Possibility of a coordinated signaling scheme in the Galaxy and SETI experiments
aa r X i v : . [ a s t r o - ph . I M ] A p r D RAFT VERSION A PRIL
2, 2019
Preprint typeset using L A TEX style emulateapj v. 10/10/03
POSSIBILITY OF A COORDINATED SIGNALING SCHEME IN THE GALAXY AND SETI EXPERIMENTS N AOKI S ETO
Department of Physics, Kyoto University, Kyoto 606-8502, Japan
Draft version April 2, 2019
ABSTRACTWe discuss a Galaxy-wide coordinated signaling scheme with which a SETI observer needs to examine a tinyfraction of the sky. The target sky direction is determined as a function of time, based on high-precision mea-surements of a progenitor of a conspicuous astronomical event such as a coalescence of a double neutron starbinary. In various respects, such a coordinated scheme would be advantageous for both transmitters and re-ceivers, and might be widely prevailing as a tacit adjustment. For this scheme, the planned space gravitational-wave detector LISA and its follow-on missions have a potential to narrow down the target sky area by a factorof 10 - , and could have a large impact on future SETI experiments. Subject headings: extraterrestrial intelligence —astrobiology —gravitational waves INTRODUCTION
Since the pioneering work by Drake (1961), significant ef-forts have been made for SETI experiments, but no definitesignal has been detected so far (see e.g., Tarter et al. 2001;Siemion et al. 2013; Harp et al. 2016). This might be partlydue to the fact that we have explored an extremely small frac-tion in the multi-dimensional phase space for SETI experi-ments, under the restrictions of available observational facil-ities and computational resources (Tarter et al. 2010; Wrightet al. 2018). For example, Tarter et al. (2010) figurativelyclaimed that we have examined only a glass of water ran-domly sampled from Earth’s oceans to find a fish (see alsoWright et al. 2018).In this paper, we discuss a search for intentionally emit-ted beamed signal from extra-terrestrial intelligence (ETI)in our Galaxy. There are on the order of 10 stars in ourGalaxy and many of them are expected to have planets. Whilenearby stars are distributed almost isotropically, distant ones( & See also https://breakthroughinitiatives.org/initiative/1. computational resources. Given the reciprocal advantages, acoordinated signaling scheme might be actually prevailing, asa tacit adjustment between involved parties, namely as theSchelling point in the game theory (Schelling 1960; Wright2018).In this paper, we first discuss how to configure a coordi-nated signaling scheme, without prior communications, bututilizing a conspicuous Galactic event (§2). Then, in §3,we point out that coalescence of a double neutron star bi-nary (DNSB) would be an attractive candidate for the ref-erence Galactic event. This is partly because the progenitorof the merger event (namely a DNSB) would be suitable fora high-precision measurement with space gravitational wavedetectors and radio telescopes, well before the occurrenceepoch of the event. After the multi-messenger observationof GW170817 (Abbott et al. 2017), the estimated merger rateof Galactic DNSBs is also within a preferable range. Withthe space gravitational wave detector LISA, the survey skyarea might be narrowed down by a factor of 10 , potentiallyincreasing the prospects for SETI relative to the searches forsignatures of primitive life (Lingam & Loeb 2019). Discoveryof radio pulsars in a short period DNSB ( .
600 sec) would bealso beneficial for the sky area restriction, and might be real-ized in an earlier time than LISA. COORDINATED COMMUNICATION SCHEME
In this section, we discuss a simple coordinated communi-cation scheme. In this scheme, we use a conspicuous Galacticastronomical event whose time of the occurrence and the spa-tial position can be accurately estimated ahead of time, byappropriate observation of its progenitor. sending cone
Let us consider a sender S and the progenitor of the ref-erence event E at a Galactic distance l (see Fig.1). For sim-plicity, we temporarily ignore the motions of both the senderand the progenitor. Also ignoring fluctuations of the metric,we introduce a rest frame covering the Galactic scale. Similarto Nishino & Seto (2018), we define the time t S , E when thesender S observes the event E with a messenger propagatingat the speed of light (e.g., electromagnetic wave or gravita-tional wave). We also introduce the relative time ∆ t S ≡ t − t S , E for describing the scheduled actions of the sender.During the time interval − l / c ≤ ∆ t S ≤
0, the sender S cantake the opening angle θ for transmitting its artificial photonsignal, as the solution to the equation below ∆ t S = − lc (1 + cos θ ) . (1)In the following, we call the time-dependent sending directionas “sending cone” (see Fig.1). It can be regarded as a ring onthe celestial sphere. Note that the sending duration 2 l / c iscomparable to the light-crossing time of the Galaxy, namelythe time required for a Galactic-scale signal transfer.With the choice (1) for the sending cone, an artificial signalfrom S (on the black solid line in Fig.1) will arrive the pur-ple dashed-circle in Fig.1 at the occurrence time of the eventE. With this condition, a receiver R ∞ at the infinity distancecatches the S’s artificial signal simultaneously with the eventE. More specifically, for any sender, the synchronization atinfinity can be realized, if and only if its signal is transmittedtowards the sending cone determined by eq.(1).Note that the sending cone moves from θ = 0 (at ∆ t S = − l / c ) to θ = π (at ∆ t S = 0), sweeping the whole 4 π -sky areaat the constant rate. Namely, we have ( d cos θ/ d ∆ t S ) = const .In this sense, the present scheme does not have a preferredsending direction. The center of the sending cone is di-rected to E for − l / c ≤ ∆ t S < − l / c , but antipodal to E for − l / c ≤ ∆ t S ≤ ∞ at an extra-Galactic distance(e.g., 40Mpc to NGC4993) much larger than the Galacticscale l = O (10) kpc, aiming a signal delivery almost syn-chronously with the event E. In this paper, we continue toapply the scheme (1), for a largely different situation, namelyintra-Galactic communication with the distance between thesender (S) and receiver (R G ) comparable to the Galactic dis-tance l (see Fig.1). In this case, the receiver R G observes theartificial signal from S earlier than the event E, with the arrivaltime difference of O ( l / c ). In fact, the present communicationscheme no longer aims a synchronous signal delivery, and,correspondingly, a sender does not need to care about the dis-tance to a potential receiver (the separation SR G in Fig.1). receiving cone Next we discuss the coordinated signaling scheme from theperspective of a receiver. For illustrative purpose, we tenta-tively suppose that the sender S in Fig.1 also attempts to re-ceive an artificial photon signal emitted by an unknown civi-lization S that follows the Galaxy-wide scheme (1). Below,for a while, we denote the receiver by S(R) to express itsdual nature (sender/receiver). As we mentioned in the pre-vious subsection, the sending cone of the unknown sender S sweeps the whole 4 π -sky, including the S → S(R) direction.The question here is which sky direction the receiver S(R)should search an artificial signal as a function of time. In re-ality, this is a simple problem, considering the possible prop-agation direction of the incoming signal (the green arrow inFig.1). At any time, the propagation direction must be in thesending cone of the receiver S(R). Otherwise the signal is notsynchronized as infinity, and this contradicts with the signal-ing scheme originally at the unknown sender S . Therefore,the receiver S(R) can limit the survey towards the antipodaldirection of its sending cone, reduced from the whole 4 π -skyarea. More specifically, with respect to the reference event E, This argument is valid for the angle ∠ ESR ∞ < ◦ . But we can easilyconfirm that eq.(1) holds also for ∠ ESR ∞ > ◦ . If the duration of the civilization is longer than 2 l / c . (cid:1)(cid:2) q (cid:1) (cid:3) (cid:1) (cid:3) ∞ F IG . 1.— Our signal transmission scheme using a Galactic reference eventE. By observing the progenitor of the reference event E, the sender S esti-mates the occurrence epoch of E and its position (including the distance l ).The sender S transmits its artificial signal to its (red colored) “sending cone”with the time-dependent opening angle θ given by eq.(1). The artificial sig-nal reaches the purple dashed-circle at the occurrence epoch of the event E.Then, the receiver R ∞ at infinity catches the artificial signal simultaneouslywith the event signal. But a Galactic receiver R G observes the event E later.The green arrow is used in §2.2 where S is assumed to be also a receiver andtemporarily denoted by S(R). the opening angle θ ′ of the receiving direction (hereafter “re-ceiving cone”) is given by θ ′ = π − θ with the solution θ foreq.(1). Of course, the sky direction θ ′ is not changed, even ifthe receiver S(R) merely searches for other Galactic civiliza-tions, without sending its own signal. Therefore, we hereafterdenote a receiver simply by R.In Fig.2, we show the geometrical relations between thesending and receiving cones. We should notice that, with thepresent scheme, a receiver can handle a specific sky directionat a time, irrespective of the distance to a sender. The inverseis true for a sender, as mentioned at the end of the previoussubsection. Considering the simplicities and merits both forthe senders and receivers, this signaling scheme (or similarones) might be actually prevailing as a tacit adjustment in thestrategy space (Schelling 1960; Wright 2018). practical effects In reality, the sending/receiving cones have a finite width δθ around the opening angle θ due to the parameter estimationerrors for the progenitor of the event E. If the sky position ofthe event E can be specified sufficiently well (as expected fortypical electromagnetic wave observations), the error width isroughly given as δθ ∼ max (cid:20) δ ll , δ ( ∆ t S )( ∆ t S ) (cid:21) (2)with the distance error δ l and the timing error δ ( ∆ t S ).Those involved in the communication (e.g., S i and R inFig.2) also need to appropriately correct own peculiar mo-tions, including the mean Galactic rotation and random com-ponents. Given its measurability, this would not be a seriousconcern. Meanwhile, a small peculiar velocity would be pre-ferred for the progenitor of E.Below, when considering a signal transmission from an-other civilizational to the Earth, we assume that the formerhas more advanced technology and the associated error width δθ is dominated by our estimation errors given by eq.(2). (cid:1) (cid:1) (cid:1) (cid:2) (cid:1) (cid:3) (cid:2) (cid:3) F IG . 2.— The sending and receiving cones for the coordinated signalingscheme. The sender S transmits its artificial photon signal to its time-varyingsending cone (red colored). Then, at the position of the receiver R, this photonmust be on the sending cone of R, for consistently satisfying the synchronouscondition at infinity. In general, once a sender transmits a photon to its send-ing cone, it will be subsequently on the corresponding sending cone at anyfuture space-time point (e.g., S → R and S → S → R). A receiver R onlyneeds to search for its time-varying receiving cone (shown with green color)antipodal to its sending cone.
Galactic plane
We now discuss the impact of the Galaxy-wide coordinatedsignaling scheme for our Galactic SETI experiments. Forcomparison, we also study the case for an uncoordinated sig-naling. We assume that, except for the time dependence ofthe sending direction, there is no difference between the twocases. For example, the Galactic structure (e.g., its plane)would be similarly respected for choosing the weight of thesending directions. Then, at any incident, the expected num-bers of transmitters whose beams are pointing to us would besimilar for the two cases (see Fig. 3). Here we should recallthat the senders do not know the positions of receivers includ-ing the Earth. Conveniently, in the coordinated case, we onlyneed to search the receiving cone with the width δθ , by au-tomatically excluding almost all the sky directions from thebeginning. Practically, in view of the Galactic structure, wewill be able to further limit our survey to the intersections be-tween the region around the Galactic plane and the receivingcone. Since the information of the Galactic structure is com-mon to the two cases, the SETI phase space would be com-pressed by a factor of δθ for the coordinated case, relative tothe uncoordinated one. REFERENCE GALACTIC EVENT
Next we discuss the basic properties that are required forthe reference Galactic event, and propose a DNSB mergeras an attractive candidate. This choice might be somewhataffected by the research background of the author and otherpossibilities would be worth exploring. In this section, we set l = 10kpc as the fiducial value. desired properties In order to less ambiguously and continually select a lim-ited number of the Galactic reference events, its Galactic rate r E should be larger than the inverse of the sending/receivingduration 2 l / c ∼ × yr. But the rate should not be over-whelmingly larger, since the compression factor δθ for thesky area would be degraded by the total number of equiva- (cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:8)(cid:9)(cid:10)(cid:11)(cid:6)(cid:2)(cid:12)(cid:13)(cid:10)(cid:4)(cid:14)(cid:11)(cid:15)(cid:6)(cid:2)(cid:16)(cid:11)(cid:6)(cid:15)(cid:1)(cid:17)(cid:3)(cid:4)(cid:7)(cid:8)(cid:8)(cid:9)(cid:10)(cid:11)(cid:6)(cid:2)(cid:12)(cid:13)(cid:10)(cid:4)(cid:14)(cid:11)(cid:15)(cid:6)(cid:2)(cid:16)(cid:11)(cid:6)(cid:15) (cid:1)(cid:2)(cid:3)(cid:2)(cid:4)(cid:5)(cid:6)(cid:4)(cid:7)(cid:8)(cid:3)(cid:2)(cid:9)(cid:10)(cid:11)(cid:10)(cid:4)(cid:10)(cid:6)(cid:12)(cid:6)(cid:9)(cid:13)(cid:7)(cid:4)(cid:14)(cid:9)(cid:10) (cid:15)(cid:10)(cid:9)(cid:16)(cid:6)(cid:9)(cid:13)(cid:7)(cid:4)(cid:14)(cid:9)(cid:10) F IG . 3.— The differences between (a) the uncoordinated (random) sig-naling scheme and (b) the coordinated scheme, in the Galactic coordinate.The filled small red circles show the transmitters directed to us at a certainmoment. Their numbers would be similar in the two cases. But, with thecoordinated signaling scheme, we can limit the survey direction on the re-ceiving cone (the green ring) whose center is occupied by the reference event(the blue triangle for − l / c ≤ ∆ t S < − l / c ). The ring has a finite width δθ due to our parameter estimation errors for the reference event. Our sendingcone (the red ring) is antipodal to the receiving cone. lent references 2 r E l / c . Namely, the preferable rate would beroughly given by r E ∼ (1 - × c / l ∼ . × − (4 - yr − . (3)Meanwhile, for a Galaxy-wide reference, the progenitor ofthe event should be easily identified as early as ∼ l / c beforethe event, at the distance of l . Additionally, its position (es-pecially the distance l ) and the occurrence epoch t S , E shouldbe estimated at high precision, to reduce the width δθ of thecones. double neutron star merger Below, from the viewpoint of mankind (as the only-knownexample of a Galactic civilization), we argue that a DNSBmerger would be suitable for the reference Galactic event.After the historical multi-messenger observation ofGW170817, the comoving merger rate of DNSBs is estimatedto be 1540 + − Gpc − yr − (Abbott et al. 2017). Using the typi-cal value 10 − Mpc − for the number density of the Milky-wayequivalent galaxies, we obtain the median value of the Galac-tic DNSB merger rate r DNSB ∼ . × − yr − . Therefore, therate r DNSB is within the preferable range (3).At 2 l / c ∼ × yr before the merger, a DNSB has orbitalperiod of ∼
600 sec. A recycled pulsar in such a short-periodorbit would be an interesting target for radio telescopes suchas SKA (Dewdney et al. 2009). But, due to a significantDoppler smearing, it would not be straightforward to find arecycled pulsar by taking a Fourier transformation of the ra-dio data (see e.g., Lorimer & Kramer 2004). The smearingeffect would not be severe for the younger (normal) pulsar ina DNSB, and subsequent identification of the recycled onewould allow us to make a desired high-precision measure-ment. However, the younger one is expected have a smallerbeaming fraction (Levin et al. 2013) and would typically havea shorter lifetime before crossing the death line. Fortunately, the DNSB emits strong a gravitational wavesignal at ∼ ∼ l ∼ ∼
500 (Taka-hashi & Seto 2002). The subsequent follow-up radio observa-tion for a recycled pulsar would be much easier than a blindsearch (Kyutoku et al. 2019). If succeeded, the radio data pro-vide us with the sky position, the residual eccentricity and theorbital inclination much better than LISA data alone. Thenthe distance l (and correspondingly the cone width δθ ) wouldbe estimated at δθ ∼ δ l / l ∼ SNR − ∼ × − with a negli-gible contribution of the timing error in eq.(2). For a DNSBat l . δθ ∼ δ l / l ∼ − , depending on the integration time.Finally, we should mention that the burst-like gravitationaland electromagnetic waves around the merger are not directlyrelevant for the present transmission scheme. This is differentfrom the extra-Galactic transmission for which the actual syn-chronization would be crucial (Nishino & Seto 2018). But, ifwe have the luck to discover a Galactic DNSB that will mergeshortly (e.g. in ∼
100 yr), it might be interesting to considerthe possibility of synchronous signal delivery. DISCUSSION
In this paper, we discussed a coordinated signaling schemein our Galaxy. This scheme would be advantageous bothfor senders and receivers, in various respects. However, not merely the possibility of their intentional signaling, buteven the existence of other Galactic ETIs is totally unclearat present. Based on our social-scientific standpoint, it mightseem reasonable that the adopted signaling scheme would de-pend on the age of the civilization and their knowledge onother Galactic civilizations obtained from their past SETI-likeactivities. But, given the large uncertainties, further detailedpresumptions about the likely forms of the signaling schemewould be far beyond the scope of this paper.If all the signaling Galactic civilizations follow the presentcoordinated scheme (as an extreme case), we need the timeinterval 2 l / c ∼ × yr to complete a single scan of theGalaxy. This is comparable to the light-crossing time in ourGalaxy, namely the typical time for Galactic communication.Unfortunately, it is much longer than our individual lifetime.In this relation, if we have totally N T signaling ETIs in ourGalaxy, the expected number n S of the scanned ones wouldbe n S ∼ N T (cid:18) lc (cid:19) − ∆ T ∼ (cid:18) N T (cid:19) (cid:18) l / c × yr (cid:19) − (cid:18) ∆ T (cid:19) (4)within the observational times ∆ T . The total number N T isquite uncertain and could be much smaller than 2000. There-fore, in reality, a practical approach would be a mixed strat-egy, assigning some faction of survey time to the specific di-rections associated with the receiving cone, in addition to thetraditional random pointing. If we succeed to detect a civiliza-tion in our receiving cone within the time span ∆ T , the totalnumber of the Galactic civilizations following the signalingscheme is roughly estimated to be ∼ l / ( c ∆ T ).This work is supported by JSPS Kakenhi Grant-in-Aid forScientific Research (Nos. 15K65075, 17H06358).).This work is supported by JSPS Kakenhi Grant-in-Aid forScientific Research (Nos. 15K65075, 17H06358).