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Acta Astronautica

Acta Astronautica 68 (2011) 366–371

0094-57

doi:10.1

� Tel.

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journal homepage: www.elsevier.com/locate/actaastro

Limits on interstellar messages

Seth Shostak �

SETI Institute, 515 N. Whisman Road, Mountain View, CA 94043, USA

a r t i c l e i n f o

Article history:

Received 27 February 2009

Accepted 19 October 2009Available online 10 November 2009

Keywords:

Seti

Active seti

Transmissions

Messages

65/$ - see front matter & 2009 Elsevier Ltd. A

016/j.actaastro.2009.10.021

: þ1 650 960 4530; fax: þ1 650 961 7099.

ail address: seth@seti.org

a b s t r a c t

Despite the fact that major efforts have been expended on passive searches for

extraterrestrial signals, few deliberate ‘‘transmissions’’ to potential alien recipients have

occurred. These have generally taken the form of simple graphics depicting such things

as our appearance, location, and biological construction. In this paper, we consider (a)

the fundamental technical and astronomical limitations to interstellar messaging—in

other words, how many ‘‘bits’’ could any society reasonably send, and (b) what might be

a likely transmission strategy. These considerations suggest approaches for SETI

programs, as well as giving insight into the types of messages we might construct for

eventual replies to received signals.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

While SETI experiments designed to find radio andoptical signals intentionally sent from other worlds havebeen conducted for more than four decades, there hasnever been a sustained, deliberate broadcasting effort.Arguments against a transmitting project range from thepractical (cost) and the philosophical (our communicationtechnology is less than a century old, so we should listenfirst), to the paranoid (it might be dangerous to betray ourlocation with a signal). A summary of some of thearguments for and against terrestrial broadcasting effortsis given in Ekers et al. [1].

Although we are not beaming signals to other starsystems ourselves, there has nonetheless been consider-able thought given to how we might reply to, or eveninitiate, any extraterrestrial communication. Varioussuggestions [2] have included encoding our message withmathematics, music, or graphics. The last has someprecedent in the pictorial messages affixed to the Pioneer10 and 11 spacecraft, as well as the analog records carriedby Voyager 1 and 2. In addition, a simple graphic was alsoused in the first, deliberate high-powered transmission todeep space, the Arecibo broadcast [3].

ll rights reserved.

Irrespective of coding schemes, one might argue thatexercises in message construction for replies are super-fluous, given that mankind has long been transmittinginformation to the stars inadvertently. Indeed, high-powered broadcasting at frequencies above �100 MHzwill traverse the ionosphere and continue into space. Theearliest television signals have already reached severalthousand star systems. However, the strength of TVsignals at light-years’ distance will be low, given thesmall gain of the transmitting antennas. For VHF broad-casts, the maximum effective radiated power is between100 and 300 Kw, and for UHF is 5 MW. At 100 light-years,these will produce signals of flux density no more than10�33–10�31 W/m2-Hz, even in the very narrow parts ofthe band where the carriers are located. The best SETIexperiments today are seven orders of magnitude toopoor to be able to detect a comparable signal. And notethat retrieving the video components of a TV broadcastwould require �104 greater antenna collecting area thanrequired to find the carriers.

Our military radars, thanks to their higher-gainantennas, produce more detectable emissions, butcover only a fraction of the sky at any one time. Finally,it has been pointed out [1] that high-powered terrestrialbroadcasting is likely to be a transitory activity, asimproved technology will soon encourage us to use eitheroptical fibers or low-power, highly targeted transmissionsto disseminate information and entertainment.

S. Shostak / Acta Astronautica 68 (2011) 366–371 367

In other words, to assume that leakage automaticallygenerates a ‘‘reply from Earth’’ to any SETI signal wemight receive is unrealistic. Consequently, it is useful toseriously consider the general nature of signals intendedfor deliberate communication between star systems, asthese might (1) elucidate the construction of any futurereplies to extraterrestrial transmissions, and (2) help togauge what sort of signals our SETI experiments mightdiscover. In this paper, we consider some realistic limitson information content that can be easily sent acrossinterstellar distances via light or radio, and suggest whatmight be reasonable signaling strategies.

2. Information content

Leaving aside for the moment the ostensible content ofan interstellar message, be it a photograph, mathematics,music, or plain text, one can ask how much informationcan be sent in a reasonable time between galactic starsystems that are separated by hundreds, or possiblythousands of light-years distance. In the case of electro-magnetic signaling (radio or light), this depends on (1)distance, (2) transmitter power, (3) transmitting beamsize and receiver collecting area, and (4) the chosenfrequency. In this paper, we do not consider the bodilytransmission of information, although as pointed out byRose and White [4], actually rocketing highly compressedinscribed data (which in the case of genetic material canreach densities of �1024 bits/kg) to deliberately chosenrecipients could convey a great deal of information at lowcost. Physical conveyance of data also has the advantagethat the signal is not transient—it does not require thatthe recipient be monitoring the communication when itarrives. On the other hand, electromagnetic signaling isfast, and—if the information conveyed is limited—can bean inexpensive way to reach very large numbers of targetstar systems, as will be shown below.

We are interested in estimating a reasonable maximum

data rate for interstellar communications, on the assump-tion that a society only modestly more advanced (a fewcenturies) than ours would have the technology toconstruct the requisite transmitting apparatus. We canthen compute the likely size of messages, a parameterthat will directly influence the type of information that issent.

2.1. Data communication at microwave frequencies

Since most SETI is conducted at microwave frequen-cies—both because the Galaxy is highly transparent inthis part of the band, and also because natural ‘‘marker’’frequencies such as that of neutral hydrogen (1,420 MHz)and the hydroxyl radical (1,612, 1,665 and 1,667 MHz)delimit this spectral region—it is instructive to computethe amount of information, and the requisite power, thatcan be conveyed in this spectral regime.

Common radio practice is that a broadcast will use abandwidth that is �5% of the carrier frequency, or in thiscase, �70 MHz. The amount of information C (bits/s) thatcan be conveyed with a channel of bandwidth W is given

by Shannon [5]

C ¼W log2ð1þ P=NÞ; ð1Þ

in which P/N is the signal power-to-noise ratio at thereceiver=TA/TS, where TA and TS are respectively, theantenna temperature produced by the source and thereceiving system temperature. So for circumstances inwhich this ratio is 1, we have C=W, or 70 megabits/s.

Note that for most SETI experiments, W�1 Hz, and P/Nis less than one, but these efforts are intended to findcarriers or very slowly pulsed signals, both of which haveextremely low information transmission rates. If sufficienttransmitter power and/or antenna gain are available toproduce a P/N �1, and if the entire 70 MHz can berecorded by those receiving the signal with high temporalresolution (�10 ns), then in the course of a day, 750 giga-bytes of information could be received, and in a year,270 terabytes.

To get some idea of how feasible this is, consider thetransmitter power required to produce TA/TS=1. We have

TA ¼ ARSn=2k; ð2Þ

where AR is the collecting area of the receiving antenna, kis Boltzmann’s constant, and Sn is the incident flux density(W/m2-Hz).

If we define PT as the transmitter power over a band W,and additionally assume that this power is uniformlydistributed over that band, then Eq. (1) becomes

C ¼W log2ð1þ ½2PTARAT�=½pkWl2D2TR�Þ; ð3Þ

where AT is the transmitting antenna area, TR is thesystem temperature of the receiver, D is the distancebetween sender and receiver, and l is the wavelength. Asexample, consider Arecibo-size (7�104 m2 area) trans-mitting and receiving antennas separated by D=100 light-years, with l=21 cm, and TR=5 K. To achieve a signal-to-noise P/N=1 requires a transmitter power density of 1 Kw/Hz, or 70 gigawatts over the entire 70 MHz band. Thelatter figure is considerable, approximately 0.5% of thetotal energy generation on Earth today, but permits a datarate of �10 megabytes/s, roughly comparable to that of ahigh-definition television signal. There are, however,several ways that an extraterrestrial transmitting societycould reduce the power demand, by using (1) a largertransmitting antenna, (2) a reduced bandwidth, or (3) areduction in the data rate, either by sending lessinformation, or by taking longer to send it. Note thatscheme (3) has some small benefit from the slow,logarithmic dependence on power implied by Eq. (3).

We have assumed Arecibo-size transmitting andreceiving antennas. This is, of course, merely an anthro-pocentric guess. There are already plans to build a radiotelescope on Earth whose maximum dimension is 1 km. Atthe transmitting end, an Arecibo-sized antenna used at21 cm wavelength has a beam that is �4,000 AU in size at100 light-years. This is enormously larger than the zonewithin which one expects to find Earth-like worlds. Itseems more reasonable to suppose that an advancedsociety bent on sending deliberate signals would focusits transmissions to cover no more than the habitablezone of the target star, defined to be of radius RH. If we

S. Shostak / Acta Astronautica 68 (2011) 366–371368

postulate that they have optimized their broadcastingeffort in this fashion, Eq. (3) then becomes independent ofdistance, and

C ¼W log2½1þ PTAR=ð2pkWR2HTRÞ�;

or, solving for PT

PT ¼ 2pkWR2HTR=ARð2

C=W� 1Þ: ð4Þ

Assuming we have a 1 km diameter receiving antenna,and using other parameters as in our example above, thepower requirement drops so that only 4 Kw is required totransmit �10 Megabytes/s, assuming RH=2 AU, whichdelimits a zone larger than the orbit of Mars in our ownsolar system. While this optimization is logical, andrewarded by a dramatic drop in power cost, thetransmitting antenna is now impressively large (a filledaperture of 300 km size for targets at 100 light-years).Nonetheless, this optimized approach gives us an estimateof the lower limit on the required power.

We have assumed that only a small fraction of themicrowave band would be modulated, as this is typicalpractice. However Jones [6] has pointed out that optimalencoding could make use of the entire free-space micro-wave window from 1 to 10 GHz. If this is done, the gain ininformation transfer rate would be �102 over ourexample, with a concomitant increase by the same factorin required power. Note also that interstellar scatteringwill smear high-frequency signal components, and thiswill require special transmission schemes if broadcastsare made over long distances in the galactic plane [7].

2.2. Data communication at optical frequencies

Optical communication using pulsed light is bothfeasible and is being looked for by SETI practitioners. Fordistances extending over many hundreds of light-years ormore, scattering by the interstellar medium argues for theuse of infrared wavelengths. However, at wavelengthsZ1mm, dispersion will broaden individual pulses, limit-ing the maximum number of pulses that can be sent persecond. The amount of the dispersion [8] is

Dt ¼ 4:1� 1015DMl2=c2 s; ð5Þ

where a typical value for the dispersion measure DM=30s�1 over �1 kpc distance. This limits pulse repetition ratesto 1012 s�1 at 1mm wavelength, and 1010 s�1 at 10mm. Wewill assume one bit per pulse because of the slow increasein data rate with power implied in the Shannon formula-tion [1] and its derivative, Eq. (4). Clearly, if energy cost isno object, higher bit rates than those we consider could beachieved.

Suppose, as above, an optimized system that targets astar’s habitable zone. We further assume that theincoming flux of photons in one pulse width t (s) at thereceiving end must be �10 times that produced duringtime t by the transmitting society’s own star, ofluminosity L*. If we send C binary bits/s (one bit perpulse), with a duty cycle for ‘‘on’’ bits of 50%, the requiredpower is

PT ¼ CtL�R2H=D2 ð6Þ

The necessary power decreases with distance D because inthis simplified calculation we have assumed that the onlynoise source is light from the transmitting society’s star.This has the counterintuitive result that targeting distantstars requires less power, which is true if the habitablezone strategy is used. Using [6], with t=10�10 s, aninformation rate of C=1010 bits/s, D=100 light-years, RH=2AU, and a solar-type star with infrared luminosityL*�1026 W, then PT=1013 W. Reducing the bit rate propor-

tionately reduces the power required, and if only one bitper second is sent, only 1 Kw is necessary to signal stars at100 light-years.

There is a minimum power requirement for signalingin the optical: the level necessary to produce one photonper pulse (‘on’ bit) in the receiving device, assuming thatthere is no noise introduced by the transmitter’s homestar. This might be the case, for instance, if the distance D

is great enough so that the star delivers 5t�1 photons/s tothe receiver’s mirror, or if the transmitter is located farenough from the home star to be cleanly resolved by thereceiver. The minimum power required is

PTmin ¼ pCR2Hhc=ðARlÞ; ð7Þ

where h is Planck’s constant and AR is, once again, the areaof the receiving mirror. Assuming l=10mm, RH=2 AU, anda 100 m diameter receiving mirror, PTmin=7�109 W forC=1010 bits/s.

Note that from (6) and (7), we can deduce that beyonda distance of

D ¼ ½tL�ARl=ðphcÞ�1=2; ð8Þ

the power requirement given by (6) reaches the minimumlevel, and no further decrease occurs. For a data rate ofC=1012 bits/s at l=1mm, and our example parameters, thishappens at D=120 light-years. For C=1010 bits/s atl=10mm, the minimum power applies for distancesgreater than D=3,700 light-years.

2.3. Radio vs. optical

In Fig. 1 we plot the required power for radio (both 5%bandwidth, and full microwave window) and two opticalregimes as a function of distance.

The straightforward considerations above have shownthat data rates from 107 to 1012 bits/s can be straightfor-wardly achieved in the radio and optical. The powerrequirements as given in Fig. 1 are considerable, particu-larly for optical, although one should bear in mind thatthese values are somewhat dependent on our assump-tions about the size of the transmitting and receivingapparatus. For all but the nearest stars, the requiredpowers are less than the current energy production onEarth (1.5�1013 W), and much less than the Earth’sinsolation (2�1017 W, above the atmosphere). These factssuggest that advanced societies could muster the energyrequired for transmitting at the given bit rates.

One aspect of Fig. 1 worth noting is that full spectrummicrowave transmissions have a bit rate comparable to10mm optical, but achieve this with four to eight orders ofmagnitude less power. However, against this energyefficiency, one must weigh the greater instrumental and

Fig. 1. Minimum power levels required for high bit-rate transmissions.

There are four regimes plotted, and all assume that the senders are

beaming to a circle of radius 2 AU centered on the target star: (a)

Microwave with a fully modulated 70 MHz bandwidth, having a data

rate of 7�107 bits/s, (b) microwave using the spectrum from 1–10 GHz,

conveying 1010 bits/s, (c) a 10 m pulsed laser with 10�10 s pulses sending

1010 bits/s, and (d) a 1 m laser with 10�12 s pulses and a data rate of

1012 bits/s. The radio examples assume a 1 km diameter receiving

antenna. Note that the power required in the optical regime flattens

with distance once the influence of noise introduced by the luminosity of

the home star (assumed to be L*=1026 W) drops to less than 1/10th

photon per pulse width collected by a 100 m diameter receiving mirror

(assumed in these examples). For comparison, terrestrial power genera-

tion is currently �1.5�1013 W.

S. Shostak / Acta Astronautica 68 (2011) 366–371 369

decoding challenges of the microwave scheme. To putinformation into 9 GHz bandwidth requires ingenuityboth in the design of hardware and in the encodingscheme to minimize the effects of dispersion. In addition,we have assumed that all transmitters will target a star’shabitable zone. At 1,000 light-years, the necessarytransmitting antenna aperture in the radio, which willvary across the 9 GHz spectrum, is 5�103 km (nearly halfEarth’s diameter) at the lowest part of the band. For 10mmoptical, the transmitting mirror would only need be 160 min diameter to properly target the habitable zone of a star1,000 light-years’ distant. These differences in implemen-tation requirements, in situations where energy is cheap,might easily favor the use of optical.

3. Possible messages

With data rates in hand, we can trivially compute thetotal information conveyed for any broadcast length. Thetypes of messages we routinely encounter in dailyintercourse are usually formulated, decoded and under-stood in a few days at most. However, such shortmessages may not be appropriate for a deliberatetransmission intended to reach other societies. If thereare 1,000–100,000 civilizations [9] spread throughout theMilky Way, then their average separation is hundreds to afew thousand light-years. The round-trip message timeswill probably lead senders to assume they are engaged inone-way communication. They will want to send every-

thing at once, since interaction with the communicantmay not occur. This encourages long messages.

But messages should not be too long, as virtually no onewill chance to pick up the signal just as the message begins,but will ‘‘tune in’’ somewhere in the middle. Consequently,repetition will be necessary, and should occur at intervalsthat are short compared with the time that the recipients willbe devoting to a single listening project. On Earth, this time isusually less than a human lifetime, suggesting messagelengths of no more than a few years.

In considering what message might be encoded byinterstellar signaling, it’s worth remarking that our ownefforts at interstellar communication have been extremelymodest, a fact that may influence how we have thoughtabout message content in general. The Pioneer 10/11 andVoyager 1/2 messages contained pictorial informationabout our appearance, culture, and location, as well assome music and verbal greetings in the case of theVoyager probes. The Voyager message was inscribed on amechanical record, of �10 megabytes carrying capacity.The earlier Pioneer plaques were engraved, and a bit maprendition of that graphic is �600 kilobytes in size. The1974 Arecibo message, which was sent digitally at about1 byte/s, comprised 210 bytes.

The data that our current radio SETI experiments couldreceive is also very limited. Project Phoenix, for example, ahighly sensitive radio scrutiny of �750 nearby starsystems, could recognize narrow-band signals that pulsedevery few seconds, and could collect no more than�10 bytes in a single observation of a target star system.On the other hand, today’s optical SETI experiments could,in principle, record short (10 min) bursts of nanosecondpulses, at 108 bytes/s, making for a total recordablemessage of �75 gigabytes.

The limitations of the radio efforts, in particular, haveseduced us into assuming that highly efficient encodingschemes would be necessary for interstellar messaging.However, this might be analogous to extrapolating SamuelF. B. Morse’s carefully weighed message in 1844, ‘‘What hathGod wrought?’’—the first telegraphic message betweencities—to present-day communication. Given the very largesize of messages that could be sent by a modestly advancedcivilization, as calculated above, it may be unnecessary to beoverly concerned about either encoding schemes or specificsof content, but rather rely on redundancy in the transmittedinformation to provide the key to understanding by therecipient.

In the face of the fact that large information transfersare possible, let us consider what sorts of messages mightbe sent, based on current human activity. Among SETIresearchers, it is occasionally (and usually off-handedly)said that altruistic societies will transmit their ‘‘Encyclo-pedia Galactica.’’ Our own encyclopedias could be sent ina matter of seconds. A more ambitious project would be totransmit the contents of a major library. The content ofthe Library of Congress is �1.4�1014 bytes [10] and couldbe sent in under an hour with the highest speed opticalsignaling link. The iconic information repository incontemporary times is the World Wide Web, and theestimated amount of immediately accessible data onservers in 2003 was comparable to that in the collections

S. Shostak / Acta Astronautica 68 (2011) 366–371370

of the Library of Congress [10], although the Web isgrowing rapidly (doubling time in the 1990s was less than6 months).

These and other possible ‘‘messages’’ are listed in Table 1.What we see is that, even at radio wavelengths, we can sendcontent as extensive as the Library of Congress in a half-year’stime or less. On the other hand, the amount of new datacurrently being stored on magnetic media is about5�1018 bytes per year [10]. While this may be only atemporary phenomenon, there’s little doubt that informationis growing at a prodigious rate. Our fastest channel, a1012 bits/s optical link, could just barely keep up with thisnew information flow. In a few years’ time, it will obviouslybe unable to do so. The implication is that, while we might beable to broadcast a comprehensive ‘‘Encyclopedia Terrestria,’’the annual updates will require editing, and the editing willbecome more severe with time.

Nonetheless, Table 1 encourages us to think that, withtransmitting times of a year or less, a society could sendenormously rich content, with enough redundancy tofacilitate decoding (in the same way that anyone receivingthe Library of Congress would eventually be able to figureout English). However, there is the serious problem ofknowing where to broadcast the information, especiallysince, as we have seen, the power requirements for highbit-rate transmissions are substantial, making multipletargeting expensive. It is well and good to say that theWeb can be sent in two days, but if one is compelled tosequentially target every star in the Galaxy, the transmit-ting project will last a billion years, and the chances thatsomeone is listening when the broadcast reaches theirplanet is small.

One means to ameliorate this unfavorable approach isto use advanced astronomical information. Extraterres-trial societies that are only a century or two beyond ourown will possibly have long lists of planets whoseatmospheres give evidence for biology, as Earth’s has for�2 billion years. This would tell them which target starshave worlds with life. However, technological societiesmight only inhabit a planet for a tiny fraction of itsbiological history, and thus even for those transmitting

Table 1Size of sample messages, and transmission time for various modes.

Message Size

(bytes)

Microwave radio n

band

Arecibo 1974 message 2�102 2�10�5 s

Pioneer plaque 6�105 6�10�2 s

Voyager record 107 1 s

Human DNA 109 2 min

Encyclopedia Britannica 5�109 10 min

Library at Alexandria �7�1011 1 day

A human memory 3�1012 4 days

New books in 1 year 5�1012 1 week

Library of Congress (17 million books) 2�1014 6 months

World Wide Web (2003) 2�1014 7 months

E-mail in 1 year 4�1017 1,500 yr

New information generated in one year

(2002)

5�1018 20,000 yr

Memory content of all human beings 2�1022 70 million yr

Some table entries are based on information found in U.C. Berkeley School of I

societies with lists of fecund worlds, the number ofpossible signaling targets could still be large (4106).

These facts incline us to suggest that only threestrategies seem appropriate for a transmitting society:

1.

arro

nfor

Develop very large energy sources (1017 W or more, foroptical transmissions) and construct a device capableof simultaneously targeting millions of likely worlds. Ifthe energy of a star (�1026 W) can be harnessed (e.g.,via a Dyson sphere), then continuous broadcasts in theoptical could be made in all directions.

2.

Transmit only to those star systems from which signalshave already been heard, confirming the presence ofintelligent recipients. In this case, it is highly unlikely thatthe Solar System is now on anyone’s target list, as Earth’sleakage signals have only reached to �60 light-years.

3.

Transmit short messages sequentially, but repeatedly. Asexample, imagine a society that ‘‘pinged’’ a million starsystems once a day (�0.1 s per ping). That would beadequate to daily convey the equivalent of the Encyclo-pedia Britannica to each of these systems using 1mminfrared as the carrier and one bit per pulse. Needless tosay, the message could be different each time.

The relative ease and economy of approach (3) suggeststhat it is a good candidate for the type of transmissionthat might be made to star systems for which the sendershave no direct proof of technically competent listeners;in other words, systems like our own, as judged by anyextraterrestrials more than �60 light-years distant. Italso suggests that SETI researchers should considerlooking for stars whose infrared luminosity regularlyspikes.

In conclusion, we have seen that instrumentation thatis technologically feasible, coupled to power sources thatan advanced society will surely command, would be ableto transmit, in a year’s time or less, quantities ofinformation comparable to the largest collections onEarth. However, unless the transmitting society is soadvanced that it can afford both the instruments and the

w- Microwave radio wide-

band

Optical

1010 bps

Optical

1012 bps

2�10�7 s 2�10�7 s 2�10�9 s

5�10�4 s 5�10�4 s 5�10�6 s

0.01 s 0.01 s 10�4 s

1 s 1 s 8�10�3 s

5 s 4 s 4�10�2 s

10 min 10 min 6 s

40 min 40 min 25 s

1 h 1 h 40 s

1 day 1 day 20 min

2 days 2 days 20 min

10 yr 10 yr 1 month

140 yr 130 yr 1 yr

0.6 million yr 0.5 million yr 5,000 yr

mation Management and Systems [10], and in Reupke [11].

S. Shostak / Acta Astronautica 68 (2011) 366–371 371

energy necessary to broadcast simultaneously to vastnumbers of stars, it will most likely adopt the strategy ofsending short, frequently repeated messages. In the caseof optical signaling, these could be gigabytes in size. Itseems reasonable to suspect that, until we make ourpresence known to others, we will have to make do withthe fact that other worlds might be sending us only anencyclopedia’s worth of information daily.

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