Constraints on the abundance of 0.01c stellar engines in the Milky Way
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Constraints on the abundance of . c stellar engines in the Milky Way Manasvi Lingam
1, 2 and Abraham Loeb Department of Aerospace, Physics and Space Sciences, Florida Institute of Technology, Melbourne FL 32901, USA Institute for Theory and Computation, Harvard University, Cambridge MA 02138, USA
ABSTRACTStellar engines are hypothesized megastructures that extract energy from the host star, typicallywith the purpose of generating thrust and accelerating the stellar system. We explore the maximumpotential speeds that could be realizable by stellar engines, and determine that speeds up to ∼ . c might perhaps be attainable under optimal conditions. In contrast, natural astrophysical phenomenain the Milky Way are very unlikely to produce such speeds. Hence, astrometric surveys of hypervelocitystars may be utilized to conduct commensal searches for high-speed stellar engines in the MilkyWay. It may be possible to derive bounds on their abundance, but this requires certain assumptionsregarding the spatiotemporal distribution of such engines, which are not guaranteed to be valid. INTRODUCTIONThe search for signatures of extraterrestrial techno-logical intelligence (ETI) - appositely termed “tech-nosignatures” by Jill Tarter in 2007 (Tarter 2007) -has been dominated by the quest for artificial electro-magnetic signals from the 1960s onward, mostly at ra-dio wavelengths (Drake 1965; Shklovskii & Sagan 1966;Tarter 2001; Worden et al. 2017; Lacki et al. 2020); inspite of the numerous searches conducted hitherto, thefraction of parameter space sampled remains minus-cule (Tarter et al. 2010; Wright et al. 2018). Since thevery inception of this field, however, the potentialityof non-radio technosignatures was recognized, and itsimportance has been increasingly underscored in the21st century (Dyson 1966; Freitas 1983; Bradbury et al.2011; Wright et al. 2014; Cirkovic 2018; Lingam & Loeb2019a).In classifying prospective ETIs, the Kardashev scalepioneered by the late Nikolai Kardashev has proven tobe a valuable metric (Kardashev 1964; ´Cirkovi´c 2015;Gray 2020). Type II ETIs, for instance, are capable ofharnessing the entire radiative energy output of theirhost star. As these ETIs are considerably more ad-vanced in terms of their technology than humans, itis conventionally anticipated that their resultant tech-nosignatures would be commensurately more striking.The best known technosignatures in this category areStapledon-Dyson spheres - these megastructures arecomposed of swarms of objects to tap the energy ofthe star (Stapledon 1937; Dyson 1960). Several searchesfor Stapledon-Dyson spheres have been undertaken to
Corresponding author: Manasvi Lingammlingam@fit.edu date, as reviewed in Wright (2020) and Lingam & Loeb(2021).Another group of megastructures belonging to a sim-ilar category are stellar engines, which draw upon thestar’s energy to extract useful work and typically gener-ate thrust. Leonid Shkadov is widely credited with thefirst design for a stellar engine wherein a gigantic mirrorwas deployed to reflect a fraction of the radiation backtoward the host star (Shkadov 1987, 1988). However,Zwicky (1957, pg. 260) explicitly articulated this sce-nario in his characteristically wide-ranging monograph:
Considering the sun itself, many changes areimaginable. Most fascinating is perhaps thepossibility of accelerating it to higher speeds,for instance km/sec directed toward α -Centauri in whose neighborhood our descen-dants then might arrive a thousand yearshence. All of these projects could be realizedthrough the action of nuclear fusion jets, us-ing the matter constituting the sun and theplanets as nuclear propellants. Looking further back in time, the qualitative notion ofstellar engines appears in Stapledon (1937, Chapter XI),as seen from the following quote:
The occasion of the first accident was an at-tempt to detach a star from its natural courseand direct it upon an inter-galactic voyage. . . Plans were therefore made for projectingseveral stars with their attendant systems ofworlds across the vast ocean of space thatseparated the two floating islets of civiliza-tion.
Stellar engines have been explored in several other pub-lications (Badescu & Cathcart 2000, 2006; Hooper 2018;Caplan 2019; Svoronos 2020) and methods for detectingthem during the course of exoplanetary transits werediscussed in Forgan (2013).In the classification scheme of Badescu & Cathcart(2000), three major classes of stellar engines were identi-fied. Class A stellar engines utilize the impulse from stel-lar radiation to generate a thrust force. The quintessen-tial example of a Class A engine is the so-called Shkadovthruster described in Shkadov (1987, 1988). Class B stel-lar engines, in contrast, harness the radiation emittedby the host star and convert it into mechanical power.Class C stellar engines combine elements of both Class Aand Class B stellar engines, and thereby generate boththrust force and mechanical power. Class D stellar en-gines, mentioned briefly in Badescu & Cathcart (2006,pg. 121), extract mass from the star by means of “masslifting” (Criswell 1985) and expel the material to gen-erate a rocket effect; such stellar engine were previouslytermed “stellar rockets” by Fogg (1989).The designs suggested for the putative stellar enginesvary from one class to another. The Shkadov thruster(Class A engine) is composed of a collection of reflectivestatites (Forward 1991), which effectively functions asa large mirror in the shape of a spherical arc; the de-sign for a Class C engine is also similar in this respect(Badescu & Cathcart 2006, Figure 1). Class D enginesoperate on the rocket effect, and can therefore be en-visioned as stellar rockets, but the engineering specificsdiffer across proposals (Caplan 2019; Svoronos 2020).We will briefly summarize one such design later in Sec.2.2.Clearly, stellar engines represent a massive engineer-ing feat, and this raises the question of why they wouldbe constructed. Before doing do, it should be notedthat the planets and moons orbiting the host star wouldneed to be accelerated as well, but this feat is relativelyeasier in comparison to the star. One possible reasonsuggested in Caplan (2019) is that stellar engines mayenable ETIs to preemptively escape the vicinity of catas-trophic phenomena (e.g., supernovas) and avoid the ad-verse consequences. This issue may be rendered moreprominent near the Galactic center, where higher stellardensities are associated with higher rates of catastrophicevents. Another option is that the ETIs might wish toundertake intergalactic travel, which is perhaps easier toundertake by moving the planetary system as a whole,in contrast to the alternative concept of building “worldships” (Hein et al. 2012). We will not speculate on thistopic further, as it partly overlaps with the poorly un-derstood fields of xenosociology and xenopsychology. For instance, theoretical models indicate that the habitability ofthe Milky Way might be affected over kpc scales due to the cu-mulative impact of tidal disruption events and a potential quasarphase at some point (Balbi & Tombesi 2017; Forbes & Loeb2018; Lingam & Loeb 2019b; Lingam et al. 2019; Pacetti et al.2020).
In this work, we explore stellar engines from a genericphysical standpoint in Sec. 2, and describe how theymay attain terminal speeds that are sub-relativistic. Wecompare these speeds against stars ejected by naturalastrophysical phenomena in Sec. 2, and argue that thelatter cannot reach such large values in the Milky Way.By making use of this proposition, we examine currentastrometric surveys to set tentative constraints on theabundance of putative ETIs that develop high-speedstellar engines in Sec. 3. We end with a summary ofour results and prospects for future work in Sec. 4. MAXIMUM ATTAINABLE STELLAR SPEEDSWe will begin with a synopsis of the maximal speedsrealizable by ejected stars and stellar engines.2.1.
Maximum speeds of ejected stars in astrophysicalsystems
The maximum speed ( v max ) achievable by starsejected after tidal disruption of a stellar binary systemby Sagittarius A* was computed in the classic analy-sis by Hills (1988), and it was concluded that v max ≈ . × − c ; see also Yu & Tremaine (2003) and Brown(2015). Subsequent numerical simulations by Sari et al.(2010, Section 8) determined that the maximum speedof the least massive object in a triple system that un-derwent ejection is given by v max ≈ . r GM R + R (cid:18) M M + M (cid:19) / , (1)where M denotes the mass of the supermassive blackhole (SMBH), while M j and R j are the masses and radiiof the stellar binary system that is subjected to tidalbreakup ( j = 2 , M < M . We adopt M ≈ × M ⊙ for Sagittarius A* (Boehle et al. 2016), andsubstituting this value into the above equation yields v max ≈ . × − c (cid:18) M M ⊙ (cid:19) / (cid:18) R + R R ⊙ (cid:19) − / × (cid:18) M + M M ⊙ (cid:19) − / , (2)and this expression is considerably simplified when M is at least a few times smaller than M , and using thescaling R ∝ M . for main-sequence stars (Tout et al.1996). In this optimal situation, we end up with v max ≈ . × − c (cid:18) M M ⊙ (cid:19) − . , (3)which implies that v max is nearly independent of M .Hitherto, we have assumed that M is a main-sequencestar, but the other extreme is to consider a stellar-massblack hole instead. The resultant maximum speed wascalculated in Guillochon & Loeb (2015, Equation 5): v max ≈ . × − c (cid:18) M M ⊙ (cid:19) / (cid:18) M M ⊙ (cid:19) − . , (4)where M is the mass of a typical stellar-mass black holeand M is the mass of the ejected star.Thus, it is apparent from the preceding formu-lae that achieving v max > . c is very unlikelyfor gravitational triple interactions in our Galaxy.In fact, even ejected stellar speeds larger than ∼ . c are rarely attained in numerical simula-tions, as seen from the probability distributions ofejected velocities in Bromley et al. (2006); Kenyon et al.(2008); Ginsburg et al. (2012); Rossi et al. (2014);Generozov & Madigan (2020). Faster speeds of & . c are realizable in theory but require one of the stars inthe stellar binary system to be replaced by a SMBHinstead (Guillochon & Loeb 2015; Loeb & Guillochon2016; Darbha et al. 2019); however, this specific scenariois manifestly not applicable to the Milky Way.Aside from the Hills mechanism and its variants men-tioned earlier, it is necessary to gauge whether otheravenues can eject stars at similar speeds. One of themost well-known processes entails the disruption of thebinary when one of the objects undergoes a core-collapsesupernova and leads to the ejection of the other objects(Blaauw 1961; Boersma 1961). Numerical simulationsindicate, however, that the maximal speeds of ejectionare . . c (Tauris 2015; Evans et al. 2020; Neunteufel2020). Another possibility is the “dynamical ejectionscenario” whereby dynamical ejection from stellar clus-ters is facilitated, typically at speeds of order . − c (Poveda et al. 1967; Leonard 1991; Oh & Kroupa 2016).Lastly, one could replace the SMBH with an intermedi-ate mass black hole or a series of stellar-mass black holes,but the resulting speeds of ejected stars are . . c (Gualandris & Portegies Zwart 2007; O’Leary & Loeb2008; Fragione & Gualandris 2019). In all these pro-cesses, the speeds attained are smaller than v max for theHills mechanism; see (3) and (4).2.2. Stellar engines: potential speeds
The Shkadov thruster, which is an example of a ClassA stellar engine, will reach the velocity v after an interval∆ t as follows (Badescu & Cathcart 2000, Equation 34): v ≈ . × − c (cid:18) ∆ t (cid:19) (cid:18) LL ⊙ (cid:19) (cid:18) M ⋆ M ⊙ (cid:19) − , (5)where L ⋆ and M ⋆ are the luminosity and mass of thestar. In order to compare the speeds of stellar enginesagainst those presented in Sec. 2.1, it is necessary toassess their maximal values.It is reasonable to assume that the maximum speedis attained when ∆ t ≈ t ⋆ , where t ⋆ denotes the main-sequence lifetime of the star. From the scaling t ⋆ ∝ M ⋆ /L ⋆ (Hansen et al. 2004, Equation 1.90), we find that v max would become independent of stellar properties;after simplification, we obtain v max ≈ . × − c . Note,however, that this estimate for v max applies only when t ⋆ < t U , where t U is the current age of the Universe; this condition is fulfilled for M ⋆ & M ⊙ . On the other hand,if this criterion is violated, the stellar engine will notbe able to achieve v ≈ v max in reality. Since the thrustgenerated by Class A and Class C engines is comparable(Badescu & Cathcart 2006, Section 3), the same upperbound also applies to the latter.Let us consider a generalized stellar engine whereina fraction ε of the total energy radiated by the star isharnessed to propel it, as suggested in Hooper (2018).This would resemble a Class C stellar engine to a certaindegree, because there is both energy extraction from thestar’s radiation and the generation of thrust force. Byapplying the conservation of energy, we obtain (Hooper2018, Equation 2.3): v ≈ . × − c √ ε (cid:18) ∆ t (cid:19) / (cid:18) LL ⊙ (cid:19) / (cid:18) M ⋆ M ⊙ (cid:19) − / , (6)and we can calculate the maximum velocity by invokingthe relation ∆ t ≈ t ⋆ from earlier, which yields v max ≈ . × − c √ ε, (7)and we reiterate that this speed is realizable in realityonly when M ⋆ & M ⊙ . As opposed to energy conversion,if the momentum of radiation is harnessed, the scalingand magnitude of v are akin to (5).We can, however, conceive of more sophisticated sys-tems. Let us suppose, for instance, that instead of utiliz-ing energy, the putative ETI extracts mass at a constantrate (denoted by ˙ M ⋆ ) via “mass lifting” (Criswell 1985).This scheme does not exhibit a clear one-to-one mappingwith any of the stellar engines described in Sec. 1 be-cause the focus is not on the energy or momentum of theemitted radiation, but rather on mass extraction and itssubsequent conversion into thrust imparted to the star.The mass thus acquired is presumed to be convertedinto energy at an efficiency µ via the mass-energy rela-tionship. In this event, provided that ˙ M ⋆ ∆ t ≪ M ⋆ toensure the mass is roughly constant, the speed achievedover the interval ∆ t is estimated to be v = s µc ˙ M ⋆ ∆ tM ⋆ . (8)In place of working with two variables in the above ex-pression, we can rewrite it as follows: we suppose thatETI modulates its mass extraction and energy conver-sion such that ˙ M ⋆ ∆ t = ζM ⋆ with ζ ≪
1, i.e., the ETIensures that the star’s mass is not significantly depletedafter the interval ∆ t . A crude upper bound on ζ is 0 . The depletion of stellar mass, among other things, may aid incontrolling the stellar luminosity, and thereby mitigating the shiftof the habitable zone around the star over time. loss), which consequently yields a maximum speed of v max ≈ . × − c √ µ (cid:18) ζ . (cid:19) / . (9)It is important to note, however, that both energy andmomentum of the system as a whole are conserved. Inthe latter case, we would have M ⋆ v ≈ ( ζµM ⋆ c ) /c bymomentum conservation, thus obtaining v max ≈ . c µ (cid:18) ζ . (cid:19) , (10)in the same manner as (9); for µ ≪
1, it is apparentthat this velocity drops below that of (9). Due to thejoint conservation of energy and momentum, it followsthat the peak velocity cannot exceed the maximum of(9) and (10) for this generic stellar engine.It is necessary to examine the potential values of µ fur-ther. In the canonical case of the proton-proton chainreaction to yield helium, it is well-known that µ ≈ . prima facie . It is worth mentioning, however, that effi-ciencies of <
42% are predicted for black holes by gen-eral relativity (Novikov & Thorne 1973). Thus, if thestellar engine is a binary with one of the objects being ablack hole, it is conceivable that µ ∼
10% could be effec-tuated, although the subsequent pathway to impartingthrust to the binary system remains indeterminate (andundoubtedly complicated) and falls outside the scope ofthis paper. What is clear, however, is that the mass ex-traction can continue as long as access to the black holeis maintained, which implies that the black hole mustalso be accelerated. Even setting aside this option, weremark that ETIs with the technological wherewithal tobuild stellar engines might find methods to raise µ by anorder of magnitude or so compared to the proton-protonchain. In case µ ∼ . v max ∼ . c .The above analysis, however, ignored the fact that acontinual mass loss ought to result in a rocket effect. Intheory, we can also conceive of thrusters propelled byjets in stellar and compact object systems, correspond-ing to the Class D stellar engines mentioned in Sec. 1.The final velocity is straightforward to calculate whenthe rocket equation holds true (Tsiolkovsky 1903): v = v ex ln (cid:18) M i M f (cid:19) , (11)where M i and M f are the initial and final masses ofthe star, whereas v ex is the velocity at which the pro-pellant is expelled. If one considers v ex that is a fewtimes higher than the stellar escape velocity, or equiva-lently the stellar wind velocity, and choose a mass ratio of ∼ we would end up with v ∼ . c . It shouldbe noted that this setup calls for an increase in the ex-haust velocities by only a factor of order unity comparedto current designs (Cassibry et al. 2015; Wurden et al.2016). From a conceptual standpoint - although theyare not readily implementable with current human tech-nology - relativistic rockets reliant on hydrogen (orits isotopes) as the fuel have the capacity to reachweakly relativistic exhaust velocities (Winterberg 2019;Holmlid & Zeiner-Gundersen 2020); in this context, therealization of v max ∼ . c does not seem wholly impos-sible.We point out that two recent designs for Class D stel-lar engines have examined the aforementioned phenom-ena in more detail (Caplan 2019; Svoronos 2020). Inthe so-called “Star Tug” proposed in Svoronos (2020,Figure 1), mass lifting is used to extract matter froma Sun-like star, which is converted into propellant byan engine located at a given distance. This propellant isemployed to generate thrust that overcomes the gravita-tional force between the engine and the star, and causesthe acceleration of the system. At perfect efficiency, theStar Tug achieved v max ≈ . c in a few Gyr, whereaslowering the efficiency to 20% still enabled a velocityof 0 . c to be achieved in approximately 10 Gyr. TheStar Tug achieved an asymptotic acceleration of ∼ − m s − at perfect efficiency when the engine was situatedfar away from the star, but this value dropped by nearlytwo orders of magnitude at 20% efficiency.Once the stellar engine has begun accelerating and itspassage through the interstellar medium (ISM) is under-way, it may be feasible to make use of other propulsionsystems to generate additional thrust and couple themto the stellar engine. The interstellar ramjet, whichscoops up interstellar material and converts the accruedmatter into fuel, represents one such possibility (Bussard1960; Long 2011). We will not delve into the technicaldetails of this putative coupling scheme, because ascer-taining the engineering technologies adopted by hypo-thetical advanced ETIs is indubitably constrained byour current level of knowledge and vision.Lastly, a comment on the effects of the ISM on stellarengines is in order. The mechanical components com-prising the stellar engine will be subject to erosion anddamage due to interactions with gas, dust and cosmicrays in the ISM. However, predicting the extent of dam-age is difficult because it depends on the relative ve-locity of the stellar engine, the distance travelled by it,the thickness and properties of the materials used tofabricate the components, and many more. There havebeen several theoretical studies of the passage of sub- Note, however, that this mass ratio (which is equivalent to ζ ∼ .
9) is at odds with the choice of ζ considered previously. We haveconsidered a deliberately high value to highlight the significanceof the rocket effect when it comes to Class D stellar engines. relativistic spacecraft through the ISM, and it might befeasible for them to remain functional over kpc distances(Hoang et al. 2017; Hoang & Loeb 2017; Hoang 2017;Hippke et al. 2018; Lingam & Loeb 2020), although sig-nificant uncertainties still remain.To summarize, there appear to be plausible designsfor stellar engines that seem capable of achieving v max ∼ . . c in principle. At the minimum, it may be ar-gued that no compelling a priori grounds exist for dis-missing the prospects for sub-relativistic stellar enginesbased on core physical principles. CONSTRAINTS ON STELLAR ENGINESIn the preceding Section, we presented arguments asto why even the fastest stars ejected from astrophysi-cal systems are unlikely to have speeds of & km/s(0 . c ), whereas stellar engines could attain such ve-locities. Hence, if one were to detect stars moving at & . c , it would be strongly indicative of ETI activ-ity and thus constitute a technosignature. The one falsepositive that ought to be taken into consideration is thata star moving at & . c may have an extragalactic ori-gin because of ejection during binary SMBH interactions(Guillochon & Loeb 2015), as explained in Sec. 2.1. Acombination of precise astrometry and chemical taggingshould, however, aid in distinguishing between extra-galactic and Galactic hypervelocity stars. This proce-dure was utilized to pinpoint the origin of HVS 3 fromthe Large Magellanic Cloud (Erkal et al. 2019).The Gaia mission was designed to accurately pin downthe positions and radial velocities of ∼ stars in theMilky Way. Gaia
DR-1 and DR-2 have already yieldeda wealth of data on this front (Gaia Collaboration et al.2016, 2018). As a rigorous assessment of the originof hypervelocity stars requires knowledge of their to-tal velocity (Brown 2015), it is necessary to measureboth their radial and tangential components.
Gaia
DR-2 has provided radial velocity information about 7million stars (Katz et al. 2019). The number of starswith data available regarding their proper motion (i.e.,tangential velocity) is ∼ . × (Lindegren et al.2018). A number of studies have already combedthrough this sample to unearth evidence for hyperve-locity stars (Bromley et al. 2018; Hattori et al. 2018;Marchetti et al. 2019; Boubert et al. 2019; Caffau et al.2020; Li et al. 2020).To the best of our knowledge, the fastest hyperveloc-ity star from any survey is S5-HVS1 from the SouthernStellar Stream Spectroscopic Survey with a velocity of ∼ × − c (Koposov et al. 2020), while HVS 22 from theMultiple Mirror Telescope survey exhibits a similar ve-locity of ∼ × − c (Kreuzer et al. 2020). Among the Gaia
DR-2 catalog, one of the fastest objects is the can-didate
Gaia
DR-2 6097052289696317952, which appearsto have a tangential velocity of ∼ . × − c (Scholz2018). Other analyses of the Gaia
DR-2 data have seem-ingly identified stars with velocities (tangential and/or radial) that are comparable to, but somewhat lower,than this object (Shen et al. 2018; Bromley et al. 2018;Du et al. 2019; Caffau et al. 2020).Thus, it would seem a safe bet to contend that allsearches conducted to date have failed to yield unam-biguous evidence of sub-relativistic stellar engines. Thisdatum enables us to derive the following constraint: N surv · f T · f SE < , (12)where N surv represents the number of stars collectivelyencompassed by all astrometric surveys, f T denotes thefraction of all stars that host ETIs with human-leveltechnology, and f SE embodies the fraction of all human-level ETIs that subsequently achieve the capability andintent to deploy sub-relativistic stellar engines. The rea-son we select human-level technology as the benchmarkis not due to the notion that we are “special”, but be-cause it constitutes a signpost that is familiar to us.Although (12) may appear simple, the estimation ofthe sample size N surv is fraught with several difficultiesand ambiguities, some of which are detailed below.1. Given that Gaia
DR-2 furnished astrometric datafor ∼ stars and radial velocity data for ∼ stars, it is tempting to specify N surv ∼ − .2. However, the stellar engines we discussed in Sec. 3reach their peak speeds of ∼ . . c only whenthe stars have masses close to that of the Sun orhigher ( M ⋆ & M ⊙ ). Among the total populationof ∼ objects spanned by the Gaia mission,only ∼ of them are solar-type main-sequencestars. Hence, the above numbers for N surv mustbe reduced by roughly an order of magnitude whenwe restrict ourselves to solar-type stars.3. The calcium triplet (CaT) is used by the Gaia mis-sion to estimate the radial velocities by measuringthe Doppler shift. The spectrograph has a band-pass of 847-874 nm (Cropper et al. 2018), therebyproviding a “buffer” of ∼ . ∼ . . c would yield Doppler shifts of ∼ . Gaia spec-trograph is liable to “reject” such stellar engineswhen the shift falls outside its bandpass. In prin-ciple, however, high tangential velocities can beinferred from measurements of the proper motionsand parallaxes (Shen et al. 2018; Scholz 2018).4. Last, but not least, (12) is expected to yield anaccurate picture only when the stellar engines areuniformly distributed in both the spatial and tem-poral realms. However, it will take . stellar engines to exit the ∼ Gaia
DR2 once their maximal velocity is at-tained, and they will eventually cross the entireMilky Way in ∼
10 Myr. Hence, it is not straight-forward a priori to derive proper constraints onthe unknown parameter(s) unless new stellar en-gines are being continually “injected” into the do-main encompassed by surveys like
Gaia .Bearing these caveats in mind, let us adopt a roughestimate of N surv ∼ with the express purpose of tak-ing the argument further; we emphasize that this valueis fiducial. By plugging this choice into (12), we obtain f T · f SE < − (cid:18) N surv (cid:19) − . (13)After the Gaia mission is complete, assuming that nostellar engines are found, we may end up with the poten-tially tightest limit of f T · f SE < − for speeds & . c under optimal circumstances, i.e., when the subtletiesdescribed in points • The first possibility is that f T is exceptionallysmall. In this case, the prevalence of human-level ETIs would be commensurately low. Thiscould arise due to any number of evolution-ary bottlenecks ranging from abiogenesis to com-plex multicellularity to technological intelligence(Smith & Szathmary 1995; Lingam & Loeb 2021). • In the second case, f SE may be minuscule, but f T may have a moderate magnitude. There are,however, different scenarios at play here. On theone hand, ETIs might have a short technologicallifetime and become extinct before they reach thestage where they can build stellar engines. Onthe other hand, it could very well be that weaklyrelativistic stellar engines have hidden engineeringobstacles that render their construction impossi-ble, or that ETIs possess the capability to buildthem but opt not to do so for other reasons. • In the third outcome, both f T and f SE are bothvery small. This situation does not warrant sepa-rate explication, because it represents an amalga-mation of the above two points.To differentiate between, and indeed shed light on,the diverse outcomes demarcated above, the practicalimportance and necessity of carrying out searches forbiosignatures and technosignatures on multiple fronts isself-evident (Frank 2018; Haqq-Misra et al. 2020).There is a fourth option that deserves to be mentionedat this juncture. In theory, it is possible that stellar en-gines might already exist in the Milky Way, but that these putative megastructures are operating at veloci-ties that fall within the bounds of known hypervelocitystars. In this setting, distinguishing between them andnaturally occurring hypervelocity stars would be an ex-tremely challenging endeavour. We will not explore thisscenario further because it calls for additional assump-tions about the preferred trajectories of stellar engines,and this requires an understanding of the motives of pu-tative ETIs, which is wholly unknown.Before moving ahead, we note that stellar engines arepotentially capable of accelerating at ∼ − m s − (Caplan 2019; Svoronos 2020). In contrast, the cen-tripetal acceleration of the Sun is ∼ − m s − . Thus,in principle, detecting anomalously high stellar acceler-ations might also be indicative of stellar engine activity,although we caution that the ratio of the two accelera-tions (i.e., an order of magnitude) is not strikingly large. CONCLUSIONWe examined various mechanisms for the ejection ofstars at high speeds, and concluded that stars ejected inthe Milky Way are very unlikely to attain speeds over & km/s (0 . c ) by any known natural astrophysicalphenomena. Next, we considered some proposed designsfor stellar engines, i.e., propulsion systems engineered byadvanced ETIs to accelerate stars, which were conceivedby Olaf Stapledon and Fritz Zwicky (among others) inthe mid-20th century. We argued that speeds of ∼ . . c may be potentially achievable by stellar enginesunder optimal circumstances.Based on the above premises, we examined currentsurveys for hypervelocity stars including the recent Gaia
DR-2 sample. In light of existing studies, we concludedthat no stars have been conclusively identified that pos-sess velocities of & . c . Taken at face value, stellarengines moving at sub-relativistic speeds appear to bequite rare but placing stringent constraints on their like-lihood is rendered difficult because of both instrumentallimitations and lack of knowledge about their spatio-temporal distribution. It might be possible that fewerthan one in ∼ stars is propelled to speeds & . c bystellar engines, although this statement is not definitivein light of the attendant uncertainties.In the future, it would seem worthwhile to pursuethe search for stars with anomalously high velocities(namely & . c ). This strategy is advantageous for twochief reasons. First, it does not necessitate any new re-sources, because it can readily piggyback on astrometricsurveys like Gaia . Second, if we do stumble upon starsmoving at such anomalously high speeds, their originwould be of great interest and significance irrespectiveof whether they have an artificial basis or not.In this regard, this search exemplifies the phi-losophy underpinning the aptly named “ FirstLaw of SETI Investigations” proposed by thelate Freeman Dyson: “
Every search for aliencivilizations should be planned to give interest- ing results even when no aliens are discovered. ”(NASA Technosignatures Workshop Participants2018), which itself echoes the earlier sentiments es-poused by Frank Drake in his neglected early treatise(Drake 1965, pg. 342): “
Thus, any project aimed atthe detection of intelligent extraterrestrial life shouldsimultaneously conduct more conventional research. ” Thus, in each of these respects alongside a few others,this search for technosignatures may score highly on theaxes of merit adumbrated in Sheikh (2020). ACKNOWLEDGMENTSWe are grateful to the two reviewers for their positiveand insightful reports, which helped improve the paper.This work was supported in part by the BreakthroughPrize Foundation, Harvard University’s Faculty of Artsand Sciences, and the Institute for Theory and Compu-tation (ITC) at Harvard University.REFERENCES
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