SETI MERIT AND THE GALACTIC PLANE

SETH SHOSTAK

SETI Institute, 2035 Landings Drive, Mountain View, CA 94043, USA

AbstractÐAn easily computed ®gure of relative merit is de®ned for stellar targets that takes intoaccount both distance and location relative to the galactic plane. It is based on stellar densities and anassumed exponential distribution of extraterrestrial transmitter powers, and can be readily computed.This parameter has been used to evaluate stellar targets for Project Phoenix to be observed at theArecibo telescope. Over a range of plausible parameters, use of this merit index produces a bettersample than simply ordering target stars by distance, even for the very nearby stars observed byPhoenix. 7 2000 Elsevier Science Ltd. All rights reserved

1. INTRODUCTION

For two decades, SETI target strategy has been lar-

gely bi-modal. On the one hand, the scheme pio-

neered by Drake [1] in Project Ozma Ð a targeted

search of nearby stars Ð continues to be pursued in

its modern incarnation, Project Phoenix. Othersearches eschew the scrutiny of speci®c targets in

favor of an all-sky (or mostly all-sky) survey. While

intermediate strategies that choose clumped neigh-

borhoods or nearby galaxies have occasionally been

adopted (e.g., [2±4]), these have comprised only asmall fraction of the total e�ort.

However, the impending completion of Project

Phoenix will shift the attention of targeted searchesbeyond the nearest 1000 Sun-like stars, those with

distances less than 0200 light-years. Some envision

a search of 104 or even 106 such targets as the next

step. This will include stars out to02000 light-years,

or more than the full-width thickness of the Galaxyat the Sun's location. Consequently, the spatial dis-

tribution of such samples will become signi®cantly

distended along the galactic plane. Larger samples

will clearly serve to modify targeted searches into de

facto examinations of the plane, a strategy now

explicitly followed in survey mode by the SouthernSERENDIP project.

Such large-scale targeted searches are yet to beundertaken. However, one can still ask if there is

any substantive advantage in choosing today's rela-

tively nearby targets on the basis of their proximity

to the galactic plane? Is the advantage reaped by

having a galactic plane ``background'' to such tar-gets worth the inevitable trade-o�, namely that clo-

ser stars o� the plane would be rejected in favor of

more distant stars in the plane?

In this paper, we set up a simple criterion for

evaluating the merit of targets which we then use to

evaluate this trade-o�. We also consider the practi-

cal application of such a criterion in the case of the

Project Phoenix targeted search, now observing atArecibo. In addition, we make a preliminary evalu-

ation of the merit in targeting stellar agglomera-

tions, such as open clusters.Earlier studies have pointed out the advantages of

searching in the galactic plane [5,6]. Sullivan andMighell used the galactic stellar model of Bahcall

and Soneira [7] to evaluate the number of star sys-tems that could be detected by a SETI search indi�erent directions. In this paper, we consider a

variation of this approach. In particular, we de®ne asimple relative ®gure of merit for target stars, basedon their position and an assumed distribution of

transmitter powers. This ®gure of merit can then beused to govern the choice of star systems for tar-geted searches.

Note that our ®gure of merit does not seek tocompare SETI observations made with di�erentinstrumentation, as does that described by Dreherand Cullers [8]. The present index is a straightfor-

ward quantity m, used to access the relative desir-ability of observing a star or group of stars at agiven distance and location. We are de®ning the

merit of targets, rather than observing setups.

2. FIGURE OF MERIT

Imagine the observation of an elemental volume dV

having a density of stars r(d ), where d is the dis-tance (in light-years). We de®ne the merit of thisvolume by

dm � r�d �g�d �dV, �1�in which g(d ) is a measure of the goodness of stellartargets located at distance d. For example, if all

alien transmitters had the same EIRP (EquivalentIsotropic Radiated Power), then g(d ) would be con-stant out to some dmax at which point (in the idealcase of perfect signal detection and no temporal

scintillation) it would drop to zero.Following Drake [9] and others, we assume a

power law distribution for the spectral density of

extraterrestrial transmitter EIRP's P(W ):

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P�W � � P0WÿadW, �2�

We further assume that there exists a maximumpower Wmax at which P(W ) becomes zero. Consider

a target at distance d0 for which the minimumdetectable power is W0. The number of detectabletransmitters from this target

n0 ��Wmax

W0

P�W �dW �3�

We de®ne the goodness of this target to be one.Then for any distance d greater than d0,

g�d � �

�Wmax

Wd

P�W �dW�Wmax

W0

P�W �dW�

g1ÿa ÿ�d

d0

� 2�1ÿa�

g1ÿa ÿ 1�4�

for a$1, and

g�d � � 1ÿ2 � ln

�d

d0

�ln�g� for a � 1 �5�

in which g0Wmax/W0. In this paper we will adopt avalue d0 0 100 light-years, at which distance

g(d )=1, and g 0 106. With this formulation, therelative merit of an observation of an individual staris m=mstar+m®eld for which

mstar � g�d �, as above: �6�

The component of merit due to the galactic stellar

background, m®eld, is computed by making an inte-gration of (1) over distance

mfield ��10

ÿrdisk�x� � rspher�x�

� � p4� B 2 � g�x�dx �7�

where rdisk and rspher are respectively the disk and

spheroid stellar densities and B is the beamwidth ofthe telescope. For these densities, we employ a sim-pli®ed version of the models developed by Bahcalland Soneira [7] and used by Sullivan and Mighell

[6]. When converted to units of light-years, these are

rdisk � rd � eÿ

x

11400 � eÿz

h lyÿ3, �8�

rspher � rs ��r

rs

�ÿ78 �eÿ7:67

�r

rs

� 14

lyÿ3: �9�

In these equations, the central stellar densities are

rd=0.0425 lyÿ3 and rs=0.332 lyÿ3. The scale heightfor disk stars at distance z above the galactic planeh = 978 ly, and the characteristic length for the

spheroidal distribution rs=8,810 ly. The distance xin the plane from the galactic center of a point dlight-years from Earth and at galactic coordinates

(l,b ) is simply computed from

x �������������������������������������������������������������������������������������������D 2 ÿ 2 � d � D � cos�b� � cos�l� � �d � cos�b�� 2

q�10�

in which D=26,000 ly is the galactic radius of theSun. The height above the plane, z, and r, the dis-tance of the point in question from the galactic cen-

ter, are given by

z � d � sin�b�, and r ������������������x 2 � z 2

p, �11�

where b is the galactic latitude. Note that through-

out this analysis we make computations based onthe total stellar density. Since ours is a relativemerit, this is justi®ed if the fraction of stars that are

suitable SETI targets does not vary with location.Integration of the above formulae to determine

the number of stars per square degree leads toresults such as in Fig. 1 and those given in Sullivan

and Mighell [6].

3. TARGET CHOICE

The above formulation can be used to assist in therational assembly of a targeted star observing list.

In particular, it permits a simple procedure to assesswhether a more distant target lying closer to thegalactic plane is to be preferred to a nearer star sys-

tem out of the plane.However, in order to quantify this assessment, an

assumption must be made on the steepness of the

power spectrum a, as used in eqn (2). As noted byearlier authors [5,9] if a > 5/2, then nearby sourcesare more easily detected, whereas if a < 5/2, morepowerful emitters from greater distance would be

most visible. A ®t to a collection of several hundredof the most powerful terrestrial radars (J. Dreher,1998, private communication) indicates an EIRP

slope at the high end of a0 0.5. If this earthly ex-perience is representative of the distribution ofextraterrestrial transmitters, then the arguments

Fig. 1. Stars per square degree as a function of longitudefor latitudes vbv=0, 5, 10, and 30 degrees (top to bottom)

computed using the model described in the text.

S. Shostak650

made in this paper Ð that greater considerationshould be given to choosing even nearby targets onthe basis of their proximity to the galactic plane Ð

would be strengthened.However, in view of our ignorance about the true

value of a, we consider two bracketing cases, a=7/

2, which biases the search in favor of close targets,and a=3/2, which favors the distant. The com-ponent merits for individual stars mstar and for the

®eld m®eld, given by eqns (6) and (7) are depicted inFigs. 2 and 3. These have been computed using abeamwidth B = 3.2 arcmin, appropriate for the

Arecibo telescope at 21 cm.In the case of a steeply falling distribution of

transmitter powers (a=7/2), the so-called ``targeted''

case, individual star merit mstar falls precipitously. Ata distance of 0500 ly, it is below the ®eld merit atany galactic latitude and longitude. In other words,

beyond this distance, a targeted search is essentiallyno more e�ective than a sky survey. From Fig. 5,we see that the number of stars within 500 ly is 02� 106. Assuming that one in ten stars is an interest-

ing SETI candidate, then targeted searches makesense even in this optimistic (a=7/2) case only ifthey comprise less than 0200,000 stars. In other

words, the cross-over point to survey mode shouldoccur long before a telescope such as Arecibo hasreached one star per beam (0107 stars over the

entire sky). Note also that for a=7/2, a survey con-®ned to low latitudes and longitudes is only slightly(050%) more e�ective than one at high latitudes.

For the so-called ``survey'' case of a less steeplyfalling EIRP distribution (a=3/2), the merit of anindividual star falls slowly, dropping by less than100 even at 5000 ly (Fig. 2). But the consequence of

this long-range detectability is that the merit of thebackground ®eld at even moderately low galactic

Fig. 2. Individual star merit mstar. The merit is given rela-tive to a star at 100 light-years de®ned as having mstar=1.The upper curve is for power law parameter a=3/2, forwhich g0dÿ1 �d� d0); the lower curve is for a=7/2, forwhich g0 dÿ3(d� d0). Note that the total merit for anobservation of a star is formed by summing mstar and m®eld.

Fig. 3. Logarithm of merit for background star ®eld m®eld,assuming a power law parameter a=7/2. The vertical axisis galactic latitude, and the horizontal axis is longitude(both in degrees). Note that there is only a slight variationacross the sky, with an improvement of about 0.2 dex=60% for regions having vbv < 15 and vlv < 120. Thea=7/2 case favors nearby objects. Once again, a singlestar, with no stellar background, at 100 ly has a merit of

1.00. The assumed beam size is 3.2 arcmin.

Fig. 4. Same as Fig. 3, but with a power law parametera=3/2. There is a merit improvement of one to two ordersof magnitude when looking at directions having vbv < 15

and vlv<120. The a=3/2 case favors distant objects.

Fig. 5. The number of stars out to a given radius, com-puted by integrating eqns (8) and (9) in a sphere centeredon the Sun. The upper curve is proportional to r 3. Thedotted curve is the actual integral. Note that at 1000 ly,

the actual curve is 70% that of the r 3 curve.

SETI merit and the galactic plane 651

longitudes and latitudes is one to two orders ofmagnitude higher than individual stars with dis-tances >500 ly. This is the regime in which choosing

a more distant star closer to the plane over a nearerone that's o� the plane pays large dividends. Anexamination of Figs. 2 and 4 will persuade the

reader. For example a star at b < 208 and 2000 lydistant is, for most longitudes, a preferable target toa star with b>608 at only 200 ly.

4. PRACTICAL CONSEQUENCES

We have applied the above analysis to the 0600stars listed for possible observation by ProjectPhoenix at Arecibo. These are almost all nearby (see

Fig. 6) and more or less uniformly distributed inright ascension between declinations 8±28 degrees.The median distance (the median is less in¯uenced

by outliers than the mean) is 147 ly. Beyond 0100ly, the sample is clearly incomplete.

These candidates were biased in favor of the near-est, Sun-like stars. However, if the distribution of

extraterrestrial EIRP's is closer to a=3/2 than toa=7/2, then we have noted that using a distance cri-terion alone will result in a signi®cantly poorer

sample than if stars are chosen on the basis of totalmerit, m=mstar+m®eld. Numerical computation of mis straightforward, and could be implemented in the

software used to select targets. In Fig. 7 are giventhe computed merits for this sample assuming a=3/2.

Even given a pre-existing target list, the analysis

presented here can be useful. It is unlikely that all ofthe0600 Arecibo targets will be observed. By rank-ing them by merit m, a better experiment can be run

with no more e�ort than simply re-ordering the pri-ority of targets.As an example, we have taken the candidate list

and computed for each star the galactic coordinatesand value of m. This was done for both a=3/2 anda=7/2. For the sample as a whole, the median valueof total merit hmi=1.8 (a=3/2) and hmi=0.15 (a=7/

2). The list was then ordered by merit and split inhalf. When the two samples were compared, theresult was that the median merits for the ®rst were

hmi=3.6 (a=3/2) and hmi=0.63 (a=7/2). For thesecond, these values were respectively hmi=1.3 and0.045. In such circumstances, it would be tempting

to toss the lesser candidates out altogether.This considerable improvement by ranking is

slightly misleading. The existing scheduling of stars

for Project Phoenix already takes note of distance,preferentially choosing the nearer stars. These close-in targets have higher values of m, of course, and itmay be thought that the current ordering by dis-

tance will e�ect the same degree of improvement asthe somewhat more complicated ranking proceduresuggested in this paper. This is only true for the

``targeted'' case (a=7/2). For the case a=3/2, evenculling the closest 300 targets still results in a valuefor hmi that is nearly 40% lower than when the same

number of targets are chosen from the completesample using the merit formulation given here.Note also that the merit of the background ®eld

m®eld 0 B 2. Consequently, the in¯uence of galactic

coordinates on the total merit of a star increaseswith larger beams. Arecibo is a large telescope hav-ing a narrow beam. Field stars behind the targets

will be fewer and relatively less e�ective in improv-ing the chances of success. The Phoenix candidatesthemselves are nearby, enhancing their individual

merit. In addition, Arecibo cannot spend more thana few hours a day observing close to the galacticplane, and consequently is fed with candidate lists

that range over all galactic latitudes. Nonetheless,even in this situation, so favorable to a targetedsearch of the nearest stars, one may disregard thegalactic coordinates of the targets without conse-

quence only in the case that ae7/2.

5. CLUSTERS

As SETI targeted searches reach to greater dis-tances, it will be tempting to observe clumps ofstars. In order to make a preliminary evaluation ofthe e�ectiveness of such searches, we have chosen 23

NGC, Berkeley and other open clusters (see, forexample, the listing in Lang [10]). These range indistance from 1200 to 34,000 ly, but the principal

criterion for including them for analysis was their

Fig. 6. The distance distribution for the 0600 stars com-prising the target list for the Project Phoenix deployment

at Arecibo. Median distance is 147 ly.

Fig. 7. Target star merit for the 0600 candidate stars forProject Phoenix observations at Arecibo. These have been

computed using a=3/2.

S. Shostak652

age. Most open clusters dissipate shortly after birth,

but those evaluated here all have estimated ages>109 years. The clusters considered are listed inTable 1.

The number of stars in these clusters rangesfrom a few dozen to nearly a thousand (in somecases a number was estimated from the total mag-

nitude of the cluster). Following the proceduresdescribed above, the relative merits were computedfor each cluster, assuming that they were observedwith only a single beam of the Arecibo telescope

and further assuming that the cluster stars followa gaussian density distribution on the sky. Themedian cluster merits were hmi=12 (a=3/2) and

hmi=0.00023 (a=7/2). For the former value of a,this is many times better than the median value ofstars in the full Arecibo sample. For the latter, it

is many times worse. This suggests that, whileclusters might be a good idea, they are an uncer-tain substitute for targeted searches of nearby

stars.This analysis naively treats clusters as simply

compact collections of individual stars whose sumis no greater than its parts. However, their desir-

ability as SETI targets is probably enhanced bythe fact that member stars will be of similar ageand are physically close. In particular, if a society

inhabiting one of the cluster's stars transmits toother planetary systems within that cluster, thenthe density of stars will have an e�ect on the

chances of a detection outside the cluster. If so-cieties target nearby planetary systems (forexample, by broadcasting with a beam that coversa star out to 5 A.U.) then these beams will cover

an amount of sky 0r 2/3star. The chance that we are

illuminated by one of these beams will be enhancedby this amount (normalized to the star density in

the ®eld), and the merit would similarly be

increased. Under such suppositions Ð in which thedesirability of an agglomeration is dependent on r 5/

3star rather than simply rstar Ð then open clusters

might be expected to become more attractive tar-gets. However, for open clusters, the e�ect is small,only 03% for the case a=7/2. This re¯ects the

rather small density enhancement of these objects.

6. CONCLUSIONS

We have de®ned a relative merit for assessing thedesirability of observing individual stellar targetsbased on their distance and galactic coordinates,

and evaluated this quantity for two bracketingvalues of the power distribution parameter, a=3/2and a=7/2. The use of this calculated merit, rather

than simply selecting stars on the basis of proximity,results in a signi®cantly improved ranking of targets,even for nearby stars, when a < 7/2. It can also beused for the automated compilation of new target

lists in which trade-o�s between distance and proxi-mity to the plane must be weighed.As targeted searches are extended to greater dis-

tance, they become less e�ective than surveys sur-prisingly quickly. Even for a steep powerdistribution (a=7/2) targeted stars have more merit

than background only when the samples contain lessthan0200,000 stars.The merit of 23 old, open clusters was computed.

It was found that the desirability of these targetswas strongly dependent on the value of a.Consequently, they comprise an uncertain substitutefor conventional stellar targets.

By quantifying and combining the e�ects of dis-tance and distribution of transmitter powers into asingle relative index, we have been able to ascertain

that even searches of nearby stars with large tele-scopes can disregard the galactic coordinates oftheir targets without consequence only in the case

that ae7/2. Since terrestrial radars evidence a shal-low power law slope (a 0 1/2), the possibility thatextraterrestrial transmitters are distributed with a<7/2 should not be ignored.

REFERENCES

1. Drake, F., The Search for Extraterrestrial Intelligence(Proceedings of an NRAO Workshop Held at theNRAO, Green Bank, West Virginia, 20±22 May,1985), eds. K. I. Kellermann and G. A. Seielstad,1986, NRAO/AUI, p. 17.

2. Sagan, C. and Drake, F. Scienti®c American, 1974,232, 80.

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Table 1. Clusters analyzed for relative merit

Name Right Ascension Declination

NGC 752 01 54.8 +37 26Berk 17 05 17.4 +30 33Berk 19 05 20.9 +29 33Berk 20 05 30.4 +00 11Basel 11 05 55.2 +21 58Berk 22 05 55.7 +07 50NGC 2141 06 00.3 +10 26NGC 2158 06 04.4 +24 06NGC 2236 06 27.0 +06 52Trumpler 5 06 34.0 +09 29Collind 110 06 35.8 +02 03Berk 29 06 50.4 +16 59Berk 32 06 55.4 +06 30NGC 2395 07 24.3 +13 41NGC 2420 07 35.5 +21 41NGC 2682 08 47.7 +12 00Berk 81 18 59.0 +00 35Berk 42 19 02.6 +01 48NGC 6791 19 19.0 +37 45NGC 6802 19 28.6 +20 10Turner 1 19 47.0 +27 10NGC 6885 20 09.9 +26 20NGC 6940 20 32.5 +28 08

SETI merit and the galactic plane 653

6. Sullivan, W. T. III and Mighell, K. J., Icarus, 1984,60, 675.

7. Bahcall, J. N. and Soneira, R. M., Ap. J. Supp., 1980,44, 73.

8. Dreher, J. W. and Cullers, D. K., Astronomical andBiochemical Origins and the Search for Life in theUniverse, eds. C. B. Cosmovici, S. Bowyer and D.

Werthimer. IAU Colloq. No. 161, 1997, EditriceCompositori, Bologna, p. 711.

9. Drake, F. In Communications with ExtraterrestrialIntelligence: CETI, ed. Carl Sagan. MIT Press,Cambridge, 1973, p. 240.

10. Lang, K. R., Astrophysical Data: Planets and Stars.Springer, New York, 1992.

S. Shostak654