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Theory of Rotating Stars. (PSA-1)

Theory of Rotating Stars. (PSA-1)

Jean-Louis Tassoul
Copyright Date: 1978
Pages: 528
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    Theory of Rotating Stars. (PSA-1)
    Book Description:

    Ever since the first observations of sunspots in the early seventeenth century, stellar rotation has been a major topic in astronomy and astrophysics. Jean-Louis Tassoul synthesizes a large number of theoretical investigations on rotating stars. Drawing upon his own research, Professor Tassoul also carefully critiques various competing ideas.

    In the first three chapters, the author provides a short historical sketch of stellar rotation, the main observational data on the Sun and other stars on which the subsequent theory is based, and the basic Newtonian hydrodynamics used to study rotating stars. Following a discussion of some general mechanical properties of stars in a state of permanent rotation, he reviews the main techniques for determining the structure of a rotating star and its stability with respect to infinitesimal disturbances. Since the actual distribution of angular momentum within stars is still unknown, Professor Tassoul considers various models of angular momentum as well as of meridional circulation. He devotes the rest of his study to the problems concerning various groups of stars and stages in stellar evolution.

    Originally published in 1979.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

    eISBN: 978-1-4008-6898-8
    Subjects: Astronomy

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-x)
  3. Preface
    (pp. xi-2)
  4. 1 An Historical Overview
    (pp. 3-15)

    The study of stellar rotation began about the year 1610, when sunspots were observed for the first time through a refracting telescope. The first public announcement of an observation came in June 1611 from Johannes Goldschmidt (1587–1615)—a native of East Friesland, Germany—who is generally known by his Latinized name Fabricius. From his observations he correctly inferred the spots to be parts of the Sun itself, thus proving axial rotation. He does not appear to have appreciated the importance of this conclusion, and pursued the matter no further.

    According to his own statement, Galileo Galilei (1564–1642) observed...

  5. 2 The Observational Data
    (pp. 16-42)

    In Sections 1.1 and 1.2 we discussed the early measurements of the axial rotation of the Sun and the stars. Remarkably, most present-day methods of reduction still largely rely upon these pioneering studies. Our intent here, then, is to present a general survey of the recent observational data pertaining to stellar rotation, and the various assumptions underlying their reduction. The Sun, the single stars, and the binaries are examined in turn. For the present, we shall not aim at completeness, but limit ourselves, rather, to the main observational features that we will need in the subsequent chapters. Specific groups of...

  6. 3 Stellar Hydrodynamics
    (pp. 43-73)

    As we may infer from the observations, most stars remain in a state of hydrostatic equilibrium under the action of their own gravitation and centrifugal force of axial rotation. However, detailed study of the Sun has demonstrated that such a balance of forces is only approximate. Indeed, the solar surface shows traces of internal motions, both around the axis of rotation and in the meridional planes (cf. cf. §2.2). Departure from strict equilibrium is also apparent during some phases of stellar evolution; and, in this respect, we may mention the pulsating stars, the novae and supernovae, and the flare stars....

  7. 4 Permanent Rotations
    (pp. 74-94)

    Let us consider a star for which rotational motion and magnetic field are completely negligible; suppose further that the self-gravitating configuration is isolated from other bodies. Then, as is well known, the system assumes a spherical shape, i.e., the surface upon which the total pressurepvanishes is a sphere. Moreover, the surfaces of constant pressure—the isobaric surfaces—can be described by means of concentric spheres. In consequence, the gravitational potentialV,the densityp,the temperatureT,and the luminosity L also possess central symmetry. (Although these assertions may not be evident to a mathematician, they are reasonably...

  8. 5 Stellar Models: Techniques
    (pp. 95-115)

    In the preceding chapter we discussed some general mechanical properties of stars in a state of permanent rotation. Although, on physical grounds, we must distinguish between barotropes and baroclines, rotation natu rally delineatesthreeclasses of stars: (i) the barotropes, (ii) the pseudobarotropes, and (iii) the genuine baroclines (cf. §4.3). The first two families are chiefly characterized by their having an angular velocity that is a constant over cylinders centered about the axis of symmetry, i.e., δΩ/δz = 0; on the contrary, the latter condition never obtains in the case of genuine baroclines. (Clearly, barotropes and pseudo-barotropes include the con...

  9. 6 Small Oscillations and Stability: Techniques
    (pp. 116-158)

    In most instances, configurations in a state of permanent rotation provide an adequate description of actual rotating stars. However, it must be borne in mind that our basic underlying assumptions were made on account of mathematical difficulties (cf. §4.2), and that they neverstrictlyobtain in nature. For instance, can we surmisea priorithat the effective gravity g always exactly balances the pressure force in a real star? As a matter of fact, not every model in a state of permanent rotation can actually occur in nature: the models must not only obey the general conservation principles of physics...

  10. 7 The Angular Momentum Distribution
    (pp. 159-187)

    As we recall from Chapter 4, many fundamental properties of a configuration in a state of permanent rotation can be derived in a straightforward manner from the condition of mechanical equilibrium. Although these results have a direct bearing on several aspects of the theory of stellar rotation, they provide no clue as to what the angular momentum distribution is in a star. Also, because we have hitherto circumvented the use of the condition of energy conservation when constructing equilibrium models, we do not know as yet whether we can apply these results, without modification, to an actual radiating star. For...

  11. 8 Meridional Circulation
    (pp. 188-218)

    This chapter is primarily concerned with large-scale meridional currents that may occur in a star perturbed away from spherical symmetry. For the sake of simplicity, we shall restrict ourselves to rotationally driven currents only, but similar large-scale motions also exist in tidally or magnetically distorted stars. The possible existence of meridional currents in the radiative regions of rotating stars was first suggested independently by Vogt and by Eddington in order to solve the problem of thermal equilibrium posed by the von Zeipel paradox (cf. §7.2). As they showed, the effect of radiative transfer alone attempting to maintain thermal equilibrium is...

  12. 9 The Solar Dififerential Rotation
    (pp. 219-232)

    The problem presented by the differential rotation of the Sun is one of long standing and many efforts have been made to formulate a plausible flow pattern that reproduces the observed fluid motions on the solar surface. As we repeatedly pointed out in the two previous chapters, very little is known thus far about the angular momentum distribution within a star; and, in spite of the recent work by Dicke and his colleagues, the Sun is no exception (cf. §11.4). Our intent, then, is to devote this brief chapter to those models that attempt to explain the mean solar rotation...

  13. 10 Solid-Body Rotation vs. Differential Rotation
    (pp. 233-272)

    So far, we have described the general principles governing the motion of rotating stars, and we have applied these principles to specific models that have level surfaces that deviate but slightly from spheres. Consider now a single star with fixed angular momentum J and mass M, within which electromagnetic effects may be neglected. To simplify matters even further, let us restrict ourselves to barotropic models and ignore all problems pertaining to energy transport (cf. §7.2). Impose the condition next that the system must rotate with some prescribed rotation law Ω = Ω(Φ), which satisfies the Hǿiland criterion for stability (cf....

  14. 11 Collapse and Fission
    (pp. 273-304)

    Although there is as yet no general agreement about the process of star formation, it is commonly accepted that stars are born out of diffuse gas and dust found in interstellar space. The most detailed theories postulate conditions in the interstellar medium such that large-scale hydrodynamical or thermal instabilities will occur over extended regions of the Galaxy. For instance, according to the classical picture first put on a quantitative basis by Jeans in 1902, the initial step in star formation is the pulling together, by gravitational forces, of some large mass of interstellar matter. This requires, in essence, that the...

  15. 12 Stellar Models: Structure and Evolution
    (pp. 305-361)

    With the advent of high-speed computers, significant advances have been made in our understanding of the structure and evolution of rotating stars. However, as we indicated in Chapter 7, the actual distribution of angular momentum within a star is still largely unknown; hence, in all models proposed to date, the rotation law is always specified in anad hocmanner. In other words, even the most detailed calculations are still very preliminary in character, their aim being essentially to evaluate the gross changes caused by rotation on stellar models. The modifications brought by rotation on the interiors of chemically homogeneous,...

  16. 13 Rotating White Dwarfs
    (pp. 362-384)

    Despite our lack of knowledge about the exact manner in which the various possible endpoints of stellar evolution are attained, great progress has been made in our basic understanding of white dwarfs as cooling degenerate dwarfs. Since a number of comprehensive papers on the theory of spherical white-dwarf models now exist, a brief survey of their properties will suffice for our purpose. As we know, a white dwarf is largely supported against gravity by the pressure provided by the kinetic energy of thedegenerateelectrons; in contrast, its luminosity is almost entirely derived from the thermal energy of thenondegenerate...

  17. 14 Oscillations and Stability
    (pp. 385-421)

    As we recall from Section 6.4, the natural oscillation frequencies of a spherical star in hydrostatic equilibrium can be classified according to several types: the (radial and nonradial)p-modes, the (nonradial)f-modes, and the (nonradial)g-modes. In the absence of any dissipative mechanism, the possible modes of instability of a spherical star are these: (i) the lowest radial mode that becomes dynamically unstable when the adiabatic exponent is less than 4/3 in a large portion of the star, and (ii) theg-oscillations that become convectively unstable when the Schwarzschild criterion for stability is violated in some part of the star...

  18. 15 Stellar Magnetism and Rotation
    (pp. 422-447)

    The role of magnetic fields in rotating stars has been considered at various places in this book. For example, in Section 11.4 we showed that magnetically controlled winds provide an efficient means for extracting angular momentum from rotating stars with convective envelopes. It is the purpose of this chapter to outline the major theoretical problems of interest in the study of rotating stars containing large-scale magnetic fields. It will in no way be an exhaustive study; however, references will be given for further pursuit. In Section 15.2, we discuss the gross changes brought by large scale magnetic fields on the...

  19. 16 Rotation in Close Binaries
    (pp. 448-469)

    The effect of axial rotation upon the structure, evolution, and stability of a single star has been the main subject matter of this book. In the preceding chapter, we showed that the presence of magnetic fields actuates extra degrees of freedom that introduce a number of new elements into the problem of axial rotation. Further challenging problems arise from the study of double stars whose components are close enough to induce tidal distortion on each other. (The main observational data pertaining to these matters was presented in Section 2.4.) Since many comprehensive surveys of the double-star problem are now available...

  20. Epilogue
    (pp. 470-474)

    The theory of rotating stars had its beginnings in the Scientific Revolution, which took place in Europe during the seventeenth century, and it has since aroused the interest of many distinguished scientists. Yet, most (if not all) problems of stellar rotation belong to what Kuhn has described as “normal science,” that is to say, a highly convergent or consensus-bound activity that is firmly based upon one or more major scientific achievements of the past and that results in a cumulative progression of new ideas developing from antecedent ideas in a logical sequence. Indeed, as can be inferred from the study...

    (pp. 475-476)
    (pp. 477-480)
    (pp. 481-482)
    (pp. 483-486)
  25. Appendix E: THE ψ-AND x-FUNCTIONS
    (pp. 487-492)
  26. Index of Names
    (pp. 493-502)
  27. Index of Subjects
    (pp. 503-506)
  28. Back Matter
    (pp. 507-507)