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SETI merit and the galactic plane
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PII:
Acta Astronautica Vol. 46, No. 10±12, pp. 649±654, 2000 7 2000 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0094-5765/00 $ - see front matter S0094-5765(00)00027-8
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 into account both distance and location relative to the galactic plane. It is based on stellar densities and an assumed 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 the Arecibo telescope. Over a range of plausible parameters, use of this merit index produces a better sample than simply ordering target stars by distance, even for the very nearby stars observed by Phoenix. 7 2000 Elsevier Science Ltd. All rights reserved
1. INTRODUCTION
For two decades, SETI target strategy has been largely bi-modal. On the one hand, the scheme pioneered by Drake [1] in Project Ozma Ð a targeted search of nearby stars Ð continues to be pursued in its modern incarnation, Project Phoenix. Other searches eschew the scrutiny of speci®c targets in favor of an all-sky (or mostly all-sky) survey. While intermediate strategies that choose clumped neighborhoods or nearby galaxies have occasionally been adopted (e.g., [2±4]), these have comprised only a small fraction of the total eort. However, the impending completion of Project Phoenix will shift the attention of targeted searches beyond 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 to 02000 light-years, or more than the full-width thickness of the Galaxy at the Sun's location. Consequently, the spatial distribution 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 Southern SERENDIP project. Such large-scale targeted searches are yet to be undertaken. However, one can still ask if there is any substantive advantage in choosing today's relatively nearby targets on the basis of their proximity to the galactic plane? Is the advantage reaped by having a galactic plane ``background'' to such targets worth the inevitable trade-o, namely that closer 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 practical application of such a criterion in the case of the Project Phoenix targeted search, now observing at Arecibo. In addition, we make a preliminary evalu-
ation of the merit in targeting stellar agglomerations, such as open clusters. Earlier studies have pointed out the advantages of searching in the galactic plane [5,6]. Sullivan and Mighell used the galactic stellar model of Bahcall and Soneira [7] to evaluate the number of star systems that could be detected by a SETI search in dierent directions. In this paper, we consider a variation of this approach. In particular, we de®ne a simple relative ®gure of merit for target stars, based on their position and an assumed distribution of transmitter powers. This ®gure of merit can then be used to govern the choice of star systems for targeted searches. Note that our ®gure of merit does not seek to compare SETI observations made with dierent instrumentation, as does that described by Dreher and Cullers [8]. The present index is a straightforward quantity m, used to access the relative desirability of observing a star or group of stars at a given 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 distance (in light-years). We de®ne the merit of this volume by dm r d g d dV,
1
in which g(d ) is a measure of the goodness of stellar targets located at distance d. For example, if all alien transmitters had the same EIRP (Equivalent Isotropic Radiated Power), then g(d ) would be constant out to some dmax at which point (in the ideal case 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 ): 649
650
S. Shostak
P W P0 W
ÿa
dW,
2
We further assume that there exists a maximum power Wmax at which P(W ) becomes zero. Consider a target at distance d0 for which the minimum detectable power is W0. The number of detectable transmitters from this target Wmax n0 P W dW 3 W0
We de®ne the goodness of this target to be one. Then for any distance d greater than d0, Wmax 2 1ÿa d P W dW g1ÿa ÿ d0 Wd g d Wmax 4 g1ÿa ÿ 1 P W dW W0
for a$1, and
d 2 ln d0 g d 1 ÿ for a 1 ln g
5
6
The component of merit due to the galactic stellar background, m®eld, is computed by making an integration of (1) over distance 1 ÿ p mfield rdisk x rspher x B 2 g xdx 7 4 0 where rdisk and rspher are respectively the disk and spheroid stellar densities and B is the beamwidth of the telescope. For these densities, we employ a simpli®ed version of the models developed by Bahcall and Soneira [7] and used by Sullivan and Mighell [6]. When converted to units of light-years, these are x z ÿ ÿ rdisk rd e 11400 e h ly ÿ3 ,
rspher
14 r ÿ 7 ÿ7:67 r r 8 s e rs ly ÿ3 : rs
q D 2 ÿ 2 d D cos b cos l d cos b 2 10
in which D=26,000 ly is the galactic radius of the Sun. The height above the plane, z, and r, the distance of the point in question from the galactic center, are given by p z d sin b, and r x 2 z 2 , 11 where b is the galactic latitude. Note that throughout this analysis we make computations based on the total stellar density. Since ours is a relative merit, 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 to results such as in Fig. 1 and those given in Sullivan and Mighell [6]. 3. TARGET CHOICE
in which g0Wmax/W0. In this paper we will adopt a value d0 0 100 light-years, at which distance g(d )=1, and g 0 106. With this formulation, the relative merit of an observation of an individual star is m=mstar+m®eld for which mstar g d , as above:
x
The above formulation can be used to assist in the rational assembly of a targeted star observing list. In particular, it permits a simple procedure to assess whether a more distant target lying closer to the galactic plane is to be preferred to a nearer star system 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 by earlier authors [5,9] if a > 5/2, then nearby sources are more easily detected, whereas if a < 5/2, more powerful emitters from greater distance would be most visible. A ®t to a collection of several hundred of the most powerful terrestrial radars (J. Dreher, 1998, private communication) indicates an EIRP slope at the high end of a 0 0.5. If this earthly experience is representative of the distribution of extraterrestrial transmitters, then the arguments
8
9
In these equations, the central stellar densities are rd=0.0425 lyÿ3 and rs=0.332 lyÿ3. The scale height for disk stars at distance z above the galactic plane h = 978 ly, and the characteristic length for the spheroidal distribution rs=8,810 ly. The distance x in the plane from the galactic center of a point d light-years from Earth and at galactic coordinates (l,b ) is simply computed from
Fig. 1. Stars per square degree as a function of longitude for latitudes vbv=0, 5, 10, and 30 degrees (top to bottom) computed using the model described in the text.
SETI merit and the galactic plane
Fig. 2. Individual star merit mstar. The merit is given relative to a star at 100 light-years de®ned as having mstar=1. The upper curve is for power law parameter a=3/2, for which g 0 d ÿ1 d d0 ); the lower curve is for a=7/2, for which g 0 d ÿ3(d d0 ). Note that the total merit for an observation of a star is formed by summing mstar and m®eld.
made in this paper Ð that greater consideration should be given to choosing even nearby targets on the 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 component merits for individual stars mstar and for the ®eld m®eld, given by eqns (6) and (7) are depicted in Figs. 2 and 3. These have been computed using a beamwidth 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''
Fig. 3. Logarithm of merit for background star ®eld m®eld, assuming a power law parameter a=7/2. The vertical axis is galactic latitude, and the horizontal axis is longitude (both in degrees). Note that there is only a slight variation across the sky, with an improvement of about 0.2 dex =60% for regions having vbv < 15 and vlv < 120. The a=7/2 case favors nearby objects. Once again, a single star, with no stellar background, at 100 ly has a merit of 1.00. The assumed beam size is 3.2 arcmin.
651
Fig. 4. Same as Fig. 3, but with a power law parameter a=3/2. There is a merit improvement of one to two orders of magnitude when looking at directions having vbv < 15 and vlv < 120. The a=3/2 case favors distant objects.
case, individual star merit mstar falls precipitously. At a distance of 0500 ly, it is below the ®eld merit at any galactic latitude and longitude. In other words, beyond this distance, a targeted search is essentially no more eective 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 interesting SETI candidate, then targeted searches make sense even in this optimistic (a=7/2) case only if they comprise less than 0200,000 stars. In other words, the cross-over point to survey mode should occur long before a telescope such as Arecibo has reached 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 eective than one at high latitudes. For the so-called ``survey'' case of a less steeply falling EIRP distribution (a=3/2), the merit of an individual star falls slowly, dropping by less than 100 even at 5000 ly (Fig. 2). But the consequence of this long-range detectability is that the merit of the background ®eld at even moderately low galactic
Fig. 5. The number of stars out to a given radius, computed by integrating eqns (8) and (9) in a sphere centered on the Sun. The upper curve is proportional to r 3. The dotted curve is the actual integral. Note that at 1000 ly, the actual curve is 70% that of the r 3 curve.
652
S. Shostak
Fig. 6. The distance distribution for the 0600 stars comprising the target list for the Project Phoenix deployment at Arecibo. Median distance is 147 ly.
longitudes and latitudes is one to two orders of magnitude higher than individual stars with distances >500 ly. This is the regime in which choosing a more distant star closer to the plane over a nearer one that's o the plane pays large dividends. An examination of Figs. 2 and 4 will persuade the reader. For example a star at b < 208 and 2000 ly distant is, for most longitudes, a preferable target to a star with b > 608 at only 200 ly. 4. PRACTICAL CONSEQUENCES
We have applied the above analysis to the 0600 stars listed for possible observation by Project Phoenix at Arecibo. These are almost all nearby (see Fig. 6) and more or less uniformly distributed in right ascension between declinations 8±28 degrees. The median distance (the median is less in¯uenced by outliers than the mean) is 147 ly. Beyond 0100 ly, the sample is clearly incomplete. These candidates were biased in favor of the nearest, Sun-like stars. However, if the distribution of extraterrestrial EIRP's is closer to a=3/2 than to a=7/2, then we have noted that using a distance criterion alone will result in a signi®cantly poorer sample than if stars are chosen on the basis of total merit, m=mstar+m®eld. Numerical computation of m is straightforward, and could be implemented in the software used to select targets. In Fig. 7 are given the 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 of the 0600 Arecibo targets will be observed. By ranking them by merit m, a better experiment can be run with no more eort than simply re-ordering the priority of targets. As an example, we have taken the candidate list and computed for each star the galactic coordinates and value of m. This was done for both a=3/2 and a=7/2. For the sample as a whole, the median value of total merit hmi=1.8 (a=3/2) and hmi=0.15 (a=7/ 2). The list was then ordered by merit and split in half. When the two samples were compared, the result was that the median merits for the ®rst were hmi=3.6 (a=3/2) and hmi=0.63 (a=7/2). For the second, these values were respectively hmi=1.3 and 0.045. 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 closein targets have higher values of m, of course, and it may be thought that the current ordering by distance will eect the same degree of improvement as the somewhat more complicated ranking procedure suggested in this paper. This is only true for the ``targeted'' case (a=7/2). For the case a=3/2, even culling the closest 300 targets still results in a value for hmi that is nearly 40% lower than when the same number of targets are chosen from the complete sample 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 increases with larger beams. Arecibo is a large telescope having a narrow beam. Field stars behind the targets will be fewer and relatively less eective in improving the chances of success. The Phoenix candidates themselves are nearby, enhancing their individual merit. In addition, Arecibo cannot spend more than a few hours a day observing close to the galactic plane, and consequently is fed with candidate lists that range over all galactic latitudes. Nonetheless, even in this situation, so favorable to a targeted search of the nearest stars, one may disregard the galactic coordinates of the targets without consequence only in the case that ae7/2.
5. CLUSTERS
Fig. 7. Target star merit for the 0600 candidate stars for Project Phoenix observations at Arecibo. These have been computed using a=3/2.
As SETI targeted searches reach to greater distances, it will be tempting to observe clumps of stars. In order to make a preliminary evaluation of the eectiveness of such searches, we have chosen 23 NGC, Berkeley and other open clusters (see, for example, the listing in Lang [10]). These range in distance from 1200 to 34,000 ly, but the principal criterion for including them for analysis was their
SETI merit and the galactic plane
age. Most open clusters dissipate shortly after birth, but those evaluated here all have estimated ages >109 years. The clusters considered are listed in Table 1. The number of stars in these clusters ranges from a few dozen to nearly a thousand (in some cases a number was estimated from the total magnitude of the cluster). Following the procedures described above, the relative merits were computed for each cluster, assuming that they were observed with only a single beam of the Arecibo telescope and further assuming that the cluster stars follow a gaussian density distribution on the sky. The median 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 of stars in the full Arecibo sample. For the latter, it is many times worse. This suggests that, while clusters might be a good idea, they are an uncertain substitute for targeted searches of nearby stars. This analysis naively treats clusters as simply compact collections of individual stars whose sum is no greater than its parts. However, their desirability as SETI targets is probably enhanced by the fact that member stars will be of similar age and are physically close. In particular, if a society inhabiting one of the cluster's stars transmits to other planetary systems within that cluster, then the density of stars will have an eect on the chances of a detection outside the cluster. If societies target nearby planetary systems (for example, by broadcasting with a beam that covers a star out to 5 A.U.) then these beams will cover an amount of sky 0r 2/3 star. The chance that we are illuminated by one of these beams will be enhanced by this amount (normalized to the star density in
Table 1. Clusters analyzed for relative merit Name NGC 752 Berk 17 Berk 19 Berk 20 Basel 11 Berk 22 NGC 2141 NGC 2158 NGC 2236 Trumpler 5 Collind 110 Berk 29 Berk 32 NGC 2395 NGC 2420 NGC 2682 Berk 81 Berk 42 NGC 6791 NGC 6802 Turner 1 NGC 6885 NGC 6940
Right Ascension 01 05 05 05 05 05 06 06 06 06 06 06 06 07 07 08 18 19 19 19 19 20 20
54.8 17.4 20.9 30.4 55.2 55.7 00.3 04.4 27.0 34.0 35.8 50.4 55.4 24.3 35.5 47.7 59.0 02.6 19.0 28.6 47.0 09.9 32.5
Declination +37 +30 +29 +00 +21 +07 +10 +24 +06 +09 +02 +16 +06 +13 +21 +12 +00 +01 +37 +20 +27 +26 +28
26 33 33 11 58 50 26 06 52 29 03 59 30 41 41 00 35 48 45 10 10 20 08
653
the ®eld), and the merit would similarly be increased. Under such suppositions Ð in which the desirability of an agglomeration is dependent on r 5/ 3 star rather than simply rstar Ð then open clusters might be expected to become more attractive targets. However, for open clusters, the eect 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 the desirability of observing individual stellar targets based on their distance and galactic coordinates, and evaluated this quantity for two bracketing values of the power distribution parameter, a=3/2 and 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 be used for the automated compilation of new target lists in which trade-os between distance and proximity to the plane must be weighed. As targeted searches are extended to greater distance, they become less eective than surveys surprisingly quickly. Even for a steep power distribution (a=7/2) targeted stars have more merit than background only when the samples contain less than 0200,000 stars. The merit of 23 old, open clusters was computed. It was found that the desirability of these targets was strongly dependent on the value of a. Consequently, they comprise an uncertain substitute for conventional stellar targets. By quantifying and combining the eects of distance and distribution of transmitter powers into a single relative index, we have been able to ascertain that even searches of nearby stars with large telescopes can disregard the galactic coordinates of their targets without consequence only in the case that ae7/2. Since terrestrial radars evidence a shallow power law slope (a 0 1/2), the possibility that extraterrestrial 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 the NRAO, 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. 3. Shostak, S., Ekers, R. and Vaile, R., Astronomical Journal, 1996, 112, 164. 4. Cohen, N. L., Malkan, M. A. and Dickey, J. M., Icarus, 1980, 41, 198. 5. Gulkis, S., The Search for Extraterrestrial Life: Recent Developments, IAU Symp. 112, ed. M. D. Papagiannis. Reidel, Dordrecht, 1985, p. 411.
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S. Shostak
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 and Biochemical Origins and the Search for Life in the Universe, eds. C. B. Cosmovici, S. Bowyer and D.
Werthimer. IAU Colloq. No. 161, 1997, Editrice Compositori, Bologna, p. 711. 9. Drake, F. In Communications with Extraterrestrial Intelligence: CETI, ed. Carl Sagan. MIT Press, Cambridge, 1973, p. 240. 10. Lang, K. R., Astrophysical Data: Planets and Stars. Springer, New York, 1992.
PII:
Acta Astronautica Vol. 46, No. 10±12, pp. 649±654, 2000 7 2000 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0094-5765/00 $ - see front matter S0094-5765(00)00027-8
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 into account both distance and location relative to the galactic plane. It is based on stellar densities and an assumed 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 the Arecibo telescope. Over a range of plausible parameters, use of this merit index produces a better sample than simply ordering target stars by distance, even for the very nearby stars observed by Phoenix. 7 2000 Elsevier Science Ltd. All rights reserved
1. INTRODUCTION
For two decades, SETI target strategy has been largely bi-modal. On the one hand, the scheme pioneered by Drake [1] in Project Ozma Ð a targeted search of nearby stars Ð continues to be pursued in its modern incarnation, Project Phoenix. Other searches eschew the scrutiny of speci®c targets in favor of an all-sky (or mostly all-sky) survey. While intermediate strategies that choose clumped neighborhoods or nearby galaxies have occasionally been adopted (e.g., [2±4]), these have comprised only a small fraction of the total eort. However, the impending completion of Project Phoenix will shift the attention of targeted searches beyond 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 to 02000 light-years, or more than the full-width thickness of the Galaxy at the Sun's location. Consequently, the spatial distribution 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 Southern SERENDIP project. Such large-scale targeted searches are yet to be undertaken. However, one can still ask if there is any substantive advantage in choosing today's relatively nearby targets on the basis of their proximity to the galactic plane? Is the advantage reaped by having a galactic plane ``background'' to such targets worth the inevitable trade-o, namely that closer 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 practical application of such a criterion in the case of the Project Phoenix targeted search, now observing at Arecibo. In addition, we make a preliminary evalu-
ation of the merit in targeting stellar agglomerations, such as open clusters. Earlier studies have pointed out the advantages of searching in the galactic plane [5,6]. Sullivan and Mighell used the galactic stellar model of Bahcall and Soneira [7] to evaluate the number of star systems that could be detected by a SETI search in dierent directions. In this paper, we consider a variation of this approach. In particular, we de®ne a simple relative ®gure of merit for target stars, based on their position and an assumed distribution of transmitter powers. This ®gure of merit can then be used to govern the choice of star systems for targeted searches. Note that our ®gure of merit does not seek to compare SETI observations made with dierent instrumentation, as does that described by Dreher and Cullers [8]. The present index is a straightforward quantity m, used to access the relative desirability of observing a star or group of stars at a given 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 distance (in light-years). We de®ne the merit of this volume by dm r d g d dV,
1
in which g(d ) is a measure of the goodness of stellar targets located at distance d. For example, if all alien transmitters had the same EIRP (Equivalent Isotropic Radiated Power), then g(d ) would be constant out to some dmax at which point (in the ideal case 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 ): 649
650
S. Shostak
P W P0 W
ÿa
dW,
2
We further assume that there exists a maximum power Wmax at which P(W ) becomes zero. Consider a target at distance d0 for which the minimum detectable power is W0. The number of detectable transmitters from this target Wmax n0 P W dW 3 W0
We de®ne the goodness of this target to be one. Then for any distance d greater than d0, Wmax 2 1ÿa d P W dW g1ÿa ÿ d0 Wd g d Wmax 4 g1ÿa ÿ 1 P W dW W0
for a$1, and
d 2 ln d0 g d 1 ÿ for a 1 ln g
5
6
The component of merit due to the galactic stellar background, m®eld, is computed by making an integration of (1) over distance 1 ÿ p mfield rdisk x rspher x B 2 g xdx 7 4 0 where rdisk and rspher are respectively the disk and spheroid stellar densities and B is the beamwidth of the telescope. For these densities, we employ a simpli®ed version of the models developed by Bahcall and Soneira [7] and used by Sullivan and Mighell [6]. When converted to units of light-years, these are x z ÿ ÿ rdisk rd e 11400 e h ly ÿ3 ,
rspher
14 r ÿ 7 ÿ7:67 r r 8 s e rs ly ÿ3 : rs
q D 2 ÿ 2 d D cos b cos l d cos b 2 10
in which D=26,000 ly is the galactic radius of the Sun. The height above the plane, z, and r, the distance of the point in question from the galactic center, are given by p z d sin b, and r x 2 z 2 , 11 where b is the galactic latitude. Note that throughout this analysis we make computations based on the total stellar density. Since ours is a relative merit, 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 to results such as in Fig. 1 and those given in Sullivan and Mighell [6]. 3. TARGET CHOICE
in which g0Wmax/W0. In this paper we will adopt a value d0 0 100 light-years, at which distance g(d )=1, and g 0 106. With this formulation, the relative merit of an observation of an individual star is m=mstar+m®eld for which mstar g d , as above:
x
The above formulation can be used to assist in the rational assembly of a targeted star observing list. In particular, it permits a simple procedure to assess whether a more distant target lying closer to the galactic plane is to be preferred to a nearer star system 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 by earlier authors [5,9] if a > 5/2, then nearby sources are more easily detected, whereas if a < 5/2, more powerful emitters from greater distance would be most visible. A ®t to a collection of several hundred of the most powerful terrestrial radars (J. Dreher, 1998, private communication) indicates an EIRP slope at the high end of a 0 0.5. If this earthly experience is representative of the distribution of extraterrestrial transmitters, then the arguments
8
9
In these equations, the central stellar densities are rd=0.0425 lyÿ3 and rs=0.332 lyÿ3. The scale height for disk stars at distance z above the galactic plane h = 978 ly, and the characteristic length for the spheroidal distribution rs=8,810 ly. The distance x in the plane from the galactic center of a point d light-years from Earth and at galactic coordinates (l,b ) is simply computed from
Fig. 1. Stars per square degree as a function of longitude for latitudes vbv=0, 5, 10, and 30 degrees (top to bottom) computed using the model described in the text.
SETI merit and the galactic plane
Fig. 2. Individual star merit mstar. The merit is given relative to a star at 100 light-years de®ned as having mstar=1. The upper curve is for power law parameter a=3/2, for which g 0 d ÿ1 d d0 ); the lower curve is for a=7/2, for which g 0 d ÿ3(d d0 ). Note that the total merit for an observation of a star is formed by summing mstar and m®eld.
made in this paper Ð that greater consideration should be given to choosing even nearby targets on the 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 component merits for individual stars mstar and for the ®eld m®eld, given by eqns (6) and (7) are depicted in Figs. 2 and 3. These have been computed using a beamwidth 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''
Fig. 3. Logarithm of merit for background star ®eld m®eld, assuming a power law parameter a=7/2. The vertical axis is galactic latitude, and the horizontal axis is longitude (both in degrees). Note that there is only a slight variation across the sky, with an improvement of about 0.2 dex =60% for regions having vbv < 15 and vlv < 120. The a=7/2 case favors nearby objects. Once again, a single star, with no stellar background, at 100 ly has a merit of 1.00. The assumed beam size is 3.2 arcmin.
651
Fig. 4. Same as Fig. 3, but with a power law parameter a=3/2. There is a merit improvement of one to two orders of magnitude when looking at directions having vbv < 15 and vlv < 120. The a=3/2 case favors distant objects.
case, individual star merit mstar falls precipitously. At a distance of 0500 ly, it is below the ®eld merit at any galactic latitude and longitude. In other words, beyond this distance, a targeted search is essentially no more eective 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 interesting SETI candidate, then targeted searches make sense even in this optimistic (a=7/2) case only if they comprise less than 0200,000 stars. In other words, the cross-over point to survey mode should occur long before a telescope such as Arecibo has reached 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 eective than one at high latitudes. For the so-called ``survey'' case of a less steeply falling EIRP distribution (a=3/2), the merit of an individual star falls slowly, dropping by less than 100 even at 5000 ly (Fig. 2). But the consequence of this long-range detectability is that the merit of the background ®eld at even moderately low galactic
Fig. 5. The number of stars out to a given radius, computed by integrating eqns (8) and (9) in a sphere centered on the Sun. The upper curve is proportional to r 3. The dotted curve is the actual integral. Note that at 1000 ly, the actual curve is 70% that of the r 3 curve.
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Fig. 6. The distance distribution for the 0600 stars comprising the target list for the Project Phoenix deployment at Arecibo. Median distance is 147 ly.
longitudes and latitudes is one to two orders of magnitude higher than individual stars with distances >500 ly. This is the regime in which choosing a more distant star closer to the plane over a nearer one that's o the plane pays large dividends. An examination of Figs. 2 and 4 will persuade the reader. For example a star at b < 208 and 2000 ly distant is, for most longitudes, a preferable target to a star with b > 608 at only 200 ly. 4. PRACTICAL CONSEQUENCES
We have applied the above analysis to the 0600 stars listed for possible observation by Project Phoenix at Arecibo. These are almost all nearby (see Fig. 6) and more or less uniformly distributed in right ascension between declinations 8±28 degrees. The median distance (the median is less in¯uenced by outliers than the mean) is 147 ly. Beyond 0100 ly, the sample is clearly incomplete. These candidates were biased in favor of the nearest, Sun-like stars. However, if the distribution of extraterrestrial EIRP's is closer to a=3/2 than to a=7/2, then we have noted that using a distance criterion alone will result in a signi®cantly poorer sample than if stars are chosen on the basis of total merit, m=mstar+m®eld. Numerical computation of m is straightforward, and could be implemented in the software used to select targets. In Fig. 7 are given the 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 of the 0600 Arecibo targets will be observed. By ranking them by merit m, a better experiment can be run with no more eort than simply re-ordering the priority of targets. As an example, we have taken the candidate list and computed for each star the galactic coordinates and value of m. This was done for both a=3/2 and a=7/2. For the sample as a whole, the median value of total merit hmi=1.8 (a=3/2) and hmi=0.15 (a=7/ 2). The list was then ordered by merit and split in half. When the two samples were compared, the result was that the median merits for the ®rst were hmi=3.6 (a=3/2) and hmi=0.63 (a=7/2). For the second, these values were respectively hmi=1.3 and 0.045. 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 closein targets have higher values of m, of course, and it may be thought that the current ordering by distance will eect the same degree of improvement as the somewhat more complicated ranking procedure suggested in this paper. This is only true for the ``targeted'' case (a=7/2). For the case a=3/2, even culling the closest 300 targets still results in a value for hmi that is nearly 40% lower than when the same number of targets are chosen from the complete sample 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 increases with larger beams. Arecibo is a large telescope having a narrow beam. Field stars behind the targets will be fewer and relatively less eective in improving the chances of success. The Phoenix candidates themselves are nearby, enhancing their individual merit. In addition, Arecibo cannot spend more than a few hours a day observing close to the galactic plane, and consequently is fed with candidate lists that range over all galactic latitudes. Nonetheless, even in this situation, so favorable to a targeted search of the nearest stars, one may disregard the galactic coordinates of the targets without consequence only in the case that ae7/2.
5. CLUSTERS
Fig. 7. Target star merit for the 0600 candidate stars for Project Phoenix observations at Arecibo. These have been computed using a=3/2.
As SETI targeted searches reach to greater distances, it will be tempting to observe clumps of stars. In order to make a preliminary evaluation of the eectiveness of such searches, we have chosen 23 NGC, Berkeley and other open clusters (see, for example, the listing in Lang [10]). These range in distance from 1200 to 34,000 ly, but the principal criterion for including them for analysis was their
SETI merit and the galactic plane
age. Most open clusters dissipate shortly after birth, but those evaluated here all have estimated ages >109 years. The clusters considered are listed in Table 1. The number of stars in these clusters ranges from a few dozen to nearly a thousand (in some cases a number was estimated from the total magnitude of the cluster). Following the procedures described above, the relative merits were computed for each cluster, assuming that they were observed with only a single beam of the Arecibo telescope and further assuming that the cluster stars follow a gaussian density distribution on the sky. The median 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 of stars in the full Arecibo sample. For the latter, it is many times worse. This suggests that, while clusters might be a good idea, they are an uncertain substitute for targeted searches of nearby stars. This analysis naively treats clusters as simply compact collections of individual stars whose sum is no greater than its parts. However, their desirability as SETI targets is probably enhanced by the fact that member stars will be of similar age and are physically close. In particular, if a society inhabiting one of the cluster's stars transmits to other planetary systems within that cluster, then the density of stars will have an eect on the chances of a detection outside the cluster. If societies target nearby planetary systems (for example, by broadcasting with a beam that covers a star out to 5 A.U.) then these beams will cover an amount of sky 0r 2/3 star. The chance that we are illuminated by one of these beams will be enhanced by this amount (normalized to the star density in
Table 1. Clusters analyzed for relative merit Name NGC 752 Berk 17 Berk 19 Berk 20 Basel 11 Berk 22 NGC 2141 NGC 2158 NGC 2236 Trumpler 5 Collind 110 Berk 29 Berk 32 NGC 2395 NGC 2420 NGC 2682 Berk 81 Berk 42 NGC 6791 NGC 6802 Turner 1 NGC 6885 NGC 6940
Right Ascension 01 05 05 05 05 05 06 06 06 06 06 06 06 07 07 08 18 19 19 19 19 20 20
54.8 17.4 20.9 30.4 55.2 55.7 00.3 04.4 27.0 34.0 35.8 50.4 55.4 24.3 35.5 47.7 59.0 02.6 19.0 28.6 47.0 09.9 32.5
Declination +37 +30 +29 +00 +21 +07 +10 +24 +06 +09 +02 +16 +06 +13 +21 +12 +00 +01 +37 +20 +27 +26 +28
26 33 33 11 58 50 26 06 52 29 03 59 30 41 41 00 35 48 45 10 10 20 08
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the ®eld), and the merit would similarly be increased. Under such suppositions Ð in which the desirability of an agglomeration is dependent on r 5/ 3 star rather than simply rstar Ð then open clusters might be expected to become more attractive targets. However, for open clusters, the eect 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 the desirability of observing individual stellar targets based on their distance and galactic coordinates, and evaluated this quantity for two bracketing values of the power distribution parameter, a=3/2 and 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 be used for the automated compilation of new target lists in which trade-os between distance and proximity to the plane must be weighed. As targeted searches are extended to greater distance, they become less eective than surveys surprisingly quickly. Even for a steep power distribution (a=7/2) targeted stars have more merit than background only when the samples contain less than 0200,000 stars. The merit of 23 old, open clusters was computed. It was found that the desirability of these targets was strongly dependent on the value of a. Consequently, they comprise an uncertain substitute for conventional stellar targets. By quantifying and combining the eects of distance and distribution of transmitter powers into a single relative index, we have been able to ascertain that even searches of nearby stars with large telescopes can disregard the galactic coordinates of their targets without consequence only in the case that ae7/2. Since terrestrial radars evidence a shallow power law slope (a 0 1/2), the possibility that extraterrestrial transmitters are distributed with a < 7/2 should not be ignored.
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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 and Biochemical Origins and the Search for Life in the Universe, eds. C. B. Cosmovici, S. Bowyer and D.
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