Astrometric study of Gaia DR2 stars for interstellar communication
aa r X i v : . [ a s t r o - ph . I M ] M a r ✐ ✐ “ija3” — 2020/3/10 — 0:45 — page 1 — ✐✐✐ ✐ ✐✐ Journal name cambridge.org/
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Key words: extraterrestrial intelligence; astrobiology© Cambridge University Press and theEuropean Microwave Association 2019
Astrometric study of Gaia DR2 stars forinterstellar communication
Naoki Seto , Kazumi Kashiyama , Department of Physics, Kyoto University, Kyoto 606-8502, Japan, Research Center for the Early Uni-verse, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan, Departmentof Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
Abstract
We discuss the prospects of high precision pointing of our transmitter to habitable planetsaround Galactic main sequence stars. For an efficient signal delivery, the future sky positions ofthe host stars should be appropriately extrapolated with accuracy better than the beam openingangle Θ of the transmitter. Using the latest data release (DR2) of Gaia, we estimate the accu-racy of the extrapolations individually for . × FGK stars, and find that the total numberof targets could be ∼ for the accuracy goal better than 1”. Considering the pairwise natureof communication, our study would be instructive also for SETI (Search for ExtraterrestrialIntelligence), not only for sending signals outward. ✐ “ija3” — 2020/3/10 — 0:45 — page 2 — ✐✐✐ ✐ ✐✐ Introduction
Even ∼ years have passed since the pioneering work by Drake,we have not succeeded to detect a convincing signature of extrater-restrial intelligence (ETI) (e.g., Drake 1961; Horowitz, & Sagan1993; Tarter 2001; Siemion et al. 2013). On one hand, this mightbe simply reflecting the possibility that the number of Galacticcivilizations is small, or even zero on our past light-cone. Onthe other hand, our observational facilities and available computa-tional resources might not be sufficient to deal with existing weaksignals in a huge parameter space (Tarter et al. 2010; Wright et al.2018). In any case, SETI programs are actively ongoing, includingrecently launched Breakthrough Listen in which ∼ Galacticstars and ∼ nearby galaxies will be analyzed (Gajjar et al.2019).In parallel with the searching efforts, artificial signals havebeen intentionally transmitted from the Earth to extraterrestrialsystems (e.g., Zaitsev 2016, see also Baum et al. 2011; Vakoch2016). For example, Polaris has been repeatedly selected as atarget. In 2008, a 70 m-dish antenna of NASA’s Deep Sky Net-work was used for a radio transmission in the X-band (wavelength λ ∼ cm). More recently, in 2016, an ESA’s antenna (dish size L = 35 m) was directed to Polaris for sending messages encodedin λ ∼ cm radio waves. Here we should comment that the1-10 GHz band (wavelength 3-30 cm) is regarded as an ideal win-dow for interstellar communication, given the background noises(Cocconi & Morrison 1959). The half opening angle of the trans-mitted beam is given by Θ ∼ λ/ (2 L ) , and we have O (100") forthe two concrete cases mentioned above.Considering the potential limitations of observational facili-ties and computational resources inversely at ETI side, it wouldbe more advantageous to increase the energy flux of our out-going signals. Here one of the solid options is to reduce thebeam opening angle Θ (e.g., Benford et al. 2010, see also Hippke2019). For example, using a phased array with an effective diam-eter comparable to the core station of SKA2, we can realize Θ ∼ . λ/ L/ − . Note that, for a given beamopening angle Θ , the size of the transmitter L could be reducedby using a shorter wavelength λ . Clark & Cahoy (2018) studiedintentional signal transmissions in the optical/IR bands for whichtypical seeing level on the surface of the earth is O (1”) . Eventhough the Sun becomes a much stronger background than in theradio band, they discussed that a facility similar to the AirborneLaser ( L = 1 . m, λ = 1315 nm, Θ ∼ . ) could be workable,depending on the size of the receiver’s telescope. Meanwhile,the lightsail propulsion has been studied as an attractive tech-nology for future interplanetary and interstellar missions. Undercertain restrictions, Guillochon & Loeb (2015) showed an opti-mal combination L = 1 . km and λ = 0 . cm for interplanetarytransportations, corresponding to Θ ∼ . . With a potential lightbeamer ( L ∼ km, λ ∼ µ m) for the Breakthrough Starshot, thediffraction would be O (0 . . a However, a target star is moving on the sky with proper motion µ , and there is an offset angle between its observed position andthe appropriate transmission direction. Given the round-trip time d/c ( d : the target distance) of photon, the offset is estimatedto be d/c × µ = 2( v t /c ) = 40”( v t /
30 km s − ) with the trans-verse velocity v t (Arnold 2013; Zaitsev 2016). Therefore, if a https://breakthroughinitiatives.org/forum/28?page=4 we use a beam Θ . ” and want to shoot a star moving atthe typical transverse velocity v t ∼
30 km s − (De Simone etal. 2004), we generally need to carefully extrapolate the futureposition of the star, by measuring its related parameters. For exam-ple, we require the precision ∆ v t ∼ .
75 km s − (Θ / for thetransverse velocity.An astrometric mission is an ideal instrument for this mea-surement. It provides us with five astrometric parameters: the skyposition ( α, δ ) , parallax ̟ and proper motion ( µ α , µ δ ) . All ofthem are indispensable for our extrapolation.In 2016, the astrometric mission Gaia released its first data(DR1). Since then, Gaia has brought significant impacts on var-ious fields of astronomy. Its unprecedented precision is expectedto also change the shooting problem drastically.In this paper, using Gaia’s latest data release (DR2, Brown etal. 2018), we estimate the number of main-sequence FGK starssuitable for the high precision shooting. These stars would havetheir habitable zones at ∼ AU. If we observe the systems at thedistances of d , the angular separation between the stars and theirhabitable planets are smaller than . d/
10 pc) − . Therefore,we can quite certainly hit the habitable planets once its host star iswithin our beam of Θ & . d/
10 pc) − . Note that ∼ % ofthe Galactic Sun-like stars could have Earth-size planets in theirhabitable zones (Petigura et al. 2013), but Gaia is unlikely to detectthese small planets by astrometric drift (Perryman et al. 2014).We expect that our study would be useful also for SETI, notonly for sending signals outward. This is because, it would beadvantageous for receivers to inversely assess the potential cri-teria and strategies of senders at selecting their targets (see e.g.,Schelling 1960; Wright 2018; Seto 2019). Astrometric observation and extrapolation
Here we briefly explain the basic astrometric parameters relevantto our study. On the celestial sphere around a target star, we locallyintroduce an orthogonal angular coordinate ( x , x ) (see Fig. 1).The parallax ̟ is the annual positional modulation on the planeand is determined by the distance d to the star as ̟ = 1 . (cid:18) d (cid:19) − mas . (1)The proper motion ( µ , µ ) corresponds to the long-term signa-ture of the time derivatives µ i = dx i /dt (i = 1 , ) and is relatedto the transverse velocity components as v t , i = µ i × d = 4 . (cid:18) µ i − (cid:19) (cid:18) d (cid:19) km sec − . (2)We put v t ≡ ( v + v ) / for the magnitude of the transversevelocity.Next we discuss the sky position of the target star for our trans-mission. We introduce a simple Galactic-scale time coordinate t .Also for simplicity, we assume that the astrometric measurementand the shooting are done at the same time t = 0 on the Earth. Butit is straightforward to incorporate the time interval (realistically ≪ d/c ) between the two operations.By an astrometric observation, we can basically obtain infor-mation of the target at t = − d/c (see Fig. 1). In contrast, our ✐ “ija3” — 2020/3/10 — 0:45 — page 3 — ✐✐✐ ✐ ✐✐ (cid:1) (cid:1) (cid:1) (cid:2) (cid:1) (cid:1) (cid:2) (cid:2) (cid:3) (cid:3) (cid:1) (cid:1) (cid:4) (cid:1) (cid:1) (cid:5) (cid:2) (cid:3) (cid:3) (cid:6) Fig. 1.
Prediction of the sky position of a target star in an orthogonal angular coordinate in the celestial sphere. We obtain astrometric information (sky position,parallax and proper motion) of the target at t = − d/c ( d : the parallax distance to the target). We then extrapolate the sky position of the target at the hitting epoch t = d/c . The directional errors are shown with gray regions. Because of the inaccuracies of the distance and the proper motion, the error size at t = d/c would bemuch larger than the original size at t = − d/c . We define ∆ as the angular size of the long axis of the error ellipsoid. To hit the target star at a single shot, we requirethat ∆ is smaller than the beam width Θ of the transmitter indicated by the radius of the dashed blue circle. signal strikes the target around t = d/c . Therefore, the followingextrapolation is required for the shooting x ie = x im + 2 d m µ im c (3) = x im + f µ im ̟ m (4)(see Fig. 1). Here we use the subscript “m” for the astrometricallyremeasured values (e.g., x im ≡ x i ( t = − d/c ) ) and ”e” for theextrapolated values for the target (e.g., x ie ≡ x i ( t = d/c ) ). If weuse the unit [mas yr − ] for µ im and [mas] for ( x ie , x im ) , we havethe numerical value f = (2 kpc / .As shown in Eq. (2), the transverse velocity is given by theproduct d m µ im = v t , im and is the primary quantity for adjust-ing the shooting direction. More specifically, as mentioned earlierand shown in Eq. (3), the offset angle for the shooting is givenby v t , im /c ) . But, in standard astrometric observations, weseparately estimate d m ∝ /̟ m and µ im .From Eq. (4), the error for the extrapolated position x ie is givenby δx ie = δx im + f δµ im ̟ m − f µ im δ̟ m ̟ . (5)The first term represents the directional error of the target at t = − d/c . The second and third terms are those associated with theextrapolation and caused by the errors for the proper motion andthe parallax respectively.The total number of Gaia DR2 sources is 1,692,919,135(Brown et al. 2018). Among them, the five astrometric parame-ters ( ̟, α, δ, µ α ∗ , µ δ ) are provided for 1,331,090,727 sources,accompanied by the estimation of the associated × errormatrix. Using these data, we can evaluate the × matrix A for the directional error δx ie A ≡ (cid:18) h δx δx i h δx δx ih δx δx i h δx δx i (cid:19) . (6)This matrix determines the error ellipse of the extrapolated posi-tion ( x , x ) in the sky, and we define ∆ as the angular size ofits long axis (given in terms of the larger eigenvalue of A ). If weuse an transmitter with a beam opening angle Θ , we should have ∆ < Θ for hitting the target at a single shot (see Fig. 1).Our discussions on the uncertainty ∆ have been somewhatabstract. Here we make an order-of-magnitude estimation for ∆ .For an astrometric observation like Gaia, we have approximaterelations for the estimation errors of the related parameters (e.g. σ ̟ ≡ h δ̟δ̟ i / ) as σ ̟ ∼ σ xi ∼ σ µ i (7)in the units mentioned after Eq. (4) (Brown et al. 2018). Therefore,in Eq. (5), the first term is ∼ ( d/ times smaller than thesecond one, and is negligible for our targets at d = O (1 kpc) dis-cussed in the next section. The ratio between the second and thirdterms in Eq. (5) is given by ( v t / . − ) with the transversevelocity v t . For its typical value v t ∼
30 km s − , Eq. (5) is dom-inated by the third term due to the parallax (distance) error, andwe have ∆ ∼ (cid:16) v t
30 km s − (cid:17) (cid:16) σ ̟ ̟ (cid:17) (8) ∼ (cid:16) v t
30 km s − (cid:17) (cid:18) d (cid:19) (cid:16) σ ̟ . (cid:17) . (9)In Eq. (9), we used the characteristic value σ ̟ ∼ . of GaiaDR2 for a star at G-magnitude G = 17 (Brown et al. 2018). Inthis manner, we can roughly estimate the angular uncertainty ∆ = O (1”) for Gaia DR2 sources at distances d = O (1) kpc. ✐ “ija3” — 2020/3/10 — 0:45 — page 4 — ✐✐✐ ✐ ✐✐ Table 1.
Numbers of our filtered sample and shooting targets filtered sampletargets ∆ < ”targets ∆ < ”targets ∆ < . ”F 2960592 2320725 888155 8065G 14224687 9183380 2603038 21441K 30251412 20315244 4819918 80339total 47436691 31819349 8311111 109945So far, we simply fixed the target distance at the observedvalue d = d m without considering its time variation. We can, inprinciple, measure the line-of-sight velocity v l of the target. But,the line-of-sight velocity v l introduces an effective change of thetransverse velocity only by O ( v l /c ) and is totally negligible, com-pared with the required accuracy level ∼ .
75 km s − (Θ / .Meanwhile the acceleration of the solar system is estimated to be O (10 mm sec − yr − ) and is dominated by the Galactic centrifu-gal acceleration (see e.g., Titov, & Lambert 2013). If we regardthis as the typical secular value for Galactic field stars, the effec-tive velocity shift becomes .
07 km sec − ( d/ and is notimportant for the accuracy goal O (1”) . In addition, the Galacticpotential could be modeled relatively well. Below certain accuracylevel, it would be required to deal with additional time-dependingfluctuations of the photon rays such as the relativistic correc-tions and non-vacuum effects (e.g., scintillation). We leave relatedstudies as our future works. Target stars in Gaia DR2
In this section, we examine the actual data set provided inGaia DR2 and estimate the numbers of stars suitable for ourhigh-precision shooting.
FGK-type stars
Gaia DR2 contains 76,956,778 sources whose effective temper-ature T eff and radii R are presented, in addition to the fiveastrometric parameters and their × noise covariance matrix. b From these sources, we further selected FGK stars potentiallyhosting habitable planets, by applying the following three filters;(i) effective temperature in the three ranges below, F-type: T eff ∈ (6000 K, 7500 K], G-type: T eff ∈ (5200 K, 6000 K] andK-type : T eff ∈ [3700 K, 5200 K],(ii) stellar radius: R ≤ . R ⊙ for F-type stars and R ≤ . R ⊙ for GK-type stars,(iii) “Priam flag” value either of the following ones: 0100001,0100002, 0110001, 0110002, 0120001 and 0120002.The filter (ii) is for removing evolved stars, and (iii) is forexcluding low quality data (Andrae et al. 2018).After the selection, we obtained . × stars, as shown inthe first column in Table 1. In the following, we call these stars“filtered sample”. They are anisotropically distributed in the skywith the averaged density ∼ − [arcsec − ] . In Fig. 2 (cyancurve), we present the G-magnitude distribution of our filteredsample. We have a sharp cut-off at G = 17 that is mainly deter-mined by the availability of the effective temperature T eff (Brown b According to Gaia DR2 site, the uncertainties are underestimated by 7-10% for faintsources with
G > outside the Galactic plane, and by up to ∼
30 per cent for brightstars with
G < .
10 12 14 16 18 2001 ´ ´ ´ ´ G - magnitude c u m u l a ti v e nu m b e r D< ² D< ² filtered sample Fig. 2.
Cumulative G-magnitude distributions of the filtered sample (cyan curve)and of the shooting targets with ∆ < ” (black curve) and < ” (orange curve). ´ ´ ´ ´ distance @ kpc D c u m u l a ti v e nu m b e r D< ² D< ² filtered sample Fig. 3.
Cumulative distance distributions of the filtered sample (cyan curve) andof the shooting targets with ∆ < ” (black curve) and < ” (orange curve). Themedian distances are . kpc and 0.92 kpc for the orange and black curves. et al. 2018). In Fig. 3 (cyan curve), we show the cumulative dis-tance distribution for the filtered sample. The median distance is1.1 kpc and 95% of the sample are within 2.1 kpc.Note that, for Gaia DR2, all stars are astrometrically analyzedas single stars, and some of the filtered sample would be unfa-vorably affected by the other members of multiple systems. Formultiple systems, more elaborate analysis is planned in the nextGaia data release, and we do not discuss the associated effects. selecting target stars Using the prescription based on the × covariance matrix (6)and the actual data provided in Gaia DR2, we evaluate the angularuncertainty ∆ for each of our filtered sample. In Fig. 4 we showthe cumulative distribution of ∆ . As expected from our order-of-magnitude estimation, the characteristic size is O (1”) . The bestvalue is ∆ = 0 . ” for a K-star at the distance of 6.7 pc with G = 7 . . Given the incompleteness of the Gaia DR2 data at G < ✐ “ija3” — 2020/3/10 — 0:45 — page 5 — ✐✐✐ ✐ ✐✐ Δ [ as ] c u m u l a ti v e nu m b e r Fig. 4.
Cumulative distributions of the uncertainty ∆ expected for our filteredsample. The two vertical dashed lines are at ∆ = 0 . ” and 1”. , we should take the lower end of ∆ just for a reference as ofnow.Now we select our shooting targets by introducing the threefiducial criterion values; ∆ = 0 . ”, 1.0” and 5.0”, taking intoaccount the specific numerical values quoted in introduction (for0.1” and 1.0”). The resulting numbers of the targets are summa-rized in Table 1. We have ∆ < ” for 67% of the filtered sample,but the fractions decrease to 18% ( ∆ < ”) and 0.2% ( ∆ < . ”)for more stringent requirements.In Figs. 2 and 3, we show the distributions of G-magnitudesand distances for our targets with ∆ < ” and 5”. The mediandistances for the two criterion values are 0.57 kpc and 0.92 kpc,respectively.To particularly examine stars hosting confirmed planets, wealso utilize the cross match between Gaia DR2 and the NASAExoplanet Archive. After applying the filters (i)-(iii) to totally1678 cross-matched stars, we obtain 1259 FGK stars as a subsetof our filtered sample. We then evaluate their angular uncertainties ∆ and obtain 26 targets with ∆ < . ”, 782 with < ” and 1220with < ”. If we limit our analysis only to host stars of confirmedhabitable planets, the subset size is reduced to 60 and we obtain 1target with ∆ < . ”, 48 with < ” and 58 with < ”. Relative tothe . × stars in our original sample, these two subsets havesmaller uncertainties ∆ . positions of the targets Here we discuss positions of our shooting targets in the Galaxy.As a representative example, we specifically pick up the sub-set of the filtered sample whose 1- σ error regions of T eff and R are simultaneously within T eff ∈ [5790 K , and R ∈ [0 . , . R ⊙ , close to the solar values. This subset contains5928 solar-type stars, and we have 2738 targets for ∆ < ” and4847 for < ”. Note that the overall data qualities of this subsetare better than our original filtered sample, because of the rela-tively strong requirements on T eff and R . Accordingly, the targetfractions of this subset are higher than those in Table 1.For graphical demonstration, we introduce a Cartesian coor-dinate ( x, y, z ) , using the distance d and the Galactic angular - - - - @ kpc D y @ kpc D - - - - @ kpc D z @ kpc D Fig. 5.
Upper panel : Spatial distribution of 5928 solar-type stars with T eff ∼ K and R ∼ R ⊙ . All stars are projected to the Galactic ( xy )plane. The orange dots represent 2738 target stars with ∆ < ” and the blackones show the additional 2109 target stars with 1” < ∆ < ”. The cyan dots arethose with ∆ > ”. The Galactic center is toward the direction of + x -axis. Theradius of the black circle is 2 kpc. Lower panel : Similarly projected to the xz -plane. The Galactic plane corresponds to the x -axis around which thenumber of stars are small due to the strong dust extinction. coordinate ( l, b ) as ( x, y, z ) = d (cos b cos l, cos b sin l, sin b ) . (10)The Galactic center is at the direction of + x -axis, and the Galacticplane corresponds to the xy -plane. In the upper panel of Fig. 5, weshow the projection of the subset sample onto the xy -plane. Mostof the orange dots (targets with ∆ < ”) have projected distancesless than . kpc, but the black dots (with 1” < ∆ < ”) are dis-tributed over ∼ . kpc. We expect that the observed anisotropy ofthe stars is mainly due to the Galactic extinction pattern and par-tially to the sampling pattern of Gaia. If we make a more detailedanalysis, we can identify a sparseness of the solar-type stars inthe range d . pc. Given the absolute G-magnitude of the ✐ “ija3” — 2020/3/10 — 0:45 — page 6 — ✐✐✐ ✐ ✐✐ Sun M G = 4 . , this is likely to be caused by the incompletesampling of Gaia for bright stars at G < .In the lower panel of Fig. 5, we show the projections of the starsonto the xz -plane. We can see a clear deficit of stars around the x -axis to which the Galactic plane is projected. This reflects thestrong extinction towards Galactic plane. In future, some of theunaccessible volume might be explored by the proposed infraredmissions such as JASMINE (Gouda 2012) and GaiaNIR (Hobbset al. 2016). Interestingly, along the x -axis, the boundary of theorange points is not distinctively covered by the black points,unlike the z -axis direction. This indicates that the boundary ismainly determined by the limitation of the temperature estimation,not by the threshold value ∆ = 1 ”.When the Sun is observed inversely by ETI on a planet arounda solar-type star plotted in Fig. 4, they will record almost the sameluminosity, interstellar extinction and transverse velocity as werecorded for the star in Gaia DR2. Therefore, if the ETI haveastrometric mission equivalent to Gaia, they can realize a simi-lar shooting accuracy ∆ as we can expect for the star. Here weignored details such as the source density and orientation of theirecliptic plane, and also assumed that the extinction pattern doesnot change drastically below the arcmin scale. In this manner, Fig.4 would be intriguing also from the view point of searching forintentional ETI signatures from solar-type stars, not just shootingthem from the Earth. Discussions
In this paper, we discussed the prospects of high precision point-ing of our transmitters to Galactic habitable planets. For a beamopening angle Θ , we practically want to estimate the future skyposition of the host stars with accuracy better than ∆ < Θ . Thisroughly corresponds to measuring the transverse velocities v t ofthe stars with a precision δv t < .
75 km sec − (Θ / muchsmaller than the typical value v t ∼
30 km sec − .In the present work, we regarded Gaia as an optimal instru-ment for our pointing problem. Fully using the astrometric dataprovided in Gaia DR2, we evaluated the size of the angularuncertainties ∆ individually for our filtered sample composed by . × FGK stars. As summarized in Table 1, we have theaccuracy ∆ < ” for 67% of the filtered sample. The fractiondecreases to 18% for ∆ < ”.Until just a few years ago, Hipparcos catalog was the bestavailable astrometric data. It includes ∼ × stars whosedistances were estimated within ∼ % errors. As shown inEq. (8), this corresponds to the extrapolation error of at least ∼ v t /
30 km sec − ) . With Gaia DR2, our target number is O (10 ) for the accuracy goal 1.0” (see Table 1), and three ordersof magnitude larger than Hipparcos era.Gaia DR2 is based on the data collected in the first 22 months ofobservation. Gaia is smoothly operating now, and the mission life-time could be extended to ∼ , limited by micro-propulsionsystem fuel. c With 10 years data, ignoring instrumental degra-dation, the signal-to-noise ratio of the sources would increase bya factor of 2.3, and the accuracies of the astrometric parame-ters would be improved by at least the same factor. The actualimprovement is expected to be better than this simple scaling,considering the advantages of the long-term observation both on c measuring the proper motion and on reducing the noise correlationbetween the parallax and other parameters. If we conservativelyuse the improvement factor 2.3 for ∆ in Fig. 4, the numbers ofour shooting targets would be 2 and 7 times larger for ∆ < ”and < . ” respectively, compared with Table 1. In addition, aswe commented earlier, information related to multiple stars wouldbe refined.In this paper, we studied interstellar communications mainlyfrom the standpoint of a sender. But a sender and a receiverare inextricably linked together, as demonstrated in Fig. 5. Inthis sense, our results would be suggestive also for SETI relatedactivities. Here, considering the rapid improvements even of ourtechnology in the past few decades, it would be more productiveto gain insights without making strong assumptions on the ETI’stechnology level. Acknowledgement.
This work has made use of data from the EuropeanSpace Agency (ESA) mission Gaia, processed by the
Gaia
Data Process-ing and Analysis Consortium (DPAC). Funding for the DPAC has beenprovided by national institutions, in particular the institutions participatingin the
Gaia
Multilateral Agreement. This research was supported by theMunich Institute for Astro- and Particle Physics (MIAPP) which is fundedby the Deutsche Forschungsgemeinschaft (DFG, German Research Founda-tion) under Germany’s Excellence Strategy EXC-2094-390783311. We alsoused the gaia-kepler.fun crossmatch database created by Megan Bedell forthe NASA Exoplanet Archive. NS thanks H. Sugiura for his help on pythoncodes. This work was supported by JSPS Kakenhi Grants-in Aid for ScientificResearch (Nos. 17K14248,17H06358,18H04573,19K03870).
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