A star is a celestial body that shines with its own light. It is a plasma spheroid that through nuclear fusion processes in its core generates energy, radiated into space in the form of electromagnetic radiation (luminosity), elementary particle flux (stellar wind) and neutrinos. Much of the chemical elements heavier than hydrogen and helium are synthesized in the nuclei of stars through the process of nucleosynthesis.
The determination of the position of the stars on the celestial sphere, with respect to appropriate coordinate systems, is a problem of astrometry, as well as it is the task of this one to study the variations of coordinates due both to the Earth (irregularities in the rotational motion of this one), and to intrinsic causes of the stars (proper motions); the nature, the structure, the physical state etc. of the stars are studied by astrophysics in the broader cosmological context.
Of a star you can directly measure the splendor, both relative in a scale of apparent magnitudes, and absolute if the distance is known, or the parallax, which can also be directly deduced from exact observations of positions on the celestial sphere for stars distant up to a hundred parsecs, or indirectly inferred from other observations in the case of more distant stars.
The absolute magnitude of a star is indicative of the total amount of radiation emitted by the star in the unit time, or luminosity. The other characteristic of a star that can be inferred directly from observations, and from which almost all physical information is taken, is its spectrum. From the examination of the spectrum it is in fact possible, by simple inspection, to deduce the presence of the various atomic elements and their state of ionization and excitation (referring of course to analogous laboratory data) and to go back, by means of relatively complex calculations, to a temperature range for the surface layers of the star (those that emit the observed and analyzed radiation) and to the numerical percentages of the various atomic elements existing therein.
Further measurements, based on the Doppler effect, allow then to determine the radial component with respect to the Earth of the velocity of the star, referring to a comparison spectrum. The knowledge of the motion of the Earth around the Sun and of the Sun in space finally allow to disregard both these motions and to calculate the absolute motion of the star in the galaxy to which it belongs.
The most important classification of stars is the so-called Harvard classification, proposed in the early years of this century by E. C. Pickering and A. J. Cannon, who also compiled the HD catalog (Henry Draper Catalogue). In the cataloging, stars are grouped in a sequence of decreasing temperatures, defined by the spectral composition of the emitted radiation. This composition of starlight is very similar to that of the black body and, since the emission maximum of the latter has different wavelengths depending on the temperature, it is possible to classify the stars according to the value of this maximum and then according to their surface temperature. The higher the temperature, the shorter is the wavelength that corresponds to the maximum emission of the star. This is Wien’s law, or displacement law, valid for blackbody spectrum.
A star with reddish appearance has therefore the maximum emission in the red, that is in the area of longer wavelengths; a star with white or blue appearance has instead the maximum in the area of shorter wavelengths. White and blue stars are therefore hotter than red ones. The Harvard sequence is a classification of stars by types or spectral classes, ordered according to decreasing values of temperature distinguished by the letters O-B-A-F-G-K-M. Although most of the ca. 255,000 stars listed in the HD catalog fall within this classification, there are some quite special ones. At the end of the sequence corresponding to the cooler stars, some stars can be associated in whose spectrum the banded spectra of carbon and cyanogen are present with strong intensity. These are the so-called C-type stars in which today are included the stars once classified as spectral class R and N, both with temperatures between 1500 and 3000 K.
The substantial difference with the M-type stars, which are at the same end of the Harvard sequence, consists in the presence in their spectrum of the characteristic bands of zirconium oxide. At the opposite end of the sequence, in correspondence of the very hot O-type stars, can be placed the so-called Wolf-Rayet stars, characterized by a spectrum in which there are large emission lines characteristic of carbon (WC stars) and nitrogen (WN stars).
In the Harvard classification each of the spectral classes is divided into 10 subclasses, from 0 to 9. In it, our Sun is for example considered to be of type G, subclass 1, i.e. G1. Since the spectral distribution of radiation emitted by a star looks very similar to that emitted by a black body, it follows that the magnitude of a star measured at a wavelength λ1 will differ, in general, from that measured at a wavelength λ2: the difference between the magnitude at a longer wavelength and the one at shorter wavelength is called color index. Between international color index (for which the measurement wavelengths are 430 and 540 nm) and spectral type there is a relationship of quasi-proportionality, in the sense that the color index has a more positive value the more advanced is the spectral type.
The measurement of the temperatures corresponding to each spectral type is done by examining the intensity of the radiation emitted by stars of each spectral type at different wavelengths and comparing the observations with the corresponding blackbody data at different temperatures. By other way, knowing at what temperature each atomic element ionizes and knowing what spectral lines it emits in each state of ionization, it is possible to trace the corresponding temperature. We have obtained temperatures ranging from a few thousand degrees for the coldest red stars (of spectral types M and N) up to a few tens of thousands of degrees for O-type stars.
Spectral analysis has shown that the chemical composition of all stars is essentially identical, in fact the presence of molecular compounds in some stars is due to the low surface temperature of these; the possible differences, with regard to the heavier elements, are between stars of different populations for which there may have been initial differences in composition. Direct measurements of stellar diameters have not yet been possible except with very refined interferometric techniques, made by A. A. Michelson in 1930 at Mount Wilson (and more recently by others) who managed to measure the diameters of some giant stars relatively close (Arcturus, Betelgeuse). It was possible to indirectly measure the size of some components of double stars, based on the duration of the eclipse, by knowing the relative orbital velocity of the two components.
Theoretically, according to Stefan and Boltzmann’s law, valid for the black body and approximated for a star, it is possible, from the knowledge of the surface temperature, to deduce the total intensity of radiation emitted per unit area and per unit time. Knowing also the absolute magnitude, by comparison with similar data for the Sun, it is possible to deduce the size. In any case, theoretical and experimental measurements have shown that the size of stars vary from the order of a hundred solar diameters, for giant and supergiant stars, to the order of the diameter of the planets; the discovery of pulsars and theoretical considerations on stellar structure, however, assume that there are also stars (neutron stars, black holes) with diameters of a dozen kilometers or less. Even the masses of stars can only be inferred indirectly.
A. S. Eddington, in 1924, found theoretically a relationship between mass and luminosity of a star, in the sense that a star is the brighter the more massive it is; this relationship was already known for the few visual double stars for which, knowing the elements of the orbit and the distance, it was possible to calculate the mass. The stellar masses vary in a rather narrow range, between about 1/10 and a few tens of solar masses. The densities of stars show much more marked variations, in correspondence with the wide range of sizes: red giant stars have average densities millions of times lower than that of water (and that of the Sun), while, at the opposite extreme, the observed white dwarf stars have densities millions of times higher; even higher densities must have neutron stars and black holes. However, it should be noted that, as was observed in the case of the Sun, the density of a star varies greatly between the interior and the surface.
The spectroscopic study of stars has allowed the discovery of some other peculiarities. The presence of emission lines in the spectrum of some of them has first of all led to believe the existence of nebulae or bright gaseous masses, distinct from the stars: the stellar spectral lines are in fact all in absorption as generated by the various atomic elements present in the stellar atmosphere (what was called inversion layer) seen in the background of the brightest and hottest central zone, which would present a spectrum all in emission. The shape of the spectral lines is then to be connected, although there is not a very precise relationship, with the size of the star: supergiant and giant stars present in fact spectra with very sharp lines, because in their extended and tenuous atmospheres are relatively unimportant the turbulence motions, which would cause, by collision, an enlargement of the spectral lines; the opposite happens in the stars of smaller size, in which the greater density of the atmospheres causes a greater number of collisions per unit time.
The enlargement of stellar spectral lines can have origin also in two other phenomena, difficult to distinguish between them and to observe. The first one is the rotation of the star on itself: in this case there is an enlargement of the spectral lines, more easily verifiable when the star is part of a double eclipse system and when the rotation axis is perpendicular to the Earth-star conjunction; it was thus possible to find that there are peripheral rotation speeds up to a few hundred km/s, which, knowing the size of the corresponding stars, lead to angular velocities of a rotation every few hours. Generally, stars of the first spectral types have higher rotational velocities; in particular, A-type stars are those with the highest rotational velocities.
The other phenomenon that can cause a broadening of spectral lines is the well-known Zeeman effect, which consists of the subdivision of spectral lines in the presence of magnetic fields. For small separations it is not possible to distinguish the individual lines produced by the subdivision of the original line, which then appears simply more enlarged. The presence of stellar magnetic fields, which can be inferred indirectly because magnetic fields exist also in sunspots, is revealed spectroscopically by equipping the spectroscope with a polarizer: the two wings of the magnetically enlarged line are in fact polarized differently.
Many stars, in particular type A, have very intense magnetic fields, up to a few thousand gauss, often variable in polarity and intensity and always associated with variability in the spectrum and peculiarities in the abundances of certain atomic elements, metallic in particular. The different physical parameters that characterize a star are all related to each other; mass, size and density are related by the relationship valid for the Sun and the planets, as well as the acceleration of gravity on the surface depends on the mass and size of the star, while it has already been observed that there is a proportionality between mass and luminosity, but not respected by supergiant, giant and dwarf stars that are in conditions of instability. Brightness L, radius R and surface temperature T of a star are related to each other by the relation \(L=4\delta T^4R^2\), where \(\delta\) is a constant.
Since the spectral type of a star depends on temperature and surface gravity acceleration, then also on surface pressure (because temperature and pressure determine on one hand the degree of ionization of atomic elements present and on the other hand the intensity of spectral lines generated), it follows that, neglecting rotation and magnetic field, probably dependent on other physical characteristics, only four parameters completely define the physical state of a star, that is mass, luminosity, size and chemical composition. Theoretically, however, only mass and chemical composition should be decisive for the structure of a star.
From the diagram of the values of two fundamental parameters, luminosity and spectral type (or equivalent parameters) observed in a homogeneous group of stars (for example belonging to a cluster), we obtain the Hertzsprung and Russell diagram (often abbreviated as H-R diagram), of extreme importance in stellar astronomy and the basis of fundamental discoveries. The H-R diagram has shown first of all that not all combinations between spectral type and absolute magnitude are allowed, because the diagram is not all uniformly occupied by the representative points of the stars, which are instead concentrated in certain areas.
Most stars are concentrated on a relatively narrow strip that lies roughly along the main diagonal of the diagram (main sequence), a relatively small number of points are scattered below the main sequence (white dwarf zone), while above this there are concentrations of points in the three roughly horizontal zones of subgiants, giants and supergiants; the main sequence is also sometimes called the dwarf star zone. Giants are characterized by higher magnitudes, higher pure size, and lower densities. Giant stars can be recognized as such based on spectrographic observations, determining, for example, the intensity and width of certain spectral lines or bands. Giant stars possess luminosity classes II or III.
Between the main sequence and the zone of the giants there is the Hertzsprung gap. The comparison between the H-R diagram for the hundred or so stars closest to the Sun and the analogous diagram for all the stars whose absolute magnitude and spectral type (or color index) are known, shows that the zone of the giants and supergiants, almost empty in the first case, is densely populated in the second: the reason for this is that the giant stars, having a very high luminosity, are observable even at much greater distances than the stars of the main sequence. The diagram relating to the stars closest to the Sun therefore gives a correct representation of the distribution of stars of various types of magnitude greater than about 11m.
It is deduced, based on simple statistical considerations, that there must exist, within a radius of about 10 parsecs from the Sun, at least 250 other stars of magnitude between 11m and 17m. The diagram, or numerical function, that links the distribution of the number of stars with their relative luminosity is called the luminosity function. This function is obtained by counting the number of stars per unit area, for example per square degree, that possess the same luminosity (or absolute magnitude). The method is obviously limited to the distance of a few hundred light years at which you can still accurately measure the distance of a star and has led, in the field of stellar statistics, to the definition of the galactic structure.
The question of luminosity leads back to the second problem for which the H-R diagram has proved useful: the fact that the diagram is only partially occupied shows that the spectral type can not be the only parameter for an experimental stellar classification (already known theoretically). Spectroscopic astrophysicists took advantage of the clear-cut zoning of the H-R diagram to attribute to these different luminosity classes and thus define a second experimental parameter usable for an experimental classification.
W. W. Morgan, P. C. Keenan and E. Kellmann (Atlas of Stellar Spectra, 1943) defined a two-dimensional stellar classification, abbreviated MKK. Compared to the traditional areas of the H-R diagram, the five brightness classes of the MKK classification correspond, respectively, to the supergiants class I, to the giants classes II and III, to the subgiants class IV and to the main sequence stars class V.
The Sun, for example, has brightness class V, and in the MKK system is classified as G1 V. Other classifications are also used for special purposes; for example, the Barbier and Chalonge classification, which is based on the measurement of spectral features sensitive to the effects of temperature and luminosity, and the Strömgren classification, which is based on the measurement of stellar splendor in narrow bands of wavelengths.
For the faintest stars it is almost impossible to measure the distance and therefore to establish what the absolute magnitude is, and for them are also impossible spectrographic observations; for these stars, however, you can easily build the H-R diagram (which assumes significance only if the stars are part of a homogeneous group), using the apparent magnitude instead of the absolute one (provided of course that they are all at the same distance) and, instead of the spectral type, the color index. The diagram thus obtained is also called color-magnitude diagram and has been used in the study of clusters and stellar associations, for which the condition of equal distance from Earth is verified, obtaining a double result: the first is that, having two H-R diagrams available, one for stars of known absolute magnitude (for example those near the Sun) and the other to be studied, it is possible to deduce the distance of the group of stars in general by simply comparing the magnitudes corresponding, on the two diagrams, to an equal spectral type.
The method can be affected by error if the magnitude measurements are altered by the presence, between the group of stars and the Earth, of interstellar gas or dust, which cause an anomalous reddening of the stars, easily detectable with multi-color photometric methods. The second result, moreover unforeseen when it was discovered by W. Baade, was the existence of groups of stars with globally different characteristics, a result that led the same Baade, in 1944, to postulate the existence of stellar populations based on the different H-R diagrams that they presented. The figure illustrates schematically what are the differences between the two basic types of populations, which include, in extreme cases, the stars of globular clusters (Population II) and open clusters (Population I).
The study of the evolution of stars is aimed at determining the different stages, from birth to death, through which a star passes during its existence. Since not all stars have a similar history, this field of astronomy, or rather of astrophysics, also has the task of determining the parameters that define the different modes of development of different types of stars. Today it is believed that stars are mostly born in groups, by condensation from clouds of gas with densities thousands of times higher than those of the common interstellar matter surrounding them: these are the Bok globules.
During the process of contraction of a Bok globule, the matter of which it is composed heats up and begins to emit radiation, but only in the infrared band. Objects of this type, with strong emission in the infrared, have been observed in the Orion Nebula, in the star V1057 of the Swan, in the Carena (the famous star Eta), in the constellation of Cassiopeia (W3-IRS5), and in numerous other centers. The process of contraction of the gaseous globules proceeds rapidly (it is the Hayashi phase, a stage of rapid contraction that, for a future star equivalent to the Sun, lasts about 30 million years, decreasing exponentially with the increase of mass) until it heats enough the gaseous concentration, so as to stimulate its brightness. At this stage, protostars are still wrapped by the nebular matrix and appear subject to strong variability: they are also identified as Herbig-Haro objects.
The actual star begins to exist when the temperature becomes high enough (many millions of degrees) to trigger thermonuclear reactions that produce energy for billions of years during the lifetime of the star. The start of the stellar phase appears marked by an impetuous “wind” of radiation that sweeps the surrounding nebular remnants, phenomenon called T Tauri phase; the star is still physically unstable. The subsequent evolution of a star will be conditioned by a series of parameters, the most important of which are the initial mass, the chemical composition, and, in particular, the relative abundance between hydrogen and helium and other elements. Since all the stars in a cluster formed at about the same time and with a similar composition, the study of stellar evolution can be conducted on the basis of the comparative study of the different H-R diagrams obtained for different clusters. In this case the determining parameter for the evolution of a given star is only its initial mass.
The study of the subsequent evolution of the star can be carried out by studying the H-R diagram for the many stars of a cluster: the state of the star is at this point represented with a point on the right of the main sequence in the H-R diagram. At the stabilization of thermonuclear reactions that have marked its birth, this point moves on the main sequence in a position higher and more to the left as the greater is the initial mass of the protostar.
The size of the nucleus, in which the reactions take place, and also the temperature, vary according to the initial mass of the star: the greater is this, the greater is the temperature reached in its interior and the smaller is the zone of energy production. Generally this is due, in higher mass stars, to the reactions of the carbon-nitrogen cycle, which require higher temperatures, while in stars of relatively small mass, of the order of that of the Sun, the proton-proton reactions prevail (direct fusion of hydrogen into helium).
A star remains on the main sequence for most of its life, in fact the main sequence of H-R diagrams is almost always overcrowded. In particular, a star of small mass (less than that of the Sun) remains on the main sequence for billions of years, while the most massive and brightest stars remain on the main sequence a few million years. If the forming star encloses a too modest amount of matter (for example below one tenth of the solar mass) will give rise to a star whose central temperature will be low and the nucleosynthesis reactions inside, simple, weak and unstable: a red dwarf will be born, with a modest surface temperature (only a few thousand K), a star similar to Proxima Centauri, or to the stars of Luyten, Wolf, Barnard.
Protostellar masses less than one hundredth of that of the Sun will never reach the thermal threshold for the initiation of energy reactions and therefore will remain in a state of progressive gravitational contraction, during which they will dissipate their internal energy, without ever shining of their own light (this is the case of the great planets Jupiter and Saturn and some stars identified recently, which, for their thermal radiation, are classified as real aborted stars, the so-called dark dwarfs).
The actual evolution of the star, i.e. the shift of its representative point on the H-R diagram, begins when all the hydrogen in the core is consumed and nuclear reactions begin to take place in an increasingly outer layer, while the core begins to contract gravitationally. The course of processes at this point differs according to the mass of the star: for a star with mass less than or slightly higher than the mass of the Sun, the contraction of the nucleus leads to a release of energy that expands the outer layers of the star, bringing it in the zone of the giants. In this phase the helium transformation reactions of the core begin, giving rise to an instability of the core itself: the temperature of the core, and of the star, increases and the star moves to the left on the H-R diagram, crossing a pulsation zone (the zone of variable stars), probably produced by the alternation of states of degeneration and normality in the core.
Subsequently, the star, exhausted all the nuclear fuel and no longer having gravitational energy to increase its temperature to trigger reactions that produce heavier elements, is transformed gradually, contracting very slowly, in a white dwarf. In massive stars all processes are accelerated and being in particular higher temperature, they are also differentiated. In fact, in massive stars, at the first episode of instability resulting from the exhaustion of nuclear hydrogen, follows an internal heating sufficient to trigger in the mass of inert helium reactions aimed at the synthesis of carbon and oxygen; and this, while the hydrogen resumes to “burn” in an outer layer. The duration of this phase of stability can be estimated in about one thousandth of the permanence in sequence of the star.
At the exhaustion of helium, a new episode of gravitational instability is produced that causes the abrupt contraction of the stellar mass and the raising of its internal temperature up to 800 million K. At these thermal levels, carbon and oxygen enter, in turn, in cycle transmuting into a series of heavy elements ranging from magnesium, sulfur, silicon. The core of the massive star in this phase is “onion skin”, i.e. in a series of concentric layers within which the reactions of nucleosynthesis are distributed according to the temperature.
The progressive depletion of nuclear fuel becomes more and more rapid with the complexity of the reacting substance (the last reactions have a duration that is around some tens of years) and gives rise to a series of collapses of the stellar mass that raises the internal temperature up to over one billion of K. When in the core of the star are triggered reactions that lead to the synthesis of iron, huge amounts of energy begin to dissipate by neutrino radiation and internal photodissociation.
The combination of iron with heavier elements is not capable of self-sustaining, because it is endothermic (unlike previous reactive cycles, of exothermic nature) that is absorbs energy, instead of producing it. Therefore, arrived at this phase, the massive astro is condemned. Deprived of any source of energy, subjected to irrepressible internal dissipation, the balance breaks abruptly and the entire mass collapses on itself, generating a flash of radiation of extraordinary intensity whose violence projects, suddenly, in space the stellar layers. The destructive phenomenon is what gives origin to a supernova.
At the destruction (more or less integral of the star) survives the former thermal core, the inert core, reduced to a compact mass of degenerate matter that gives rise to a neutron star, characterized by very high density (1014 g/cm3) associated with very small geometric dimensions (10-15 km radius) and very high gravitational acceleration of the surface (1010 g); endowed with an intense magnetic field, from this star can emanate impulsive flows of synchrotron radiation (pulsar effect). The critical mass, from which it becomes possible the formation of a neutron star, has been determined by S. Chandrasekhar, and is equivalent to 1.44 solar masses.
In stars of mass comparable to that of the Sun, the core temperatures cannot rise too high; so that the reaction cycle stops at the helium cycle, the collapse of the star is not catastrophic, and the star is reduced to a white dwarf, a planet-sized body of degenerate matter. Following the supernova event and, most likely, also during the red giant stage – especially if it is a close binary system – a star ejects part of its mass in the form of stellar wind producing the spectroscopic phenomenon called P Cygni effect. It is therefore reasonable to foresee that the matter diffused by stars, also composed of elements heavier than hydrogen goes to be part of stars that are formed later; this is particularly true for the most massive stars, which have an accelerated evolution and that, since there is a galaxy, could have reformed several times. Thus it is realized that the most recent stars possess a different chemical composition. This is also the reason for the differentiation between stars of different populations: the oldest stars of Population II, belonging for example to globular clusters, are less rich in heavy elements than Population I stars of the most recent open clusters, in which these elements have been observed.
Atmosphere and structure of stars
The part perhaps most studied from the theoretical point of view is the atmosphere, generically defined as that part of a star from which we directly receive radiation. In fact, the radiation produced in the core of a star is transported outward by differentiated mechanisms. The interior of a star much less massive than the Sun (red dwarf) is probably entirely stirred by convection, and such is the thermal mechanism that puts it in equilibrium with the exterior; while solar-rank stars show to have – around the core – at least two zones with different equilibrium: radiative in the inner one, convective in the outer one.
In higher mass stars, on the contrary, a convective core surrounded by a radiative envelope is expected. In energy transport by radiative way, radiation is repeatedly absorbed and re-emitted by the atoms that compose the star and, each time, it gives up part of its energy transforming itself in radiation of shorter and shorter wavelength.
The knowledge of the absorption coefficient of stellar matter is essential to study the internal structure of a star. The absorption coefficient of the matter of stellar nuclei is so great that a layer of matter a few centimeters thick, in those conditions of temperature and pressure (millions of degrees and hundreds of thousands of atmospheres), is perfectly opaque; it should be noted that, given the high temperatures involved, the radiation inside a star has a very short wavelength (X or gamma rays and ultraviolet): absorption in this case occurs by ionization, electron acceleration and Compton effect.
Once arrived in the outer layers of a star, the radiation meets the layers whose opacity is low enough to allow to cross them (also because the radiation is degraded from very short wavelengths to visible wavelengths or almost). Even in these conditions the absorption of radiation is important, with the difference that, while in the inner layers the absorption is continuous, in the outer layers it becomes important also the selective absorption, depending on the chemical nature of the elements present and the physical state in which they are: it is thus produced a spectrum of lines, observable with a spectroscope, and that so far has been the only means of information about the structure of stellar atmospheres. Only from a certain depth, which also depends on the wavelength of radiation, this can leave the star without being reabsorbed.
The stellar atmospheres, in which the spectral lines are formed, are layers of gas with thicknesses ranging from a few hundred or thousands of kilometers for main sequence stars (or less for dwarf stars) up to sizes comparable with the size of the stars themselves in red supergiants with extended atmosphere (such as Arcturus or Capella).
The thickness of the atmosphere is also variable according to the wavelength of observation, since the opacity of the matter composing the atmosphere depends on the wavelength; moreover, the central part of the most intense stellar spectral lines (a stellar spectrum is in absorption) is generated, statistically, by photons coming from the most superficial layers, while the radiation quanta forming the continuous part of the spectrum also come from the deepest layers. This fact demonstrates that the atmosphere of a star has not homogeneous structure and that it is not in thermal equilibrium, as it is also demonstrated by the impossibility to deduce, with different methods, a single value for the surface temperature: for example, the Sun, spectral type G1, has temperatures that vary between 4800 K and 7000 K according to the method used for the determination.
Particularly studied is the mechanism of absorption and re-emission of radiation. Also in this case, the use of models, some of which proposed by K. Schwarzschild and A. S. Eddington, which account for the shape of the spectral lines, led to the solution of the problem of the structure of stellar atmospheres. At present the general picture of the phenomena involved in attributing to each stellar atmosphere its characteristic structure can be considered almost complete, while the interpretation of the single phenomena is in progress, as well as of the peculiarities often encountered in the spectroscopic and photometric observation of stars.
The internal structure of stars, although not directly observable, can however be deduced theoretically in its essential lines and with increasing precision. The matter forming a star, given the conditions of high temperature and high pressure, can only exist in the gaseous state: this mass of gas, for a star to be stable, must be in conditions of hydrostatic equilibrium, that is in each point of the star the gravitational pressure exerted by the overlying layers must be balanced by the pressure of expansion of the internal gases acting in the opposite direction.
The temperature, the pressure and the density of a star are therefore related to each other by the equation of state, in which also the chemical composition is involved; the latter is generally expressed by three parameters that give the abundance of hydrogen, helium and all other elements (that astronomers improperly call metals), considered globally. Despite the high density in which stellar gas is found, it can still be considered as perfect gas, formed by nuclei and electrons, at least in normal stars. The stellar gas, in addition to hydrostatic equilibrium, must be in thermal equilibrium and this leads to consider the mechanisms, radiative and convective, with which the transport of energy from the nucleus to the atmosphere takes place. In white dwarfs and even more in neutron stars – in which it is necessary to take into account the relativistic effects – the electron gas becomes degenerate and in this case the pressure becomes independent of temperature.
- Binary star