Universe

UNIVERSE. - It is the totality of everything that exists in space and time; also called "world," which in itself means a part of the U.

In the earliest Greek poets the main problem was the origin of the world, generated from Chaos (Hesiod) or from Time (Orphics). As the problem became more precise among the first Ionian philosophers, Anaximander has the infinite succession of worlds generated from the infinite, ἀπειρον (H. Di Is, Frag. d. Vors., Berlin 1934, 12, A, 14). Infinite worlds originate from atoms ceaselessly in motion in the infinity of space and time, according to the atomistic doctrines (ibid., 54, A, 21). Plato teaches one world, made in imitation of the ideas by the Demiurge; and outside it are the eternal ideas, while Aristotle models the material U. according to his metaphysics: unique, eternal, arranged in concentric spheres moving around the earth, enclosed within the sphere of the fixed stars (De Caelo), moved by the unmoved mover, God, who is external to it (Phys., VIII). According to the school of Epicurus, and the infinite series of times, from the boundless chance whirl of atoms falling in infinite space infinite worlds arise (Epicurus, Ad Erod., 45, 73; Lucretius, De rerum natura, II, 1048 ff.; V, 528); the Stoa, on the other hand, thinks of a U. (τὸ πᾶν) that comprises the world (τὸ ὅλον) as unique, finite, round, mobile, compact, animated and, outside the world, the infinite, incorporeal void (Diogenes Laertius, VII, 140). The material U. is unique, according to Plotinus, emanated from the One, through the soul that orders and vivifies it; beyond it is the spiritual empyrean U. (Eum., III, 2). The Middle Ages, outside the outermost sphere of the material U., conceived according to the Aristotelian schema, but created and ordered by God, admits the empyrean world (St. Thomas, Dante Alighieri). St. Thomas affirms the unity and uniqueness of the U. as necessary, because all bodies must have a reciprocal spatial order (Sum. Theol., I, q. 47, a. 3); St. Bonaventure, on the other hand, affirms as possible, at least in the abstract, the existence of two or more U. without reciprocal spatial relation (In Sent., I, dist. 37, a. 2, q. 3); the same opinion was held by the nominalists G. Buridan, Albert of Saxony, Marsilius of Inghen, Paul of Venice, etc.

In the Renaissance N. Cusanus calls the U. a "contraction of divinity" (De docta ignor., II, 4) and denies, with G. of Occam, the incorruptible celestial matter of Aristotelianism; God is the center and circumference of the world, which has its center everywhere and its circumference nowhere, because God is everywhere and in no place (ibid., II, 12); therefore the U. is infinite in the privative sense, in that it has no limits (ibid., II, 1). Cusanus influenced Giordano Bruno, for whom the U. is infinite, with innumerable worlds (De immenso et innumerabilibus, I, II), is an "animal magnum," whose soul is God; and also R. Descartes, who calls his mechanistic U. indefinite, but in fact it is infinite (Princ. Phil., II, 21). Subsequently the concept of an infinite U. dominates in realistic conceptions, down to the whole of the 19th century.

In the Critique of E. Kant, the U. or world is the second idea of pure reason, it is "the mathematical whole of all phenomena and the totality of their synthesis" (Crit. d. rag. pura, Bari 1945, p. 343), and contains, according to H. Maier, four elements, the concept of the real, the system of the laws of being, the system of real individualities and the system of the origin of individuals (H. Maier, Wahrheit und Wirklichkeit, Tübingen 1926, p. 491).

In the theory of relativity, the U. is the set of all possible quadruples of the values of the coordinates x, y, z, t (that is, of all points) of space-time (O. Minkowski), or else the four-dimensional manifold constituted by the sets of physical events (P. Langevin). It is unlimited but finite, curved in four dimensions, just as analogously a spherical surface is in three dimensions.

In logic A. De Morgan (Formal logic or the calculus of inference, London 1847) introduced the concept of the U. of discourse: the set of elements and logical classes taken into consideration in a discourse; for example, the winged horse is an object of the U. of discourse of myth and not of zoology.

Roberto Masi

SCIENCE

From the restricted meaning it had in ancient times, with particular reference to the Earth, the word U. has progressively extended its meaning to include all celestial objects whose existence is in any case established. However, it is appropriate to distinguish at once between container and content. The container is the space-time platform, or the substrate, in which the matter that constitutes the content is distributed. Therefore, if by the word U. one wished to mean only this spatial platform, the subject would essentially concern mathematics and metaphysics, and upon it it would be possible to make all the hypotheses that logic and reasoning permit. Always with the understanding, naturally, that in the U. thus obtained it is possible to identify the physical space that surrounds us.

The first and most natural hypothesis that can be made is that this physical space is Euclidean, that is, such that the line representing the shortest path between two points (namely the geodesic of this space) is given by the straight line, as it is considered by ordinary geometry, called precisely "Euclidean." In that case the sum of the interior angles of a triangle is exactly equal to two right angles; from a point one and only one parallel can be drawn to a given line, etc.; that is, in this space all the properties that are deduced from Euclid's "fifth postulate" hold. In that case space is infinite and unbounded; the straight line too is infinite therein. Euclidean geometry adapts itself very well to the study of the physical world. Astronomers have availed themselves of it and still do.

The deductions they make with the use of this geometry accord fully with the results of observations. On the other hand, however, the space of the astronomers, that is, that part of space which astronomers have been able to explore, is a very small thing compared with the entire space constituting the U. It is perhaps because of this smallness of its that it appears Euclidean to us, just as in a gulf or an inlet the calm water appears flat, while it is known that that of the whole sea, to which the gulf belongs, is spherical. Therefore one could say that Euclidean geometry works well on a small scale, but perhaps would not adapt itself equally well on a large scale, giving to "large" and "small" the meaning just stated.

If the whole of space is not Euclidean, one must think that one of the other two non-Euclidean geometries that can be obtained must be adapted to it, the hyperbolic or the elliptic. In the first, the sum of the interior angles of a geodesic triangle is less than two right angles; in the second, it is greater; in the first, from a point one can draw infinitely many geodesics parallel to a given geodesic; in the second, from a point one cannot draw any parallel to a given geodesic. Hyperbolic space is infinite, as the geodesic therein is infinite; whereas in elliptic geometry space is unbounded but finite, as the geodesic therein is likewise finite. It remains to be seen to which of these types of spaces, conceived by mathematicians, the physical space in which we are immersed corresponds.

In the theory of relativity, Einstein suggested a type of space called "Riemannian" (after the mathematician Riemann), with four dimensions, in which time too is considered as a dimension (a second depth), and he showed that, while to a first approximation the geometry in this space is confounded with Euclidean geometry, so that it does not contradict the numerous and excellent deductions made with it, to a second approximation it would give the key to the explanation, not previously given, of certain phenomena and to the connection of many others, among which no relation had at first appeared. From a conceptual point of view, there would be a simple experiment to decide whether this geometry of Einstein is the right one, that is, whether it is the one that truly adapts itself to the description of the U., and it would consist in measuring the three interior angles of a cosmic triangle, having its vertices at three points of our U., and seeing whether their sum is less than, equal to, or greater than two right angles. But in practice such an experiment (already attempted, moreover, by Gauss) is perhaps illusory. It follows in fact from geometrical considerations that the difference between the sum of the three angles of a triangle and two right angles is proportional to the area of the triangle and is inversely proportional to the square of the radius of curvature of space. Since this radius of curvature (which would be infinite for Euclidean space) is immensely great, one would have to use triangles having extremely large sides, so that the difference considered might acquire values such as to be perceptible to our measuring instruments (without counting, moreover, the difficulty of carrying these instruments to other "fixed" points of the cosmic U.). In short, it seems that, for now at least, there is no possibility of deciding anything about the nature of the physical space in which we are immersed, that is, of the "container," whereas astronomers are in a position to say something more certain and positive about the second part of the question, namely about the "content" and therefore about the constitution of the cosmic U.

1. The metagalactic U. The galaxies

If until a few years ago the investigation of astronomers had been limited only to our own stellar system (the Milky Way, or Galaxy; v. below), at present one also speaks of the metagalactic U. or metagalaxy, that is, of what exists outside and beyond, up to the distance of a billion light-years (or perhaps even 2 billion light-years, as seems to appear from the "new scale of cosmic distances" [1953], which would double all extragalactic distances) where the telescope with a mirror 5 meters in diameter of Mount Palomar in California reaches. In the metagalaxy the unit is precisely constituted by the gigantic stellar systems, similar to our own, which in the telescope or on the photographic plate appear as nebulae (extragalactic nebulae), but are more modernly called galaxies, from the Greek name of the Milky Way, the Galaxy par excellence.

The metagalactic U. has so far appeared uniformly filled with galaxies, which are nevertheless at notably great distances from one another. The average number of stars in a galaxy seems to be of the order of 10 billion, although there are very great dispersions. There are supergiant galaxies, like the Milky Way, which can contain more than 100 billion stars, while there are also dwarf galaxies that have no more than 10 million. The average distances between the stars in galaxies are relatively much greater with respect to their diameters than the distances between galaxies are with respect to their dimensions. In a normal region of the metagalaxy, the distance between one galaxy and another is of the order of 100 galaxy diameters (in some richer region the average distance even falls below 10 diameters), whereas the average distance between star and star in the neighborhood of the Sun is greater than 10 million solar diameters (the density of the stars in a galaxy is like that of a wood in which the trees are 15 km from one another). Newton wrote: "He who ordered the U. has separated the fixed stars by immense distances, fearing that, by the force of gravitation, they should fall upon one another."

Although the average distribution of galaxies in space (at least in the part explored so far) is appreciably uniform, in some region of the metagalaxy many galaxies appear closely crowded together, forming true "clusters of galaxies." In the northern part of the constellation of Virgo there is a group of about 200 brilliant galaxies, which covers an area of more than 10 square degrees in the sky. Even more numerous, in the same region of the sky, are the less brilliant galaxies: more than 80,000 in 360 square degrees of sky down to stellar magnitude 17.6, and still several thousand fainter ones. North of the Virgo group there is another well-distinct and diffuse cluster of galaxies, in the constellations from Coma Berenices to Ursa Major and Canes Venatici. The most extensive cluster of galaxies is found in the southern sky, in the constellation of Centaurus, and seems to have actual dimensions greater than 5 million light-years.

The Milky Way too is part of a "local group" of galaxies, to which belongs the Andromeda nebula (at a distance of 1.5 million light-years [according to the new scale], which is the only galaxy barely visible to the naked eye, since it is a supergiant galaxy) and another dozen or so smaller nebulae. Of the whole group, at least half are irregular galaxies (not spirals) and 5 of them are very brilliant. Among the latter are to be included the two Magellanic Clouds, which are the galaxies closest to us (at 100,000 light-years the Large Cloud and at 200,000 light-years the Small Cloud), so much so that some astronomers considered them outright satellite galaxies of the Milky Way.

Galaxies appear to observation quite varied in dimensions and in structural organization; nevertheless the inaccessibility of the greater part of them, and therefore the scant knowledge that is still had of them, means that they are classified into a relatively small number of types: elliptical, spherical, spiral and irregular. But the great majority appear, even in long-exposure photographs obtained with the largest instruments, as small indistinct specks; whence the more distant objects can be classified only on the basis of their apparent dimensions and on the basis of the existence or not of a certain central condensation. Fortunately, the few thousand nearer galaxies, observable therefore with greater detail, have permitted the analysis and a fairly detailed classification of these celestial objects. It is then natural to think that they constitute a truthful sample of all the galaxies existing within a billion light-years. It is thought that at the maximum distance reached so far, the number of photographable galaxies is at least 200 million (in a sphere of 100 million light-years from the Earth at least a million galaxies).

In galaxies not all matter is condensed into stars; this depends on the evolutionary stage in which the galaxy finds itself, that is, on its age. In the Milky Way it is thought that beyond the 100 billion stars there is still diffuse matter, in the form of gas and of extremely minute cosmic particles, for a total mass perhaps greater than that condensed into stars. But the Milky Way is a giant galaxy; an average galaxy will have a mass of 10 billion times that of our Sun (which is an average star). Whence one may infer that the average density of the matter of the metagalactic space explored so far is of the order of 10^{-30} to 10^{-31} grams per cubic centimeter. Such a value naturally has only the meaning of an order of magnitude; some astronomer in fact considers it too small, assigning in the end to the average density of the matter of all space the value of 10^{-28} gr/cm³. That is, the U. is on average substantially empty, enormously emptier than it is possible to obtain in terrestrial laboratories.

2. The Milky Way (Galaxy)

As has already been mentioned, it is the stellar system, one of the galaxies of the U., to which our Sun belongs. This galactic system presents itself as an agglomeration of stars and of diffuse matter (gas and interstellar smoke) of roughly spheroidal shape and with very strong flattening, which rotates about an axis perpendicular to the galactic plane, defined by the luminous ring of the Milky Way. It is drawn in the sky as a faintly luminous band along a great circle that forms with the celestial equator an angle of about 62°.

In the telescope, the Milky Way appears constituted by a multitude of stars, individually invisible to the naked eye; photography reveals in it veritable stellar clouds. Such apparent concentration of the stars in the median plane of the Milky Way is however due only to an effect of perspective, depending on the position of the Sun within the system itself. The Sun is in fact located more or less in the equatorial plane of the system, but very far from the center, at a distance from it of about 30,000 light-years. In the sky, the center of the Galaxy is projected in the direction of the constellations of Scorpio-Sagittarius, where indeed the Milky Way appears richer and densely populated with stars. The dimensions of the Galaxy considered most probable are the following: diameter of about 100,000 light-years, thickness at the center about 10,000 light-years. In reality a certain number of stars have still been found that should be situated outside this lenticular system, constituting as it were a sort of halo; therefore the equatorial diameter of the whole system would come to exceed 150,000 light-years and the thickness 120,000, that is, the Galaxy would in the end be almost spherical.

Recent research also seems to show that the Galaxy has in the end a decidedly spiral shape, thus bringing out its analogy with the other external galaxies, in which the spiral shape predominates. Such conclusions were recently (1952) supported by the actual discovery of the spiral arms of the Galaxy, a discovery obtained both directly (Bok and collaborators of the Harvard Observatory) and by means of the observation of the hydrogen emissions, by such arms, of radioelectric waves (at the wavelength of 21 cm), which, arriving as far as our Earth after having passed the ionospheric barrier, have been revealed by suitable radio-receiving apparatus.

All around the galactic system proper there are then the globular clusters, singular clusters of stars of appreciably spherical shape and with very strong central concentration constituted by a very great number of stars, which many times, not even with the largest telescopes, can be distinctly separated. About a hundred (exactly 103) globular clusters are known, and there are good reasons for holding that they are all that exist. Globular clusters seem to accompany all galaxies: Hubble and Baade have proved the existence of at least 300 similar objects around the Andromeda nebula, which is a galaxy similar to the Milky Way (although of much larger dimensions, according to the "new scale"). Of the globular clusters around our Galaxy, the best known is the cluster of Hercules (named after the constellation in which it is projected in the sky), which is also visible to the naked eye as a small luminous patch. The great telescopes have revealed in it more than 40,000 stars outside the extremely dense and unrealizable central nucleus. In the sky it appears under a diameter of about 30°, that is, of the apparent diameter with which the Sun and the Moon are shown to us. The two brightest globular clusters, however, are found in the southern celestial hemisphere. Of all the clusters, the two nearest are at a distance of 40,000 light-years and the farthest at 500,000 light-years. They are, however, all concentrated around the Galaxy, so much so that the galactic center coincides perfectly with the centroid (barycenter) of the globular clusters (Shapley).

Besides these globular clusters, generally external to the Galaxy, there are then other clusters of stars, which are called precisely galactic clusters, both because they are generally inside the system (the farthest is at about 40,000 light-years, that is, appreciably at the distance of the nearest globular cluster), and because they are generally close to the equatorial plane of the Galaxy. They are also called open clusters, because of their less dense and compact constitution than the globular clusters, from which they are also distinguished by the "quality" of the stars that compose them and by the number of these stars, which are in general only a few tens or at most a few hundred. Such stars moreover present common physical characteristics and a noticeable equality of their movements in space. More than 300 galactic clusters are known; the one nearest to the earth is that of the Hyades in the constellation of Taurus, which is located at 108 light-years. Very well known too is the cluster of the Pleiades, clearly visible also to the naked eye. The study of galactic clusters is always very interesting, and from it fundamental discoveries have been obtained at various times, such as that (1950) of the absorption of light in interstellar space, which then led to the discovery of interstellar amorphous matter.

Interstellar matter is found diffused almost generally throughout the Galaxy, but particularly in the vicinity of its equatorial plane, where it forms a denser and more noticeable layer of the thickness of a few hundred light-years. Such matter is composed of gas and dust. The existence of interstellar gas is demonstrated by the spectra of distant stars, which present characteristic absorption lines, called precisely "interstellar lines", or "stationary" lines, since they present a Doppler shift different from the other lines due to the star itself, the radial motion of the interstellar gas being naturally generally different from that of the stars. By such methods calcium, sodium, potassium, titanium have been identified, and then also molecular compounds formed of carbon, hydrogen, nitrogen. But the most abundant element in interstellar matter (as also in matter already condensed into stars) is hydrogen, which however has been revealed only recently (1939), since its absorption lines all fall in the ultraviolet regions of the spectrum, which our atmosphere totally absorbs, and also because interstellar hydrogen must generally be found deprived of its single electron owing to the ultraviolet irradiation of the hottest stars that are diffused throughout the Galaxy. However, if a hydrogen nucleus encounters an electron, the recombination will be accompanied by the emission of radiation, which can be observed. Moreover, from interstellar hydrogen comes also a good part of the so-called galactic radio waves that are received with the appropriate "radio telescopes" (v. below). O. Struve gives the following relative abundances for cosmic matter: in stars, 6 atoms of calcium, nitrogen and oxygen, compared with 500 atoms of helium and 5000 of hydrogen; in interstellar matter, in a million cubic inches, 10 million atoms of hydrogen, 100 of calcium, 60 of sodium, 4 of potassium, 2 of titanium.

As regards then the presence of interstellar dust (smoke), proof of it is had through the general and selective absorption that it exerts on the light of distant celestial objects. Although the measurements are extremely difficult and delicate, in the regions where interstellar matter is most abundant (galactic plane), one finds on average that 50% of the light is absorbed after a path of 3000 light-years. Moreover the selective absorption (reddening of distant stars) depends on the dimensions of the absorbing particles, which has led to attributing to them a diameter of the order of a tenth of a micron. According to some astronomers, such particles would be composed of metallic corpuscles, such as iron. The average density of interstellar matter is extremely low, of the order of 10⁻²⁴ gr/cm². A volume as large as the Earth would represent barely the weight of a kilogram. On the whole, one atom of interstellar matter per cubic centimeter. But since the distances between the stars are immensely great, in the end, the total mass of the matter diffused in the Galaxy would be more or less equal to the mass of all the stars. In it, the mass of the interstellar dust (which would be found only in limited places) would be a little greater than the mass of the gases.

Many times these interstellar gases are found gathered and condensed in the form of nebulae, which appear dark if they are not excited by any star, and constitute in that case thick clouds of absorbing matter; they are nothing other than the numerous "black holes" that appear here and there in the luminous face of the Milky Way. More than 1500 dark nebulae have been counted so far, among them the Coalsack in the southern sky, near the Southern Cross, which is located at only about 50 light-years, and then the dark clouds in the constellation of Ophiuchus, also very close, and still the dark nebulae of Cygnus at 250 light-years.

Many times these gaseous clouds become luminous because the gas is excited by some brilliant stars that are found in the vicinity and become luminous by luminescence. These are the galactic nebulae or diffuse nebulae, which appear in the form of more or less vast and more or less dense luminous patches. The most important is the nebula of Orion, visible also to the eye in the constellation of the same name. The spectrum of diffuse nebulae is generally composed of a certain number of bright lines belonging to hydrogen, helium, carbon, nitrogen.

The origin of some lines remained for a long time unknown and mysterious, so much so that it was attributed to a hypothetical element, the "nebulium", which is not found on Earth. Then it was discovered (Bowen, 1929) that these mysterious lines are due to oxygen ionized once or twice, and precisely to the so-called "forbidden lines", which are not obtained under the usual laboratory conditions, because they require the absolute absence of collisions with atoms of matter and therefore an extremely weak density of the gases. Some diffuse nebulae, such as the one that surrounds the stars of the Pleiades, give instead an absorption spectrum, analogous to that of the stars. In this case we are dealing with "reflection nebulae", because they simply reflect the light of a central star, which is not hot enough to emit ultraviolet radiation that causes the luminescence of the gas.

Besides the diffuse nebulae, the Galaxy also contains planetary nebulae (of which the ring nebula in Lyra is characteristic), so called because they have the appearance of a small luminous disk, elliptical or noticeably circular, very similar to the appearance of a planet. About a hundred of these objects are known, all of faint luminosity. At their center there is generally a very hot star. The origin of these singular celestial objects is still mysterious; some think that they are the remnants of ancient novae, the present gases having been expelled from the star at the time of their explosion.

3. The stars

But the fundamental constituents of the Galaxy are the stars, which are made up of colossal gaseous globes produced by the concentration and condensation of cosmic gas, and within which is produced all the energy that they radiate into space.

From the point of view of appearance (from our Earth), the stars (as indeed also the other galactic and extragalactic objects), while participating in the diurnal motion of the celestial sphere, do not show appreciable displacements in their respective positions or in the configurations they present in the sky (constellations). As such, they were called by the ancients stellae fixae to distinguish them from the planets or "wandering stars" (the ancients counted among these also the Sun, which instead is itself a star).

The stars, in the sky, are also distinguished from the planets by their generally more vivid and brilliant light, by their greater scintillation, and by not presenting — whatever the size of the telescope — an apparent disk or a perceptible diameter (naturally abstracting from the inevitable diffraction disk). This is because, given their very great distance (the nearest star, Proxima Centauri, is at a distance of 4.3 light-years, a light-year being the distance traveled by light in one year, that is, about 10 thousand billion km, exactly 9,461.10¹² km), even the very strongest magnifications can only increase the light they send out. In fact the stars are not fixed in space, but are endowed, besides their apparent motions (diurnal rotation and annual revolution), with small angular movements (called stellar proper motions; the record is held by Barnard's "Arrow Star," whose proper motion is 10'.2 per year), which correspond, given the great stellar distances, to spatial velocities sometimes extremely high.

The apparent brightness of the stars is measured in stellar magnitudes, denoted by numbers on a decreasing scale starting from the most luminous (−2, −1, 0, 1, 2, 3...). The ratio of light between one magnitude and the next is equal to about two and a half times (precisely 2.2+2). With the naked eye (for a sharp sight and on a dark night) stars are visible down to the 6th magnitude. With the largest telescope (the 5 m at Palomar) and by means of long-exposure photography, one has reached down to the 25th magnitude.

As regards the nomenclature of the stars, only the most luminous (about a hundred) have received a proper name (generally of Arabic, Egyptian or Oriental origin), while the others are indicated by the letters of the Greek alphabet followed by the name of the constellation to which they belong, e.g. α Orionis (Sirius). This too applies only to stars visible to the naked eye (about 5,500 in both celestial hemispheres); for all the others one indicates the star catalog in which they are contained and their respective order number, or else one gives their celestial coordinates (right ascension and declination, referred to a given equinox), generally adding the symbol of the constellation that contains them.

All the knowledge we have about the physical characteristics of the stars depends on the results of spectral analysis, which, inaugurated by G. Donati (1860) with direct-vision ocular prisms, immediately after G. R. Kirchhoff with the discovery of the Fraunhofer lines had opened the way to the chemical analysis of celestial bodies (1859), then received a decisive impulse from Fr. A. Secchi S.J., to whom the first spectral classification of the stars is due. Stellar spectra generally present (like the Sun) a bright continuous background furrowed by dark lines, which come from the absorption of light operated by the gases contained in the "atmosphere" of the stars, while the continuous spectrum is generated by the deeper layer, open to our direct investigation and called, as in the Sun, the "photosphere." From Fr. Secchi's first examinations, it was expected to find a different spectrum for each star, but it was soon noticed that all spectra could be classified into a few "types" or "spectral classes," which show progressive variations of certain characteristics, these being then directly linked with the physical characteristics (color, temperature, etc.) of the stars. The spectral classes are designated arbitrarily by capital letters, which are in the order O, B, A, F, G, K, M, there being then in each class successive subdivisions expressed by the numbers from 0 to 9.

Generally speaking, the spectral class of a star depends essentially on its surface temperature. Thus, whereas the ancient astronomers believed that the relative intensity of the spectral lines depended on the abundance of the elements, and that there were therefore helium stars, hydrogen stars or stars with metallic components, it is known today that the spectral variations indicate variations of temperature — and, to a lesser degree, variations of pressure — rather than a real difference of chemical constitution. This depends on the fact that, for example, the lines of hydrogen appear intense only when the hydrogen atoms that produce them are in physical conditions such as to produce an intense absorption, and this occurs only when the temperature is sufficiently high. In general, the photospheric temperature of the stars decreases progressively from class O to class M, while the number of absorption lines increases.

Some stars show, superimposed on the continuous spectrum, bright lines or "emission lines" in place of the usual dark Fraunhofer lines. Generally these are lines of hydrogen, and these lines are found both among the hottest stars and among the coldest, while they are absolutely exceptional among the intermediate ones.

Spectral analysis of the stars makes it possible to investigate not only their qualitative structure but also their quantitative one, that is, to evaluate the relative abundances of the various chemical elements. Although the results are not yet definitive, two important facts seem conclusively established: 1) in the stars, as in the Sun, only the chemical elements known on Earth are found: for those among them that have not yet been found directly, their absence is explained by considering that they are either very rare elements or heavy elements (and therefore probably located in the central regions of the stars), or else elements whose spectral lines fall in regions of the spectrum that are still inaccessible; 2) hydrogen is by far the predominant element in the stars, forming in the majority of them at least 80% of all the atoms. Moreover, there seems to be no reason to think that the chemical composition of the stars varies from one to another, and therefore it should be analogous to that fairly well established for our Sun, which naturally — given its great proximity — is the best studied and best known star. Nevertheless, some discrepancy seems to persist, but it is limited to a few very hot stars (of spectral class O) or to cold stars (class M, and the other special classes N, R, S characterized by spectral bands analogous to those of class M). In short, it would be erroneous to deduce from the examination of a stellar spectrum that a given element is predominant in the spectrum of a star merely because its spectral lines are very intense there; nevertheless, the intensity of these lines depends, at least in part, on the abundance of the corresponding element. And here, briefly, are the main characteristics of the various spectral classes, beginning with class B, since the first class O comprises only a small number of stars still hotter than B.

Class B: blue stars, with surface temperatures of the order of 30,000°; the spectral lines, few in number, belong to hydrogen and helium. The metallic lines are weak or absent, because owing to the high temperature the metals become ionized and could give intense lines only in the regions of the far ultraviolet, which is not observable. Examples: Rigel (β Orionis), the three stars of Orion's belt, Spica (α Virginis).

Class A: white stars, with surface temperatures from 16,000° to 20,000°; the spectrum is characterized by the lines of hydrogen, which appear broad and diffuse. Examples: Sirius (α Canis Maioris), Vega (α Lyrae), Castor (α Geminorum).

Class F: white-yellowish stars, with temperatures of the order of 10,000°. The hydrogen lines are less intense than in A and the metallic lines begin to appear; the most intense are the two ultraviolet lines of ionized calcium, which, according to the Fraunhofer nomenclature used in solar spectroscopy, are designated by the letters H and K. Examples: Procyon (α Canis minoris), Canopus (α Argus).

Class G: yellow stars with temperatures close to 7000°; the Sun belongs to this class (temperature ca. 6000°). The spectrum is characterized by very intense metallic lines: some, such as H and K, are distinctly more intense than the hydrogen lines. Examples: the Sun, Capella (α Aurigae).

Class K: yellow-orange stars, with temperatures of the order of 4000° and a spectrum analogous to that of G; however, the lines of neutral metals increase in intensity relative to those of ionized metals. Moreover, certain spectral "bands" begin to appear, typical of molecules not dissociated into atoms. Examples: α Bootis, Aldebaran (α Tauri).

Class M: red stars with temperatures of ca. 3000°. The spectrum has a "fluted" appearance (the "columnar" aspect of Fr. Secchi), due to the presence of numerous absorption bands. The violet end of the spectrum is very weak. Examples: Betelgeuse (γ Orionis), Antares (α Scorpii).

The intrinsic luminosity of the stars varies; it is expressed by means of their absolute magnitude, that is, the stellar magnitude that each star would have if it were brought to a given distance, the same for all, arbitrarily chosen as 10 parsecs (the parsec, an abbreviation of parallax equal to one second [of arc], is a unit of measurement for great celestial distances, equal to that which a star would have if it had a parallax [the angle under which the semi-major axis of the Earth's orbit would be seen from the star] of one second of arc: a parsec is therefore equal to 3.26 light-years, that is, to ca. 30 thousand billion km). The Sun therefore has an absolute magnitude of - 4.85, which is equivalent to saying that, if it were at a distance of 10 parsecs, it would appear only as a rather faint star, barely visible to the naked eye. Many other stars are intrinsically more luminous than the Sun; the record is held by a star that is more than a billion times more luminous than the Sun, and in the opposite sense by a star with absolute magnitude + 19, that is, ca. one million times less luminous than the Sun.

However, the luminosities of the stars are not distributed at random; in fact, by relating these luminosities (or the corresponding absolute magnitudes) to the respective spectral classes, one obtains a singular characterization defined by the so-called "Hertzsprung-Russell diagram," in which the majority of the stars are distributed along a rather narrow strip that crosses the figure almost diagonally, and to which the name "main sequence" is given. A relatively small number of stars is then distributed along a second almost horizontal strip between spectral classes F and M. This second strip joins the first toward the point that corresponds to the star Sirius of class A o. Since such stars are intrinsically more luminous than those, of the same spectral class, belonging to the main sequence, they are called giant stars, while the corresponding ones of the main sequence (at least those of classes F to M) are called dwarf stars. The Sun, which belongs to the main sequence and is located almost at the center of the diagram, must therefore be considered a yellow dwarf star. The gap between giants and dwarfs is mainly notable for the colder stars, so the luminosity ratio between the dwarf stars of class M o, such as Proxima Centauri, and the red giants of the same class reaches a million. This Hertzsprung-Russell diagram is substantially verified for the stars that are found in the regions of the Galaxy where the Sun is found, that is, in the regions of the nebular "arms." These are called stellar population I (Baade), to distinguish them from another category of stars (population II), which instead predominate in the central regions (nucleus) of the Galaxy, in globular clusters, etc., and which present a "spectrum-luminosity diagram" different from the classic Hertzsprung-Russell one.

Some stars, finally, present characteristics that correspond neither to the main sequence nor to the branch of the giants of the diagram. They are either stars even more luminous than the giants (40-50 times more), and to which the name supergiants is given (e.g., Antares of class M o and Rigel of class B 8); or else also (fairly numerous and widespread) very singular stars, which have a white color and extremely dense matter gathered in a small volume, whence they are called white dwarfs (e.g., the companion of Sirius). The mass of the white dwarfs is of the order of that of the Sun, while their volume is rather similar to that of a planet. Their density is therefore extremely high, reaching even 100,000 times that of water. Such hyperdense matter, constituted by atomic nuclei and electrons tightly packed together, exhibits characteristic properties quite different from ordinary stellar matter. This matter (called "degenerate" matter, or also "Fermi gas," after the physicist who first studied it) proves to be compressible despite its great density, and the pressure within it is no longer given, as in ordinary stellar matter, by the perfect gas equation, but instead is appreciably independent of temperature. This matter, moreover, does not radiate energy; but the weak radiation that we receive from these stars is due to a thin outer envelope of normal matter surrounding the inner core, from which derives the weak luminosity of these stars, which has so far made their discovery rather difficult. Nevertheless, the statistical investigations carried out in recent times, on the assumption that the percentage of white dwarfs observed in the vicinity of our Sun (where it is naturally easier to discover them) should reasonably be extended to the entire Galaxy, would give for this singular class of stars an enormous number, on the order of several billion. This means that there would be approximately 8-10 white dwarfs for at least every hundred stars (Luyten, 1952).

From knowledge of the absolute magnitude of stars and their apparent luminosity, one can easily arrive at an estimate of stellar diameters (which, moreover, can often also be measured directly by means of stellar interferometers). Thus enormous diameters have been found for red giants and small diameters for red dwarfs. Among the former, Capella of class G (like the Sun), Arcturus of class K or and Aldebaran of class K 5 have diameters respectively 16, 22 and 35 times greater than that of the Sun.

Even larger are the supergiants: Antares has a diameter equal to about 400 times that of the Sun (and therefore a volume 60 million times greater), so much so that the Earth's orbit around the Sun would fit comfortably within it. The record is held by the star α Aurigae, which has a diameter 2000 times greater than that of the Sun, and therefore greater than that of the orbits of Jupiter and Saturn. Red dwarf stars, on the other hand, generally have dimensions smaller than the Sun, such as Proxima Centauri, which has a diameter 30 times smaller. However, the smallest stars are the white dwarfs: the satellite of Sirius has a diameter only a few times that of the Earth. Dwarf stars, yellow or red, are the most numerous, but giants are far more luminous than dwarfs and form the majority of stars visible to the naked eye.

The mass of stars can be determined directly only for a very small number of them (about 500), and precisely only for those "double stars" (v. below) whose orbital elements are well known.

From these observed values it has nevertheless been possible to derive (Eddington, 1924) a general law: the absolute magnitude of stars varies regularly as a function of their mass (mass-luminosity relation). This law has made it possible to evaluate the masses of the majority of stars (with the exception of white dwarfs), finding that they have a mass of the same order of magnitude as the Sun, and precisely between 1/5 and 5 times the mass of the Sun. The record is held by the star of Plashett (discovered in 1921), which would have a mass 139 times greater than that of the Sun. It follows therefore that red giant stars, which have such a great volume, have a very low density. Antares has a density 50,000 times less than that of ordinary air, that is, equal to a "good vacuum" obtained in our laboratories.

Although spectral analysis allows us to know only the constitution of the surface layers of stars, research in theoretical astrophysics has made it possible to obtain fairly satisfactory and conclusive information about the internal constitution of stars, since stellar matter enjoys relatively simple properties. This matter, given the nearly complete ionization of its atoms, which have lost almost all the electrons surrounding the nucleus, behaves like a gas even when its density is equal to or greater than that of water. In stellar matter, almost completely ionized, the space occupied by the atoms is very small compared with usual conditions, so that this matter must prove compressible up to densities much higher than those of ordinary liquids and solids and therefore still retain the properties of gases. Moreover, again because of this highly advanced ionization, stellar matter exhibits the singular property of having a density almost independent of its composition. In fact, the mean atomic mass of an ionized gas is about 2, whatever the nature of the atoms composing it. For example, iron has an atom whose atomic mass is 56, being formed of a nucleus and 26 electrons. When it is completely ionized, it gives rise to 27 particles, whose mean atomic mass is precisely 56/27=2.1. Only hydrogen and helium give rather low values upon ionization, but their effect is compensated, on the whole, by the incomplete ionization of the heavy elements. On the other hand, in the internal equilibrium of stars, radiation pressure intervenes, which increases with the fourth power of the temperature. This pressure therefore contributes significantly to supporting the weight of the outer gaseous layers of the star.

In the end, it has been possible to determine and calculate the temperature, pressure and density that must be found in the central regions of stars. In the case of the Sun, for example, there is a central temperature on the order of 20 million degrees, a density 80 times that of water (the mean density of the Sun is only 1.41) and a pressure of 100 billion kg/cm². Such central temperatures are appreciably of the same order for all stars of the main sequence (from 15 to 30 million degrees), while they are distinctly lower (1-5 million degrees) for red giants and supergiants.

4. Double and variable stars

Many stars (it is thought even one in three or four), examined with a telescope, or with spectroscopic or photometric methods, prove to be composed of two nearby stars, e.g. Castor, Antares, Rigel. Sometimes the proximity is only apparent, depending on the fact that the two stars happen to be aligned with the Earth ("optical doubles"); but in the majority of cases, the two stars form a real physical system, being linked to each other by the force of Newtonian attraction, as are the Earth and the Moon or the Sun and the planets. They then form a double star or a binary system; analogously there are ternary, quaternary systems, etc. Double stars that can be seen and studied directly, either with a visual telescope or on a photographic plate, are called visual double stars. Many double stars, however, are so closely approached to each other that no telescope can separate them, while their duplicity is revealed only by the spectroscope, which shows the superposition of two distinct spectra, and they are called precisely spectroscopic doubles. Finally, a third category of double stars is constituted by the binaries or photometric doubles or, better still, eclipsing doubles, since the orbit of the double presents itself to us in profile or nearly so, in such a way that one of the components periodically hides the other during the revolution that the satellite star performs around the principal one. Of these latter, the best known is Algol (β Persei), whose light variations (therefore eclipsing binaries are also false "variables") were discovered in 1783, but whose name, which in Arabic means "the demon," would indicate that they were known for a very long time before.

Historically, the first known (visual) double star is Mizar (η Ursae Maioris), whose duplicity was discovered by Fr. Riccioli around the middle of the 8th century. Sirius, the brightest star in the entire sky, is also a double star, whose companion is a white dwarf.

Variable stars, or simply variables, are those stars whose brightness is subject to continuous variations. The first known variable was Mira Ceti (ο Ceti), discovered in 1596 by Fabritius. At present many thousands of variables are known, and their number is continually growing. Besides eclipsing variables, which are in fact double stars, the "physical" variables, in which the variation in brightness is intrinsic and real to the star itself, being accompanied by corresponding variations in temperature and spectral class, can be divided into two fundamental groups: regular or periodic variables and irregular variables. The most important are the former, in which the light variations occur regularly according to determined periods. According to the length of this period they are further divided into three great classes: short-period (about half a day), less short (about a week), and long-period (about 280 days). The short-period ones are also called "cluster variables" because they are particularly numerous in globular star clusters, although they are also found in other regions of the sky. None of them is visible to the naked eye. The most important, however, are those of the second class, also called cepheids (from the name of the typical star of the group, δ Cephei, whose stellar magnitude varies regularly by 0.7 units in 5.37 days), whose brightness variations are due to genuine stellar pulsations, that is, to periodic expansions and contractions of the star's atmosphere (or at least of its outermost layers), the cause of which is nevertheless still unknown. These pulsations are accompanied by regular variations in the star's temperature, which produce the observed brightness variations. At the same time, corresponding variations of the spectrum and regular displacements of the spectral lines occur. The cepheids are particularly important because a law of proportionality exists between the variations of their apparent luminosity and the period (Miss H. Leavitt's law, discovered in 1910). And since this law then translates into a relation between absolute magnitude and period, it allows one to determine their distance from the examination of the photometric variations of the cepheids alone. Moreover, since such stars are found and can be observed even in distant celestial objects, such as globular clusters and extragalactic nebulae (external galaxies), from the study of cepheids considerable information is obtained about the distances of these celestial objects. Precisely from a more accurate determination of the "zero-point" of the scale of cosmic distances, based on the observation of cepheids in the Andromeda nebula, the necessity of the "new scale" was shown (Baade, 1952-1953), which would double all the distances and dimensions of extragalactic objects.

Among the regular long-period variables, which are generally red giant stars of spectral class M, is Mira Ceti, the first variable discovered, which has a light variation period of about 330 days with variations in luminous intensity in a ratio of 1 to 250. These variables too are perhaps pulsating stars, although the theory of pulsations is not yet able to explain all their characteristics. Note the very remarkable fact that almost all (physical) variable stars are giant stars.

5. New and supernew stars

Novae (formerly also called "temporary stars") are the name given to particular stars that suddenly undergo an exceptional increase in brightness, which sometimes brings them to become visible even to the naked eye (whence the name "new stars" assigned to them by the ancient astronomers). After this rapid explosion, the nova slowly returns to the initial conditions of a telescopic star. The variations in stellar magnitude undergone by the star during the explosion phase sometimes reach 13 magnitudes, which would correspond to an intrinsic increase in luminosity of the order of 50-100 thousand times its original one. The cause of the phenomenon is not yet known with precision, but it would seem natural to think of an instability of the star that produces in it a sort of explosion with ejection and expulsion of the outermost layers of its atmosphere. This would seem to be proved by the spectral variations that always accompany the light variations of the nova. Moreover, in some of them the phenomenon of the explosion repeats periodically (recurrent novae).

On the other hand, the phenomenon of novae seems much more frequent than the appearance of the most spectacular novae would suggest. Over a hundred new stars have been recorded (generally by photography) in the last fifty years; but certainly very many others remain unknown. So that, in the end, it is thought that at least 20-30 novae explode every year in our Galaxy. Note furthermore that nearly all the observed novae seem to favor the regions of the galactic plane. Given the high frequency of the phenomenon, some astronomers have been led to the conclusion that almost all the stars of our galactic system must have passed through the nova stage in the course of the last billion years, or else, if the phenomenon cannot affect all stars, those observed must have suffered it repeatedly, and therefore the majority of novae would be recurrent.

Many times the phenomenon of the explosion becomes more conspicuous and exceptional, the star reaching in a short time a luminosity even a hundred million times greater than the Sun, that is, as luminous as an entire galaxy. So much so that many times the phenomenon becomes observable even in other galaxies. One then speaks of supernovae, and indeed the tendency of modern astronomers is to classify supernovae in a decidedly different way from that of ordinary novae, considering them as a completely separate and distinct class, showing clearly different spectral and luminosity characteristics. Certainly a supernova must have been the famous star of Tycho Brahe, which appeared suddenly in 1572 in the constellation of Cassiopeia and became visible even in broad daylight. Another supernova must also have been the star that appeared in Oct. 1604 (this time observed by Galileo), and finally also the famous star observed by the Chinese in 1654, which gave rise to the present gaseous nebula of Cancer. This nebula for a long time aroused the attention and curiosity of astronomers, since it appeared clearly different in nature from that of every other known nebula, all the more so because it showed itself to be in rapid expansion, developing at a speed of over 1000 km/sec. In the end, three supernovae have certainly appeared in our Galaxy in the course of the last millennium; and this percentage corresponds roughly to that established for the average frequency of their appearances in external galaxies: two supernovae every hundred years. So far several tens of such mysterious and singular stars have been recorded (besides the three galactic supernovae), which represent, according to H. N. Russell, "the most terrifying phenomenon known to the human spirit." The energy released by these stars is in fact of the order of 10⁴⁸-10⁴⁹ erg, that is, of the order of magnitude of the total energy contained in an ordinary star.

6. The origin of stellar energy

The Sun and the stars continuously diffuse into space an enormous flux of energy, whose origin and sources remained for a long time entirely unknown. A first hypothesis was that it came from chemical reactions, such as combustion: however, if the Sun were made solely of carbon and burned in an atmosphere of oxygen, it would have been consumed in a few thousand years. The meteoritic hypothesis, according to which the Sun's energy would have been supplied by the fall of meteorites onto the Sun itself, was also soon abandoned. Finally, the hypothesis of gravitational contraction met a similar fate, according to which solar heat would be produced by the compression of gaseous masses derived in turn from the contraction of the Sun due to gravitational attraction: it has been easily calculated that such a contraction would suffice to supply the energy radiated by the Sun for only about twenty million years. This would absolutely not be a sufficient period, because the age of the Earth is 3,350 million years (Holmes, 1948) and geologists hold that at least a billion years must have been necessary for the evolution of life on our planet.

The problem of the origin of stellar energy could be solved only around 1940, when it was recognized that it comes from the nuclear reactions that take place in their interior. By now, in our laboratories we know how to produce such reactions by bombarding atoms and atomic nuclei with appropriate devices and projectiles. In the interior of the stars, the energy with which the particles must be endowed in order to be able to enter the interior of the nuclei is supplied by the extremely high temperature in which the central regions of the stars find themselves. Hence in these, thermonuclear reactions occur spontaneously, capable of releasing energies thousands of times greater than chemical reactions. In effect, such nuclear reactions are accompanied by relatively important variations of mass, and since, according to Einstein's formula: E = c²M, there is equivalence of mass with energy, the coefficient of proportionality being given by the square of the speed of light. Therefore the value of the energy obtained from the transformation of matter is absolutely enormous; one gram corresponds to over 25 million kw.

Among all the nuclear reactions known to physicists, it is thought, however, that in the interior of the Sun and of the stars only a small number can be triggered, and particularly the reactions of combination of protons or hydrogen nuclei with the nuclei of light elements. In the majority of stars, that is, in those belonging to the main sequence of the Russell diagram (such as the Sun), these thermonuclear reactions, six in number, form what is called the carbon-nitrogen cycle, or Bethe-Weisäcker cycle (from the names of the two physicists who identified it). In it, four hydrogen nuclei, combining successively with carbon and nitrogen nuclei, are finally converted into one helium nucleus. Now, the atomic weight of hydrogen is 1.00813, while the atomic weight of helium is 4.00386; deducting the outer electrons, the corresponding nuclear masses are 1.00758 and 4.00276, so that in the reaction a fraction of the mass, equal to 4.00758 - 4.00276 = 0.02866, that is 1/141 of the initial mass, is no longer found in the helium nucleus formed by the union of the 4 hydrogen nuclei. This "mass defect" must therefore appear, according to Einstein's principle of equivalence, in the form of energy released by the reaction. As for the carbon and nitrogen nuclei, they are found regenerated at the end of the reaction itself, behaving like the catalysts of ordinary chemical reactions. In short, the thermonuclear reactions that are produced in the interior of the stars lead to a slow transmutation of hydrogen into helium. It is these reactions that maintain the irradiation of the stars and that, in particular, produce the heat and light necessary for life. In reality, the nuclear reactions do not directly give light, but only gamma rays. These are then absorbed by the stellar matter and re-emitted in the form of radiations of greater wavelength. Before therefore arriving at the surface of the stars, the radiations are absorbed and re-emitted a great number of times. In the end, the radiation emitted is appreciably in equilibrium with the surface temperature.

7. Stellar evolution

Knowing the nuclear reactions that take place in the interior of the stars, one can examine their effects and in a certain way foresee how they may be triggered successively, provoking in the stars the evolutionary processes that characterize their "life". Indeed, the new knowledge of physics has profoundly modified the traditional ideas on the evolution of the stars. In the case of the Sun, and therefore also for the majority of normal stars (those distributed along the main sequence of the Russell diagram), it was formerly believed that it would slowly and progressively cool, since the contraction, which was held to be the sole source of energy, had to progressively slow down. It is now established, on the other hand, that gravitational contraction has importance only in the first phase of the life of the stars (phase of contraction), allowing the initiation of the first thermonuclear reactions by raising the temperature at the center of the stars themselves. Once, however, the sub-atomic or nuclear phase has begun, the thermonuclear reactions (in particular that of the carbon-nitrogen cycle) suffice to produce all the energy radiated, transforming hydrogen into helium. Now, the reserves of hydrogen contained in normal stars are so great as to allow, for example, the life of the Sun for at least another 10 billion years. Moreover, instead of a slow decline, it is foreseen that the slow transmutation of hydrogen into helium must have the effect — by progressively increasing the opacity of the stellar matter — of progressively increasing the central temperature and therefore the irradiation. Consequently, the Sun is headed rather toward a phase of heating, before definitively beginning its final decline. In a few billion years, the Sun will probably be a hundred times more luminous. Its intrinsic luminosity will be comparable with that of Sirius. The increase in the Sun's temperature will entail an increase in the temperature of the Earth, which it is thought must reach at least 1,300°, causing every trace of life to disappear on it. Life, therefore, is destined to disappear from the Earth not because of cold, as was formerly believed, but because of heat (note: the "fire" of the Scriptures).

8. Radio sources and cosmic radio noise

The use of suitable radio-receiving apparatus, called precisely radiotelescopes, has revealed the emission, on the part of celestial bodies (in particular the Sun) and on the part of diffuse cosmic matter, of electromagnetic radiations of radioelectric frequency that manage to reach our Earth, after having overcome the barrier constituted by the terrestrial ionosphere. Moreover, the existence of radio-emitting sources of limited dimensions and not corresponding to any known celestial body has also been revealed. The first discovery is by Rey, Parsons and Philips (1946), subsequently confirmed by the observations of the Australians Bolton and Stanley (1948) and of Ryle and Smith (1948). In these first experiments it was found that the angular diameter of the two most intense sources observed must not exceed 6 minutes of arc. Subsequent observations, obtained with special interferometric radiotelescopes, while on the one hand they have increased the number of these singular dark bodies that emit only at radiofrequency, have progressively led to limiting more and more the effective diameter of the sources, to which the name of radio stars had initially been given. But since present-day radiotelescopes do not permit one to affirm or deny whether these are dark bodies without apparent diameter, the less committal designation of cosmic radio sources is preferred, all the more so since for some of them it has been possible to ascertain the coincidence with particular celestial objects (such as the famous "Crab Nebula") or with small gaseous nebulae. It should be noted furthermore that the hertzian irradiation that reaches the Earth from these radio sources is generally far more intense (on average 100 million times greater) than that which reaches us from the Sun (the so-called "radio-Sun"), in which — given its proximity — such irradiation is particularly intense. Moreover, it is still under discussion whether the radio sources are galactic or extragalactic bodies (sometimes it has indeed been possible to ascertain that some of the weakest radio sources coincide in position with certain extragalactic nebulae); many, however, incline to the view that they are predominantly "new bodies" distributed within our Galaxy, in which the radio emissions are more intense than those of the Sun, while much smaller is their visual emission. It is also presumed that such bodies are widely distributed both in our Galaxy and in the external galaxies.

Galactic radio noise is due instead to radiofrequency emissions on the part of interstellar matter, and in particular from the vast hydrogen clouds whose great diffusion throughout all space has been ascertained. The definitive confirmation of this great diffusion was obtained in 1952 with the discovery of radiation at a wavelength of 21 cm made by H. Ewen and E. M. Purcell (and then subsequently also by others). To understand well how this was possible it is necessary to recall that the outer electron of the hydrogen atom can move only on a determined number of orbits around the central nucleus, and that moreover it can jump from one orbit to another. To each of these jumps there corresponds an absorption or an emission of radiation (ultraviolet, visible, infrared or even hertzian). Some of these radiations are rather complex, showing themselves to be constituted by two or three (or even a greater number) of radiations extremely close to one another. The complexity of these radiations must be justified by the fact that, instead of single quantum orbits, there must in reality be groups of orbits of dimensions very close to one another. Indeed, theoretical physicists have shown that even the "normal" orbit, that is the one closest to the nucleus, must be double, and the "transition" of the electron between these two orbits must precisely be revealed by a radiation of 21 cm wavelength (Van Hulst). Such a transition, however, is one of the so-called "forbidden" transitions, since under the usual laboratory conditions they are generally hindered by some other event, such as e.g. the collision with another atom. But in interstellar space, in which the density of matter is extremely low, similar perturbing events are exceptionally rare; whence the electron ends up carrying out the forbidden jump.

9. The age of the U

This expression is inexact, since astronomers prefer rather to speak of the scale of cosmic time, a more appropriate expression that implies an attempt to establish points of reference in the past, rather than to fix an absolute beginning of cosmic time. On the other hand, the possibilities of success in resolving the problem of the scale of time are intimately connected with the ideas that we are forming, with ever greater precision, about the very origin of the cosmic world.

The beginning must be traced back to a fairly simple creative act; probably that of the elementary particles (protons, electrons, perhaps neutrons) and of the "fields" that interact among them, that is of the laws that govern these particles. The primeval matter of the U. should therefore have been constituted by a gigantic nebula of hydrogen, cold and extremely rarefied (the matter inanis et vacua of the Mosaic Genesis: et tenebrae erant super faciem abyssi), in which there then came to be formed the partial condensations that gave origin to the galaxies, and therefore, through successive evolutions, to the stars with which the U. is today seen to be populated.

Now, hydrogen still constitutes today the most widespread element of the U., not only in the matter already condensed into stars (in some of which it represents up to 70 per cent), but — as has been seen — also in the amorphous interstellar matter, where it reaches concentrations of 80 per cent. Such primitive hydrogen is slowly being transformed into helium and into the other elements, whence the abundance of hydrogen that we still observe is good testimony for the "young age" of the U. This view is furthermore supported by the considerations of H. Shapley and of other equally authoritative astronomers, according to which the development of stellar systems, that is of the galaxies, must be understood as reversed with respect to the scheme previously accepted by astronomers. The galaxies, that is, are born as spiral nebulae, and then, progressively losing the arms that wind around the central nucleus, they slowly transform into elliptical and spherical galaxies (this fact has also been demonstrated theoretically by G. Armellini). Our Galaxy too is itself a spiral nebula, whose arms attempts are being made to delineate (an important contribution was brought in 1952 by the study of the radioelectric emissions of 21 cm wavelength of interstellar hydrogen), in one of which the Sun has its dwelling, in an eccentric position and far from the central nucleus. Now, observations have clearly brought out the enormous numerical preponderance of spiral galaxies, which represent over 80 per cent of all galaxies. Such abundance should therefore indicate a relatively recent stage of the evolution of these stellar systems, and hence the "young age" of the whole U.

But it is still possible to define these concepts quantitatively. In the first decades of this century — when the problem of the age of the U. began to be posed in a concrete way — astronomers seemed to agree that our galactic system, and also all the other galaxies, must have existed, more or less in their present form, for a fairly long time, at least for some trillion (10¹²) years. The reasons supporting these views were provided — besides a supposed apparent equipartition of kinetic energy among the stars — mainly by the incorrect application of the Einstein relation E = c²M, which quantitatively links matter and energy. This relation implied, for example, that the Sun, which has a mass of 10²³ grams, could have maintained the luminosity currently observed (10²³ erg/sec) for a time of at least 10²¹ seconds, that is, for a period of quadrillions (10¹²) of years. Subsequent developments in nuclear physics have shown instead that the release of energy does not involve the entire mass of the star; whence results of the order of billions of years (10⁹-10¹⁶) were reached.

On the other hand, stellar dynamics teaches that the mass of a celestial body cannot exceed a certain limit, otherwise the radiation pressure becomes so strong as to produce a breakdown of equilibrium. In particular, calculation shows, and observations confirm, that a mass only slightly more than a hundred times the mass of the Sun must be considered dangerous and already close to breakdown. From this it follows that the age of the Sun could not go back more than 8 trillion years (8.10¹²). Taking an average among the values obtained, J. Jeans held that the age of the stars was of the order of 5 trillion years (5.10¹²). This value, moreover, seemed corroborated by the knowledge of the time regarding the distribution of stellar velocities and the evolution of galactic clusters. Hence, at the end of the 1920s, Jeans summarized the current ideas of astronomers in the view that the history of the U. could be described backward for at least a thousand times the value established for the age of the solar system and of the Earth, an age which, mainly on the basis of the results from radioactive elements in terrestrial rocks and meteorites, is reasonably held to be of the order of three or four billion years (3350 million years: Holmes, 1948).

Around 1930 it became evident that a complete re-examination of the problem of the scale of cosmic time was necessary. The initial impulse was given by the development of the hypothesis of the expansion of the U. formulated by Lemaître and De Sitter precisely in those years. In effect, granting the Riemannian nature of space, having determined the radius of curvature on the basis of relativity theory, and having "ascertained," according to Lemaître, that this radius of curvature is not a fixed and immutable quantity but is expanding with increasing rapidity, it appeared natural to place the beginning of the U. at the epoch when the distance of the galaxies was minimal. Now, the theory of the expansion of the U. indicates that the "catastrophe" should have occurred two or three billion years ago; and therefore one was led to place the origin of the stars and stellar systems at the epoch of this catastrophe. In other words, there was a tendency toward the transition from the "long" time scale (of the order of trillions of years, 10¹²-10¹³) to a "short" scale (of the order of billions of years, 10⁹).

At present, the theory of expansion has lost much of its original favor among astronomers, owing, among other things, to the numerous doubts that have arisen concerning the interpretation of the phenomenon of the red shift of the spectral lines of extragalactic nebulae (the greatest experimental support for expansion), which, interpreted as a Doppler effect, would indicate a recession velocity of the galaxies of tens of thousands of km per second. The velocities, moreover, would appear (at least up to the depth of exploration of the U. reached) to be proportional to the distances of the galaxies themselves. E. Hubble himself (discoverer, together with Slipher and Humason, of the phenomenon) never accepted such an interpretation for what has taken his name as the "Hubble effect"; and he even thought that it originates from some new and still unknown physical principle. The thought of contemporary astronomers can be summarized in the recent phrase of H. Shapley: "That the hypothesis of expansion is correct and refers to all the space we have explored so far is probable, but it has not been possible to demonstrate it conclusively" (Scientific Monthly, 67 [1948], p. 243).

On the other hand, the evidence in favor of the shortening of the scale of cosmic time has been increasing, particularly on the basis of new knowledge about the dynamics of stellar systems, and principally galactic rotation and the statistics of binary systems. Theoretical considerations and experimental evidence have shown that all spiral nebulae, that is, external galaxies, are endowed with a motion of rotation about an axis perpendicular to the plane of their nebular arms. Such rotation has been ascertained (Oort-Lindblad) also for our Galaxy; it does not occur, however, as with a rigid body, that is, with identical angular velocity for all stars, but in a "differential" manner, so that stars closer to the galactic center complete their rotation in a shorter time than that taken by more distant stars. Our Sun, with its retinue of planets, and the stars near it, take about 250 million years, a period given the name cosmic year.

This differential rotation of the Galaxy produces a process of disintegration and dissolution in galactic star clusters, which therefore must be celestial objects with a rather short average life, of the order of a dozen cosmic years. Open galactic clusters are subject to disintegration through the effect of galactic tidal forces, while the denser ones (such as the Pleiades) tend to break up mainly through internal causes (gradual depletion of the cluster through the expulsion of its members as a result of their interactions). In short, ten or fifteen cosmic years appear to be a significant interval in the development of these clusters. Therefore, the presence of some hundreds of them in our galactic system should be very convincing testimony in favor of the "short" scale of cosmic time for galactic development.

The second important corroboration is provided by double stars, which are very numerous in the sky. Chandrasekhar gave a fundamental formula for the problem of the stability of "wide" binary systems, a formula that links the semi-major axis of the orbit described by the satellite star with the probable "time of dissolution" of the binary system. According to this formula, a binary system with a semi-major axis equal to a thousand astronomical units will dissolve, through the effect of tidal forces caused by stellar "encounters" ("encounter" does not necessarily imply contact or collision, but only close approach with considerable dynamical effects), over the course of 700 billion years; while a binary system with a semi-major axis 10 times greater, that is, 10,000 astronomical units (a "wide" binary system) will dissolve in only two billion years (the astronomical unit is the mean Earth-Sun distance). On the other hand, it is possible to determine the theoretical and observed frequency function of double stars, from which it would appear that the dissolution of binary systems has barely begun; whereas under the assumption of the "long" scale of cosmic time, that is, of trillions of years, one should not find such a large percentage of "wide" double stars as current statistics show.

In conclusion, the results that astronomers have reached can be summarized as follows: the cosmic U[niverse] is very young and — setting aside also the results of the expansion of the U[niverse], still sub indice — its ancient history should not exceed a few billion years, at most 10 billion (10.10²). The normal stars, like our Sun, would be perhaps slightly younger (much younger, on the other hand, are the red supergiants, some of which should still be "being born" even now), and roughly coeval is the entire planetary system, of which the Earth is a part. For the latter one can also specify a "geological time scale," which is two billion years, to which the solidification of the Earth's crust should date back. Still for our Earth, there is then a "biological time scale," on the order of a billion years, to which the appearance of life dates back, and finally an "anthropological time scale" of one million years, to which the appearance of man dates back.

10. Modern astronomy and the Mosaic Genesis

The enormous progress that, following upon physics, astronomy has been making from 1939 onward, besides making ever clearer and more precise the vision of the cosmic U[niverse], also makes possible attempts to delineate in an ever more concrete way the processes of its evolution and even the problems of its origin. For this origin one is also beginning to "see" in a scientific way the necessity of an initial creation, to which it may be possible to "hook" the chain of processes that led from the uniform and disorganized U[niverse] of the "beginning" to the differentiated and organized U[niverse] that we presently have before our eyes. This first creative act must have concerned the creation of matter, and with it of space and time, that is, of the environmental platform that constitutes the "container" of the U[niverse].

Indeed, one of the greatest successes of modern astronomy perhaps lies in having finally made possible the interpretation of the first page of the Mosaic Genesis, showing a perfect agreement (G. Armellini calls it "surprising") between the Mosaic words and the conclusions reached by modern astronomical cosmogony. Naturally, the Mosaic account has a distinctly anthropic character, describing in popular language what a man would have seen who had witnessed the unfolding of events while observing them from the Earth. An important observation may find a place here (Gialanella). In the Mosaic Genesis two terms have been employed, clearly distinct from each other: one is creavit (in Hebrew bāra) and the other fiat (in Hebrew jēkā). The first, creavit, has been used only three times, to indicate: 1) the "creation" of the Earth and the Heaven, that is, of the original matter (the protons and electrons or, if one prefers, rather the neutrons, from which electrons and protons were then derived by natural "decay," or, if one prefers again, hydrogen); 2) the "creation" of living beings; 3) the "creation" of man. In all the other passages, on the other hand, the fiat is used: "fiat lux, fiat firmamentum," etc. Now, it is possible to "reconstruct," for example, solely through the applications of the laws of physics, light from the "formless and void" matter of the original creation, as the result of the first thermonuclear reactions that occurred in the interior of the stars by virtue of the increased temperature and the strong density reached following gravitational contraction. "Fiat lux": the light has come about, but naturally, without any need of a direct creation.

The physical laws alone, however, are no longer enough to explain the origin of life, and a new bāra is then required, the second, that is, a second intervention of the creative power. Nor is it any longer possible to pass, by physical and natural laws alone, from purely animal life — even if through all the complex evolutionary forms — to conscious and rational life, that is, to man. And here the third wondrous bāra was necessary. — See plate LXXXIV.