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MacCone C.,International Academy of Astronautics IAA
Acta Astronautica | Year: 2012

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 A 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 SgrA at about three light-years and having an estimated mass of 1,300 solar masses. These two big black holes could be our Galaxys antennae for communications with alien civilizations harboring in other nearby galaxies. We mathematically show that the following radio bridges may be created between SgrA and the supermassive black hole located at the center of the nearby galaxies: The SgrA-Andromedas (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.The SgrA-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.The SgrA-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.The SgrA-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.The SgrA-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 light-years. 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 SgrA 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. Source


MacCone C.,International Academy of Astronautics IAA
Acta Astronautica | Year: 2012

The Drake equation, first proposed by Frank D. Drake in 1961, is the foundational equation of SETI. It yields an estimate of the number N of extraterrestrial communicating civilizations in the Galaxy given by the product N=Ns×fp×ne×fl×fi×fc×fL, where: Ns is the number of stars in the Milky Way Galaxy; fp is the fraction of stars that have planetary systems; ne is the number of planets in a given system that are ecologically suitable for life; fl is the fraction of otherwise suitable planets on which life actually arises; fi is the fraction of inhabited planets on which an intelligent form of life evolves; fc is the fraction of planets inhabited by intelligent beings on which a communicative technical civilization develops; and fL is the fraction of planetary lifetime graced by a technical civilization. The first three terms may be called the astrophysical terms in the Drake equation since their numerical value is provided by astrophysical considerations. The fourth term, fl, may be called the origin-of-life term and entails biology. The last three terms may be called the societal terms inasmuch as their respective numerical values are provided by anthropology, telecommunication science and futuristic science, respectively. In this paper, we seek to provide a statistical estimate of the three societal terms in the Drake equation basing our calculations on the Statistical Drake Equation first proposed by this author at the 2008 IAC. In that paper the author extended the simple 7-factor product so as to embody Statistics. He proved that, no matter which probability distribution may be assigned to each factor, if the number of factors tends to infinity, then the random variable N follows the lognormal distribution (central limit theorem of Statistics). This author also proved at the 2009 IAC that the Dole (1964) [7] equation, yielding the number of Habitable Planets for Man in the Galaxy, has the same mathematical structure as the Drake equation. So the number of Habitable Planets follows the lognormal distribution as well. But the Dole equation is described by the first FOUR factors of the Drake equation. Thus, we may divide the 7-factor Drake equation by the 4-factor Dole equation getting the probability distribution of the last-3-factor Drake equation, i.e. the probability distribution of the SOCIETAL TERMS ONLY. These we study in detail in this paper, achieving new statistical results about the SOCIETAL ASPECTS OF SETI. © 2011 Elsevier Ltd. All rights reserved. Source


Maccone C.,International Academy of Astronautics IAA
Proceedings of the International Astronautical Congress, IAC | Year: 2014

The KLT (acronym for Karhunen-Loève Transform) is a mathematical algorithm superior to the classical FFT in many regards: 1) The KLT can filter signals out of the background noise over both wide and narrow bands. That is in sharp contrast to the FFT that rigorously applies to narrow-band signals only. 2) The KLT can be applied to random functions that are non-stationary in time, i.e. whose autocorrelation is a function of the two independent variables t1 and t2 separately. Again, this is a sheer advantage of the KLT over the FFT, inasmuch as the FFT rigorously applies to stationary' processes only, i.e. processes whose autocorrelation is a function of the absolute value of the difference of t1 and t2 only. 3) The KLT can detect signals embedded in noise to unbelievably small values of the Signal-to-Noise Ratio (SNR), like 10-3 or so. This particular feature of the KLT is studied in detail in this paper. An excellent filtering algorithm like the KLT, however, comes with a cost that one must be ready to pay for especially in SETI: its computational burden is much higher than for the FFT. In fact, it can be shown that no fast KLT transform can possibly exist and, for an autocorrelation matrix of size N, the calculations must be of the order of N2, rather than N∗log(N). Nevertheless, for moderate values of N (in the hundreds) the KLT dominates over the FFT, as shown by the numerical simulations. Finally, an important and recent (2007-2008) development in the KLT theory, called the "Bordered Autocorrelation Method" (BAM) is presented. This BAM-KLT method gets around the difficulty of the N2 brunt calculations and ends up in the following unexpected theorem: the KLT of a feeble sinusoidal carrier embedded into a lot of white stationary noise is given by the Fourier transform of the derivative of the largest KLT eigenvalue with respect to the bordering index. This basic result is fully proved analytically in the final sections of this paper. Source


MacCone C.,International Academy of Astronautics IAA | MacCone C.,SETI Permanent Study Group of the IAA
Acta Astronautica | Year: 2011

The gravitational lens of the Sun is an astrophysical phenomenon predicted by Einstein's general theory of relativity. It implies that if we can send a probe along any radial direction away from the Sun up to the minimal distance of 550 AU and beyond, the Sun's mass will act as a huge magnifying lens, letting us "see" detailed radio maps of whatever may lie on the other side of the Sun even at very large distances. The recent book by this author (Claudio Maccone, Deep Space Flight and Communications, 414 pages, Praxis-Springer, 2009) describes such future FOCAL space missions to 550 AU and beyond. In this paper, however, we want to study another possibility yet: how to enable the future interstellar radio links between the solar system and any future interstellar probe by utilizing the gravitational lens of the Sun as a huge antenna. In particular, we compare the bit error rate (BER) across interstellar distances with and without using the gravitational lens effect of the Sun. The conclusion is that only when we will exploit the Sun as a gravitational lens we will be able to communicate with our own probes (or with nearby Aliens) across the distances of even the nearest stars to us in the Galaxy and that at a reasonable bit error rate. Furthermore, we study the radio bridge between the Sun and any other Star that is made up by the two gravitational lenses of both the Sun and that Star. The alignment for this radio bridge to work is very strict, but the power saving is enormous, due to the huge contributions of the two stars' lenses to the overall antenna gain of the system. For instance, we study in detail: The SunAlpha Cen A radio bridge.The SunBarnard's star radio bridge.The SunSirius A radio bridge.The radio bridge between the Sun and any Sun-like star located in the galactic bulge.The radio bridge between the Sun and any Sun-like star located inside the Andromeda galaxy (M 31). The conclusion is that a radio interstellar communications network can indeed be built if the gravitational lenses of all stars involved are exploited. Then, the new question arises: has any advanced civilization already built such a radio telecommunication network? If so, our current and future SETI searches should be tuned-up to match with this newly realized possibility. © 2010 Elsevier Ltd. All rights reserved. Source


Maccone C.,International Academy of Astronautics IAA
Acta Astronautica | Year: 2015

Darwinian evolution over the last 3.5 billion years was an increase in the number of living species from 1 (RNA?) to the current 50 million. This increasing trend in time looks like being exponential, but one may not assume an exactly exponential curve since many species went extinct in the past, even in mass extinctions. Thus, the simple exponential curve must be replaced by a stochastic process having an exponential mean value. Borrowing from financial mathematics ("Black-Sholes models"), this "exponential" stochastic process is called Geometric Brownian Motion (GBM), and its probability density function (pdf) is a lognormal (not a Gaussian) (Proof: see Ref. [3], Chapter 30, and Ref. [4]). Lognormal also is the pdf of the statistical number of communicating ExtraTerrestrial (ET) civilizations in the Galaxy at a certain fixed time, like a snapshot: this result was found in 2008 by this author as his solution to the Statistical Drake Equation of SETI (Proof: see Ref. [1]). Thus, the GBM of Darwinian evolution may also be regarded as the extension in time of the Statistical Drake equation (Proof: see Ref. [4]). But the key step ahead made by this author in his Evo-SETI (Evolution and SETI) mathematical model was to realize that LIFE also is just a b-lognormal in time: every living organism (a cell, a human, a civilization, even an ET civilization) is born at a certain time b ("birth"), grows up to a peak p (with an ascending inflexion point in between, a for adolescence), then declines from p to s (senility, i.e. descending inflexion point) and finally declines linearly and dies at a final instant d (death). In other words, the infinite tail of the b-lognormal was cut away and replaced by just a straight line between s and d, leading to simple mathematical formulae ("History Formulae") allowing one to find this "finite b-lognormal" when the three instants b, s, and d are assigned. Next the crucial Peak-Locus Theorem comes. It means that the GBM exponential may be regarded as the geometric locus of all the peaks of a one-parameter (i.e. the peak time p) family of b-lognormals. Since b-lognormals are pdf-s, the area under each of them always equals 1 (normalization condition) and so, going from left to right on the time axis, the b-lognormals become more and more "peaky", and so they last less and less in time. This is precisely what happened in Human History: civilizations that lasted millennia (like Ancient Greece and Rome) lasted just centuries (like the Italian Renaissance and Portuguese, Spanish, French, British and USA Empires) but they were more and more advanced in the "level of civilization". This "level of civilization" is what physicists call ENTROPY. In Refs. [3] and [4], this author proved that, for all GBMs, the (Shannon) Entropy of the b-lognormals in his Peak-Locus Theorem grows LINEARLY in time. At last, we reach the new, original result justifying the publication of this paper. The Molecular Clock, well known to geneticists since 50 years, shows that the DNA base-substitutions occur LINEARLY in time since they are neutral with respect to Darwinian selection. In simple words: DNA evolved by obeying the laws of quantum physics only (microscopic laws) and not by obeying assumed "Darwinian selection laws" (macroscopic laws). This is Kimura's neutral theory of molecular evolution. The conclusion of this paper is that the Molecular Clock and the b-lognormal Entropy are the same thing. And, on exoplanets, molecular evolution is proceeding at about the same rate as it did proceed on Earth: rather independently of the physical conditions of the exoplanet, if the DNA had the possibility to evolve in water initially. © 2015 IAA. Published by Elsevier Ltd. All rights reserved. Source

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