the Sun viewed from a distance of ten parsecs is - 0 . 0 0 1 arc sec. The intensity pattern produced by the interferometer is of the form

I(0)oCsin2(~ -0) , (3.14)

where 0 here is the angle off the optical axis of the interferometer and O is the angle between successive maxima (or minima) in the I(O) pattern. For S - 8 m, O-~ -~ 1 arc sec. The effective brightness ratio He~r between planet and star is

KTi r f [ IrO"~ d O ' ] , "EFr=---T~, [Ji sin2 (~'j) dg2/ I,I(O.) sin2 \--~- ] (3.15)

where the interferometer intensity pattern is integrated over the two bodies, K is a constant, I(0) is normalized intensity of the star as a line source and 0. is the angular

70 DAVID C. BLACK

size of the star. Taking the star image to be a uniformly bright disk, the integral over the star becomes

1 ---~-, ] sin e \--~--] d ~ ' - 64/9 e . (3.16)

The corresponding integral over the much smaller planet is simply the solid angle of the planet as seen from the Earth. Thus,

H KTi [ ~i ~ 64~92 EFF ~ " ~ ~7/ '~O,J " (3 .17 )

If we consider the Sun-Jupiter pair as viewed from a distance of ten parsec, Hef t - 60. That is, the interferometer nulls the stellar signal to the extent that the planetary signal is about 60 times stronger than the stellar signal.

This pronounced increase in H obtains if the optical axis of the interferometer can be perfectly pointed. However, the stellar contribution to the received signal increases rapidly with increasing pointing error. For example, a pointing error

0.005 arc see in the case of the Sun-Jupiter example cited above is sufficient to raise the stellar signal to a level comparable to that of the planetary signal. Present space technology is not sufficient to attain pointing precision ~< 0.005 arc see. Thus, any real space-based intefferometer is likely to have He~ < 1.

The interferometer scheme discussed in Orion incorporates a signal modulation approach to recovering a planetary signal in the presence of a stronger stellar signal. If the interferometer is rotated at a fixed frequency o~ about its optical axis, the signal from objects which lie close to the optical axis (i.e., 0 << O) will be sinusoidal with a characteristic frequency of 2to. The planetary signal modulation can be made markedly different from that due to a slightly off-axis star by making the interference fringe pattern so that the planet is K fringe spacings away from the star. Variations in K can be obtained by changing the interferometer baseline or the wavelength. The signal from the planet would be of the form sin 2 [(K~') cos wt]. The second harmonic content of this waveform is distinctly enhanced; in fact it is possible to choose K so as to suppress the fundamental component at 2w completely. On the other hand, the signal due to the star, which is closer to the rotation axis, will be much more nearly sinusoidal with a fundamental frequency 2to. Hence, by filtering the data for the 4w component, a frequency that is very precisely known, it should be possible to identify the planetary signal. This approach also has the advantage of relaxing the pointing accuracy requirement on the spinning intefferometer.

3.2.3. Detection of Non-Thermal Planetary Radiation

This form of DD need not be attempted from a space-based platform, certain limited ground-based searches can be attempted. We have discussed two examples of non-thermal planetary radiation, viz., magnetic field related decametric radiation and molecular maser radiation. A search for analogs to the Jovian decametric bursts can be mounted using existing receivers. As noted in Section 2, current detector


sensitivities at these wavelengths are such that signals comparable in strength to the strongest Jupiter bursts would only be detectable from planetary companions to

nearby (D - 1-2 parsec) stars. There is a practical problem attendant to this method, namely, one does not know a priori the frequency at which to search. The frequency scales with the magnetic field of the planet, and that is a highly uncertain parameter.

Concerning planetary molecular maser type emission, ground-based observations will be limited to specific wavelength windows in the transmission function of the Earth's atmosphere. It would perhaps be a good idea to construct a list of known molecules which are candidates for stimulated emission. This list would identify wavelengths at which observations might be made (e.g. 10.6 ~m). Some uncertainty in wavelength will still exist due to Doppler shifting of potential radiation. If the kinematics of the star under study are well known, a correction to the rest wavelength of a given molecular line can be made. The only unknown source of Doppler shift is that due to the orbital motion of the planet relative to the star. However, the fractional change in wavelength AA/A ~ v /c is likely to be small (v/c ~ 10 -3) for such motion. A possibility exists that some of the planned space-based infrared survey satellites, such as IRAS (Aumann and Walker, 1977), may detect intense planetary maser radiation. One difficulty with the survey systems is that their detectors are fairly broadband and would therefore tend to dilute any such signal. The IRAS survey will in any case set upper limits on the nature of this type of source.

3.3. I N D I R E C T D E T E C T I O N T E C H N I Q U E S

It was remarked in Section 3.1 that unlike the majority of the DD techniques, the ID techniques can for the most part be carried out on the ground with relatively little loss in sensitivity. An exception to this is the technique of astrometry which does appear to have limitations set by the Earth's atmosphere.

3.3.1. Detection of Transit Events

A rather detailed exposition of sources of noise, astrophysical, atmospheric, and instrumental, as well as of strategy for conducting a photometric search for other planetary systems has been given elsewhere (Rosenblatt) and will not be repeated here. The principal advantage of this technique would seem to be that a detailed short term ( - 1 yr) observing program concentrating on late spectral type stars would yield a high probability of detecting a relatively large (di ~> dNeptune) planetary companion to one of these stars provided that the orbital period of the companion is ~< 1 yr and that a large fraction of the stars under study do have planetary companions. In order to observe a sufficient number of stars ( - 2 x 10 3) with a rapid

enough sampling rate ( - 2 / d a y ) , one would need several telescopes suitably distributed over the Earth. The telescopes need not be large aperture devices, sugges- ting the possibility of using facilities which are presently little used for research at several existing observatories. An alternative approach would be to construct a battery consisting of three or four small aperture telescopes located in one geo- graphical area. This battery could be computer controlled and cycled rapidly over


independent sets of stars. Observation of a candidate transit by one telescope could

be immediately checked using the other telescopes. The Ear th 's a tmosphere does limit the accuracy of photometr ic studies but not at a

level which is likely to be significant in terms of detecting large planets. For example, Young (1967) has shown that typical scintillation effects will give rise to an r.m.s.

error of 0.001 mag. for a ten second observation with a 0.4 m aperture. This assumes

unit air mass and sea level observation near the zenith. (The error scales as air mass to the 23- power and aperture to the 4 - 3 power). A more serious error source is that of

turbidity variation (i.e., variation in the amount of dust, haze, etc.), which can lead to

photometr ic variations - 0 . 0 1 mag. over time intervals of ~< 1 hr (Rosenblatt). However, it seems likely that careful simultaneous monitoring of comparison stars

would provide adequate information to model this error source well enough to

reduce it to < 0.001 mag. If one wished to detect Am values < 0.001 mag., these atmospheric sources of noise pose significant but not insurmountable obstacles. As

turbidity effects are likely to be significant over time scales - a fraction of an hour (effects due to strong wind gusts are an exception) and as most seeing or scintillation

effects are significant on time scales ~> 0.1 s, it would seem that rapid sampling could

aid in minimizing errors due to these atmospheric phenomena.

3.3.2. Detection of Radial Velocity Effects

The accuracy of most stellar radial velocity studies is of order several hundred to a thousand m s -1, which as we have seen is far too poor to be of use in a search for other

planetary systems. However , there is no fundamental reason why the accuracy of radial velocity studies cannot be significantly improved, and many noteworthy

improvements and ideas have recently evolved in this area.

Griffin and Griffin (1973) describe means by which the accuracy of conventional photographic stellar spectroscopy can be significantly improved, perhaps to the

+ 10 m s -1 level. The essential element for any form of high accuracy stellar

spectroscopy is that the wavelength calibration must be impressed upon the stellar

light before it enters the spectrograph (cf., Serkowski, 1972; Griffin and Griffin, 1973; Young, 1974). The scheme discussed by Griffin and Griffin utilizes telluric

lines as the calibration source, requiring one to observe in regions of the spectrum where the telluric and stellar lines are thoroughly intermingled. They present radial

velocity results based on existing plates (that were not taken for high precision radial

velocity studies) that are accurate to ~:50-60 m s -1. Griffin (1976) indicates that if proper care is taken in obtaining the photographic data, one could expect to achieve

+ 10 m s -~ accuracy. A variant on this type of stellar spectroscopy involves photoelectrically measured

radial velocities. Although Griffin and Gunn (1974) were among the first to fabricate and use a photoelectric system for this purpose, the basic concept can be traced to earlier papers by Fellgett (1953) and Babcock (1954). The Griff in-Gunn device utilizes a mask with many narrow apertures that are arranged so as to transmit only absorption lines when it is in register with a stellar spectrum. The stellar spectrum is


scanned across the mask and the light t ransmitted by the mask is monitored with a

photomultiplier. The transmission is a minimum when the stellar absorption lines are

in register with the mask. Stellar velocities are determined differentially with respect

to a standard (e.g., a helium lamp). This technique routinely yields relative stellar radial velocities accurate to a few hundred m s -1 in studies which are not directed at

maximizing accuracy. Griffin (1976) has indicated that the use of a 1-1.5 m aperture

dedicated telescope employing the mask or similar photoelectric techniques should

be able to achieve + 10 m s accuracy.

Serkowski (1972, 1976) has discussed a polarimetric method of wavelength

calibration that could be used to obtain high precision radial velocity data. However , after experimentat ion with this technique he has concluded (Serkowski, 1978) that it

will not yield the required accuracies. The principal failings of the polarimetric

approach are: (1) a dependency of the wavelength calibration accuracy on the incident stellar flux and line shape; (2) the unavailability of uniformly birefringent

crystals; and (3) the complexity of the optics and data reduction. Serkowski is currently operating a Fabry-Perot spectrometer (Serkowski, 1978) which has been

used to measure the rotation rate of the a tmosphere of Venus with an accuracy of

4- 6 m s -1. There is every reason to suspect that the level of accuracy can be improved to - • 1 m s -1 (Connes, 1978).

One of the principal sources of error in radial velocity work is the inability to

obtain a uniform image of the star under study. If a slit is used which is - � 8 9 1 arc sec as projected on the sky, seeing and /o r guiding effects cause the illumination centroid to wander about so as to introduce significant radial velocity errors (several

tens to hundreds of m s -a depending on the specific system). One can use narrower

slits to obtain more uniform illumination, but this requires greater integration times to obtain a specified number of photons. One could also introduce a controlled high

frequency sweeping of the image over the slit as a way to obtain uniform illumination.

However , Connes (1978) has recently per formed laboratory tests using high quality light pipes as image scramblers and finds that advances in fiber optic technology now

makes it possible to fabricate low loss fibers that are nearly ideal image scramblers.

Application of this concept to radial velocity studies should eliminate what has been a major error source in high accuracy radial velocity work. The Ear th 's

a tmosphere does not appear to offer any meaningful limitation to the accuracy of

ground-based radial velocity observations (in fact it can be used as a calibration

source).

3.3.3. Detection of Astrometric Effects

Astrometr ic techniques can be divided into those of absolute and relative astrometry. In absolute astrometry, stellar positions on the sky are measured relative

to a system of coordinates defined by the direction of the Ear th 's axis of rotation and the vertical at the place of observation. As in most other fields, absolute measurements are generally much less accurate than are relative measurements . In relative

astrometry, the position of a star is measured relative to positions of other stars

74 D A V I D C . B L A C K

situated in close angular proximity to it on the sky. Relative astrometry, with its

inherently higher precision, is a more suitable approach than absolute astrometry for

detecting planetary induced wobble in the motion of a star. The errors of measurements in relative astrometry can be traced principally to the

following four sources: (i) inaccuracy of devices used for measuring the relative positions of star images

formed by a telescope; (ii) changes in relative positions of star images caused by instabilities of the optical

components of a telescope; (iii) effects of the Ear th 's a tmosphere; and (iv) duplicity and /o r variable color or brightness of reference stars.

Concerning item (iv), we only note that although variable color and brightness of

reference stars is a problem for photographic detection systems, it is much less of a problem for photoelectric detection systems of the type which will be ment ioned

below. The duplicity aspect of reference stars is not a problem at the current level of

astrometric accuracy, but will be a problem as more accurate systems are made

available, specifically, if as the Ab t -Levy study indicates, the vast majori ty of stars are binaries, then at some level of accuracy one will begin to see this binary character

reflected in the form of periodic motion of the reference stars. A rigorous analysis of

this reference f rame noise problem has not been carried out, but a preliminary unpublished analysis by the author indicates that reference frame motion may be a

problem at accuracy levels of order 0.000 05 arc sec. We will not discuss this error

source further except to note that it does not present a fundamental limitation. Use of

a large number of reference stars for a given target star will permit modeling of this

noise source to an accuracy level well below 0.000 05 arc sec. It is now fairly clear that one of the major limitations to the accuracy of astrometric

observations is the use of conventional photographic plates as a detector. The

traditional approach has been to use long exposure times (minutes) to obtain a

precise measure of the centroid positions for the reference and target stars. However , a recent study at the Allegheny Observatory has shown that the error o- in

astrometric data taken with photographic plates can be represented as o -z= 2 2 =(o- t / t )+o-0, where O-o is a t ime-independent error arising from the plate, t is

observing time and trt is an error due to the Ear th 's atmosphere. For values of

t ~> 60 s, tr - o'0. The value of tr0 varies depending on the type of plate, and the exact source of tro is unclear. Currently available plate material seems to be characterized by O-o ~> 0 .01-0 .02 arc sec. As the error term trt arises from statistically independent

atmospheric effects, one is led to the conclusion that higher accuracy could be obtained from taking very short observations (t ~ 0.1 s) which have values of o- >> O-o, and reducing the value of tr for a total observation time ~- by a factor -x /~ - t through the statistical independence of these short term observations. This is not to say that the photographic plate has no role in the future of astrometry; the archival character of a plate is unmatched by any photoelectric system and the possibility exists that

plate technology will advance so as to significantly reduce O-o.


Rather than discuss each of the principal error sources given above, we shall briefly discuss some techniques which may lead to significantly improved accuracy in astrometric studies. These techniques can generally be subdivided into two cate-

gories, viz., interferometric and non-interferometric. There are two non-interferometric schemes which have recently been advanced.

Both rely on photoelectric rather than photographic detection, both techniques employ the use of a mask, and both techniques appear to be limited in terms of accuracy by effects in the Earth's atmosphere at a level - 0.000 1 arc sec per yearly normal point. These two techniques do differ in certain key ways as well, but we shall concentrate here on the basic aspects common to both, as it is these common factors which are primarily responsible for any significant increase in accuracy. One of these techniques is currently being tested and developed by Gatewood and co-workers at Allegheny Observatory, the other is due to Connes and is outlined in detail in a thought provoking, unpublished manuscript (Connes, 1976).

The Allegheny concept evolved from a suggestion made by Frank Drake during the first Oreenstein-Black workshop on planetary detection. The essential aspects of this scheme are:

(1) use of a single optical system for observation of target and reference stars; (2) simultaneous observation of the target and reference stars; (3) placement of all active optical components at the pupil of the system; and (4) use of relative reduction techniques. The first of the above allows a study of systematic errors in the optical system by

analysis of residuals in the reference star positions. The second point assures that the effects of transient conditions will equally affect both the reference and target star's apparent positions. The third factor assures that temporal and- -or fabrication defects in the optics will affect all star images in a uniform manner. The fourth factor makes it possible to remove all but second and higher order terms from the data by means of standard reduction techniques.

The detector scheme employed by Gatewood consists of a precise Ronchi ruling that is scanned back and forth over a set of photomultipliers. The positions of the photomultipliers in the focal plane is predetermined based on a photograph of the star field under study. This initial placement of the photo detectors need not be precise, it suffices to determine their relative placement to within an integer number of lines on the Ronchi ruling. As the ruling is driven across the focal plane, light will be transmitted to a given photomultiplier only when the transparent portion of the ruling is in register with the stellar image associated with that multiplier. Considering just two stars of equal intensity, one would expect to observe an output from the associated photomultipliers which varies in time as shown schematically in Figure 17. The measurement of the relative positions of these two stars is converted into a measurement of the relative phase between the centroids of the respective photomultiplier output. This procedure is carried out simultaneously for all stars (target plus reference). As the ruling scans over each photomultiplier, one obtains successive, real time, statistically independent measurements of the relative positions

76 D A V I D C . B L A C K

' J _ J ',..2Z_J

Fig. 17. A schematic of the output from two photomultipliers exposed to two stars of equal intensity. The output varies in time as a Ronchi ruling with alternate opaque and clear regions is moved through the field of view of the photomultiplier tubes. The linear separation of the two stars is directly related to the

difference in phase of the centroids of the respective photomultiplier output signals.

between stars. This multichannel astrometric photometer (called MAP by Gatewood and co-workers) system has the additional characteristic of being a self-improving

system; the more the system is used on differing star fields, the more accurately

known is the ruling structure. Current plans call for use of a linear ruling which thus

requires the observer to rotate the ruling by 90 ~ in order to obtain angular

separations in two orthogonal coordinates. An alternative would be to use a

pseudo-random ruling, such as employed in radar astronomy. Such a ruling would provide true angular separations without the need for rotating the ruling of the

expense of more complex data reduction. The exciting possibility presented by both the MAP and the system outlined by Connes is that of astrometric observations

limited principally by photon statistics. It should also be noted that a somewhat similar concept, relying on a rotating grating has been considered and tested at the

University of Virginia. Several interferometric approaches to astrometry have emerged recently. One

approach involves speckle interferometric observations of visual binaries with separations ~< 3 arc sec (McAlister, 1977). The basic concept centers around the fact that a visual binary system will produce a fringe structure when studied with speckle

interferometric techniques and these fringes permit one to measure angular separations with an accuracy of - 0.002 arc sec. If one of these stars has a dark companion, the variation in the motion of that star would be detectable as a variation in the separation of the binary components. McAlister points out that the technique need not be limited to binary systems; it can also be used to study 'single' stars which have a suitably bright background star within a 3 arc sec field of view centered on the target star. It is of interest to note that the level of accuracy quoted for this technique is comparable to that of the best astrometric observations to date, and that accuracy


level is reached in only 0.5 min of observing on a 4 m telescope whereas the

equivalent accuracy for standard astrometric studies involves a year of observations. The major limitation to this approach is the rather narrow field of view (~< 3 arc sec) engendered by the requirement that the two stars be within the isoplanatic patch.

A. second type of interferometric approach attempts to overcome atmospheric effects on relative astrometry observations by using a long baseline. The Project Orion Imaging Stellar Interferometer was designed to minimize the effects of thermal turbulence in the atmosphere on astrometric observations by having a baseline of 50m, that is a baseline comparable to the outer scale length of

atmospheric thermal turbulence. A similar scheme has been discussed by Currie (1976), however, his concept involves baselines - 1 km. A detailed discussion of how these long baseline devices aid in minimizing the errors introduced by atmospheric turbulence is outside the scope of this review. Interested readers are referred to the Project Orion report for such a discussion. One other novel interferometric approach is under development by Shao at MIT (Shao, 1978). Rather than utilize a long baseline to minimize atmospheric effects on astrometric observations, Shao proposes to make simultaneous observations over a baseline of 10 m in two colors. Data from these two colors will be used to correct for atmosphere refraction. Field tests of this concept are underway at the time of this writing and preliminary results are expected early in 1979.

4. Summary and Conclusions

4.1. SUMMARY

The rapidly increasing awareness in the scientific community of the fact that technology has advanced to the stage where one can seriously consider undertaking a search for effects as small as these associated with planets revolving about other stars renders any detailed discussion of instrumentation or specific techniques obsolete by the time of publication. Rather we have attempted here to indicate both the range of phenomena which appear to be amenable to observational study and the range of methodology which is currently being considered to implement these observational studies.

To summarize, the major aspects of this review are: (1) A search for other planetary systems involves many diverse scientific fields.

This involvement ranges from the incidental (i.e., contributions to astronomy unrelated to a search per se, but derived from observations made possible with instrumentation developed for a search) to the intentional. Knowledge of the frequency of occurrence and distribution (as a function of, say, spectral type of star) of planetary systems would provide a valuable test of our concepts of the process o f star formation. Such knowledge, especially knowledge concerning which specific

stars have planetary companions, would be very useful (but not essential) to any

attempt to search for extraterrestrial intelligence. Finally, a search will provide us with perhaps the only means whereby we can meaningfully test various hypotheses concerning the origin of the solar system.


(2) There exists a rather broad range of observational techniques which might be used to detect other planetary systems. It appears to be feasible to directly image planets revolving about other stars, the most promising wavelength regimes being the visual and infrared. Detection of rather exotic, non-thermal types of planetary radiation (e.g., analogs to Jovian decametric bursts) is a possibility. However, these phenomena would have to be more energetic than they are in the solar system if they are to be detected with existing telescopes. Indirect detection of other planetary systems by observation of their central stars also appears feasible.

(3) If observations yield detection, the information content of these observations could reveal useful data concerning discovered planets; such as planetary mass, temperature, orbit, and with less certainty planetary size and very rudimentary inferences concerning planetary atmosphere. However, no single technique will yield all of this information. Generally speaking, the information content potentially available by direct detection techniques is complementary to that available by indirect detection techniques.

(4) The direct detection technique which appears to offer the most promise in terms of both information content and likelihood of detection is that of infrared observations.

(5) Advances in radial velocity techniques now make it possible to make observations with accuracies - 1 m s ~, sufficient to detect the effects of relatively large planets. The principal uncertainty concerning radial velocity studies involves the interpretation of results; the major problem being a lack of understanding concerning sources of radial velocity variations at the level of 10 m s -1 which are intrinsic to

stars. (6) Use of the photographic plate as detector is one of the major sources of error in

astrometric observations at the level of accuracy required to detect planets revolving about other stars. Interest in detecting other planetary systems has led to the development of several novel approaches to astrometry involving photoelectric detectors. A great deal of preliminary work remains to be done on these approaches. A major concern regarding the intefferometric approaches is whether the systems will be able to locate and track the fringes formed by the interferometer.

(7) Effects intrinsic to the Earth's atmosphere make it necessary to undertake direct detection observations from space (see discussion in Section 3 concerning exceptions to this). The Earth's atmosphere does not appear to offer any significant limitation to radial velocity observations, nor does it pose a major problem for photometric studies. A limit to the accuracy of ground-based astrometric observations does appear to derive from effects associated with the atmosphere, although further study is needed to quantify that limit.

4.2. CONCLUSIONS

An important question relating to a search for other planetary systems concerns the magnitude of the effort. If one is only concerned whether there exist planetary systems nearby the Sun, and is not concerned with obtaining statistical information


on planetary systems as a general phenomenon and all that that statistical knowledge portends for our understanding of the origin of the solar system, then a rather modest effort will provide answers. If one is concerned with addressing the more fundamen-

tal, statistical aspects of the question, a larger scale effort will be required. The magnitude of a search effort relates also to questions of information content and verification of observations. In order to recover the maximum information content about any planetary systems that are discovered, one would want to use at least one DD and ID technique. The effects which are potentially observable are extremely small, and in view of the scientific and philosophical impact attendant to discovery of another planetary system, there is likely to be a general tendency to require corroboration of any discovery of a planetary system using one method by observations using an independent method.

Based on all of these factors, it seems likely that a space-based system of some type must be employed in a comprehensive search strategy. Are any of the planned or

currently considered space-based telescopes of help in this regard? Unfortunately, the answer appears to be no. The Space Telescope (ST) has both imaging and astrometric capability. However, ST's imaging capability is primarily at visual wavelengths, where the H values are least favorable, and the optical system of the ST is not designed to deal with the type of imaging problems posed by planetary detection. The astrometric capabilities of the ST, either using the fine guidance system or one of the principal camera systems, are - 0 . 0 0 1 arc sec. This is only slightly better than current ground-based astrometric studies in terms of accuracy (although that accuracy limit is reached in only 15 min of observing with the ST systems), and is significantly worse than the capabilities of ground-based astrometric systems now under study. There is a dedicated astrometric satellite currently under consideration by the European Space Agency. This system, known as Hipparcos, is designed primarily to carry out a short term ( - 2 yr) mission with emphasis on parallax measurements. Baum (1978) has discussed the potential use of Hipparcos in a search for other planetary systems. The principal limitations of Hipparcos are the short duration of the mission and the accuracy of the system ( - 0 . 0 0 1 5 arc sec) is comparable to that of the ST astrometry systems. As noted previously, there is a possibility that the infrared survey satellite (IRAS) will discover some exotic form of non-thermal planetary radiation. It would appear that a special, but general purpose space system needs to be developed.

A renewed interest in one of the oldest aspects of astronomy is clearly underway and there is every reason to believe that we will soon begin to have answers to some of the more intriguing and far-reaching questions that have perplexed mankind. The fact that we will obtain answers is one of the strong points in favor of undertaking a search.

Acknowledgements

Numerous people have contributed to this review and to my involvement in this


exciting topic. The cont r ibut ions of J. Bi l l ingham, R. Bracewell, A. G. W. Cameron ,

G. D. Gatewood, J. L. Greens te in , B. M. Oliver, and K. Serkowski to m a n y aspects

of this work are greatly appreciated. I wish to acknowledge part icular ly the interest

of I. S. Rasool and T. Young, who recognized at an early stage that a search for other

p lane ta ry systems offers the oppor tun i ty to unde r t ake an activity that would contr i-

bute to both the scientific and philosophical advancemen t of mank ind .

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In search of other planetary systems