Jim Benford’s study of ‘lurkers’ — possibly ancient probes that may have been placed here by extraterrestrial civilizations to monitor our planet’s development — breaks into two parts. The first, published Friday, considered stars passing near our Sun in the lifetime of the Solar System. Today Dr. Benford looks at the Drake Equation and sets about modifying it to include the lurker possibility. Along the way, he develops a quantitative way to compare conventional SETI with the strategy called SETA — the search for extraterrestrial artifacts. Both articles draw on recently published work, the first in JBIS, the second in Astrobiology. The potential of SETA and the areas it offers advantages over traditional SETI argue for close observation of a number of targets close to home.

by James Benford


“To think in a disciplined way about what we may now be able to observe astronomically is a serious form of science.” –Freeman Dyson

I propose a version of the Drake Equation for Lurkers on near-Earth objects. By using it, one can compare a Search for Extraterrestrial Artifacts (SETA) strategy of exploring for artifacts to the conventional listening-to-stars SETI strategy, which has thus far found no artificial signals of technological origin. In contrast, SETA offers a new perspective, a new opportunity: discovering past and present visits to the near-Earth vicinity by ET space probes.

SETA is a proposition about our local region in the solar system. SETA is falsifiable in its specific domain: ET probes to investigate Earth would locate on the nearest objects down to a specified resolution. SETI, on the other hand, is about messages sent from distant stars. For example, one can falsify a proposition such as “Are signals being sent to Earth at this moment within 100 ly?” But there is the region beyond 100 ly and beyond 1000 ly, etc. So SETI is falsifiable only within larger and larger domains. Of course other factors can also weaken falsification: our sensitivity might be inadequate, duty cycle might be small, and of course frequency coverage will always be incomplete.

Rose and Wright pointed out the energy efficiency of an inscribed physical artifact vs. an EM signal, because the artifact has persistence and the EM signal has to be transmitted indefinitely (Rose & Wright, 2004). Here I point out that artifacts are not only energy efficient, but increase the chance of contact. Rose and Wright did not explore where to locate the artifact so it would be identified; here I suggest there are attractive locations near Earth where they might be readily observable.

In a recent paper, I introduced the term ‘Lurker’: an unknown and unnoticed observing probe from an extraterrestrial civilization, which may well be dead, but if not, could respond to an intentional signal. And/or it may not, depending on unknown alien motivations (Benford, 2019). Lurkers include self-replicating probes, based on von Neumann’s theory of self-replicating machines, which is why they are often called von Neumann probes (Von Neumann, 1966). Recently concepts have appeared for self-replicating probes that could be built in the near future (Borgue & Hein, 2020).

Another pioneering work on this concept was of course famously developed in “2001 A Space Odyssey” (Clarke, 1968). A ‘solarcentric’ Search for Extraterrestrial Artifacts advocated by Robert A. Freitas, who coined the term SETA for it in the 1980s (Freitas & Valdes, 1985). There are also the papers from the mid-1990s by Arkhipov (Arkhipov , 1995, 1998a, 1998b). Scot Stride has shown that autonomous instrument platforms (i.e. robotic observatories) to search for anomalous energy signatures can be designed and assembled using commercial off-the-shelf hardware and software. That provides an economical, flexible and robust path toward collecting reliable data (Stride 2001a and 2001b). Further analysis has appeared recently (Haqq-Misra & Kopparapu, 2012, Lingam & Loeb, 2018, Cirkovic et al. 2019, Shostak, 2020).

Near-Earth objects could provide an ideal way to watch our world from a secure natural object (Benford, 2019). They are attractive locations for extraterrestrial intelligence to locate a platform to observe Earth while not being easily seen.

2. Drake Equations

2.1 The Standard Drake Equation estimates the number of radiating civilizations that are detectable, NC , as the product of the rate of creation of such radiating civilizations (Drake, 1965),

This modified Drake Equation is:

I replace the usual Drake Equation symbol for time over which they radiate L, with TR. And I also multiply by:

fR = fraction that actually do radiate signals that might be observable at Earth. That is, they radiate with the intention of trying to communicate. Leakage radiation is unintentional, but comes in two types: radar, which has no message, and broadcasts, which come from many incoherent sources which cancel out, such as TV.

These parameters are listed in Table 1:

Table 1: Drake Equation Parameters. Subscripts are italicized letters in definitions

2.2 A Drake Equation for Alien Artifacts An equivalent to the Drake equation for the number of Lurkers in our solar system, NL, can similarly be expressed as the rate of creation of radiating civilizations, times the fraction that also develop interstellar probe technology fip, times the sojourn that Lurkers would be in the solar system, TL:

fip = fraction that also develop interstellar probe technology and launch them

TL = time that Lurkers could reside in the solar system

(Note that for such civilizations, fC =1; a civilization with the capability to build such probes surely can build interstellar transmitters.)

Then a Drake equation for alien artifacts is

The new parameters are listed in Table 2:

Table 2 Drake Alien Artifact Equation Parameters

In the ratio of equations 1 and 2, of the number of Lurkers in our solar system to the number of radiating civilizations, most terms, in the first bracket, cancel so:

This initial result is that the ratio of civilizations sending probes that are now resident in our solar system to the number sending messages is the product of two ratios: A ratio of motives:

the fraction that also develop interstellar probe technology and launch them, divided by fraction that only radiate, so fip/fR < 1,

and a ratio of times:

the time Lurkers are present in the solar system/ the time ET civilizations release electromagnetic signals. Surely a civilization with the capability to build such probes can build interstellar transmitters, so I will argue that TL/TR > 1.

Our own civilization has been capable of radiating for about 50 years, including message-free Cold War radar transmissions and inadvertent leakage radiation has been emitted for a long time (Quast, 2018). Intentional messages have also been sent but are difficult to detect with Earth–scale receiver systems (Billingham and Benford, 2014). We cannot yet build interstellar probes capable of traveling to and decelerating into a star system and conducting operations there. But that may be possible in the next century. If so, relatively soon we will be capable of both radiating to the stars and sending probes to explore nearby star systems.

However, equation 4 does not take account of the space volumes that the two groups operate in.

2.3 Space Volume Factor

Another factor must be included: Equation 4 must be modified for VL, the volume over which Lurkers can travel, and its corresponding range RL vs. VB, the volume over which Beacons can transmit and be plausibly detected, and its corresponding range RB. Lurker probes traveling at a small fraction of the speed of light should be compared to the transmissions from an interstellar Beacon propagating at the speed of light. That means that the volumes from which signals can be detected from Beacons is much larger than the volume over which Lurker could travel.

For example, assume that interstellar probes could operate at ~10% c, the speed of light, as contemporary concepts of fusion rockets are designed for. An example: for the Icarus Firefly magnetically confined Z-pinch concept at 4.7% c, traveling 10 ly would take about two centuries (Freeland & Lamontagne, 2015). Starshot, which is a flyby probe concept, at 0.2 c takes more than 20 years to arrive at the Centauri system. Assuming the attention span of the civilization is measured in centuries, a rough estimate of the distance over which probes will be launched is tens of lightyears. (The signal from the probe reporting back to its origin would travel at the speed of light, of course.) If it is possible for probes to move close to c, then the beacon volume to probe volume would be close to unity.

In contrast, the electromagnetic waves of an interstellar Beacon, be it light, millimeter-wave or microwave, propagate ~20 times faster, at the speed of light. For example, we can estimate the range over which a Beacon would be used to be hundreds of light years. By that I again mean that the attention span of a civilization might be measured in centuries.

I define the volumes and ranges in Table 3:

Table 3 Space Volume Factor Parameters

Therefore equation 3 must be multiplied by the ratio of these 2 volumes, VL/VB:

As volume scales as the cube of the distance to them, RL/RB:

This is a ‘Success Ratio’ of searching for artifacts compared to listening to stars. It allows us to quantitatively evaluate their relative merits. Although the volume ratio would argue that long-range Beacons will be much more likely to be detected than probes that come to observe Earth, the time ratio tends to mitigate that advantage.

2.4 Decision Tree Parameters

The ratio of the number of lurkers to the number of radiating civilizations can be estimated using the three factors in equation 5, which have the following’s sizes:

So the ‘Success Ratio’, Eq. 5, will depend on choices for these parameters.

The key parameters making up these factors can be divided into objective and subjective components, where ‘objective’ means it can be quantified or at least estimated and ‘subjective’ means it’s a matter of opinion. Here is a Table of the parameters:

Table 4: Objective and subjective SETA Parameters and determining factors

The issues determining the objective parameters are listed; subjective parameters are a matter of taste and underlying assumptions.

By making choices among the objective and subjective parameters, one constructs a decision tree: A set of parameter choices leads to a conclusion about the success ratio for SETA and SETI strategies, as embodied in equation 6. Because ET civilizations will vary enormously in motivations, we can expect a variety of outcomes for the Success Ratio.

2.41 Estimates of TR, time that ETI Beacons radiate

In the literature, estimates of TR fall between a hundred and 100 million years, a very wide range. Michael Shermer estimated TR by averaging the lifespans of 60 Earth civilizations, getting 420 years, (Shermer, 2002). Using 28 civilizations since the Roman Empire, he gives ~300 years for “modern” civilizations. But Shermer’s number for the lifetime of societies is not relevant if new societies arise to replace old ones.  In that case, one should take the summation of existence times for all the technological cultures on a planet. Note that the longest operating institution still existing on Earth is the Catholic Church, ~2,000 years. We’ll take the times to be 300-10,000 years, an order of magnitude range.

2.42 Estimates of TL, time Lurkers could reside in the solar system

A key point is that Lurkers will still be discoverable even though dead for a long time. That’s not true of an EM transmission, which is simply passing through at the speed of light. That fact weighs to the advantage of the Lurker search strategy.

The time that Lurkers would be in the solar system, TL, will be limited by the lifetime of the orbits they are in, which provides an upper bound. The Moon, Earth Trojans and co-orbitals of Earth lifetimes are:

The Moon

Our Moon is thought to have formed about 4.5 billion years ago. For TL we use the time that life became evident in our atmosphere, 0.65 109 < t1 < 2.5 109 years.

Earth Trojans

There may be many objects in the Earth Trojan region (Malhotra, 2019). Their lifetime in Trojan orbits is likely to be on the order of billions of years, and some objects there may be primordial, meaning that they are as old as the Solar System, because of their very stable orbits about the Lagrange Points (?uk et al., 2012, Dvorak et al., 2012, Marzari & Scholl, 2013, Zhou et al. 2019). Orbital calculations show that the most stable orbits reside at inclinations < 0° to the ecliptic; there they may survive the age of the solar system, ~2.5 Gyr.

Earth Co-orbitals

Morais and Morbidelli, estimate lifetimes to run between 1 thousand and 1 million years (Morais and Morbidelli, 2002). With a mean lifetime of 0.33 million years. Morbidelli says that no further studies have been done on their approach (A. Morbidelli, personal communication).

3. Scenarios for Success Ratio Estimates

Here we show several scenarios, some of which show that the two strategies, SETA and SETI, are competitive.

Scenario 1: Choosing via relative costs at equal ranges:

Assume that:

1) The ratio of fractions of ET civilizations would be proportional to the cost of interstellar probes vs. Beacons. The cost of interstellar probes will be substantially more than the cost of interstellar Beacons. Stated differently, Beacons will have substantially longer range for a fixed cost.

2) RL and RC are equal.

If we take as an example a Beacon at 100 ly and a Lurker probe launched from 100 ly, then RL and RC in Eq. 5 cancel out. For Beacons that have a range of 100 ly the cost is of order $1 billion. This is from extrapolations, based on current cost scaling and costs (Benford, 2010, Billingham and Benford, 2014). The Firefly interstellar fusion rocket has an estimated cost of $60 billion. Two thirds of that cost is fuel to accelerate and decelerate (A. Lamontagne, personal communication). Therefore the cost ratio is ~100 in favor of Beacons. If cost is the deciding factor, then fP/fR = 1/100 and Eq. 5 reduces to

Next, one chooses an orbital location for the Lurker: Our Moon is thought to have formed about 4.5 billion years ago, long before life appeared. So we use the time life became evident in our atmosphere, 0.65 109 < TL < 2.5 109 years.

Next, one guesses the transmit time of the Beacon: estimates of civilization radiating times TC vary from ~300 -105 years. Here the ‘dash’ means the range of credible values:

So for these parameter choices, a Lurker search is much more likely to be successful. Note, however, that if we assume the Beacon civilization is at 100 ly, and the probe-building civilization is at 10 ly, a factor of 1/1,000 reduces the ratio to 0.1 to 100.

Scenario 2: What if cost doesn’t matter? That would be at variance with all we know of economics on Earth, but is a hypothetical we could consider. If cost doesn’t matter, then a civilization wanting to investigate the life of Earth or whether civilization was here could build probes to investigate the ecosystem, visible in spectra of our atmosphere, and also build Beacons to broadcast to us. In such a case, fP/fR = 1, and, as we’re talking about a single civilization, RL/RC = 1. Consequently the Success Ratio NL/NC = TL/TC, which would surely be >>1. Again, lurker strategy is likely to be more successful. In this scenario, the time ratio is the important factor.

Scenario 3: Early spacefaring civilizations: A civilization such as ours, which is presently capable of only interplanetary speeds, cannot build interstellar probes as envisioned by some of our starship concepts. Starships are centuries into our future and will always be more expensive than Beacons. They could be only a radiating society and might build Beacons. In this case the success ratio NL/NC = 0, and a listen-only strategy is appropriate.

Scenario 4: Supercivilizations capable of fast interstellar flight: The opposite extreme from scenario 3 is a civilization where starships can travel at a large fraction of the speed of light. In this case, Beacons, although still cheaper, would serve to reveal our civilization only if we respond by sending a message back to them. At about the same time their probes would be arriving and could be reporting the existence of our civilization. This could’ve occurred over geological time frames, so in this case NL/NC >>1, and we would expect to find dead Lurkers on the nearby objects described in 2.42.1, and we would expect to find dead Lurkers on the nearby objects described in 2.42.

Scenario 5: Lurkers in Co-orbitals and short radiating time: Instead of a Trojan or the Moon, we choose one of the co-orbitals, which have a mean lifetime TL ~0.33 million years. 1) For TR , choose the 300-year lifetime estimate of Shermer for the Beacon to radiate. Then TL/TR = 1,000. 2) Let’s assume that starship probes are launched from a civilization 10 ly away. (A probe such as Firefly, traveling at 0.2c and decelerating into our solar system, would take 50 years to come 10 ly.) 2) Assume the Beacon civilization is at 100 ly, and the probe-building civilization is at 10 ly. So RL/RB = 0.1. 3) Further, again assume that the willingness of civilization to undertake the expense would be determined by economics. A continuous Beacon at hundred light-years would cost about $1 billion and a Firefly probe is estimated to cost $60 billion (M. Lamontagne, personal communication), so fP/fR = 0.01. Therefore the Success Ratio, eq. 5, is:

For this case listening-to-stars has a higher success ratio. But if one assumes that the radiating civilization also develops interstellar probes, fR~fp, the two strategies have a roughly equal success ratio:

So one’s assumptions of the parameters in the Table determine the answer.

Scenario 6: Lurkers in Co-orbitals and long radiating time: If we use the band of estimates in the literature for co-orbital lifetime, ~105 years, and estimates of civilization radiating times TC vary from 102 – 105, then TL/TR varies from 1 to 1,000. For the previous 100 ly/10 ly distance ratio, Eq. 5 then gives a Drake Equation ratio of

And the listening strategy will be preferred.

It is clear from these scenarios that 1) the two strategies, SETA and SETI, are competitive, 2) the Moon and the Earth Trojans have a greater probability of success than the co-orbitals.

5. Research for Finding Alien Artifacts

I advocate a sequence of tasks:

  • We have had the Lunar Reconnaissance Orbiter in low orbit around the Moon since 2009. It has taken about 2 million images at high sub-meter resolution (M. Revine, personal communication). We can see where Neil Armstrong walked! The vast majority of the photos have not been inspected by the human eye. Searching these millions of photographs for alien artifacts would require an automatic processing system. Development of such an AI is a low-cost initial activity for finding alien artifacts on the Moon, as well as Earth Trojans or the co-orbitals (Davies & Wagner, 2011, Lesinkowski et al., 2020). Note the recent AI analysis of 2 million images from LRO which revealed rockfalls over many regions of the Moon (Bickel et al., 2020).
  • Conduct passive SETI observations of these nearer-Earth objects in the microwave, infrared and optical.
  • Use active planetary radar to investigate the properties of these objects
  • Conduct active simultaneous planetary radar ‘painting’ and SETI listening of these objects.
  • Launch robotic probes to conduct inspections, take samples of Earth Trojans and the co-orbitals. The low delta-V, 3-5 km/sec, make this an attractive early option, is well within present capability (Stacey & Conners, 2009, Venigalla et al., 2019). China plans a mission to co-orbital 2016 HR 3 in the middle of this decade (Zxiaojing, et al., 2019).

6. Conclusion

Clearly looking for alien artifacts in the region of the solar system near Earth is a credible alternative approach, a strategy of ETI archeology. The formulation given here is a way of discussing the SETA strategy and comparing it to SETI.

The listening-to-stars strategy that SETI researchers have been following for over 50 years, is now being pursued very vigorously by Breakthrough Listen. What has SETI learned so far about life in the universe? Only that there is no intelligent life broadcasting signals toward Earth at the time we’ve listened, within the sensitivity levels, duty cycles and frequencies we have observed. If the ongoing SETI listening program continues to not hear a signal, the case for looking for Lurkers will grow ever stronger.

The SETA strategy was not pursued after it was suggested in the 1980’s, because listening to stars is easier and observing technologies and spacecraft were not sufficiently developed to pursue it. But now SETA is more attractive:

  • Close inspection of bodies in these regions can now be done with 21st Century observatories and spacecraft.
  • The great virtue of searching for Lurkers is their lingering endurance in space, long after they go dead.
  • The Moon and the Earth Trojans have a greater probability of success than the co-orbitals.
  • There are differences in detection in the two strategies: in the artifact case we should listen to those objects and image them in the optical or radar from Earth or send probes to visit them. In SETI, we can only listen.
  • SETA is a concept that can be falsified, a fundamental requirement for a science. SETA can be falsified or verified in practice by precisely specifying what one is looking for. For example, the statement “No artificial objects larger than 1 m exist on the surface of the Earth Trojan” can be verified by observing that object at that resolution. Smaller objects wouldn’t be resolved. If we conduct the efforts described in Section 5, and don’t find artifacts, the SETA concept is disproven for the near-Earth region, where it is most credible. If we find them, it’s verified.


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