Fast Radio Bursts from Extragalactic Light Sails

0.16 MB·

by  Manasvi Lingam

Draftversion February28,2017
TypesetusingLATEXtwocolumnstyleinAASTeX61
FAST RADIO BURSTS FROM EXTRAGALACTIC LIGHT SAILS
Manasvi Lingam1,2 and Abraham Loeb2
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1 1Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA
0 2Harvard-Smithsonian CenterforAstrophysics, TheInstitute forTheory andComputation, 60Garden Street,Cambridge, MA 02138, USA
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b ABSTRACT
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We examine the possibility that Fast Radio Bursts (FRBs) originate from the activity of extragalactic civilizations.
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OuranalysisshowsthatbeamsusedforpoweringlargelightsailscouldyieldparametersthatareconsistentwithFRBs.
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The characteristic diameter of the beam emitter is estimated through a combination of energetic and engineering
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constraints, and both approaches intriguingly yield a similar result which is on the scale of a large rocky planet.

Moreover, the optimal frequency for powering the light sail is shown to be similar to the detected FRB frequencies.
]
E These ‘coincidences’ lend some credence to the possibility that FRBs might be artificial in origin. Other relevant
H quantities, such as the characteristic mass of the light sail, and the angular velocity of the beam, are also derived. By
. usingthe FRBoccurrencerate,weinferupperbounds onthe rateofFRBsfromextragalacticcivilizationsinatypical
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galaxy. The possibility of detecting fainter signals is briefly discussed, and the wait time for an exceptionally bright
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FRB event in the Milky Way is estimated.
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Correspondingauthor: ManasviLingam
[email protected]
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1. INTRODUCTION Webeginbydenotingthedistanceofthebeamsource
from the Earth by r. One of the primary observable
Ever since the first discovery of Fast Radio Bursts
parameters for FRBs is the dispersion measure (DM),
(FRBs) over a decade ago (Lorimer et al. 2007),
defined through a line-of-sight integral,
there has been a great deal of interest in uncover-
ing their origin. Currently, only 17 FRBs have been r
recorded, and a summary of their properties can be DM= ne(s)ds=n¯er, (1)
found in Petroff et al. (2016).1 Hypotheses put for- Z0
ward for FRBs range from supramassive neutron stars of the mean number density of free electrons n¯e. Ig-
(Falcke & Rezzolla 2014) to gamma-ray bursts (Zhang noring contributions from the source, its host galaxy
2014)andstellarflares(Loeb et al.2014). Regardlessof and the Milky Way, one may adopt the mean comov-
their actual origin, it is now widely accepted that most ingelectrondensityfortheintergalacticmedium(IGM),
FRBs are at cosmological distances (Thornton et al. n¯e ≈ 2×10−7cm−3 (Planck Collaboration et al. 2016;
2013), particularly owing to the recent localization of Fialkov & Loeb 2016). For simplicity, we assume that
the repeating FRB 121102 to a dwarf galaxy at a red- the FRBredshiftsare<1,anddropthe redshiftfactors
shift of z ∼0.2 (Chatterjee et al. 2017; Tendulkar et al. in the context of our order-of-magnitude estimations.
2017). Most sources in the FRB catalog (Petroff et al. 2016)
The unusually high brightness temperature of FRB have DM values of order hundreds of cm−3 pc. Using
sources at cosmological distances (Katz 2016a) implies equation (1), the distance can be estimated as,
that their radio emission mechanism must be coherent −1
asknowntoexistinpulsarsorhuman-maderadiotrans- r∼1Gpc DM n¯e . (2)
mitters. Despite the diversity of explanations advanced (cid:18)200cm−3pc(cid:19)(cid:18)2×10−7cm−3(cid:19)
for FRBs, the possibility that they may be of artificial
This distance is alsoconsistentwith moreaccurateesti-
originhas not been specifically investigated,apart from
mates (Petroff et al. 2015, 2016).
Section V of Luan & Goldreich (2014).
Next,wesupposethatthebeamhasanangularwidth
In this Letter, we examine the possibility that FRBs
θ and a radiated (peak) power P. The beam angle is
areartificialbeams2 whichhavebeensetupasbeacons,
expressible as some factor η times the minimum value
or for driving light sails. The idea that extraterrestrial
set by the diffraction limit,
civilizations may be using radio beams (manifested as
c
dispersed pulses) is certainly not a new one, as it dates θ =η , (3)
back to the pioneering paper by Cocconi & Morrison (cid:16)νD(cid:17)
(1959). This idea was extended by researchers engaged where ν is the frequency of the radiation, D is the di-
intheSearchforExtraterrestrialIntelligence(SETI),ac- ameter of the beam emitter, and η ≥ 1. The spectral
counts of which can be found in Drake & Sobel (1992) flux density is given by,
and Tarter (2001) (see also Siemion et al. 2012). In
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addition to traditional, radio-based SETI, many other Sν =η−2 D αενP, (4)
approaches have been advanced for detecting alien civ- (cid:18)cr(cid:19)
ilizations (e.g Dyson 1960; Schwartz & Townes 1961;
where α = dlnS/dlnν is the spectral index needed for
Howard et al. 2004; Benford et al. 2010; Wright et al.
the relation αP/ν = Pν and ε is the fraction of P that
2014; Lingam & Loeb 2017).
is emitted as FRB radiation (radiative efficiency). We
In Section 2, we show that the parameters required
haveassumedthat∆ν/ν ∼1andwilluseεα∼1hence-
for generating artificial beams (to possibly power light
forth (Luan & Goldreich 2014; Katz 2016a), which im-
sails) are compatible with FRB constraints. We discuss
plies that the artificial beams are broadband. This un-
the implications and predictions in Section 3, and sum-
orthodox assumption, which is contrary to current ter-
marize our conclusions in Section 4.
restrial engineering design, will be central to our anal-
2. COMPATIBILITY OF FAST RADIO BURSTS ysis, and does represent a significant conceptual chal-
AND BEAMS lenge as to why civilizations would opt for broadband
emission.3 The mean spectrum of FRBs is observed to
We start by examining whether some of the major
FRB constraints are consistent with the assumption of
artificial beams, and then explore the possibility that
3 Potential reasons include: (i) photon recycling for multiple
these beams may be used to power light sails.
passes between the spacecraft and the planet. Each cycle yields
the standard kick but one gains by the number of cycles relative
2.1. FRB constraints and requirements
tothe casewherethebeam isdispersedafteronereflection. The
frequencywillbeDopplershiftedineachpass,andoncethespace-
craftreachesrelativisticspeedsthebeamcouldbebroadbandbe-
cause it will include a mix of photons with different number of
1 http://www.astronomy.swin.edu.au/pulsar/frbcat/ passes. (ii) optimization of engineering and economic costs and
2Alternatively,FRBscouldalsobepulsarbeams(Katz2016b). functionality(Benfordetal.2010;Messerschmitt2012).
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be Gaussian-shaped, centered on a frequency of a few words, the beam emitter is an object akin to a planet;
GHz (Law et al. 2017). While being consistent with an more precisely, it lies fairly close to the boundary be-
artificial origin, this spectral shape is puzzling for pul- tween super-Earths and mini-Neptunes (Rogers 2015).
sarormagnetar-likesourceswhichareexpectedtoshow Another possibility worth considering is that the emit-
power-law spectra. Inverting equation (4) yields,4 ter could have been fashioned along the lines of the
Stapledon-Dyson sphere (Stapledon 1937; Dyson 1960).
P∼1025ergs−1 r 2 ν −1 Sν To summarize,we assumedthat: (i) the emissionwas
(cid:18)1Gpc(cid:19) (cid:16)1GHz(cid:17) (cid:18)1Jy(cid:19) broadband, (ii) stellar energy was used to power the
−2 beams, and (iii) water was used as a coolant. A subtle
D
×η2 , (5) distinction is that (i) relies on advanced technological
(cid:18)3×109cm(cid:19)
choices(andunderpinnings),whilst(ii)and(iii)aretan-
tamount to statements about the availability and use-
where the value of D was normalized to the size of a
fulness of raw materials.
large rocky planet (Winn & Fabrycky 2015) for reasons
explained below.
2.2. What is the purpose of these beams?
First, let us suppose that extraterrestrialcivilizations
adopt the strategy of harnessing stellar energy (Lubin The preceding discussion concluded that some of the
2016) to power the beams, thereby leading to majorobservablesforFRBsareconsistentwiththeidea
thattheymaybemanifestationsofextragalacticbeams.
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P ∼SD2 ∼1025ergs−1 S D , (6) However,thisstillfailstoanswertheimportantquestion
(cid:18)S⊙(cid:19)(cid:18)3×109cm(cid:19) of why they would be extant.
Thefirst,andmostimmediate,possibilityisthatthey
whereSisthestellarirradiance,whichshouldbecloseto serve the purpose of ‘beacons’, and are thus meant to
thesolarvalueS⊙ inthehabitablezone. Thecharacter- broadcast the presence of alien civilizations. But, why
isticvalueofDisfoundfrom(4)and(6)bysubstituting would a civilization want to broadcast its presence? In
the typical values for all other parameters. Benford et al. (2010), a variety of motives were consid-
Astheapertureefficiencyisε,afraction(1−ε)would ered, many of them of a sociological origin, such as a
be dissipated, amounting to a power per unit area of call for help, a desire to proclaim their technological
(1−ε)P/D2 at the base of the emitter. If we assume achievements, etc. Although these possibilities cannot
that this excess heat is radiated awaythermally, we get (and ought not) be ruled out, there are some inherent
difficulties. Theyrelyoncomplex(anthropocentric)rea-
(1−ε)P
=σT4, (7) sons to some degree, and are thus not easily testable.
D2
Moreover, equation (5) demonstrates that a power of
where T is the surface temperature of the beamer. If 1025ergs−1 is required, representing a fairly high ex-
thevalueofT istoohigh,structuraldamagemayfollow. penditure. Hence, it seems rather implausible that this
Hence,anupperboundonT translatestoalowerbound powerwouldbeexpendedonmerelybroadcastingaciv-
on D. This leads us to ilization’s existence.
Instead,weconsidertheideadiscussedinBenford et al.
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P =1025ergs−1 1 D T , (2010), further elaboratedin Guillochon & Loeb (2015)
(cid:18)1−ε(cid:19)(cid:18)3×109cm(cid:19) (cid:18)373K(cid:19) and Benford & Benford (2016), that these beams may
(8) power light sails. Suppose that a civilization wishes to
andacomparisonwith(5)and(6)revealsthatthesame construct a light sail capable of attaining relativistic
power estimate follows for D ∼3×109 cm. This repre- speeds. In Guillochon & Loeb (2015), it was argued
sents the minimum aperture diameter that is required that an efficient strategy for achieving the largest pos-
to keep the system running. Note that the value of T sible velocity for a limited acceleration value leads to
has been normalized to the boiling temperature of wa-
ter, since it is widely used as a coolant in many beamer vmax = 2amaxdF, (9)
designs (Weber et al. 1998). p
Thus, we have shown that the characteristic value of where vmax andamax arethe maximumvelocityandac-
D ∼ 3×109 cm is obtained in two very different ways, celerationrespectively,whilstdF =νD2/cistheFresnel
from energetic and engineering requirements. This al- distance. The above expression takes advantage of the
ready constitutes a remarkable coincidence. It is ren- constant beam diameter in the near-field Fresnel region
dered more unique because of a third coincidence - the (with the sail size matching D) out to dF, where the
valueis abouttwicethe diameterofthe Earth. Inother beamentersthe Fraunhofer(far-field)regimeandstarts
todivergewithanopeningangleθ. InSection2.1,wear-
guedthatD shouldbenormalizedinunitsof3×109 cm
4WeobtainEq. (20)inLuan&Goldreich(2014),althoughthe for a multitude of reasons;this amounts to dF ∼0.1pc.
factorofb−1 shouldbecorrectedtob−2 inthatpaper. Using this value along with the characteristicvalues for
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vmax and amax, we arrive at Thisimpliesthatthemassofthesailisapproximately
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10 tons. In deriving this estimate, we have assumed a
vmax 2 amax −1 D −2 rough equipartition of the total mass between the sail
ν =1.5GHz (cid:16) c (cid:17) (cid:18)1gee(cid:19) (cid:18)3×109cm(cid:19) , and the payload, implying that the latter is also ∼ 106
(10) tons. If the payload’s density is akin to that of the
having normalized the acceleration in the anthropic International Space Station, the dimensions must be of
units of 1 gee. Remarkably, the above frequency coin- order 100 meters.
cideswithcharacteristicvalue of1 GHz consideredthus The mass is rather high by human standards; most
far, whichimplies that the beam frequency that is opti- estimatesforlightsailpropulsionaretwoordersofmag-
mal for powering the light sail falls within the range of nitudelower(Crawford1990;Vulpetti et al.2015). This
FRB frequencies. Thus, it seems somewhat reasonable estimate is approximately equal to the early fission-
tohypothesizethatthebeamscanbeusedtopowerlight basedrocketsconsideredintheliterature,whichposited
sails, and the ensuing implications are explored next. a total weight of up to 107 tons (Dyson 1968). Thus, if
thebeamwasindeedusedtopoweraspaceship,thelat-
3. DISCUSSION ter would possibly have to be very large - an “interstel-
Next, we delve into some of the other consequences lar ark” or “world ship” of sorts, although their typical
arising from our prior analysis. masses(∼1011tons)aremuchhigher(Hein et al.2012).
3.1. The angular velocity of the beam 3.3. Implications for the number of advanced
Hitherto, we have not discussed any of the temporal civilizations
aspectsofthebeam. WebeginbynotingthatFRBsare
Equation (2) and the DMs listed in the FRB catalog
detected as pulses with a duration ∆t that is typically
implythatthecharacteristicdistancetoFRBsisoforder
milliseconds. Suppose that the beam sweeps across the
afewcomovingGpc(Petroff et al.2016)andthesurvey
sky with an angular velocity Ω that is related to ∆t volume is of order ∼ 4π(3 Gpc)3 ∼ 100 Gpc3. Since
3
(Benford & Benford 2016) via we know that there are ∼ 1010 habitable Earth-size
ηc planets in our Galaxy (Dressing & Charbonneau 2015;
=θ =Ω∆t. (11) Burke et al. 2015; Winn & Fabrycky 2015), and ∼1020
νD
intheentireHubblevolume(Behroozi & Peeples2015),
Alternatively, we can introduce the time period τ = it is fair to assume that there are NE ∼ 1019 habit-
2π/Ω,whichcanbedeterminedfromtheaboveformula, able Earth-size planets within a volume ∼ 100 Gpc3.
and is given by Of these, suppose that a fraction f of these planets are
broadcasting beams, manifested as FRBs.
7.3days ν D ∆t
τ = . (12) Next, note that the characteristic beam solid angle
η (cid:16)1GHz(cid:17)(cid:18)3×109cm(cid:19)(cid:18)1ms(cid:19) is θ2 = η210−16 steradians, based on the characteristic
parametersfromtheprevioussectionsandEquation(3).
Thus, the beam has a characteristic angular velocity of
10−5 rad/s, viz. a time period around one week. Sincetheskyiscomprisedof4πsteradians,andthereare
f ·NE broadcasting planets, at any given point in time
The derivedsweeptime of the beam direction reflects
∼ (10−16/4π)fη2NE beams are visible. Each beam is
the spin or orbital motion of the beamer footprint rel-
visible for∆t∼1ms,whichimpliesthatapproximately
ative to the receding sail (which cause the direction of
1010fη2 beams should be visible in a day. The latest
the beam to change relative to the observer). Sweep-
estimates suggest that there are ∼ 104 FRBs per day
ingislikelytobeoperationalduringtherelativelyshort
(Scholz et al. 2016). If we posit that not every FRB
acceleration and deceleration stages.
arises from extragalactic civilizations, then we find,
3.2. On the dimensions of the potential light sail
fη2 ≤10−6. (14)
The total beam power required for driving a sail of
total mass ms and maximum acceleration amax can be
easilycomputed,assumingthatthereflectivityisperfect Since we know, by definition, that η ≥ 1, we arrive
(Benford 2013; Guillochon & Loeb 2015). at the conclusion that f ≤ 10−6. If each civilization
broadcasts only a single beam, this allows us to place
P =3×1025ergs−1 ms amax , (13) a bound on the number of technologically sophisticated
(cid:18)2×106tons(cid:19)(cid:18)1gee(cid:19) civilizations. Using this value of f in conjunction with
thefactthatthereare∼1010 habitableEarth-sizeplan-
and the same characteristicvalue of amax from (10) has ets in our Galaxy leads us to the conclusion that there
beenutilized. Notethatmshasbeennormalizedbythat arelessthan104FRB-producingcivilizationsinagalaxy
particularamounttoensurethatequation(13)matches similar to our own. These civilizations must belong to
the other estimates, namely equations (5), (6) and (8). the Kardashev I class (Kardashev 1964) at the mini-
5
mum,5 asseenfromthecharacteristicpowerrequiredin (although the use of a broad range of frequencies might
equation (5). Although this number is undoubtedly on smear these signals).
the higher side, it is consistent with the earlier, more We suggest that initiatives such as Breakthrough
optimistic studies involving the famous Drake equation Listen6 could be first directed towards the repeating
(Drake & Sobel1992);someofthecurrenttheorieshave FRB 121102 (Spitler et al. 2016; Scholz et al. 2016;
also yielded similar values (Forgan2009; Lingam 2016). Chatterjee et al. 2017; Tendulkar et al. 2017). This
We reiterate that the above value is an upper bound. proposition is reasonable since astrophysical explosions
There exist at least three factors which can lower it: tend to produce single bursts, while artificial beacons
can repeat.
• Itispossiblethatthebeamangleisnotdiffraction
limited. Even a fairly modest choice of η ≈3 can 3.5. Looking beyond FRBs
lower the value of fmax by an order of magnitude, In our analysis thus far, we have explicitly worked
as evident from (14).
with parameters that were characteristic of FRBs, such
as Sν ∼ 1 Jy. If all other quantities were held fixed
• Not all FRBs have an artificial origin - only a
in equation (4) except for the power which is lowered
fraction of them could correspond to alien ac-
significantly, Sν would be much smaller.
tivity. As an example, one may need to sin-
If the beam is assumedto power a light sail, equation
gle out only those FRBs that repeat, such as
(13) implies that the light sail’s mass or its maximum
FRB121102(Maoz et al.2015;Spitler et al.2016;
acceleration should be reduced to lower the power. In
Chatterjee et al. 2017; Tendulkar et al. 2017).
turn, this implies that the spacecraft would not be ca-
pable of interstellar travel on short timescales; instead,
• Acivilizationcansetupmorethanonebeamemit-
it would be more likely to operate over interplanetary
ter. Althoughitmayseemunlikely,thiscouldvery
distances. Hence, there may be a large number of in-
well happen if a civilization has progressed to the
terplanetary spacecrafts operating at extragalactic dis-
Kardashev II or III stages.
tances that are too faint to be detected. In contrast,
An interesting corollary also follows: since we have suchspacecrafts(andbeams)within ourGalaxyarepo-
assumed that FRBs are of planetary origin, the rate of tentially detectable (Guillochon & Loeb 2015).
FRBsis thereforesetbythe numberofplanetswithad- Finally, we end our discussion with an interesting
vanced civilizations. This is in contrast to other mod- observation. There are approximately 109 L⋆ galax-
3 4
els of FRBs, such as gamma-ray bursts (Zhang 2014; ies within 100 Gpc , and approximately 10 FRBs per
DeLaunay et al. 2016), whose occurrence rate is deter- day, as discussed in Section 3.3. Thus, each Galaxy
mined by the formation rate of massive stars. has a probability of 10−5 FRBs/day. Hence, an FRB
emanating from our own Galaxy can be detected every
3.4. Detecting FRBs of an artificial origin 105days ≈ 300years (Maoz & Loeb 2017). A Galactic
FRB at a distance of 10-20 kpc would be truly spec-
Thepower‘leakage’fromthelightsailswouldbehigh, tacular since the expected value of Sν would be 1010-
comparable to the beam power, because of broadband 1011 Jy, and are detectable by low-cost radio receivers
emission since the diffraction limit is different for each
(Maoz & Loeb 2017). This striking event could reveal
frequency, unlike the idealized case of monochromatic
everything that can be known about the true origin of
emission studied in Guillochon & Loeb (2015).
FRBs, and thereby settle this FRB origin debate once
It should be possible to distinguish between FRBs of
and for all.
natural and artificial (light sail) originbased on the ex-
pected shape of the pulse, as the beam sweeps by to 4. CONCLUSIONS
power the light sail (Guillochon & Loeb 2015). More
InthisLetter,wehavepositedthatFastRadioBursts
specifically, the sail would casta moving shadow on the
arebeamssetupbyextragalacticcivilizationstopoten-
observed beam, thereby leading to a diffraction pat-
tially power light sails.
tern and multiple peaks in the light curve based on
InSection2,weshowedthattheFRBparameterswere
the sail geometry (Manchester & Loeb 2016). A se-
consistent with the assumption that they are artificial
ries of short symmetric bursts would be observed as
beams. We alsodemonstratedthatthere existeda‘nat-
the beam’s path intersects with the observer’s line of
ural’sizefortheemitterwhichwasapproximatelytwice
sight (Guillochon & Loeb 2015). Hence, looking for
the diameter of the Earth. This value was obtained by
similar signatures in the signal could help determine
adopting two contrasting estimates - the first from en-
whetherFRBsarepoweredbyextragalacticcivilizations
ergyconsiderations,whilstthe secondfollowedfromen-
gineering constraints. Subsequently, we illustrated that
5Recently,extensivestudieshavebeenundertakenwhichplace
stringentconstraintsonthenumberofKardashevIIIcivilizations
(Wrightetal.2014;Zackrissonetal.2015). 6 https://breakthroughinitiatives.org/Initiative/1
6
the frequency needed to power the light sail was con- rate of FRBs, we argued that an FRB might originate
sistent with those observed for FRBs, lending further within the Milky Way once every several centuries.
credence to our hypothesis. Although the possibility that FRBs are produced by
Our analysis gave rise to many interesting conse- extragalactic civilizations is more speculative than an
quences. It was shown that the payload of the light astrophysical origin, quantifying the requirements nec-
sail and the beam’s characteristic period should be ap- essary for an artificial origin serves, at the very least,
proximately 106 tons and 7 days respectively. More- the important purpose of enabling astronomers to rule
over,under certain simplifying assumptions, we derived it out with future data.
an upper bound on the total number of intelligent civi-
lizations in a galaxy (akin to the Milky Way). We also
WethankJamesBenford,JamesGuillochon,Jonathan
suggested that smaller light sails may be widely preva-
Katz,ZacManchester,DaniMaoz,AndrewSiemion,Ja-
lent, which are presently undetectable as their spectral
son Wright and the referees for helpful comments. This
fluxdensitiesaretoolow. Usingtheallskycosmological
workwaspartiallysupportedbyagrantfromtheBreak-
through Prize Foundation for the Starshot Initiative.
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