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SETI among galaxies by virtue of black holes
Acta Astronautica 78 (2012) 109–120
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SETI among galaxies by virtue of black holes$ Claudio Maccone a,b,n a b
International Academy of Astronautics (IAA), Italy SETI Permanent Committee of the IAA, Italy
a r t i c l e i n f o
abstract
Article history: Received 31 January 2011 Received in revised form 30 July 2011 Accepted 24 October 2011 Available online 3 December 2011
In two recent papers (Refs. Maccone (2011, 2009) [1,2]) this author proved that the radio communications among any pair of stars within our Galaxy are feasible with modest transmitted powers if the gravitational lenses of both stars are exploited. In the present paper we extend those innovative results to the case of radio communications among nearby galaxies. We show that the radio communications among galaxies may become feasible if the supermassive black holes, usually located at the center of galaxies, are exploited as gravitational lenses. In other words, a massive black hole may be regarded as a huge focusing device for radio waves being transmitted out of that galaxy and/or being received from another galaxy. This happens because a black hole is such a highly massive and compact object that all electromagnetic waves flying by its surface are highly deflected by its gravitational field and made to focus at a comparatively short distance from the black hole itself. Next we consider the possibility of building radio bridges between our own Galaxy (the Milky Way) and other nearby galaxies. This possibility is serious because, since 1974, astronomers have come to known that a supermassive black hole called Sagittarius An does exist at the center of our Galaxy. In 2002 its mass was estimated to be of the order of 2.6 million solar masses, and in 2008 this estimate was increased to 4.31 million solar masses. Furthermore, in 2004 a team of astronomers reported the discovery of a potential intermediate-class black hole called GCIRS 13E orbiting around SgrAn at about three lightyears and having an estimated mass of 1,300 solar masses. These two big black holes could be our Galaxy’s ‘‘antennae’’ for communications with alien civilizations harboring in other nearby galaxies. We mathematically show that the following radio bridges may be created between SgrAn and the supermassive black hole located at the center of the nearby galaxies:
Keywords: Gravitational lens Bit error rate Interstellar radio links Intergalactic radio links Black holes
(1) The SgrAn-Andromeda’s (M31) P2 Black Hole radio bridge, having the distance of 2.5 million light years. The P2 Andromeda black hole is estimated to have a mass of about 40 million solar masses. (2) The SgrAn-M32 (a dwarf elliptical galaxy satellite of Andromeda-M31) radio bridge, with a 2.65 million light year distance. The M32 black hole is estimated to have a mass of about 3 million solar masses. (3) The SgrAn-M106 (also called NGC 4258, a spiral galaxy with anomalous arms) radio bridge, at about 24 million light years. The M106 black hole is estimated to have a mass of about 40 million solar masses.
$ n
Second IAA Symposium on Searching for Life Signatures Held at Chicheley Hall, Buckinghamshire, UK, 6–7 October 2010. Correspondence to: Via Martorelli 43, 10155 Torino, TO, Italy. Tel.: þ 39 0112055387. E-mail addresses: [email protected], [email protected] URL: http://www.maccone.com/
0094-5765/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2011.10.011
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C. Maccone / Acta Astronautica 78 (2012) 109–120
(4) The SgrAn-Sombrero Galaxy (also called M104 or NGC 4594, an unbarred spiral galaxy) at a distance of 29.3 million light years. Its black hole is estimated to have a mass of 1 billion solar masses. (5) The SgrAn-M87 radio bridge. M87 is the supergiant elliptical galaxy located at the center of the super-cluster of galaxies to which we belong, i.e. the Local Super Cluster, at the edge of which we are located. The distance between M87 and us is 53.5 million light years in the direction of the constellation of Virgo, which is why M87 and its surrounding clusters of galaxies are sometimes referred to as the Virgo Super Cluster. At the center of M87 is a supermassive black hole estimated to have a mass of 6.4 billion solar masses. M87 is also well known as ‘‘the jet galaxy’’ since a jet of energetic plasma originates at the core and extends out at least 5000 lightyears. The conclusion that we draw from the mathematics describing these radio bridges across huge inter-galactic distances is surprising: they all perform better that the simple Sun–Alpha Cen A radio bridge, first studied in detail by this author in Ref. [1]. In other words, the powers necessary to keep the radio link between SgrAn and all of the above big black holes located in other nearby galaxies are smaller than the powers requested to keep the radio bridge between the Sun and Alpha Cen A. In other words still, despite inter-galactic distances are huge with respect to ordinary interstellar distances within the Milky Way, the black hole masses in the game are so much huger than the stellar masses than the intergalactic bridges perform better than the interstellar bridges. This unexpected and new result might have profound consequences on SETI done currently by Humans on Earth. In fact, more advanced civilizations might already have built such intergalactic radio-bridges. Thus our SETI searches should be tuned-up to match with this new situation, and the conclusion is that the possibility of SETI signals reaching us from other galaxies should not be ruled out. & 2011 Elsevier Ltd. All rights reserved.
1. An introduction to radio communications in space (LINK)
is an antenna gain:
In two recent papers (Refs. [1,2]), this author proved that the radio communications among any pair of stars within our Galaxy are feasible with modest transmitted powers if the gravitational lenses of both stars are exploited. In this introductory section we review the mathematical theory set up in Refs. [1,2] and get ready to apply it to intergalactic distances rather than just to interstellar distances. Consider a radio transmitter that radiates a Power Pt isotropically and uniformly over a bandwidth Bt. Then, at a distance r it produces a flux density given by Pt : Bt 4pr 2
ð1Þ
A receiving antenna of effective aperture Aer at a distance r can collect a power given by (1) multiplied by both the effective aperture of the receiving antenna and its bandwidth, namely the received power Pr is given by Pr ¼
Pt Aer Br : Bt 4pr 2
ð2Þ
It is assumed that the receiving bandwidth Br. is smaller or, at best (in the ‘‘matched bandwidths’’ case) equal to the transmitting bandwidth Bt, that is Br rBt . So far, we have been talking about an isotropic radiator. But let us now assume that the transmitting antenna has a directivity D (see, for instance, the Wikipedia site http://en. wikipedia.org/wiki/Directivity or Chapter 1 of Ref. [3]) that
D¼
4pAet
:
l2
ð3Þ
The received power Pr is then increased by just such a factor due to the directivity of the transmitting antenna, and so (2) must now be replaced by a new equation where the right-hand side is multiplied by such an increased factor, that is Pr ¼
4pAet
Pt
l2 Bt 4pr 2
Aer Br :
ð4Þ
Rearranging a little, this becomes Pr ¼
P t Aet Aer Br : 2 r 2 l Bt
ð5Þ
This is the received signal power expression. For the matched bandwidths case, i.e. for Br ¼ Bt , this is called the Friis transmission formula, since it was first published back in 1946 by the American radio engineer Harald T. Friis (1893–1976) of the Bell Labs. In space missions, we of course know exactly both Bt and Br and so we may construct our spacecraft so that the two bands match exactly, i.e. Br ¼ Bt . Thus, for the case of telecommunications with a spacecraft (but not necessarily for the SETI case) we may well assume the matched bandwidths and have (5) reducing to Pr ¼
P t Aet Aer 2
r2 l
:
ð6Þ
Let us now rewrite (6) in such a way that we may take into account the gains (i.e. directionalities) of both the transmitting and receiving antennae, that is, in agreement
C. Maccone / Acta Astronautica 78 (2012) 109–120
with (3) 8 < Gt ¼ 4pA2 et l
: Gr ¼
that is
4pAer
l2
8 < Aet ¼
Gt l 4p
: Aer ¼
Gr l2 4p
2
:
ð7Þ
Replacing the last two expressions into (6), we find that (6) is turned into Pr ¼
P t Gt Gr ð4pÞ2 r 2
l2 :
This may finally be rewritten in the more traditional form Pr ¼
P t Gt Gr : Lðr, lÞ
ð8Þ
if one defines Lðr, lÞ ¼ ð4pÞ2
r2
l
: 2
which is the Path Loss (or path attenuation), i.e. the reduction in power density (attenuation) of the electromagnetic waves as they propagate through space. Path loss is a major component in the analysis and design of the link budget of a telecommunication system, see for instance the Wikipedia site http://www.en.wikipedia.org/ wiki/Path_loss. Next we define the Bit Error Rate (BER). Then, by virtue of a numerical example, we show that, even at the distance of the nearest star (Alpha Cen at 4.37 AU) the telecommunications would be impossible by the ordinary powers available today for interplanetary space flight. But in the next section we shall show that the telecommunications would become feasible if we could take advantage of the magnification provided by the Sun’s gravity lens, i.e. if we would send out to 550 AU a FOCAL relay spacecraft (see, for instance, Ref. [3]) for each target star system that we wish to communicate with. This was the key new result presented in Ref. [1]. So, let us start by defining the Bit Error Rate or BER. In telecommunication theory an error ratio is the ratio of the number of bits, elements, characters, or blocks incorrectly received to the total number of bits, elements, characters, or blocks sent during a specified time interval. Among these error ratios, the most commonly encountered ratio is the bit error ratio (BER) – also called bit error rate – that is the number of erroneous bits received divided by the total number of bits transmitted. At the bit error rate Wikipedia site: http://www.en.wikipedia.org/wiki/Bit_error_rate it is shown that the likelihood of a bit misinterpretation pe ¼ pð091Þp1 þpð90Þp0 :
could be the antenna of a precursor interstellar space probe that was sent out to some light years away. (2) n ¼frequency of the electromagnetic waves used in the telecommunication link. The higher this frequency, the better it is, since the photons are then more energetic (E¼hn). In today’s practice, however, the highest n for spacecraft links (like the link of the Cassini probe, now at Saturn) are the ones in the Ka band, that is: nKa 32 GHz. (3) Pt is the power in watts transmitted by the Earth antenna, typically a NASA Deep Space Network antenna 70 m in diameter. (4) The complementary error function ercf(x) is defined by the integral Z 1 2 2 erf cðxÞ ¼ pffiffiffiffi et dt, ð12Þ
p
ð9Þ
ð10Þ
(believing that we have received a 0 while it was a 1 or the other way round) is basically given by the ‘‘complementary error function’’ or erfc(x) as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 1 Eb ðd, n,Pt Þ BERðd, n,Pt Þ ¼ erf c : ð11Þ 2 N0 In this equation one has: (1) d ¼distance between the transmitting station on Earth and the receiving antenna in space. For instance, this
111
x
(for more maths, see the relevant Wikipedia site: http://www.en.wikipedia.org/wiki/ Complementary_error_function). (5) Eb(d, n, Pt) is the received energy per bit, that is the ratio Eb ðd, n,P t Þ ¼
Pr ðd, n,Pt Þ : Bit_rate
ð13Þ
(6) Finally, N0 is given by the Boltzmann’s constant k multiplied by the noise temperature of space far away from the Sun and from any other star. This ‘‘empty space noise temperature’’ might be assumed to equal, say, 100 K. This is the analytical structure of the MathCad code that this author wrote to yield the BER. Let us now consider the input values that he used in practice: (1) Suppose that a human space probe has reached the Alpha Cen system at 4.37 light year distance from the Sun: then, d¼4.37 light years. (2) Suppose also that the transmitting antenna from the Earth is a typical NASA Deep Space Network (DSN) antenna having a diameter of 70 m (like those at Goldstone, Madrid and Canberra), and assume that its efficiency is about 50%. (3) Suppose that the receiving antenna aboard the spacecraft is 12 m in diameter (it might be an inflatable space antenna, as we supposed in Ref. [3] for the FOCAL spacecraft) and assume a 50% efficiency. (4) Suppose that the link frequency is the Ka band (i.e. 32 GHz), as for the Cassini highest frequency. (5) Suppose that the bit rate is 32 kbps ¼32,000 bit/s. This is the bit rate of ESA’s Rosetta interplanetary spacecraft now on its way to a comet. (6) And finally (this is the most important input assumption) suppose that the transmitting power Pt is moderate: just 40 W. Then: (1) The gain of the transmitting NASA DSN antenna (at this Ka frequency) is about 84 dB.
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C. Maccone / Acta Astronautica 78 (2012) 109–120
(2) The gain of the spacecraft antenna is about 69 dB. (3) The path loss at the distance of Alpha Cen is 395 dB (a very high indeed path loss with respect to today’s interplanetary missions, of course). (4) The power received by the spacecraft at that distance is 2.90 10 23 W. (5) The received energy per bit (lowered by the noise temperature of the space in between the Sun and Alpha Cen) is 1.3 10 37 J. (6) And finally the BER is 0.49, i.e. there is a 50% probability of ERRORS in the telecommunications between the Earth and the probe at Alpha Cen if we use such a small transmitting power! In other words, if these are the telecommunication links between the Earth and our probe at Alpha Cen, then this precursor interstellar mission is worthless. The key point in this example is that, for all calculations, (8) and (9) were used WITHOUT TAKING THE GAIN OF THE SUN GRAVITY LENS INTO ACCOUNT, because this was a DIRECT link and NOT a FOCAL mission. 2. Bit error rate at the Alpha Centauri distance enhanced by the magnification provided by the Sun’s gravity lens (FOCAL space mission to 550 AU and beyond) The disappointing BER results of the previous section are totally reversed, however, if we suppose that a FOCAl
space mission has been previously sent out to 550 AU in the direction opposite to Alpha Cen. These topics were fully described by the author in his recent book [3], so we will not repeat them here. We now have the MAGNIFICATION provided by the Sun’s Gravity Lens playing in the game. Mathematically, this means that we must introduce a third multiplicative gain at the numerator of (8): the Sun’s Gravity Lens GAIN, given by (8) of Ref. [1], that is GSun ¼ 4p2
r Schwarzschild_of _Sun
l
,
ð14Þ
where the Schwarzschild radius of the Sun is given by r Schwarzschild_of _Sun ¼
2GMSun : c2
ð15Þ
This new gain is huge at the Ka band frequency: GSun ðnKa Þ ¼ 12,444,837 70 dB,
ð16Þ
and so the received power (8) at Alpha Cen, with the usual Earth-transmitted power of just 40 W becomes P r ¼ 2:9 1023 W,
ð17Þ
and the relevant BER becomes absolutely acceptable: BER ¼ 0:000000526387845:
ð18Þ
This should convince anybody that the FOCAL space mission is indispensable to keep the link at interstellar distances equal or higher than Alpha Cen Figs. 1–3.
BER with and without the Sun Magnification at Alpha Cen for Pt = 40 watt 0.4 BER_with_Sun(d, νKa, Pt)
0.3
BER_without_Sun(d, νKa, Pt)
0.2 0.1 0
0
0.02
0.04
0.06 0.08 d DISTANCE of interstellar probe from the Sun (light years)
0.1
Fig. 1. The Bit Error Rate (BER) (upper, blue curve) tends immediately to the 50% value (BER¼ 0.5) even at moderate distances from the Sun (0–0.1 light years) for a 40 W transmission from a DSN antenna that is a DIRECT transmission, i.e. without using the Sun’s Magnifying Lens. On the contrary (lower red curve) the BER keeps staying at zero value (perfect communications!) if the FOCAL space mission is made, so as the Sun’s magnifying action is made to work. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
BER with and without the Sun Magnification at Alpha Cen for Pt = 40 watt 0.4 BER_with_Sun(d, νKa, Pt)
0.3
BER_without_Sun(d, νKa, Pt)
0.2 0.1 0
0
2
4
6 8 d DISTANCE of interstellar probe from the Sun (light years)
10
Fig. 2. Same as in Fig. 1, but for probe distances up to 10 light years. We see that at about 9 light years away the BER curve starts being no exactly flat any more, and starts increasing slowly.
C. Maccone / Acta Astronautica 78 (2012) 109–120
113
BER with and without the Sun Magnification at Alpha Cen for Pt = 40 watt 0.4 BER_with_Sun(d, νKa, Pt)
0.3
BER_without_Sun(d, νKa, Pt)
0.2 0.1 0
0
20
40
60 80 100 d DISTANCE of interstellar probe from the Sun (light years)
Fig. 3. Same as in Fig. 2, but for probe distances up to 100 light years. We see that, from 9 light years onward, the Sun-BER increases, reaching the dangerous level of 40% (Sun–BER ¼0.4) at about 100 light years. Namely, at 100 light years even the Sun’s Lens cannot cope with this very low transmitted power of 40 W.
3. ‘‘Radio bridge’’ between the Sun and Alpha Cen A by using the two gravitational lenses of both just matched to each other In this section we provide one more new result: we define the radio bridge between the Sun and Alpha Cen A by using BOTH gravitational lenses! In other words, suppose that in the future we will be able to send a probe to Alpha Cen A and suppose that we succeed in placing this probe just on the other side of Alpha Cen A with respect to the Sun and at the minimal focal distance typical of Alpha Cen A. This distance is NOT 550 AU obviously because both the radius and the mass of Alpha Cen A are different (actually slightly higher) than the values of the Sun: ( r Alpha_Cen_A ¼ 1:227r Sun : ð19Þ M Alpha_Cen_A ¼ 1:100MSun Replacing these values into the minimal focal distance (see Eq. (1) of Ref. [1]) (obviously rewritten for Alpha Cen A), the relevant minimal focal distance is found df ocal_Alpha_Cen_A
c2 r 2Alpha_Cen_A 4GM Alpha_Cen_A
749 AU:
ð20Þ
The Schwarzschild radius for Alpha Cen A is given by 2GM Alpha_Cen_A r Schwarzschild_Alpha_Cen_A ¼ ¼ 3:248 km: c2
ð21Þ
And so the gain, provided by (14), turns out to equal r Schwarzschild_Alpha_Cen_A GAlpha_Cen_A ðnKa Þ ¼ 4p2
lKa
¼ 13,689,321:
ð22Þ
Having found the Alpha Cen A gain (23) we are now able to write the new equation corresponding to (8) for the Sun–Alpha Cen bridge. In fact, we must now put at the numerator of (8) three gains: (1) the Sun gain at 32 GHz, (2) the Alpha Cen A gain at 32 GHz, and (3) the 12-meter FOCAL antenna gain at 32 GHz raised to the square because there are two such 12-m antennas: one at 550 AU from the Sun and one at 749 AU from Alpha Cen A, and they must be perfectly aligned with the axis passing thru both the Sun and Alpha Cen A. Thus, the received power given by (8) now reads Pr ¼
Pt GSun GAlpha_Cen_A ðG12_meter_antenna_at_Ka Þ2 : Lðr, lÞ
ð24Þ
where obviously r equals 4.37 light years and l corresponds to a 32 GHz frequency. Let us now go back to the BER and replace (8) with (24) in the long chain of calculations described in Section 1. Since the received power Pr has now changed, clearly both (13) and (11) yield different numerical results. But now: (1) The link frequency has been fixed at 32 GHz (Ka band), and so no longer is an independent variable in the game. (2) Also the distance d has been fixed (it is the distance of Alpha Cen A) and so is no longer an independent variable in the game. (3) It follows that, in (13) and (11), the only variable to be free to vary is now the transmitted power, Pt.
That is GAlpha_Cen_A ðnKa Þ 71 dB:
ð23Þ
Incidentally, we chose Alpha Cen A, and not B or C, because it has the highest mass, and so the highest gain, in the whole Alpha Cen triple system. The future telecommunications between the Sun and the Alpha Cen system are thus optimized by selecting Alpha Cen A as the star on the other side of which to place a FOCAL spacecraft at the minimal distance of 750 AU. That FOCAL spacecraft would then easily relay its data anywhere within the Alpha Cen system.
Let us re-phrase the last sentence in different terms. Practically, we are now studying the BER as a function of the transmitted power Pt only and, physically, this means that: a. We start by inputting very low transmission powers in watts, and find out that the BER is an awful 50%, i.e. the telecommunication between the Sun and Alpha Cen is totally disrupted. This is of course because the energy per bit is so much lower than the empty space noise temperature.
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C. Maccone / Acta Astronautica 78 (2012) 109–120
0.4 BER_bridge_Alpha_Cen(Ptr)
0.3 0.2 0.1 0 1×10–10 1×10–9
1×10–8
1×10–7 1×10–6 Ptr·watt
1×10–5
1×10–4
1×10–3
Fig. 4. Bit Error Rate (BER) for the double-gravitational-lens system giving the radio bridge between the Sun and Alpha Cen A. In other words, there are two gravitational lenses in the game here: the Sun one and the Alpha Cen A one, and two 12-meter FOCAL spacecrafts are supposed to have been put along the two-star axis on opposite sides at or beyond the minimal focal distances of 550 AU and 749 AU, respectively. This radio bridge has an OVERALL GAIN SO HIGH that a miserable 10 4 W transmitting power is sufficient to let the BER get down to zero, i.e. to have perfect telecommunications! Notice also that the scale of the horizontal axis is logarithmic. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
b. We then increase the transmitted power, at a certain point the BER starts getting smaller than 50%. And so it gets smaller and smaller until the transmitted power is so high that the BER gets down to zero and the telecommunications are just perfect. c. But the surprise is thaty for the Sun–Alpha Cen direct radio bridge exploiting both the two gravitational lenses, this minimum transmitted power is incrediblyy small ! Actually it just equals less than 10 4 W, i.e. one tenth of a milliwatt is enough to have perfect communication between the Sun and Alpha Cen through two 12-m FOCAL spacecraft antennas (Fig. 4). How is that possible? d. Well, that is the ‘‘miracle’’ given to Humanity by the Gravitational Lenses to both explore the universe and keep the link with other stars, you know! Just remember that, in 2009, the discovery of the first extrasolar planet in the Andromeda galaxy (M31) was announced because of the gravitational lens caused by something in between!
To understand what SgrAn is and how it came to be discovered little by little in the last few decades, this author’s suggestion to the reader is to watch the instructive You Tube video entitled ‘‘Cosmic Journeys: Supermassive Black Hole in the Milky Way Galaxy’’: http:// www.youtube.com/watch?v=KCADH3 56eE. After watching that, a reading of the Wikipedia site about SgrAn would complete one’s basic knowledge: http://en.wikipedia.org/wiki/Sagittarius_A* . Having so said, we may now go back to our mathematical description of SgrAn and point out its key properties: (1) Distance from the Sun in the Milky Way: dSgrAn_Sun ¼ 25,900 ly:
ð25Þ
(2) Mass: MSgrAn ¼ 4:521 106 UM Sun ¼ 8:993 1036 kg:
ð26Þ
(3) Schwarzschild radius, i.e. black hole event horizon: 4. ‘‘Radio bridges’’ between the supermassive black hole of the Milky Way galaxy (SgrAn) and others In Ref. [1], the author made a detailed study of: (1) (2) (3) (4)
The Sun–Alpha Cen A radio bridge. The Sun–Barnard’s Star radio bridge. The Sun–Sirius A radio bridge. The radio bridge between the Sun and any Sun-like star located in the Galactic Bulge. (5) The radio bridge between the Sun and any Sun-like star located inside the Andromeda galaxy (M31). The conclusion was that a radio interstellar communications network can indeed be built if the gravitational lenses of all stars involved are exploited. In this paper, we take a much bolder step still. Given that each big galaxy has a supermassive black hole at its center, we calculate the antenna gain of that supermassive black hole and then build up the huge-distance radio bridge between that black hole and Sagittarius An (from now on abbreviated SgrAn), i.e. the supermassive black hole located at the center of our own Milky Way galaxy.
r Schwarzschild_SgrAn ¼
2GM SgrAn c2
¼ 0:089AU:
(4) Antenna Gain of the black hole: r Schwarzschild_SgrAn : GSgrAn ðnÞ ¼ 4p2 lðnÞ
ð27Þ
ð28Þ
(5) Black hole antenna gain at the Ka band frequency: GSgrAn ðnKa Þ 137:5 dB:
ð29Þ
5. ‘‘Radio bridge’’ between SgrAn and the Andromeda (M31) galaxy’s P2 black hole The Andromeda galaxy (M31) nucleus (please see http://en.wikipedia.org/wiki/Andromeda_Galaxy) is known to have two mass concentrations separated by 1.5 parsecs (4.9 ly). The brighter concentration, designated as P1, is offset from the center of the galaxy. The dimmer concentration, P2, falls at the true center of the galaxy and contains a black hole measured at 3–5 107 M in 1993 and at 1.1–2.3 108 M in 2005. The following picture of
C. Maccone / Acta Astronautica 78 (2012) 109–120
them is taken from the above Wikipedia site about M31 (Fig. 5). So, the data about the bigger (P2) black hole at the exact center of M31 read:
ð30Þ
GM31P2 ðnKa Þ 146:9dB:
Pr ¼
(2) Mass: M M31P2 ¼ 4 107 UM Sun ¼ 7:956 1037 kg:
ð31Þ
r Schwarzschild_M31P2 ¼
2GMM31P2 ¼ 0:78 AU: c2
ð32Þ
(4) Antenna Gain of the black hole: r Schwarzschild_M31P2 : lðnÞ
ð34Þ
Pt GSgrAn GM31P2 ðG12_meter_antenna_at_Ka Þ2 : Lðr, lÞ
ð35Þ
After repeating for (35) the string of calculations previously done in Section 3 to obtain the Sun–Alpha Cen A radio bridge, we finally arrive at the new graph, shown in the following Fig. 6. This shows both the same orange curve already found in Fig. 4 for the Sun–Alpha Cen A radio bridge and the new curve (in red) corresponding to the SgrAn–M31P2 radio bridge. We thus immediately see that the SgrAn–M31P2 radio bridge performs better than the Sun–Alpha Cen A radio bridge, in that just a power of about 10 7 W is sufficient to keep the link between SgrAn and M31P2 while a power of 10 4 W is necessary to keep the Sun–Alpha Cen A bridge. This is a startling result, taking into account that the SgrAn–M31P2 distance is 572,082 times larger than the Sun–Alpha Cen A distance. Clearly, this ‘‘miracle’’ occurs because the antenna gains of the two supermassive black holes are so much larger than the antenna gains of the Sun and Alpha Cen A that they more than compensate even for the abysmally larger distance in between.
(3) Schwarzschild radius, i.e. black hole event horizon:
GM31P2 ðnÞ ¼ 4p2
(5) Black hole antenna gain at the Ka band frequency:
Next we write the equation corresponding to (24) for the received power over the radio bridge between SgrAn and M31P2. That is:
(1) Distance: dSgrAn _M31P2 ¼ 2:54 106 ly:
115
ð33Þ
6. ‘‘Radio bridge’’ between SgrAn and the dwarf elliptical galaxy M32 small satellite of Andromeda
Fig. 5. HST image of the Andromeda Galaxy core showing possible double structure. NASA/ESA photo.
M32 (http://en.wikipedia.org/wiki/Messier_32) or Messier 32 (also known as NGC 221 and Le Gentil) (see Fig. 7) is a dwarf elliptical galaxy about 2.4970.08 Mly (763724 kpc) away in the constellation of Andromeda. M32 is a satellite galaxy of the Andromeda Galaxy (M31) and was discovered by Le Gentil in 1749. M32 measures only 6.570.2 kly in diameter at the widest point. Like most elliptical galaxies, M32 contains mostly older faint red and yellow stars (like the
0.4 BER_bridge_Alpha_Cen(Ptr) BER_bridge_SgrAstar_M31P2(Ptr)
0.3 0.2 0.1 0 1×10–12
1×10–10
1×10–8
1×10–6
1×10–4
Ptr·watt Fig. 6. Bit Error Rate (BER) (thin solid curve) for the double-gravitational-lens INTERGALACTIC radio bridge between the supermassive black hole at the center of our Milky Way galaxy (called SgrAn) and the corresponding P2 supermassive black hole located at the center of the Andromeda galaxy (here called M31P2). We immediately see that this intergalactic radio bridge performs about 3 orders of magnitude better than the ‘‘simple’’ radio bridge between the Sun and Alpha Cen A (thick solid curve, just the same as in Fig. 4). This startling new result paves the way to the feasibility of doing SETI among any couple of nearby galaxies, if the two supermassive black holes located at their two centers are well exploited for intergalactic communications by those ET civilizations living close to them in their respective galaxies.
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Sun) with practically no dust or gas and consequently no current star formation. It does, however, show hints of star formation in the relatively recent past, so ‘‘Earths’’ could be there, as well as ET civilizations on some of them. The structure and stellar content of M32 is difficult to explain by traditional galaxy formation models. Recent simulations suggest a new scenario in which the strong tidal field of M31 can transform a spiral galaxy into a compact elliptical. As a small spiral galaxy falls into the central parts of M31, most of the outer layers of the smaller spiral are stripped away. The central bulge of the galaxy is much less affected and retains its morphology. Tidal effects trigger a massive star burst in the core, resulting in the high density of M32 we observe today. There is also evidence that M32 has an outer disk. Most important for us, M32 contains a supermassive black hole. Its mass has been estimated to lie between 1.5 and 5 million solar masses. So, we may now start with the mathematics of the M32–Milky Way radio bridge by writing down the following equations:
(2) Mass: MM32 ¼ 3:25 106 UM Sun ¼ 6:463 1036 kg:
(3) Schwarzschild radius, i.e. black hole event horizon: r Schwarzschild_M32 ¼
2GMM32 ¼ 0:06 AU: c2
(4) Antenna Gain of the black hole: r GM32 ðnÞ ¼ 4p2 Schwarzschild_M32 : lðnÞ
ð38Þ
ð39Þ
(5) Black hole antenna gain at the Ka band frequency: GM32 ðnKa Þ 136:1 dB:
ð40Þ
These data yield the following Fig. 8, namely just the same as Fig. 6 but the addition of the new blue curve showing the BER for the SgrAn–M32 radio bridge. As we see, this still performs better than the Sun–Alpha Cen A bridge, though not as well as the SgrAn–M31P2 radio bridge.
(1) Distance: dSgrAn _M32 ¼ 2:49 106 ly:
ð37Þ
ð36Þ
7. ‘‘Radio bridge’’ between SgrAn and the M106 galaxy (NGC4258), half way in distance between Andromeda and the Virgo supercluster center (M87) We are now going much further out than the Andromeda system: we consider the ‘‘anomalous arms’’ M106 galaxy (or NGC4258) (see the Wikipedia site: http://en. wikipedia.org/wiki/Messier_106) located half way in between the distance of Andromeda and the distance of the center of the local supercluster of galaxies, namely the giant elliptical galaxy M87 in Virgo that we will consider in detail in Section 10. As our reader may expect already, we are going to show that both of these huge radio bridges are ‘‘feasible’’ for SETI communications. A composite radio image of M106, taken from the above Wikipedia site, is shown in Fig. 9.
Fig. 7. The dwarf elliptical galaxy M32.
0.4 BER_bridge_Alpha_Cen(Ptr) BER_bridge_SgrAstar_M31P2(Ptr)
0.3 0.2
BER_bridge_SgrAstar_M32BH(Ptr)
0.1 0 1×10–12
1×10–10
1×10–8
1×10–6
1×10–4
Ptr·watt
Fig. 8. Bit Error Rate (BER) (thin dash–dot curve) for the double-gravitational-lens INTERGALACTIC radio bridge between the supermassive black hole at the center of our Milky Way galaxy (called SgrAn) and the corresponding supermassive black hole located at the center of M32, the dwarf elliptical galaxy shown in Fig. 7 and a satellite of the Andromeda galaxy M31. We immediately see that this intergalactic radio bridge still performs about 1.5 orders of magnitude better than the ‘‘simple’’ radio bridge between the Sun and Alpha Cen A (thick solid curve, just the same as in Figs. 4 and 6). This new result paves the way to the feasibility of doing SETI among the center of the Milky Way and M32. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
C. Maccone / Acta Astronautica 78 (2012) 109–120
(5) Black hole antenna gain at the Ka band frequency:
The M106 astrophysical data are as follows:
GM106 ðnKa Þ 140 dB:
(1) Distance: ð41Þ
(2) Mass: M M106 ¼ 107 M Sun ¼ 1:988 1037 kg:
ð42Þ
(3) Schwarzschild radius, i.e. black hole event horizon: 2GM M106 ¼ 0:197 AU: c2
ð43Þ
(4) Antenna Gain of the black hole: GM106 ðnÞ ¼ 4p2
ð45Þ
These data yield the new Fig. 10 here below.
dSgrAn _M106 ¼ 25 106 ly:
r M106 ¼
117
r Schwarzschild_M106 : lðnÞ
ð44Þ
8. ‘‘Radio bridge’’ between SgrAn and the M104 ‘‘Sombrero’’ Galaxy M104 (NGC4594), again half way in distance between Andromeda and the VIRGO supercluster center (M87) The ‘‘Sombrero Galaxy’’ M104 (see Fig. 11, from: http://en. wikipedia.org/wiki/Sombrero_Galaxy) is again at a distance about half way between Andromeda and M87, namely 29.3 million light-years. In the 1990s, a research group led by John Kormendy demonstrated that a supermassive black hole is present within the Sombrero Galaxy. Using spectroscopy data from both the CFHT and the Hubble Space Telescope, the group showed that the speed of revolution of the stars within the center of the galaxy could not be maintained unless a mass 1 billion times the mass of the Sun, or 109 M, is present in the center. This is among the most massive black holes measured in any nearby galaxies. The following list of data thus emerges: (1) Distance: dSgrAn _M104 ¼ 29:3 106 ly:
Fig. 9. M 106 and its anomalous arms. Composite of IR, x-ray, radio and visible light view (X-ray—blue, Optical—gold, IR—red, Radio—purple; Image credit: NASA/CXC/University of Maryland. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
BER_bridge_Alpha_Cen (Ptr) BER_bridge_SgrAstar_M31P2(Ptr) BER_bridge_SgrAstar_M32BH(Ptr) BER_bridge_SgrAstar_M106BH(Ptr)
ð46Þ
Fig. 11. The Sombrero Galaxy (M104) as observed by the Spitzer. Credit: HST/NASA/ESA.
0.4 0.3 0.2 0.1 0 1×10–12
1×10–10
1×10–8 Ptr·watt
1×10–6
1×10–4
Fig. 10. Bit Error Rate (BER) (dash-dash thin curve) for the double-gravitational-lens INTERGALACTIC radio bridge between the supermassive black hole at the center of our Milky Way galaxy (SgrAn) and the corresponding supermassive black hole located at the center of M106 galaxy with anomalous arms shown in Fig. 9. We immediately see that this intergalactic radio bridge virtually performs just as well as the ‘‘simple’’ radio bridge between the Sun and Alpha Cen A (thick solid curve, just the same as in Figs. 4 and 6) since the new violet curve almost exactly overlaps the orange curve of the Sun–Alpha Cen A bridge. This result also paves the way to the feasibility of doing SETI among the center of the Milky Way and M106. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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C. Maccone / Acta Astronautica 78 (2012) 109–120
(2) Mass: 9
M M104 ¼ 10 UMSun ¼ 1:98 10
39
kg:
ð47Þ
(3) Schwarzschild radius, i.e. black hole event horizon: r M104 ¼
2GMM104 ¼ 19:7 AU: c2
ð48Þ
(4) Antenna Gain of the black hole: r G104 ðnÞ ¼ 4p2 Schwarzschild_M104 : lðnÞ
ð49Þ
(5) Black hole antenna gain at the Ka band frequency: GM106 ðnKa Þ 160 dB:
ð50Þ
source of multiwavelength radiation, particularly radio waves. A jet of energetic plasma originates at the core and extends out at least 5000 light-years, which is why M87 is sometimes called ‘‘the jet galaxy’’ (Fig. 14). The stars in this galaxy form about one sixth of M87’s mass. They have a nearly spherical distribution, while the density of stars decreases with increasing distance from the core. The galactic envelope extends out to a radius of about 490 kly, where it has been truncated. Between the stars is a diffuse interstellar medium of gas that has been chemically enriched by elements emitted from evolved stars. Any dust formed within the galaxy is destroyed within 46 million years by the X-ray emission from the core, although optical filaments of dust have been observed. Orbiting the galaxy is an abnormally large population of about 12,000 globular clusters, compared to 150–200 globular clusters orbiting the Milky Way. Since this is the largest giant elliptical
These data yield the new Fig. 12 here after. This is of course the same as Fig. 10 except the new cyan curve for the BER of the Sombrero–Milky Way radio bridge, that again performs about two orders of magnitude better than the Sun–Alpha Cen A radio bridge, tough not as well as the M32–Milky Way one. 9. ‘‘Radio bridge’’ between SgrAn and the supergiant elliptical galaxy M87 (NGC4486) at the VIRGO supercluster center We finally reached the ‘‘top’’, i.e. the supergiant elliptical galaxy M87 located at the center of our own Local Supercluster of galaxies (the Milky Way and Andromeda are just at the outskirts of it, or, if you prefer, we are just at the periphery of the periphery) (Fig. 13). From http://en.wikipedia.org/wiki/Messier_87, the M87 Wikipedia site, we learn that M87 was discovered in 1781 by French astronomer Charles Messier (1730–1817). The largest and brightest galaxy within the northern Virgo Cluster, it is located about 53.5 million light years away from Earth. Unlike a disk-shaped spiral galaxy, M87 has no distinctive dust lanes and it has an ellipsoidal shape. At the core is a supermassive black hole, which forms the primary component of an active galactic nucleus that is a strong
BER_bridge_Alpha_Cen(Ptr)
BER_bridge_SgrAstar_M31P2(Ptr) BER_bridge_SgrAstar_M32BH(Ptr)
Fig. 13. The M87 elliptical supergiant galaxy at the center of the Local Supercluster of galaxies to which we belong.
0.4 0.3 0.2
BER_bridge_SgrAstar_M106BH(Ptr) BER_bridge_SgrAstar_M104BH(Ptr)
0.1 0 1×10–12
1×10–10
1×10–8 Ptr·watt
1×10–6
1×10–4
Fig. 12. Bit Error Rate (BER) (thin dot–dot curve) for the double-gravitational-lens INTERGALACTIC radio bridge between the supermassive black hole at the center of our Milky Way galaxy (SgrAn) and the corresponding supermassive black hole located at the center of the M104 ‘‘Sombrero’’ galaxy shown in Fig. 11. This intergalactic radio bridge performs two orders of magnitude better than the ‘‘simple’’ radio bridge between the Sun and Alpha Cen A (thick solid curve, just the same as in Figs. 4, 6, 8 and 10). This result also paves the way to the feasibility of doing SETI among the center of the Milky Way and M104. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
C. Maccone / Acta Astronautica 78 (2012) 109–120
galaxy near Earth and is one of the brightest radio sources in the sky, M87 is a popular target for both amateur astronomy observations and professional astronomy study. The M87 astrophysical data of interest to us are thus: (1) Distance: dSgrAn _M87 ¼ 53:5 106 ly:
ð51Þ
(2) Mass:
119
(3) Schwarzschild radius, i.e. black hole event horizon: r M87 ¼
2GMM87 ¼ 130 AU: c2
ð53Þ
(4) Antenna Gain of the black hole: r GM87 ðnÞ ¼ 4p2 Schwarzschild_M87 : lðnÞ
ð54Þ
(5) Black hole antenna gain at the Ka band frequency: 9
M M87 ¼ 6:6 10 UMSun ¼ 1:98 10
39
kg:
GM87 ðnKa Þ 169 dB:
ð52Þ
ð55Þ
The radio bridge between the huge black hole at the center of M87 and SgrAn is represented in the following Fig. 15 by the new brown curve. We thus see that the M87-SgrAn radio bridge performs better than anyone else, with the exception of the P2 one at the center of the Andromeda galaxy. It performs about 2.5 times better than the Sun–Alpha Cen A bridge. 10. Conclusion
Fig. 14. This Hubble Space Telescope photo shows the jet of matter ejected from M87 at nearly light speed and nearly towards us, as it stretches 5000 light years from the galactic core.
BER_bridge_Alpha_Cen(Ptr)
We have shown that telecommunications between galaxies up to 60 million light-years apart are indeed feasible with modest transmission powers if each galaxy’s supermassive black hole is exploited as a gravitational magnifying lens. This is an important step ahead with respect to ‘‘classical’’ SETI searches that assumed huge transmission powers to be available to ET’s. Human SETI searches might therefore concentrate in the directions of nearby galaxies where a supermassive and central black hole is known to exist. In addition, this line of thought clearly shows that the central massive black hole of every galaxy is by far the most important ‘‘resource’’ of that galaxy for SETI purposes. In fact, it is like the ‘‘central radio station’’ of that galaxy that every civilization living in that galaxy would
0.4
BER_bridge_SgrAstar_M31P2(Ptr) BER_bridge_SgrAstar_M32BH(Ptr) BER_bridge_SgrAstar_M106BH(Ptr)
0.3 0.2
BER_bridge_SgrAstar_M104BH(Ptr) BER_bridge_SgrAstar_M87BH(Ptr)
0.1 0 1×10–12
1×10–10
1×10–8
1×10–8
1×10–4
Ptr·watt Fig. 15. Bit Error Rate (BER) (average thick/thin solid curve) for the double-gravitational-lens INTERGALACTIC radio bridge between the supermassive black hole at the center of our Milky Way galaxy (SgrAn) and the corresponding supermassive black hole located at the center of the M87 ‘‘Jet’’ galaxy shown in Figs. 13 and 14. This intergalactic radio bridge performs about two and a half orders of magnitude better than the ‘‘simple’’ radio bridge between the Sun and Alpha Cen A (orange curve, just the same as in Figs. 4, 6, 8, 10 and 12). This result also paves the way to the feasibility of doing SETI among the center of the Milky Way and M87. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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C. Maccone / Acta Astronautica 78 (2012) 109–120
like to control in order to keep in touch with other aliens living in nearby galaxies. This idea also explains the Fermi paradox in some sense. In fact, one might argue that every important civilization in a galaxy would like to live close to the central supermassive black hole, rather than in the outskirts, as we Humans do with respect to our SgrAn. The conclusion is thus that current Human SETI searches should look for ET signals coming from nearby galaxies known to have both a supermassive black hole at their center and for SgrAn and its surroundings.
Acknowledgment The author is indebted to many colleagues for conversations and suggestions, but, in particular, he would like to
thank Paul Gilster for maintaining his terrific Centauri Dreams web site: http://www.centauri-dreams.org. References [1] C. Maccone, Interstellar radio links enhanced by exploiting the Sun as a Gravitational Lens, Acta Astronaut. 68 (2011) 76–84. [2] C. Maccone, Interstellar radio links enhanced by exploiting the Sun as a gravitational lens, paper #IAC-09.D4.1.8 presented by the author at the 60th International Astronautical Congress held at Daejeon, Republic of Korea, October 12–16th, 2009, and distributed to all participants as a CD-ROM file, but not published in a printed form. [3] C. Maccone, Deep space flight and communications—exploiting the Sun as a gravitational lens, a 400-pages treatise about the FOCAL space mission that embodies and updates all previously published material about FOCAL. ISBN 978-3-540-72942-6, published by Springer, Berlin, Heidelberg, New York, 2009. Library of Congress Control Number: 2007939976. & Praxis Publishing Ltd, Chichester, UK, 2009.
Contents lists available at SciVerse ScienceDirect
Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro
SETI among galaxies by virtue of black holes$ Claudio Maccone a,b,n a b
International Academy of Astronautics (IAA), Italy SETI Permanent Committee of the IAA, Italy
a r t i c l e i n f o
abstract
Article history: Received 31 January 2011 Received in revised form 30 July 2011 Accepted 24 October 2011 Available online 3 December 2011
In two recent papers (Refs. Maccone (2011, 2009) [1,2]) this author proved that the radio communications among any pair of stars within our Galaxy are feasible with modest transmitted powers if the gravitational lenses of both stars are exploited. In the present paper we extend those innovative results to the case of radio communications among nearby galaxies. We show that the radio communications among galaxies may become feasible if the supermassive black holes, usually located at the center of galaxies, are exploited as gravitational lenses. In other words, a massive black hole may be regarded as a huge focusing device for radio waves being transmitted out of that galaxy and/or being received from another galaxy. This happens because a black hole is such a highly massive and compact object that all electromagnetic waves flying by its surface are highly deflected by its gravitational field and made to focus at a comparatively short distance from the black hole itself. Next we consider the possibility of building radio bridges between our own Galaxy (the Milky Way) and other nearby galaxies. This possibility is serious because, since 1974, astronomers have come to known that a supermassive black hole called Sagittarius An does exist at the center of our Galaxy. In 2002 its mass was estimated to be of the order of 2.6 million solar masses, and in 2008 this estimate was increased to 4.31 million solar masses. Furthermore, in 2004 a team of astronomers reported the discovery of a potential intermediate-class black hole called GCIRS 13E orbiting around SgrAn at about three lightyears and having an estimated mass of 1,300 solar masses. These two big black holes could be our Galaxy’s ‘‘antennae’’ for communications with alien civilizations harboring in other nearby galaxies. We mathematically show that the following radio bridges may be created between SgrAn and the supermassive black hole located at the center of the nearby galaxies:
Keywords: Gravitational lens Bit error rate Interstellar radio links Intergalactic radio links Black holes
(1) The SgrAn-Andromeda’s (M31) P2 Black Hole radio bridge, having the distance of 2.5 million light years. The P2 Andromeda black hole is estimated to have a mass of about 40 million solar masses. (2) The SgrAn-M32 (a dwarf elliptical galaxy satellite of Andromeda-M31) radio bridge, with a 2.65 million light year distance. The M32 black hole is estimated to have a mass of about 3 million solar masses. (3) The SgrAn-M106 (also called NGC 4258, a spiral galaxy with anomalous arms) radio bridge, at about 24 million light years. The M106 black hole is estimated to have a mass of about 40 million solar masses.
$ n
Second IAA Symposium on Searching for Life Signatures Held at Chicheley Hall, Buckinghamshire, UK, 6–7 October 2010. Correspondence to: Via Martorelli 43, 10155 Torino, TO, Italy. Tel.: þ 39 0112055387. E-mail addresses: [email protected], [email protected] URL: http://www.maccone.com/
0094-5765/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.actaastro.2011.10.011
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C. Maccone / Acta Astronautica 78 (2012) 109–120
(4) The SgrAn-Sombrero Galaxy (also called M104 or NGC 4594, an unbarred spiral galaxy) at a distance of 29.3 million light years. Its black hole is estimated to have a mass of 1 billion solar masses. (5) The SgrAn-M87 radio bridge. M87 is the supergiant elliptical galaxy located at the center of the super-cluster of galaxies to which we belong, i.e. the Local Super Cluster, at the edge of which we are located. The distance between M87 and us is 53.5 million light years in the direction of the constellation of Virgo, which is why M87 and its surrounding clusters of galaxies are sometimes referred to as the Virgo Super Cluster. At the center of M87 is a supermassive black hole estimated to have a mass of 6.4 billion solar masses. M87 is also well known as ‘‘the jet galaxy’’ since a jet of energetic plasma originates at the core and extends out at least 5000 lightyears. The conclusion that we draw from the mathematics describing these radio bridges across huge inter-galactic distances is surprising: they all perform better that the simple Sun–Alpha Cen A radio bridge, first studied in detail by this author in Ref. [1]. In other words, the powers necessary to keep the radio link between SgrAn and all of the above big black holes located in other nearby galaxies are smaller than the powers requested to keep the radio bridge between the Sun and Alpha Cen A. In other words still, despite inter-galactic distances are huge with respect to ordinary interstellar distances within the Milky Way, the black hole masses in the game are so much huger than the stellar masses than the intergalactic bridges perform better than the interstellar bridges. This unexpected and new result might have profound consequences on SETI done currently by Humans on Earth. In fact, more advanced civilizations might already have built such intergalactic radio-bridges. Thus our SETI searches should be tuned-up to match with this new situation, and the conclusion is that the possibility of SETI signals reaching us from other galaxies should not be ruled out. & 2011 Elsevier Ltd. All rights reserved.
1. An introduction to radio communications in space (LINK)
is an antenna gain:
In two recent papers (Refs. [1,2]), this author proved that the radio communications among any pair of stars within our Galaxy are feasible with modest transmitted powers if the gravitational lenses of both stars are exploited. In this introductory section we review the mathematical theory set up in Refs. [1,2] and get ready to apply it to intergalactic distances rather than just to interstellar distances. Consider a radio transmitter that radiates a Power Pt isotropically and uniformly over a bandwidth Bt. Then, at a distance r it produces a flux density given by Pt : Bt 4pr 2
ð1Þ
A receiving antenna of effective aperture Aer at a distance r can collect a power given by (1) multiplied by both the effective aperture of the receiving antenna and its bandwidth, namely the received power Pr is given by Pr ¼
Pt Aer Br : Bt 4pr 2
ð2Þ
It is assumed that the receiving bandwidth Br. is smaller or, at best (in the ‘‘matched bandwidths’’ case) equal to the transmitting bandwidth Bt, that is Br rBt . So far, we have been talking about an isotropic radiator. But let us now assume that the transmitting antenna has a directivity D (see, for instance, the Wikipedia site http://en. wikipedia.org/wiki/Directivity or Chapter 1 of Ref. [3]) that
D¼
4pAet
:
l2
ð3Þ
The received power Pr is then increased by just such a factor due to the directivity of the transmitting antenna, and so (2) must now be replaced by a new equation where the right-hand side is multiplied by such an increased factor, that is Pr ¼
4pAet
Pt
l2 Bt 4pr 2
Aer Br :
ð4Þ
Rearranging a little, this becomes Pr ¼
P t Aet Aer Br : 2 r 2 l Bt
ð5Þ
This is the received signal power expression. For the matched bandwidths case, i.e. for Br ¼ Bt , this is called the Friis transmission formula, since it was first published back in 1946 by the American radio engineer Harald T. Friis (1893–1976) of the Bell Labs. In space missions, we of course know exactly both Bt and Br and so we may construct our spacecraft so that the two bands match exactly, i.e. Br ¼ Bt . Thus, for the case of telecommunications with a spacecraft (but not necessarily for the SETI case) we may well assume the matched bandwidths and have (5) reducing to Pr ¼
P t Aet Aer 2
r2 l
:
ð6Þ
Let us now rewrite (6) in such a way that we may take into account the gains (i.e. directionalities) of both the transmitting and receiving antennae, that is, in agreement
C. Maccone / Acta Astronautica 78 (2012) 109–120
with (3) 8 < Gt ¼ 4pA2 et l
: Gr ¼
that is
4pAer
l2
8 < Aet ¼
Gt l 4p
: Aer ¼
Gr l2 4p
2
:
ð7Þ
Replacing the last two expressions into (6), we find that (6) is turned into Pr ¼
P t Gt Gr ð4pÞ2 r 2
l2 :
This may finally be rewritten in the more traditional form Pr ¼
P t Gt Gr : Lðr, lÞ
ð8Þ
if one defines Lðr, lÞ ¼ ð4pÞ2
r2
l
: 2
which is the Path Loss (or path attenuation), i.e. the reduction in power density (attenuation) of the electromagnetic waves as they propagate through space. Path loss is a major component in the analysis and design of the link budget of a telecommunication system, see for instance the Wikipedia site http://www.en.wikipedia.org/ wiki/Path_loss. Next we define the Bit Error Rate (BER). Then, by virtue of a numerical example, we show that, even at the distance of the nearest star (Alpha Cen at 4.37 AU) the telecommunications would be impossible by the ordinary powers available today for interplanetary space flight. But in the next section we shall show that the telecommunications would become feasible if we could take advantage of the magnification provided by the Sun’s gravity lens, i.e. if we would send out to 550 AU a FOCAL relay spacecraft (see, for instance, Ref. [3]) for each target star system that we wish to communicate with. This was the key new result presented in Ref. [1]. So, let us start by defining the Bit Error Rate or BER. In telecommunication theory an error ratio is the ratio of the number of bits, elements, characters, or blocks incorrectly received to the total number of bits, elements, characters, or blocks sent during a specified time interval. Among these error ratios, the most commonly encountered ratio is the bit error ratio (BER) – also called bit error rate – that is the number of erroneous bits received divided by the total number of bits transmitted. At the bit error rate Wikipedia site: http://www.en.wikipedia.org/wiki/Bit_error_rate it is shown that the likelihood of a bit misinterpretation pe ¼ pð091Þp1 þpð90Þp0 :
could be the antenna of a precursor interstellar space probe that was sent out to some light years away. (2) n ¼frequency of the electromagnetic waves used in the telecommunication link. The higher this frequency, the better it is, since the photons are then more energetic (E¼hn). In today’s practice, however, the highest n for spacecraft links (like the link of the Cassini probe, now at Saturn) are the ones in the Ka band, that is: nKa 32 GHz. (3) Pt is the power in watts transmitted by the Earth antenna, typically a NASA Deep Space Network antenna 70 m in diameter. (4) The complementary error function ercf(x) is defined by the integral Z 1 2 2 erf cðxÞ ¼ pffiffiffiffi et dt, ð12Þ
p
ð9Þ
ð10Þ
(believing that we have received a 0 while it was a 1 or the other way round) is basically given by the ‘‘complementary error function’’ or erfc(x) as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 1 Eb ðd, n,Pt Þ BERðd, n,Pt Þ ¼ erf c : ð11Þ 2 N0 In this equation one has: (1) d ¼distance between the transmitting station on Earth and the receiving antenna in space. For instance, this
111
x
(for more maths, see the relevant Wikipedia site: http://www.en.wikipedia.org/wiki/ Complementary_error_function). (5) Eb(d, n, Pt) is the received energy per bit, that is the ratio Eb ðd, n,P t Þ ¼
Pr ðd, n,Pt Þ : Bit_rate
ð13Þ
(6) Finally, N0 is given by the Boltzmann’s constant k multiplied by the noise temperature of space far away from the Sun and from any other star. This ‘‘empty space noise temperature’’ might be assumed to equal, say, 100 K. This is the analytical structure of the MathCad code that this author wrote to yield the BER. Let us now consider the input values that he used in practice: (1) Suppose that a human space probe has reached the Alpha Cen system at 4.37 light year distance from the Sun: then, d¼4.37 light years. (2) Suppose also that the transmitting antenna from the Earth is a typical NASA Deep Space Network (DSN) antenna having a diameter of 70 m (like those at Goldstone, Madrid and Canberra), and assume that its efficiency is about 50%. (3) Suppose that the receiving antenna aboard the spacecraft is 12 m in diameter (it might be an inflatable space antenna, as we supposed in Ref. [3] for the FOCAL spacecraft) and assume a 50% efficiency. (4) Suppose that the link frequency is the Ka band (i.e. 32 GHz), as for the Cassini highest frequency. (5) Suppose that the bit rate is 32 kbps ¼32,000 bit/s. This is the bit rate of ESA’s Rosetta interplanetary spacecraft now on its way to a comet. (6) And finally (this is the most important input assumption) suppose that the transmitting power Pt is moderate: just 40 W. Then: (1) The gain of the transmitting NASA DSN antenna (at this Ka frequency) is about 84 dB.
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C. Maccone / Acta Astronautica 78 (2012) 109–120
(2) The gain of the spacecraft antenna is about 69 dB. (3) The path loss at the distance of Alpha Cen is 395 dB (a very high indeed path loss with respect to today’s interplanetary missions, of course). (4) The power received by the spacecraft at that distance is 2.90 10 23 W. (5) The received energy per bit (lowered by the noise temperature of the space in between the Sun and Alpha Cen) is 1.3 10 37 J. (6) And finally the BER is 0.49, i.e. there is a 50% probability of ERRORS in the telecommunications between the Earth and the probe at Alpha Cen if we use such a small transmitting power! In other words, if these are the telecommunication links between the Earth and our probe at Alpha Cen, then this precursor interstellar mission is worthless. The key point in this example is that, for all calculations, (8) and (9) were used WITHOUT TAKING THE GAIN OF THE SUN GRAVITY LENS INTO ACCOUNT, because this was a DIRECT link and NOT a FOCAL mission. 2. Bit error rate at the Alpha Centauri distance enhanced by the magnification provided by the Sun’s gravity lens (FOCAL space mission to 550 AU and beyond) The disappointing BER results of the previous section are totally reversed, however, if we suppose that a FOCAl
space mission has been previously sent out to 550 AU in the direction opposite to Alpha Cen. These topics were fully described by the author in his recent book [3], so we will not repeat them here. We now have the MAGNIFICATION provided by the Sun’s Gravity Lens playing in the game. Mathematically, this means that we must introduce a third multiplicative gain at the numerator of (8): the Sun’s Gravity Lens GAIN, given by (8) of Ref. [1], that is GSun ¼ 4p2
r Schwarzschild_of _Sun
l
,
ð14Þ
where the Schwarzschild radius of the Sun is given by r Schwarzschild_of _Sun ¼
2GMSun : c2
ð15Þ
This new gain is huge at the Ka band frequency: GSun ðnKa Þ ¼ 12,444,837 70 dB,
ð16Þ
and so the received power (8) at Alpha Cen, with the usual Earth-transmitted power of just 40 W becomes P r ¼ 2:9 1023 W,
ð17Þ
and the relevant BER becomes absolutely acceptable: BER ¼ 0:000000526387845:
ð18Þ
This should convince anybody that the FOCAL space mission is indispensable to keep the link at interstellar distances equal or higher than Alpha Cen Figs. 1–3.
BER with and without the Sun Magnification at Alpha Cen for Pt = 40 watt 0.4 BER_with_Sun(d, νKa, Pt)
0.3
BER_without_Sun(d, νKa, Pt)
0.2 0.1 0
0
0.02
0.04
0.06 0.08 d DISTANCE of interstellar probe from the Sun (light years)
0.1
Fig. 1. The Bit Error Rate (BER) (upper, blue curve) tends immediately to the 50% value (BER¼ 0.5) even at moderate distances from the Sun (0–0.1 light years) for a 40 W transmission from a DSN antenna that is a DIRECT transmission, i.e. without using the Sun’s Magnifying Lens. On the contrary (lower red curve) the BER keeps staying at zero value (perfect communications!) if the FOCAL space mission is made, so as the Sun’s magnifying action is made to work. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
BER with and without the Sun Magnification at Alpha Cen for Pt = 40 watt 0.4 BER_with_Sun(d, νKa, Pt)
0.3
BER_without_Sun(d, νKa, Pt)
0.2 0.1 0
0
2
4
6 8 d DISTANCE of interstellar probe from the Sun (light years)
10
Fig. 2. Same as in Fig. 1, but for probe distances up to 10 light years. We see that at about 9 light years away the BER curve starts being no exactly flat any more, and starts increasing slowly.
C. Maccone / Acta Astronautica 78 (2012) 109–120
113
BER with and without the Sun Magnification at Alpha Cen for Pt = 40 watt 0.4 BER_with_Sun(d, νKa, Pt)
0.3
BER_without_Sun(d, νKa, Pt)
0.2 0.1 0
0
20
40
60 80 100 d DISTANCE of interstellar probe from the Sun (light years)
Fig. 3. Same as in Fig. 2, but for probe distances up to 100 light years. We see that, from 9 light years onward, the Sun-BER increases, reaching the dangerous level of 40% (Sun–BER ¼0.4) at about 100 light years. Namely, at 100 light years even the Sun’s Lens cannot cope with this very low transmitted power of 40 W.
3. ‘‘Radio bridge’’ between the Sun and Alpha Cen A by using the two gravitational lenses of both just matched to each other In this section we provide one more new result: we define the radio bridge between the Sun and Alpha Cen A by using BOTH gravitational lenses! In other words, suppose that in the future we will be able to send a probe to Alpha Cen A and suppose that we succeed in placing this probe just on the other side of Alpha Cen A with respect to the Sun and at the minimal focal distance typical of Alpha Cen A. This distance is NOT 550 AU obviously because both the radius and the mass of Alpha Cen A are different (actually slightly higher) than the values of the Sun: ( r Alpha_Cen_A ¼ 1:227r Sun : ð19Þ M Alpha_Cen_A ¼ 1:100MSun Replacing these values into the minimal focal distance (see Eq. (1) of Ref. [1]) (obviously rewritten for Alpha Cen A), the relevant minimal focal distance is found df ocal_Alpha_Cen_A
c2 r 2Alpha_Cen_A 4GM Alpha_Cen_A
749 AU:
ð20Þ
The Schwarzschild radius for Alpha Cen A is given by 2GM Alpha_Cen_A r Schwarzschild_Alpha_Cen_A ¼ ¼ 3:248 km: c2
ð21Þ
And so the gain, provided by (14), turns out to equal r Schwarzschild_Alpha_Cen_A GAlpha_Cen_A ðnKa Þ ¼ 4p2
lKa
¼ 13,689,321:
ð22Þ
Having found the Alpha Cen A gain (23) we are now able to write the new equation corresponding to (8) for the Sun–Alpha Cen bridge. In fact, we must now put at the numerator of (8) three gains: (1) the Sun gain at 32 GHz, (2) the Alpha Cen A gain at 32 GHz, and (3) the 12-meter FOCAL antenna gain at 32 GHz raised to the square because there are two such 12-m antennas: one at 550 AU from the Sun and one at 749 AU from Alpha Cen A, and they must be perfectly aligned with the axis passing thru both the Sun and Alpha Cen A. Thus, the received power given by (8) now reads Pr ¼
Pt GSun GAlpha_Cen_A ðG12_meter_antenna_at_Ka Þ2 : Lðr, lÞ
ð24Þ
where obviously r equals 4.37 light years and l corresponds to a 32 GHz frequency. Let us now go back to the BER and replace (8) with (24) in the long chain of calculations described in Section 1. Since the received power Pr has now changed, clearly both (13) and (11) yield different numerical results. But now: (1) The link frequency has been fixed at 32 GHz (Ka band), and so no longer is an independent variable in the game. (2) Also the distance d has been fixed (it is the distance of Alpha Cen A) and so is no longer an independent variable in the game. (3) It follows that, in (13) and (11), the only variable to be free to vary is now the transmitted power, Pt.
That is GAlpha_Cen_A ðnKa Þ 71 dB:
ð23Þ
Incidentally, we chose Alpha Cen A, and not B or C, because it has the highest mass, and so the highest gain, in the whole Alpha Cen triple system. The future telecommunications between the Sun and the Alpha Cen system are thus optimized by selecting Alpha Cen A as the star on the other side of which to place a FOCAL spacecraft at the minimal distance of 750 AU. That FOCAL spacecraft would then easily relay its data anywhere within the Alpha Cen system.
Let us re-phrase the last sentence in different terms. Practically, we are now studying the BER as a function of the transmitted power Pt only and, physically, this means that: a. We start by inputting very low transmission powers in watts, and find out that the BER is an awful 50%, i.e. the telecommunication between the Sun and Alpha Cen is totally disrupted. This is of course because the energy per bit is so much lower than the empty space noise temperature.
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0.4 BER_bridge_Alpha_Cen(Ptr)
0.3 0.2 0.1 0 1×10–10 1×10–9
1×10–8
1×10–7 1×10–6 Ptr·watt
1×10–5
1×10–4
1×10–3
Fig. 4. Bit Error Rate (BER) for the double-gravitational-lens system giving the radio bridge between the Sun and Alpha Cen A. In other words, there are two gravitational lenses in the game here: the Sun one and the Alpha Cen A one, and two 12-meter FOCAL spacecrafts are supposed to have been put along the two-star axis on opposite sides at or beyond the minimal focal distances of 550 AU and 749 AU, respectively. This radio bridge has an OVERALL GAIN SO HIGH that a miserable 10 4 W transmitting power is sufficient to let the BER get down to zero, i.e. to have perfect telecommunications! Notice also that the scale of the horizontal axis is logarithmic. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
b. We then increase the transmitted power, at a certain point the BER starts getting smaller than 50%. And so it gets smaller and smaller until the transmitted power is so high that the BER gets down to zero and the telecommunications are just perfect. c. But the surprise is thaty for the Sun–Alpha Cen direct radio bridge exploiting both the two gravitational lenses, this minimum transmitted power is incrediblyy small ! Actually it just equals less than 10 4 W, i.e. one tenth of a milliwatt is enough to have perfect communication between the Sun and Alpha Cen through two 12-m FOCAL spacecraft antennas (Fig. 4). How is that possible? d. Well, that is the ‘‘miracle’’ given to Humanity by the Gravitational Lenses to both explore the universe and keep the link with other stars, you know! Just remember that, in 2009, the discovery of the first extrasolar planet in the Andromeda galaxy (M31) was announced because of the gravitational lens caused by something in between!
To understand what SgrAn is and how it came to be discovered little by little in the last few decades, this author’s suggestion to the reader is to watch the instructive You Tube video entitled ‘‘Cosmic Journeys: Supermassive Black Hole in the Milky Way Galaxy’’: http:// www.youtube.com/watch?v=KCADH3 56eE. After watching that, a reading of the Wikipedia site about SgrAn would complete one’s basic knowledge: http://en.wikipedia.org/wiki/Sagittarius_A* . Having so said, we may now go back to our mathematical description of SgrAn and point out its key properties: (1) Distance from the Sun in the Milky Way: dSgrAn_Sun ¼ 25,900 ly:
ð25Þ
(2) Mass: MSgrAn ¼ 4:521 106 UM Sun ¼ 8:993 1036 kg:
ð26Þ
(3) Schwarzschild radius, i.e. black hole event horizon: 4. ‘‘Radio bridges’’ between the supermassive black hole of the Milky Way galaxy (SgrAn) and others In Ref. [1], the author made a detailed study of: (1) (2) (3) (4)
The Sun–Alpha Cen A radio bridge. The Sun–Barnard’s Star radio bridge. The Sun–Sirius A radio bridge. The radio bridge between the Sun and any Sun-like star located in the Galactic Bulge. (5) The radio bridge between the Sun and any Sun-like star located inside the Andromeda galaxy (M31). The conclusion was that a radio interstellar communications network can indeed be built if the gravitational lenses of all stars involved are exploited. In this paper, we take a much bolder step still. Given that each big galaxy has a supermassive black hole at its center, we calculate the antenna gain of that supermassive black hole and then build up the huge-distance radio bridge between that black hole and Sagittarius An (from now on abbreviated SgrAn), i.e. the supermassive black hole located at the center of our own Milky Way galaxy.
r Schwarzschild_SgrAn ¼
2GM SgrAn c2
¼ 0:089AU:
(4) Antenna Gain of the black hole: r Schwarzschild_SgrAn : GSgrAn ðnÞ ¼ 4p2 lðnÞ
ð27Þ
ð28Þ
(5) Black hole antenna gain at the Ka band frequency: GSgrAn ðnKa Þ 137:5 dB:
ð29Þ
5. ‘‘Radio bridge’’ between SgrAn and the Andromeda (M31) galaxy’s P2 black hole The Andromeda galaxy (M31) nucleus (please see http://en.wikipedia.org/wiki/Andromeda_Galaxy) is known to have two mass concentrations separated by 1.5 parsecs (4.9 ly). The brighter concentration, designated as P1, is offset from the center of the galaxy. The dimmer concentration, P2, falls at the true center of the galaxy and contains a black hole measured at 3–5 107 M in 1993 and at 1.1–2.3 108 M in 2005. The following picture of
C. Maccone / Acta Astronautica 78 (2012) 109–120
them is taken from the above Wikipedia site about M31 (Fig. 5). So, the data about the bigger (P2) black hole at the exact center of M31 read:
ð30Þ
GM31P2 ðnKa Þ 146:9dB:
Pr ¼
(2) Mass: M M31P2 ¼ 4 107 UM Sun ¼ 7:956 1037 kg:
ð31Þ
r Schwarzschild_M31P2 ¼
2GMM31P2 ¼ 0:78 AU: c2
ð32Þ
(4) Antenna Gain of the black hole: r Schwarzschild_M31P2 : lðnÞ
ð34Þ
Pt GSgrAn GM31P2 ðG12_meter_antenna_at_Ka Þ2 : Lðr, lÞ
ð35Þ
After repeating for (35) the string of calculations previously done in Section 3 to obtain the Sun–Alpha Cen A radio bridge, we finally arrive at the new graph, shown in the following Fig. 6. This shows both the same orange curve already found in Fig. 4 for the Sun–Alpha Cen A radio bridge and the new curve (in red) corresponding to the SgrAn–M31P2 radio bridge. We thus immediately see that the SgrAn–M31P2 radio bridge performs better than the Sun–Alpha Cen A radio bridge, in that just a power of about 10 7 W is sufficient to keep the link between SgrAn and M31P2 while a power of 10 4 W is necessary to keep the Sun–Alpha Cen A bridge. This is a startling result, taking into account that the SgrAn–M31P2 distance is 572,082 times larger than the Sun–Alpha Cen A distance. Clearly, this ‘‘miracle’’ occurs because the antenna gains of the two supermassive black holes are so much larger than the antenna gains of the Sun and Alpha Cen A that they more than compensate even for the abysmally larger distance in between.
(3) Schwarzschild radius, i.e. black hole event horizon:
GM31P2 ðnÞ ¼ 4p2
(5) Black hole antenna gain at the Ka band frequency:
Next we write the equation corresponding to (24) for the received power over the radio bridge between SgrAn and M31P2. That is:
(1) Distance: dSgrAn _M31P2 ¼ 2:54 106 ly:
115
ð33Þ
6. ‘‘Radio bridge’’ between SgrAn and the dwarf elliptical galaxy M32 small satellite of Andromeda
Fig. 5. HST image of the Andromeda Galaxy core showing possible double structure. NASA/ESA photo.
M32 (http://en.wikipedia.org/wiki/Messier_32) or Messier 32 (also known as NGC 221 and Le Gentil) (see Fig. 7) is a dwarf elliptical galaxy about 2.4970.08 Mly (763724 kpc) away in the constellation of Andromeda. M32 is a satellite galaxy of the Andromeda Galaxy (M31) and was discovered by Le Gentil in 1749. M32 measures only 6.570.2 kly in diameter at the widest point. Like most elliptical galaxies, M32 contains mostly older faint red and yellow stars (like the
0.4 BER_bridge_Alpha_Cen(Ptr) BER_bridge_SgrAstar_M31P2(Ptr)
0.3 0.2 0.1 0 1×10–12
1×10–10
1×10–8
1×10–6
1×10–4
Ptr·watt Fig. 6. Bit Error Rate (BER) (thin solid curve) for the double-gravitational-lens INTERGALACTIC radio bridge between the supermassive black hole at the center of our Milky Way galaxy (called SgrAn) and the corresponding P2 supermassive black hole located at the center of the Andromeda galaxy (here called M31P2). We immediately see that this intergalactic radio bridge performs about 3 orders of magnitude better than the ‘‘simple’’ radio bridge between the Sun and Alpha Cen A (thick solid curve, just the same as in Fig. 4). This startling new result paves the way to the feasibility of doing SETI among any couple of nearby galaxies, if the two supermassive black holes located at their two centers are well exploited for intergalactic communications by those ET civilizations living close to them in their respective galaxies.
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Sun) with practically no dust or gas and consequently no current star formation. It does, however, show hints of star formation in the relatively recent past, so ‘‘Earths’’ could be there, as well as ET civilizations on some of them. The structure and stellar content of M32 is difficult to explain by traditional galaxy formation models. Recent simulations suggest a new scenario in which the strong tidal field of M31 can transform a spiral galaxy into a compact elliptical. As a small spiral galaxy falls into the central parts of M31, most of the outer layers of the smaller spiral are stripped away. The central bulge of the galaxy is much less affected and retains its morphology. Tidal effects trigger a massive star burst in the core, resulting in the high density of M32 we observe today. There is also evidence that M32 has an outer disk. Most important for us, M32 contains a supermassive black hole. Its mass has been estimated to lie between 1.5 and 5 million solar masses. So, we may now start with the mathematics of the M32–Milky Way radio bridge by writing down the following equations:
(2) Mass: MM32 ¼ 3:25 106 UM Sun ¼ 6:463 1036 kg:
(3) Schwarzschild radius, i.e. black hole event horizon: r Schwarzschild_M32 ¼
2GMM32 ¼ 0:06 AU: c2
(4) Antenna Gain of the black hole: r GM32 ðnÞ ¼ 4p2 Schwarzschild_M32 : lðnÞ
ð38Þ
ð39Þ
(5) Black hole antenna gain at the Ka band frequency: GM32 ðnKa Þ 136:1 dB:
ð40Þ
These data yield the following Fig. 8, namely just the same as Fig. 6 but the addition of the new blue curve showing the BER for the SgrAn–M32 radio bridge. As we see, this still performs better than the Sun–Alpha Cen A bridge, though not as well as the SgrAn–M31P2 radio bridge.
(1) Distance: dSgrAn _M32 ¼ 2:49 106 ly:
ð37Þ
ð36Þ
7. ‘‘Radio bridge’’ between SgrAn and the M106 galaxy (NGC4258), half way in distance between Andromeda and the Virgo supercluster center (M87) We are now going much further out than the Andromeda system: we consider the ‘‘anomalous arms’’ M106 galaxy (or NGC4258) (see the Wikipedia site: http://en. wikipedia.org/wiki/Messier_106) located half way in between the distance of Andromeda and the distance of the center of the local supercluster of galaxies, namely the giant elliptical galaxy M87 in Virgo that we will consider in detail in Section 10. As our reader may expect already, we are going to show that both of these huge radio bridges are ‘‘feasible’’ for SETI communications. A composite radio image of M106, taken from the above Wikipedia site, is shown in Fig. 9.
Fig. 7. The dwarf elliptical galaxy M32.
0.4 BER_bridge_Alpha_Cen(Ptr) BER_bridge_SgrAstar_M31P2(Ptr)
0.3 0.2
BER_bridge_SgrAstar_M32BH(Ptr)
0.1 0 1×10–12
1×10–10
1×10–8
1×10–6
1×10–4
Ptr·watt
Fig. 8. Bit Error Rate (BER) (thin dash–dot curve) for the double-gravitational-lens INTERGALACTIC radio bridge between the supermassive black hole at the center of our Milky Way galaxy (called SgrAn) and the corresponding supermassive black hole located at the center of M32, the dwarf elliptical galaxy shown in Fig. 7 and a satellite of the Andromeda galaxy M31. We immediately see that this intergalactic radio bridge still performs about 1.5 orders of magnitude better than the ‘‘simple’’ radio bridge between the Sun and Alpha Cen A (thick solid curve, just the same as in Figs. 4 and 6). This new result paves the way to the feasibility of doing SETI among the center of the Milky Way and M32. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
C. Maccone / Acta Astronautica 78 (2012) 109–120
(5) Black hole antenna gain at the Ka band frequency:
The M106 astrophysical data are as follows:
GM106 ðnKa Þ 140 dB:
(1) Distance: ð41Þ
(2) Mass: M M106 ¼ 107 M Sun ¼ 1:988 1037 kg:
ð42Þ
(3) Schwarzschild radius, i.e. black hole event horizon: 2GM M106 ¼ 0:197 AU: c2
ð43Þ
(4) Antenna Gain of the black hole: GM106 ðnÞ ¼ 4p2
ð45Þ
These data yield the new Fig. 10 here below.
dSgrAn _M106 ¼ 25 106 ly:
r M106 ¼
117
r Schwarzschild_M106 : lðnÞ
ð44Þ
8. ‘‘Radio bridge’’ between SgrAn and the M104 ‘‘Sombrero’’ Galaxy M104 (NGC4594), again half way in distance between Andromeda and the VIRGO supercluster center (M87) The ‘‘Sombrero Galaxy’’ M104 (see Fig. 11, from: http://en. wikipedia.org/wiki/Sombrero_Galaxy) is again at a distance about half way between Andromeda and M87, namely 29.3 million light-years. In the 1990s, a research group led by John Kormendy demonstrated that a supermassive black hole is present within the Sombrero Galaxy. Using spectroscopy data from both the CFHT and the Hubble Space Telescope, the group showed that the speed of revolution of the stars within the center of the galaxy could not be maintained unless a mass 1 billion times the mass of the Sun, or 109 M, is present in the center. This is among the most massive black holes measured in any nearby galaxies. The following list of data thus emerges: (1) Distance: dSgrAn _M104 ¼ 29:3 106 ly:
Fig. 9. M 106 and its anomalous arms. Composite of IR, x-ray, radio and visible light view (X-ray—blue, Optical—gold, IR—red, Radio—purple; Image credit: NASA/CXC/University of Maryland. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
BER_bridge_Alpha_Cen (Ptr) BER_bridge_SgrAstar_M31P2(Ptr) BER_bridge_SgrAstar_M32BH(Ptr) BER_bridge_SgrAstar_M106BH(Ptr)
ð46Þ
Fig. 11. The Sombrero Galaxy (M104) as observed by the Spitzer. Credit: HST/NASA/ESA.
0.4 0.3 0.2 0.1 0 1×10–12
1×10–10
1×10–8 Ptr·watt
1×10–6
1×10–4
Fig. 10. Bit Error Rate (BER) (dash-dash thin curve) for the double-gravitational-lens INTERGALACTIC radio bridge between the supermassive black hole at the center of our Milky Way galaxy (SgrAn) and the corresponding supermassive black hole located at the center of M106 galaxy with anomalous arms shown in Fig. 9. We immediately see that this intergalactic radio bridge virtually performs just as well as the ‘‘simple’’ radio bridge between the Sun and Alpha Cen A (thick solid curve, just the same as in Figs. 4 and 6) since the new violet curve almost exactly overlaps the orange curve of the Sun–Alpha Cen A bridge. This result also paves the way to the feasibility of doing SETI among the center of the Milky Way and M106. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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(2) Mass: 9
M M104 ¼ 10 UMSun ¼ 1:98 10
39
kg:
ð47Þ
(3) Schwarzschild radius, i.e. black hole event horizon: r M104 ¼
2GMM104 ¼ 19:7 AU: c2
ð48Þ
(4) Antenna Gain of the black hole: r G104 ðnÞ ¼ 4p2 Schwarzschild_M104 : lðnÞ
ð49Þ
(5) Black hole antenna gain at the Ka band frequency: GM106 ðnKa Þ 160 dB:
ð50Þ
source of multiwavelength radiation, particularly radio waves. A jet of energetic plasma originates at the core and extends out at least 5000 light-years, which is why M87 is sometimes called ‘‘the jet galaxy’’ (Fig. 14). The stars in this galaxy form about one sixth of M87’s mass. They have a nearly spherical distribution, while the density of stars decreases with increasing distance from the core. The galactic envelope extends out to a radius of about 490 kly, where it has been truncated. Between the stars is a diffuse interstellar medium of gas that has been chemically enriched by elements emitted from evolved stars. Any dust formed within the galaxy is destroyed within 46 million years by the X-ray emission from the core, although optical filaments of dust have been observed. Orbiting the galaxy is an abnormally large population of about 12,000 globular clusters, compared to 150–200 globular clusters orbiting the Milky Way. Since this is the largest giant elliptical
These data yield the new Fig. 12 here after. This is of course the same as Fig. 10 except the new cyan curve for the BER of the Sombrero–Milky Way radio bridge, that again performs about two orders of magnitude better than the Sun–Alpha Cen A radio bridge, tough not as well as the M32–Milky Way one. 9. ‘‘Radio bridge’’ between SgrAn and the supergiant elliptical galaxy M87 (NGC4486) at the VIRGO supercluster center We finally reached the ‘‘top’’, i.e. the supergiant elliptical galaxy M87 located at the center of our own Local Supercluster of galaxies (the Milky Way and Andromeda are just at the outskirts of it, or, if you prefer, we are just at the periphery of the periphery) (Fig. 13). From http://en.wikipedia.org/wiki/Messier_87, the M87 Wikipedia site, we learn that M87 was discovered in 1781 by French astronomer Charles Messier (1730–1817). The largest and brightest galaxy within the northern Virgo Cluster, it is located about 53.5 million light years away from Earth. Unlike a disk-shaped spiral galaxy, M87 has no distinctive dust lanes and it has an ellipsoidal shape. At the core is a supermassive black hole, which forms the primary component of an active galactic nucleus that is a strong
BER_bridge_Alpha_Cen(Ptr)
BER_bridge_SgrAstar_M31P2(Ptr) BER_bridge_SgrAstar_M32BH(Ptr)
Fig. 13. The M87 elliptical supergiant galaxy at the center of the Local Supercluster of galaxies to which we belong.
0.4 0.3 0.2
BER_bridge_SgrAstar_M106BH(Ptr) BER_bridge_SgrAstar_M104BH(Ptr)
0.1 0 1×10–12
1×10–10
1×10–8 Ptr·watt
1×10–6
1×10–4
Fig. 12. Bit Error Rate (BER) (thin dot–dot curve) for the double-gravitational-lens INTERGALACTIC radio bridge between the supermassive black hole at the center of our Milky Way galaxy (SgrAn) and the corresponding supermassive black hole located at the center of the M104 ‘‘Sombrero’’ galaxy shown in Fig. 11. This intergalactic radio bridge performs two orders of magnitude better than the ‘‘simple’’ radio bridge between the Sun and Alpha Cen A (thick solid curve, just the same as in Figs. 4, 6, 8 and 10). This result also paves the way to the feasibility of doing SETI among the center of the Milky Way and M104. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
C. Maccone / Acta Astronautica 78 (2012) 109–120
galaxy near Earth and is one of the brightest radio sources in the sky, M87 is a popular target for both amateur astronomy observations and professional astronomy study. The M87 astrophysical data of interest to us are thus: (1) Distance: dSgrAn _M87 ¼ 53:5 106 ly:
ð51Þ
(2) Mass:
119
(3) Schwarzschild radius, i.e. black hole event horizon: r M87 ¼
2GMM87 ¼ 130 AU: c2
ð53Þ
(4) Antenna Gain of the black hole: r GM87 ðnÞ ¼ 4p2 Schwarzschild_M87 : lðnÞ
ð54Þ
(5) Black hole antenna gain at the Ka band frequency: 9
M M87 ¼ 6:6 10 UMSun ¼ 1:98 10
39
kg:
GM87 ðnKa Þ 169 dB:
ð52Þ
ð55Þ
The radio bridge between the huge black hole at the center of M87 and SgrAn is represented in the following Fig. 15 by the new brown curve. We thus see that the M87-SgrAn radio bridge performs better than anyone else, with the exception of the P2 one at the center of the Andromeda galaxy. It performs about 2.5 times better than the Sun–Alpha Cen A bridge. 10. Conclusion
Fig. 14. This Hubble Space Telescope photo shows the jet of matter ejected from M87 at nearly light speed and nearly towards us, as it stretches 5000 light years from the galactic core.
BER_bridge_Alpha_Cen(Ptr)
We have shown that telecommunications between galaxies up to 60 million light-years apart are indeed feasible with modest transmission powers if each galaxy’s supermassive black hole is exploited as a gravitational magnifying lens. This is an important step ahead with respect to ‘‘classical’’ SETI searches that assumed huge transmission powers to be available to ET’s. Human SETI searches might therefore concentrate in the directions of nearby galaxies where a supermassive and central black hole is known to exist. In addition, this line of thought clearly shows that the central massive black hole of every galaxy is by far the most important ‘‘resource’’ of that galaxy for SETI purposes. In fact, it is like the ‘‘central radio station’’ of that galaxy that every civilization living in that galaxy would
0.4
BER_bridge_SgrAstar_M31P2(Ptr) BER_bridge_SgrAstar_M32BH(Ptr) BER_bridge_SgrAstar_M106BH(Ptr)
0.3 0.2
BER_bridge_SgrAstar_M104BH(Ptr) BER_bridge_SgrAstar_M87BH(Ptr)
0.1 0 1×10–12
1×10–10
1×10–8
1×10–8
1×10–4
Ptr·watt Fig. 15. Bit Error Rate (BER) (average thick/thin solid curve) for the double-gravitational-lens INTERGALACTIC radio bridge between the supermassive black hole at the center of our Milky Way galaxy (SgrAn) and the corresponding supermassive black hole located at the center of the M87 ‘‘Jet’’ galaxy shown in Figs. 13 and 14. This intergalactic radio bridge performs about two and a half orders of magnitude better than the ‘‘simple’’ radio bridge between the Sun and Alpha Cen A (orange curve, just the same as in Figs. 4, 6, 8, 10 and 12). This result also paves the way to the feasibility of doing SETI among the center of the Milky Way and M87. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
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like to control in order to keep in touch with other aliens living in nearby galaxies. This idea also explains the Fermi paradox in some sense. In fact, one might argue that every important civilization in a galaxy would like to live close to the central supermassive black hole, rather than in the outskirts, as we Humans do with respect to our SgrAn. The conclusion is thus that current Human SETI searches should look for ET signals coming from nearby galaxies known to have both a supermassive black hole at their center and for SgrAn and its surroundings.
Acknowledgment The author is indebted to many colleagues for conversations and suggestions, but, in particular, he would like to
thank Paul Gilster for maintaining his terrific Centauri Dreams web site: http://www.centauri-dreams.org. References [1] C. Maccone, Interstellar radio links enhanced by exploiting the Sun as a Gravitational Lens, Acta Astronaut. 68 (2011) 76–84. [2] C. Maccone, Interstellar radio links enhanced by exploiting the Sun as a gravitational lens, paper #IAC-09.D4.1.8 presented by the author at the 60th International Astronautical Congress held at Daejeon, Republic of Korea, October 12–16th, 2009, and distributed to all participants as a CD-ROM file, but not published in a printed form. [3] C. Maccone, Deep space flight and communications—exploiting the Sun as a gravitational lens, a 400-pages treatise about the FOCAL space mission that embodies and updates all previously published material about FOCAL. ISBN 978-3-540-72942-6, published by Springer, Berlin, Heidelberg, New York, 2009. Library of Congress Control Number: 2007939976. & Praxis Publishing Ltd, Chichester, UK, 2009.