Abstract

The rate of nuclear reactions depends on the influence of the surrounding particles that compose the plasma. At high densities the situation is far from being satisfactory and the influence of electron polarization has not been completely elucidated. In particular, it is shown that the possibility of an accretion induced collapse of a carbon-oxygen white dwarf instead of a supernova explosion completely depends on the screening factors and pycnonuclear rates that are adopted. Similarly, the possibility of detecting isolated neutron stars that accrete matter from the interstellar medium depends on the adopted pycnonuclear rates. Low rates allow the formation of a metastable layer that can release energy explosively and produce aγ-ray burst. Nevertheless, current rates seem to prevent such a situation.

Le taux des réactions nucléaires dépend de l'influence exercée par les particules voisines qui composent le plasma. A haute densité, la situation est loin d'être satisfaisante et l'influence de la polarization electronique n'est pas sufisamment claire. En particulier, on montre que la possibilité d'obtenir un collapse non explosif d'une naine blanche de carbone oxygène dépend des facteurs d'écrantage et des taux pycnonucléaires adoptés. Egalement, la possibilité de détecter des étoiles à neutrons isolées dépend des taux pycnonucléaires adoptés. Des petites valeurs favorisent la formation d'une couche metastable qui peut libérer de l'energie explosivement et produire une éruption gamma. Quand-même, les taux actuels semblent empêcher cette situation.

In the Internal Constitution of the Stars, published in 1926, Eddington gave a central temperature of white dwarfs of several billions degrees. The Fermi-Dirac statistics appeared just one year later, in 1927, and the new equation of state for degenerate matter provided the explanation of white dwarfs.

The solution of the problems we have to consider presently are probably not relevant of the same kind of intellectual jump. But who knows! Anyhow, the time of the perfect gas law is definitely over. It is possible, in many cases, to get astrophysical orders of magnitude, using simple or oversimple relations betwen physical quantities. However, modeling correctly observational results has become, nowaday, more and more difficult. Data are of a better precision and provide more information, would it be chemical abundances, evolutionary tracks or those wonderful helioseismological data. An elementary statement is that, in order to look Inside the Stars (the title of a recent colloquium), we need more accurate descriptions of basic physical laws: equation of state, opacities, thermonuclear reactions.

We are still facing many difficulties in the field, and we can give a few examples: we do not have a theory which decribes consistently both the equation of state of a plasma and the level population of the atoms; we still have to improve the theory of screening effects in dense plasmas; we have now a description of cold, dense, weakly ionized matter of brown dwarfs, but it is still incomplete.

Abstract

The DENIS survey will survey the southern sky in the near-IR J (1.2 micron) and K (2.2 microns) bands at 3” resolution and to limiting magnitudes in J and K of respectively 16 and 14.5 (lmJy in both cases), and at 1” resolution in the red I band (0.9 microns). Astrophysical motivation is provided by basic problems concerning structure and evolution of galaxies, of types ranging from our own to active galaxies, and concerning specific stellar populations including stars with low temperature photospheres, those still embedded in their protostellar envelopes, and those currently losing mass on the AGB.

Scientific objectives

The release of large 2D detector arrays sensitive in the near infrared provides the first opportunity to undertake a deep survey of the sky in the non-thermal infrared range (1 to 2.5 microns). This underexplored spectral range will provide crucial insights into fundamental problems in stellar and galactic astrophysics. Theere is no recent all-sky atlas of data between the visible and the IRAS 12 microns band. The 25 year-old IRC catalog remains the state of the art effort in the near IR despite its limitations. Our objective is to carr y a 3 colour (IJK) survey of the complete southern sky, improving on the pioneering IRC sensitivity by 4 orders of magnitude and improving on its spatial resolution by a factor of 20.

There are two main motivations for a deep near IR sky survey: the near IR brightness is the best tracer of mass in stellar form, and the interstellar extinction is reduced by a factor of 10 with respect to the visible V band.

Abstract

We report the results of a nonlinear inversion of solar oscillation data that enable us to detect nonideal Coulomb interactions between particles, including pressure ionization, in the solar convection zone.

Introduction

Precise measurements of solar oscillation frequencies provide data for accurate inversions for the sound speed in the solar interior. Except in the very outer layers, the stratification of the convection zone is almost adiabatic. There, the sound-speed profile is governed principally by the specific entropy, the chemical composition and the equation of state, being essentially independent of the uncertainties in the radiative opacities. The inversions thus reveal, via tiny effects on the adiabatic compressibility of the solar plasma, physical processes that influence slightly the equation of state. We have carried out a nonlinear inversion based on a recent accurate asymptotic description of intermediate- and high-degree solar p modes (Brodsky & Vorontsov 1993; Gough & Vorontsov 1993), using the observational data of Libbrecht, Woodard & Kaufman (1990).

The equations of state (EOS) used in the analysis

In the reference models, we use the following equations of state. We are mostly brief, with the exception of the pressure-ionization model used in the helioseismic calibration.

• Saha EOS: a free-energy-minimization type realization for a mixture of reacting ideal gases, with ground-state-only partition functions of the bound species. Note that by assuming only ground states we are using the term ‘Saha’ in a rather restricted sense.

• […]

Abstract

Accurate measurements of observed frequencies of solar oscillations are providing a wealth of data on the properties of the solar interior. The frequencies depend on the solar structure, and on the properties of the plasma in the Sun. Except in the very outer layers, the stratification of the convection zone is almost adiabatic. There, the sound-speed profile is governed principally by the specific entropy, the (homogenous) chemical composition and the equation of state. It is therefore essentially independent of the uncertainties in the radiative opacities. The sensitivity of the observed frequencies is such that it enables to distinguish rather subtle features of the equation of state. An example is the signature of the heavy elements in the equation of state. This opens the possibility to use the Sun as a laboratory for thermodynamic properties.

Les fréquences observées des oscillations solaires constituent une base de données extrêmement riche qui nous permet d'étudier les propriétés de l'intérieur du soleil. Les fréquences dépendent de la structure solaire et des propriétés locales du plasma (surtout de la vitesse du son). Sauf dans les couches très exterieures, la structure de la zone convective du soleil est essentiellement adiabatique. Le profil de la vitesse du son est done donné par l'entropie spécifique, la composition chimique (homogène) et l'équation d'état. L'opacité radiative ne joue pas de rôle. Grace à la grande précision des fréquences observées on arrive à distinguer des phénomènes assez subtiles dans l'équation d'état, comme la signature faible des élements lourds.

Abstract

Coulomb interactions for the Free Helmholtz energy and the pressure are studied in a partial new formulation which described more exactly the numerical evaluation of many body theories.

Introduction

With regard to the EOS many activities have been developed to yield results which consider different phenomena, for instance pressure dissoziation and ionisation, degeneracy, relativity, Coulomb- and non-Coulombic interactions, pair production and charge mixing in different chemical compositions.

Various theoretical approaches are used in order to include exchange and correlation effects for fully ionized or partially ionized matter (see e.g. Salpeter and Zapolski 1967, Graboske et al. 1969, Hansen 1973, Pokrant 1977, Fontaine et al. 1977, March and Tosi 1984, Perrot and Dharmawardana 1984, Hubbard and Dewitt 1985, Dandrea et al. 1986, van Horn 1987, Kraeft et al. 1986, Ichimaru et al. 1987, Rogers and DeWitt 1987, Däppen et al. 1988, Ichimaru 1990, Eliezer and Ricci 1991, Saumon and Chabrier 1992).

For many applications (e.g. stellar evolution calculations or astroseismology) it is necessary either to have algebraic formulae for the EOS or extensive tables which supply the input, informations at any density and temperature. As a, first step we present an analytical EOS for fully ionized multicomponent plasmas covering a large density-temperature range. The EOS includes non-ideal effects due to exchange-correlation interactions of charged particles at any degeneracy and is applicable to any chemical mixture. Relativistic effects as well as ionic quantum corrections are taken into account.

Introduction

In Chapter 18, we showed that we can make a convincing case that the high energy electrons which are observed at the top of the atmosphere represent a sample of the high energy electrons present throughout the interstellar medium and which are responsible for the diffuse Galactic synchrotron radio emission. Our task in this chapter is to interpret these observations in terms of the propagation of these particles from their sources through the interstellar medium and the energetics of possible energy sources within the Galaxy. The key diagnostic tools are aging processes, which can result in features in the energy spectra of the electrons and estimates of the energy requirements of sources of synchrotron radiation. In this chapter, we will develop these tools in the context of the origin of the Galactic radio emission and the study of supernovae as sources of high energy electrons. These tools are, however, of very general applicability to the whole of high energy astrophysics. We will use them repeatedly in our discussion of the physics of radio sources and active galactic nuclei.

Energy loss processes for high energy electrons

High energy electrons are subject to a number of energy loss processes as they propagate from their sources through the interstellar medium. The loss processes cause distortions of the injection energy spectra of the particles from their sources and thus potentially provide information about the life histories of the high energy electrons.

The formation of dead stars

The types of stars described in Chapters 13 and 14 are held up by the thermal pressure of hot gas, the source of energy to provide the pressure being nuclear energy generation in their cores. As evolution proceeds off the main sequence, up the giant branch and towards the final phases when the outer layers of the star are ejected, the nuclear processing continues further and further along the route to using up the available nuclear energy resources of the star. The more massive the star, the more rapidly it evolves and the further it can proceed along the path to the formation of iron, the most stable of the chemical elements. An intriguing question is whether or not the star is disrupted by the various ‘flashes’ which are expected to take place as new regimes of nucleosynthesis are switched on, for example, at the points E and G in Fig. 13.19. In the most massive stars, M ≥ 10M⊙, it is likely that the nuclear burning can proceed all the way through to iron, whereas, in less massive stars, the oxygen flash, which occurs when core burning of oxygen begins, may be sufficient to disrupt the star. In any case, at the end of these phases of stellar evolution, the core of the star runs out of nuclear fuel, and it collapses until some other form of pressure support enables a new equilibrium configuration to be attained.

The possible equilibrium configurations which can exist when the star collapses are white dwarfs, neutron stars and black holes.

Synchrotron radiation

The synchrotron radiation of relativistic and ultrarelativistic electrons is the process which dominates high energy astrophysics. It is the radiation emitted by very high energy electrons gyrating in a magnetic field. It was originally observed in early betatron experiments, in which electrons were first accelerated to ultrarelativistic energies. This same mechanism is responsible for the radio emission from the Galaxy, from supernova remnants and extragalactic radio sources. It is also responsible for the non-thermal optical emission observed in the Crab Nebula and possibly for the optical and X-ray continuum emission of quasars. The reasons for these assertions will become apparent in the course of this chapter.

The word non-thermal is used frequently in high energy astrophysics to describe the emission of high energy particles. I find this an unfortunate terminology, since all emission mechanisms are ‘thermal’ in some sense. The word is conventionally taken to mean ‘continuum radiation from particles, the energy spectrum of which is not Maxwellian’. In practice, continuum emission is often referred to as ‘nonthermal’ if it cannot be accounted for by the spectrum of thermal bremsstrahlung or black-body radiation.

It is a very major undertaking to work out properly all the properties of synchrotron radiation, and that is beyond the scope of this book. For details, I refer the enthusiast to the books by Bekefi (1966), Pacholczyk (1970) and Rybicki and Lightman (1979) and the three review articles by Ginzburg and his colleagues (see the References section for this chapter).

Introduction

In this chapter, we look in a little more detail into some aspects of stellar evolution which will be important for studies of high energy astrophysical processes in our Galaxy and in extragalactic systems. For example, we need to know how far we can trust the theory of stellar structure and evolution; we need to know more details of the processes of nucleosynthesis in stars in order to understand the origin of the chemical composition of the interstellar gas and of the cosmic rays; we need to study what is known about the processes of mass loss from stars and the processes which can lead to the formation of dead stars; we need to investigate binary star systems in order to contrast their properties with those of X-ray binary systems containing neutron stars and black holes, and to discuss how such close binary stars can be formed. This survey is in no sense complete, and reference should be made to the texts recommended at the end of the book for more details.

The Sun as a star

Granted the outline of stellar evolution presented in Section 13.3, how well can the theory account for the properties of our own Sun? As by far the brightest star from our location in the Universe, it can be studied in much more detail than any other star, and is a benchmark for the theory of stellar structure and evolution. Until the last 20 years, the study of the Sun and the stars was largely confined to the interpretation of their surface properties.

Introduction – a global view of the interstellar medium

Hendrik van de Hulst, the theorist who predicted the 21-cm line of neutral hydrogen, once remarked that, if you set out to detect an emission or absorption line from an atom, ion or molecule in astronomy, you are bound to discover it somewhere in the Universe. This statement is particularly true of the interstellar medium because it is now understood that it is far from equilibrium and that a very wide range of densities and temperatures are present – those found largely reflect the characteristics of the observing tools used by the astronomer. It is no surprise, therefore, that there is a great deal of physics to be studied. Astrophysically, the understanding of the nature and properties of the interstellar gas is of the first importance, since it is out of this medium that new stars are formed. It is continually replenished because of mass loss from stars, and so the medium plays a key role in the birth-to-death cycle of stars. The same astrophysics is applicable to the study of diffuse gas anywhere in the Universe, be it galaxies, the intergalactic gas or the gas clouds in the vicinity of active galactic nuclei. These diagnostic tools are essential for determining the physical conditions in which high energy astrophysical processes take place. Furthermore, interstellar gas will prove to be an essential ingredient of the fuelling mechanisms for active galactic nuclei.

The interstellar medium amounts to about 5% of the visible mass of our Galaxy.

γ-ray observations of the Galaxy

Just as the Galactic radio emission outlines the distribution of high energy electrons and magnetic fields in the Galaxy, so the distribution of γ-radiation can provide information about high energy protons and the overall distribution of interstellar gas. As described in Section 5.4, in collisions between high energy particles and protons and nuclei of atoms and molecules of the interstellar gas, pions of all charges, π+, π0 and π-, are produced. The positive and negative pions decay into positive and negative muons, which, in turn, decay into positrons and electrons with relativistic energies (see Fig. 5.11). The latter may make a contribution to the low energy electron spectrum, and the predicted presence of positrons provides a direct test of the importance of the pion production mechanism in interstellar space. The neutral pions decay almost instantly into two γ-rays. In proton-proton collisions, the cross-section for the production of a pair of high energy γ-rays is roughly the geometric size of the proton, σγ ≈ 10-30 m2. The spectrum of γ-rays produced in such collisions is shown in Fig. 20.1. The characteristic signature of this process is that the spectrum of γ-rays has a broad maximum at about 70 MeV. Knowing the physical conditions in the interstellar gas, the γ-ray production rates by various mechanisms can be worked out. Stecker (1977) has carried out these calculations assuming an interstellar gas density of 106 particles m-3 and a local energy density of starlight of 4.4 × 105 eV m-3.

Distances in astronomy

The unit of distance used in astronomy is the parallax-second, or parsec. It is defined to be the distance at which the mean radius of the Earth's orbit about the Sun subtends an angle of one second of arc. In metres, the parsec, abbreviated to pc, is 3.0856 × 1016 m. For many purposes, it is sufficiently accurate to adopt 1 pc = 3 × 1016 m. The parsec is a recognised SI unit and it is often convenient to work in kiloparsecs (1 kpc = 1000 pc = 3 × 1019 m), megaparsecs (1 Mpc = 106 pc = 3 × 1022 m) or even gigaparsecs (where 1 Gpc = 109 pc = 3 × 1025 m).

Sometimes, it is convenient to measure distances in light-years, which is the distance light travels in one year: 1 light-year = 9.4605 × 1015 m. Thus, 1 pc = 3.26 light-years.

Another commonly used distance unit in astronomy is the astronomical unit, abbreviated to AU, which is the mean radius of the Earth's orbit about the Sun: 1 AU = 1.49578 × 1011 m. The very nearest stars to the Earth are at a distance of about 1 pc, and so they are about 2 × 105 times as far away as the Earth is from the Sun.

Accurate distances are among the most difficult measurements to make in astronomy, and there must, therefore, exist corresponding uncertainties in all the derived physical properties of astronomical objects.