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ETI an for passed guideposts ably interesting as structure regarded temporal be inverted can this Given burst). a observing ein ont esta n rsn f4 of headings: present Subject one than less to down regions esuya neselrsgaigshm hc a origina was which scheme signaling interstellar an study We A A UGUST T E ERHFRGLCI IIIAIN SN ITRCLSUPERN HISTORICAL USING CIVILIZATIONS GALACTIC FOR SEARCH tl mltajv 12/16/11 v. emulateapj style X ∼ 1. 0 er g,sm ftehsoia uenvemgtallow might supernovae historical the of some ago, years 100 INTRODUCTION ,2021 4, xrtretilitliec —astrobiology intelligence extraterrestrial ∼ ∼ 0mn ol ea interesting an be could min) 10 0yas(e ..Dae1961; Drake e.g. (see years 60 eateto hsc,KooUiest,Koo6680,J 606-8502, Kyoto University, Kyoto Physics, of Department after bevn eeec us,i otatt h rgnlpro original the to contrast in burst, reference a observing π rudtornsi h sky. the in rings two around , rf eso uut4 2021 4, August version Draft need erv- ABSTRACT up- vor N a h m- nt. ng ce o- n- AOKI l. t, t. g - - - S aatcsproa eoddi h at20 years 2000 past the in recorded supernovae Galactic , ETO uu srnmclbrt ihu ro communica- prior without burst, astronomical cuous n ie emil s h ih er(.. o h ntof unit put the also for We (l.y.) pc. l.y.=0.307 year 1 light conversion the the use with length mainly we to time, devoted is and 5 Section 1006. SN error for discussion. estimation and study summary distance case the a burst of make reference effects and the the o as discuss scenario SNe also the We discuss Galactic we historical 4, the Section obse applying In high-priorit after burst. time the reference elapsed evaluate a the of ing the we function a of 3, as viewpoint Section direction search In the from point. scheme Schelling signaling concurrent SN. per the sky coul whole regions the target of 1% the than that less show typically surve be and preferred the present, out at figure directions also We reference. past signaling the a in recorded SNe Galactic six ∼ up pick intent We detecting signals. for ETI guideposts interesting as Galax regarded our gi be in Now, inten- (SNe) receive supernovae burst. historical and reference possibility, transmit the this us observing allows after that signals way tional can a scheme signaling in original refined the be that show We sender-search system. the burst of geometry underlying the reconsidered of 2020) analysis al. recent et. the (Abbott considering observation Galact wave small, of gravitational too rate merger be the might addition, LIS NSBs In detector 2019). wave al. gravitational next et space the (Kyutoku the in of binary launch a the such fore detect to difficult be ol ehgl datgosfrbt edr n receivers scheme and signaling senders both concurrent for This advantageous highly o be irrespective senders. would signals, the the to distances record collectively can latter receiver the and h pe flight. of speed the h pta oiin nteln.I h edr ntespa- the on senders the If line. (e.g., coordinate the line the on tial introduce We positions 1). spatial Fig. straight the arbitrary (see an Galaxy along the signals in duration short of sions nti ae,t aiymk ovrin ewe distance between conversions make easily to paper, this In revisit we 2, Section In follows. as organized is paper This w point, Schelling the of perspective the from paper, this In npicpe h iigajsmn a edn yletting by done be can adjustment timing the principle, In sasml opnn oe,ltu osdrtransmis- consider us let model, component simple a As 00yas n ics hte aho hmi utbefor suitable is them of each whether discuss and years, 2000 hl h etuepro fS 9 a presum- has 393 SN of period use best the While l rpsdb eo(09 n fcetylinks efficiently and (2019) Seto by proposed lly ,teshm a erfie ota intentional that so refined be can scheme the s, 2.1. 2. S OCRETSGAIGSCHEME SIGNALING CONCURRENT 1 rgnlpooa nSt (2019) Seto in proposal original R and 1 st opciyteEIsurvey ETI the compactify to us nw h eieytm eoead the beforehand, time delivery the knows apan S 2 nFg )snhoietersignals their synchronize 1) Fig. in OVAE oa ( posal before ∼ 5yas be- years, 15 can y ional the f x c line ven for rv- er- as ic A s. s, d y y e f . 2
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FIG. 2.— Spatial configuration of the burst site (B), the senders (Si) and ͬ ]Q1 1QJ the Earth E (as a receiver). The green line represents the spatial projection of the null geodesic mentioned in Fig. 1. The closest approach C should FIG. 1.— Space-time diagram for the concurrent signaling scheme. We be the geometrically distinctive option for the datum position xD. The closest consider intentional signals propagating along a straight spatial line, corre- approach distance BC would be the unique length scale existing in the system. sponding to the horizontal axis with the positional coordinate x. The red diagram shows a null geodesic, and the signal from the sender S2 is emit- ted in phase with that from S1. The receiver R1 can concurrently record the ateness of the Galactic NSBs in relation to their merger rate. signals from S1 and S2. This adjustment can be done by commonalizing the datum point D for the senders and receivers. In 2019, Seto estimated that the number of NSBs available for the references would be 1. He used the volume averaged NSB merger rate reported∼ by the LIGO-Virgo collaboration (Abbott et al. 2017). However, if using their most recent rate the signals commonly through a specific position x = xD at a specific time t = t (and appropriately extended in the fu- (Abbott et al. 2020), the number of reference NSBs in our D Galaxy is decreased by a factor of five and could be much less ture direction e.g. for S2 in Fig. 1). Therefore, the question is whether the senders and receivers can converge the datum than unity. Therefore, at this moment, it would be fruitful to examine applicability of astrophysical burst events other than point (tD,xD) without prior communication. Below, we dis- cuss this interesting possibility. NSB mergers. First, we consider a rest frame covering the whole Milky- way Galaxy, ignoring kinematical and gravitational effects. It 2.2. refinement would be reasonable to presume that the datum time tD should Explosions of Galactic SNe are conspicuous events and be fixed by the time slice t = tB containing a conspicuous as- have attracted attentions of human beings at least in the past tronomical event that is well localized both temporally and 2000 years (Stephenson & Green 2002). One might wonder spatially (a burst-like event). whether∼ a future SN (e.g. to be observed around AD3000) Then, the remaining question is how to choose the datum can be currently used as the reference burst, just like a short- position xD on the straight line. Here, for suppressing am- period NSB. Unfortunately, in contrast to an inspiral of an biguities, we want to keep the involved parties as small as NSB, the physical processes up to a SN explosion are much possible (e.g. excluding an additional usage of the Galactic more complicated (in particular the late-time evolution of a center). Actually, we have the geometrically unique point on massive star compared with type Ia SNe). As a result, even the line, given the burst site. That is the closest approach for advanced civilizations, it would not be straightforward to C (with x = xC) as illustrated in Fig. 2. The combination make a high precision prediction for the future explosion time 3 (tD,xD)=(tB,xC) is what was effectively proposed in Seto of a SN (e.g. with accuracy of 1 yr at 10 yr before ob- (2019). However, as understood from Fig. 2, with this choice, serving a SN). ∼ ∼ both the transmission and reception of an intentional signal Therefore, we want to refine the original concurrentscheme must be completed before observing the reference astronomi- so that both the senders and receivers work only after observ- cal burst (unless the burst site, sender and receiver are on the ing a SN. If there exists a simple solution that is also robust in same line in this order). More specifically, for the combina- the context of the Schelling point, it might be already prevail- tion (tB,xC), the intentional signals are synchronized with the ing as a tacit adjustment. The question here can be rephrased astrophysical burst only at infinite distance (see Fig. 2). In as whether we can introduce a common time unit in order to fact, rather than commonalizing the datum point (tB,xC), Seto delay the datum time tD from the original burst epoch tB. (2019) proposed this simple asymptotic condition for the sig- Let us take another look at Fig. 2 for the geometry of the nal adjustment. system composed by a signaling line and the reference burst Partly influenced by the broad impacts of the multi- site. In fact, we can readily identify the geometrically unique messenger event GW170814, Seto (2019) pointed out that time interval owned by the system. That is the closest ap- a merger of an NSB would be ideal for the reference burst proach distance BC divided by the speed of the light c. This (see also Nishino and Seto 2018). In the signaling scheme, to choice has no ambiguity and would be preferable for a tacit cover the whole sky, we can use a Galactic NSB for the time adjustment (Schelling 1960). In addition, the time interval duration 2l/c 105 yr before the arrival of the merger signal l sinθ/c can be well estimated with a high-precision measure- (l: distance to∼ the NSB size of the Galaxy). Gravitational ment of the burst distance l. wave from such a short-period∼ NSB can be easily detected by We thus expect that the closest approach C would be the LISA, and we can estimate the required parameters at high unique datum position xD and the shifted time tB +q l sinθ/c × precision (Kyutoku et al. 2019). But we have to wait 15 yr would be a reasonable expression for the datum time tD. Here before the launch of LISA, in spite of the recent momentum∼ q is the scaling parameter, and the choice q =1 would be the of SETI related activities. primary option, in addition to the original one q = 0. Below, Furthermore, there appeared a concern about the appropri- we call the choice q = 1 by the primary mode and the original 3 one q = 0 by the zero mode. q=0 Actually, the SN signal reaches the closest approach C at 1/8 the time given by q = 1. Therefore, in Fig. 2, the segment 150 CE corresponds to the portion of the signaling line where the 1/4 primary mode can be transmitted after observing the reference burst. We define the corresponding length 1/2
dq=1 = l cosθ (1) ] 1 100 as the effective depth of the potential civilizations for the 2 degree search direction θ π/2. [ Note that, for our≤ signaling scheme, we have the axial sym- metry with respect to the line connecting the SN site and a civilization. Therefore, at any time, the target sky directions 50 would be rings centered at the SN or its antipodal direction.
2.3. comments on earlier studies Here it might be instructive to mention some earlier dis- 0 cussions on the potential use of Galactic SNe for interstellar -2 -1 0 1 2 communication (Tang 1976; McLaughlin 1977; Makovetskii 1980; Lemarchand 1994, see also Hippke 2020), while they E are totally different from the concurrent signaling scheme. FIG. 3.— The target offset angle θ away from the burst direction, as func- tions of the normalized time τE . The results are presented for some scaling The basic idea of these studies is to transmit intentional sig- 2 parameters q 0. We must have τE p1 + q − 1 for the existence of a nals around the observation epoch of a SN explosion. In such solution θ. ≥ ≤ a method, unlike the concurrent scheme, a receiver needs to estimate the arrival times of intentional signals individually for potential senders by using their distances. Therefore, ex- cally, for the time range cept for the case when the senders are at the direction of the + 2 − SN, the signal search would be much more demanding than 0 τE 1 q 1 (6) the concurrent method. Furthermore a sender needs to omni- ≤ ≤ we have the two solutions θ = θ− and θ+ given by directionally transmit their signals in a short period of time p around the observational epoch of the SN. 1 + τE θ± = arctan[q] arccos . (7) 3. SEARCH AND SENDING DIRECTIONS IN THE SKY ± " 1 + q2 #
3.1. search directions 2 In contrast, Eq. (5) has no solutionp for τE > 1 + q − 1. Now, we assume that some Galactic senders apply the re- The critical epoch 1 + q2 − 1 is 0.41 for the primary mode p fined concurrent signaling scheme, employing a specific ref- q = 1. In Figure 3, we plot the relation (5) for various choices erence burst (not limited to a SN in this section). We discuss of q. For the zerop mode (q = 0) studied in Seto (2019), where in the celestial sphere we should search for their inten- we have the search window −2 τE 0 (corresponding to tional signals at a certain moment on the Earth. We put l as ≤ ≤ −2l/c ∆tE 0), covering the whole sky, as mentioned in the distance between the Earth and the burst site (see Fig. 2) ≤ ≤ ∆ the previous section. and define tE as the time difference (on the Earth) from the For the specific angles θ =0 and 180◦, the closest approach arrival epoch of the burst signal. As explained in the previ- distance vanishes, and the observational epoch τE does not ous section, we want to search for an intentional ETI signal at depend on the parameter q in Fig. 3. Meanwhile, for θ = 90◦, ∆tE 0. ≥ ∆ the Earth becomes the closest approach C. Using Fig. 2, we can obtain the expression for tE as a Now, using Fig. 4, we make an intuitive explanation for the function of the offset angle θ time evolution of the target search directions in the celestial l sinθ l cosθ l sphere. In this figure, the angle θ corresponds to the opening ∆tE = tB + q + − tB + (2) angle from the burst direction, and our target directions are × c c c composed by the inner ring with θ = θ− and the outer ring l with θ = θ+. = (cosθ + qsinθ − 1). (3) ◦ c At the arrival time of the burst τE = 0, we have θ− =0 and the inner ring is formed at the direction of the burst with the Here we introduce the normalized time τE by effective depth dq=1 = l cosθ− = l (see Eq. (1)). Meanwhile the ◦ −1 outer ring emerges as the great circle at θ+ = 90 away from l + τE ∆tE . (4) the burst with the effective depth dq=1 = l cosθ = 0. ≡ c − In the time range 0 < τE < √2 1, the inner ring expands Then we have and the outer ring shrinks as shown in Fig. 3. Then, at the time τE = √2 − 1, the two rings merge and the time window τE = cosθ + qsinθ − 1. (5) for the primary mode (q = 1) is closed.
For a given epoch τE (and the parameter q), we can in- 3.2. sending directions versely solve the offset angle θ from the burst. More specifi- 4
G%` R1`VH 1QJ In the second column of Table 1, we show the Galactic co- ordinate for each remnant, as the combination of the Galactic Q% V``1J$^ͮ_ longitude lG and the Galactic latitude bG. The latter will be 1JJV``1J$^ͯ_ important in §4.3 where we discuss the intersections of the inner/outer rings with the Galactic plane. U In the third and fourth columns of Table 1, we presented the estimated distances l to the SN sites and their relative er- rors δl/l (respectively from Yuan et al. 2014; Leike et al. :C:H 1H]C:JV 2020; Winkler et al. 2003; Trimble 1973; Tian & Leahy 2011; Sankrit et al. 2016). These reference values do not always U represent the most conservative estimations. In the fifth column of Table 1, for each SN, we present the normalized time τE = c∆tE /l at present. SN393 has the largest value τE 0.44(> 0.41), reflecting the long elapsed ∼ time ∆tE 1600 yr and the shortest distance l. Indeed, for SN 393, we∼ have presumably lost accessibility to the primary FIG. 4.— The search directions in the celestial sphere for the primary mode mode (even if the actual distance is . 7% larger than the listed (q = 1). We have the two separate (inner and outer) rings centered at the burst value). In contrast, SN1604 has the smallest elapsed time direction with the offset angles θ− and θ+ given by Eq. (7). The inner ring ∆t 400 yr and the largest distance l, and its normalized ∂ θ ∂ θ E expands ( t − > 0) with time and the outer ring shrinks ( t + < 0). They time∼ is only =0.025. τ − θ θ ◦ τE merge at the time E = √2 1 with − = + = 45 . We put the intersections In the sixth column of Table 1, except for SN393, we show between the Galactic plane in the sky and the outer ring by C+A and C+B (see C− C− the two solutions θ+ and θ− given by Eq. (7) for q =1. The §4.3). Similarly, we put A and B for the intersections of the Galactic ◦ plane with the inner ring, but they do not exist in this illustration. summations of the two solutions become 90 , reflecting the symmetry of Eq. (5) for q = 1.
4.2. parameter estimation errors So far, we studied the relation between τE and θ± from the viewpoint of a receiver. In this subsection, we briefly discuss By using the normalized time τE = c∆tE /l and Eq. (7), the directions for the signal transmission from the Earth. In we can determine the offset angles θ± for the inner and the signaling scheme, on a signaling line in Fig. 2, the timing outer rings. However, because of the estimation errors δl is identical for transmission and reception, and our expres- and δ(∆tE ), the angles contain uncertainties δθ±, and the two sions in the previous subsection can be basically used also for rings would have the finite widths 2θ±. If the remnant is senders. Correspondingly, in Fig. 4, the sending directions correctly identified for a reference∼ SN with an elapsed time −4 are just antipodal to the search directions, so that we can syn- ∆tE > 300 yr, we will have δ(∆tE )/∆tE < 10 . Thenwe can chronize our intentional signals with the potential incoming expect δl/l δ(∆tE )/∆tE, and the angular errors are roughly signals. given by δθ±≫ O(δl/l). More precisely, taking the derivative For the primarymode (q =1), at the burst arrivaltime τE =0, of Eq. (5) for∼q = 1, we obtain we should transmit to the antipodal direction of the burst and ◦ 90 away from the burst (overlapping with the outer search τE δl δθ± = − (8) ring only at τE =0). In the time interval 0 τE (√2−1), we cosθ± sinθ± l can cover the half-sphere centered at the≤ antipodal≤ direction | | (an identical result for θ+ and θ−). Therefore, a high-precision of the burst. distance measurement is crucial for compactifying the target At this point, we look back on the integrated structure of the sky direction. refined concurrent signaling scheme. We should notice that, In reality, some of the remnants in Table 1 contain large for the propagation line in Fig. 2, the offset angle θ and the relative errors δl/l. For example, we still have δl/l 0.2 SN distance l depend on the positions of the senders/receivers. for the Crab nebula (Kaplan et al. 2008). In principle,∼ the But, individually following the simple rule (5), we can make imaging parallax of the Crab pulsar could be a solid approach a globally adjusted signaling system. Given the simplicity for its distance estimation, but the performance is limited with and effectiveness, we expect that this could be a promising current radio telescopes of relatively small fields of views (see Schelling point for the interstellar signaling. Kaplan et al. 2008 for details). This is due to the high system 4. HISTORICAL GALACTIC SNE temperature caused by the hot nebula around the pulsar and also by the absence of reference extra-Galactic sources. In 4.1. basic information contrast, SKA is designed to have a large number of small In the past 2000 years, Galactic SNe have been recorded dish telescopes (wider field views) and would provide us with around the world∼ (Stephenson & Green 2002). In Table 1, much better distance estimation to the Crab pulsar. Here we we present the six historical SNe for which real-time obser- should note that the Crab system is highly important also for vations were actually made and the corresponding remnants a broad range of astrophysics. The high-precision estimation are identified relatively reliably. Following theses two crite- of its distance is awaited not only for SETI. ria, we didnot includeSN386andSN1181in viewof debates RX J1713.7-3946 is considered to be the remnant of on their remnants (see also Ritter et al. (2021) for the former SN393. Leike et al. (2020) recently claimed to constrain with the parallax distance 7500l.y.). We also excluded the its distance at (3.65 0.03) 103 l.y. (corresponding to SN resulting in Cassiopeia∼ A. Due to the strong interstellar AD1890-1920 for the± expiration× date of the primary mode extinction, we do not have a secure real-time record for this search). They used the light extinction pattern of Gaia stars SN (see also Ashworth 1980). around the dusty environment associated with the remnant. 5
TABLE 1 BASIC PARAMETERS FOR THE SIX HISTORICAL SUPERNOVAE
supernova Galactic coordinate distance l [l.y.] uncertainty δl/l τE in 2021 θ+ and θ− for q = 1 SN 185 G315.4-2.3 8300 0.10 0.23 75.3◦, 14.7◦ SN 393 G347.4-0.6 3700 0.01 0.44 N/A SN 1006 G327.6+14.6 7100 0.04 0.14 81.1◦, 8.9◦ SN 1054 (Crab) G184.6-5.8 6500 0.18 0.15 80.7◦, 9.3◦ SN 1572 (Tycho) G120.1+1.4 8970 0.09 0.051 87.1◦, 2.9◦ SN 1604 (Kepler) G4.5+6.8 16600 0.14 0.025 88.5◦, 1.5◦
TABLE 2 SEARCHREGIONSFORTHEPRIMARYMODE (q = 1)
supernova δθ± sky fraction (α,δ) for C+A and C+B (α,δ) for C−A and C−B SN 185 1.8◦ 0.04 (07 : 44,−24.0◦),(18 : 47,−2.0◦) (12 : 34,−62.8◦),(16 : 04,−52.5◦ ) SN 1006 0.4◦ 0.008 (19 : 20,13.7◦), (08 : 00,−29.7◦) N/A SN 1054 1.9◦ 0.04 (22 : 23,57.3◦),(08 : 54,−44.8◦) (05 : 39,31.2◦),(06 : 12,18.6◦) SN 1572 0.28◦ 0.005 (18 : 52,0.1◦),(06 : 41,5.1◦) (24 : 49,62.9◦),(24 : 05,62.4◦) SN 1604 0.21◦ 0.004 (21 : 25,50.5◦),(09 : 39,−52.5◦) N/A
The Galactic plane intersects the outer search ring at C+A and C+B and the inner search ring at C−A and C−B. Their sky directions are presented in the equatorial coordinate (α,δ).
90 ° 185 1006 1054 75 ° 1572 1604 60 °
45 ° Galactic Plane
30 °
15 °
12 h 14 h 16 h 18 h 20 h 22 h 2 h 4 h 6 h 8 h 10 h 12 h -15 °
-30 °
-45 °
-60 °
-75 °
-90 °
FIG. 5.— The search directions associated with the five historical SNe in the equatorial coordinate. We have the inner and outer rings for each SN. The directions of the SN remnants are at the centers of the inner (small) rings. The black curve shows the Galactic plane, and its intersections with the rings are listed in Table 2. The Galactoc center is at (17:46, −28.9◦).
Using the ongoing and forthcoming astrometric projects, we (Binney & Merrifield 1998). Therefore, we might correct the might continue similar approach for SN remnants. effects related motions, from the viewpoint of an implicit ad- So far, we had not taken into account the motions of in- justment. volved parties. But, they cause effects such as aberration of 4 light. For an interstellar transmission of distance & 10 l.y., 4.3. case study for SN1006 the Galactic rotation would be the dominant contribution of O(100kms−1), and the aberration effect could be 10−3 rad (a To provide a concrete picture of the proposed method, we few arcmin). In future, when the distance errors are reduced make a case study for SN1006 (Winkler et al. 2003). Its down to δl/l 10−3, we need to consider the aberration effect estimated distance is l = 7100l.y. with an error δl/l 0.04 ∼ that is relatively small in Table 1. At present, the normaliz∼ ed . But the Galactic rotation can be modeled well, and the su- ◦ time is τE = c(2021 − 1006)/l =0.14, and we have θ− =8.9 perimposed peculiar motion can be also estimated statistically ◦ and θ+ = 81.1 for the inner and outer rings of the primary 6 mode. The effective depths in Eq. (1) are respectively given systems suitable for reference bursts. by 7000l.y. and 1100l.y.. From Eq. (8), the widths of the In this paper, we reconsider the underlying geometry of the ◦ ringsare estimated to be 2δθ± 0.78 . The sky area currently system and identify the unique time unit corresponding to the covered by the two rings is given∼ by closest approach distance between the reference burst and the signal line. We can slide the datum time tD (in Fig. 1) with δΩ =4πδθ+(sinθ+ + cosθ+) 0.098sr, (9) ∼ a parameter q. Its primary option would be q = 1 from the and its fraction to the entire sky is about δΩ/(4π) 0.8%. viewpoint of the Schelling point. Under this scenario, we The accessibility to the primary mode will be lost∼ around can search (or transmit) intentional signals after observing a AD4000 with 1006 + 0.41 7100 4000. reference burst. More specifically, we can determine the tar- × ∼ get directions by using the distance to the reference l and the On the two rings in the sky, the regions around the Galac- ∆ tic plane would be particularly important, given the enhanced elapsed time tE after observing the burst. stellar density (see also Seto 2019). The Galactic latitude Now, the historical records of Galactic SNe in the past ◦ 2000 years can be regarded as invaluable assets for SETI with∼ of SN1006 is bG = 14.6 , representing its angular separation ∆ from the Galactic plane (see Fig. 4). Since we currently have the accurate knowledge on the elapsed times tE . We found that for SN393, the accessibility to the primary mode (q = 1) θ− < bG <θ+, only the outer ring intersects the Galactic plane (as illustrated in Fig. 4). In the Galactic coordinate, the two was likely to be lost about 100 years ago, but we still have ◦ ◦ multiple SNe applicable for the primary mode search. intersections C+A and C+B are given by (lG,bG) = (48.4 ,0 ) and (246.8◦,0◦), corresponding to (α,δ)=(19:20,13.7◦) and Given the estimated Galactic SN rate ( 1 per 100 years; − ◦ Tammann et al. 1994), a SN might be∼ suitable for an (08 : 00, 29.7 ) in the equatorial coordinate. In Fig. 5, we 4 show the inner and outer rings with the red curves in the intermediate-distance transmission (e.g. l . 10 l.y.) in our equatorial coordinate. Since the preferred sending directions Galaxy. Otherwise we have too many references at any mo- are antipodal to the search directions, it would be efficient to ment, and cannot compactify the target sky directions. Con- − ◦ sidering the time duration l/c to cover a large fraction of transmit signals to the sky around (α,δ)=(07:20, 13.7 ) ∼ and (20 :00,29.7◦). the sky, the selection of a reference burst might depend also We can make similar studies for other SNe listed in Table on the self-estimated lifetime of the transmitting civilization. Here we should notice that astronomical events other than 1. For SN185, SN1054 and SN1572,we have bG <θ− <θ+ and the Galactic plane intersects also with the| inner| search SNe might be also used for the signaling reference, particu- ∆ ring (see also Fig. 5). In Table 2, we present the errors δθ± larly if the two parameters l and tE can be estimated accu- of the rings, the total sky fraction of the two rings and the rately (e.g. those associated with orbital motions around Sgr equatorial coordinates for the intersections (including those A*). Furthermore, we might not need to exclude the possibil- with the inner search rings for reference). The errors δθ± are ity of using a negative q for predictable bursts such as BNS mergers. small for SN1572 and SN1604, due to the relation δθ± τE (see Eq. (8)). ∝ In this paper, we have concentrated on the geometrical as- pects of the system. This is partly because of the less ambigu- 5. SUMMARY AND DISCUSSION ous nature of the consideration and the resultant compatibility with the Schelling point argument. But it might be fruitful to A tacit adjustment on intentional signaling can significantly discuss possibilities of other tacit adjustments from different reduce the required costs both for the senders and searchers viewpoints. and could be actually prevailingin our Galaxy. In this context, Seto (2019) pointed out the possibility of the concurrent sig- naling scheme that is controlled by astronomical bursts such The author would like to thank the anonymous reviewer for as BNS mergers. But, in the original scheme, we need to his/her comments and suggestions. This work is supported complete operations basically before observing the reference by JSPS Kakenhi Grant-in-Aid for Scientific Research (Nos. bursts themselves. This would severely limit astrophysical 15K65075, 17H06358).
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