Revealing the life cycle of a massive stellar cluster

High-resolution x-ray images from the Chandra X-ray Observatory and XMM-Newton elucidate all stages in the life cycles of massive stars—from ultracompact H II (UCHII) regions to supernova remnants—and the effects that those massive stars have on their surroundings.

Introduction: Uncertainties

The stellar initial mass function (IMF) is difficult to measure because of systematic uncertainties, selection effects, and statistical variance. Stars in clusters may all have the same age and distance, making their masses relatively straightforward to determine, but mass segregation, field star contamination, variable extinction, and small number statistics can be problems in determining the IMF.

The interstellar medium

Although to all intents and purposes a single or binary star may be regarded as evolving isolated in empty space, not only is it a member of a very large system of stars – a galaxy – but it is also immersed in a medium of gas and dust, the interstellar medium. This background material (mostly gas) amounts, in our Galaxy, to a few percent of the galactic mass, some 109 M ⊙, concentrated in a very thin disc, less than 103 light-years in thickness (we recall that 1 ly ≃ 9.5 × 1015 m), and ∼105 light-years in diameter, near the galactic midplane. Its average density is extremely small, about one particle per cubic centimetre, corresponding to a mass density of 10−21 k gm−3 (10−24 g cm−3); in an ordinary laboratory it would be considered a perfect ‘vacuum’. The predominant component of galactic gas – of which stars are formed – is hydrogen, amounting to about 70% of the mass, either in molecular form (H2), or as neutral (atomic) gas (HI) or else as ionized gas (HII), depending on the prevailing temperature and density. Most of the remaining mass is made up of helium. The interstellar material is not uniformly dispersed, but resides in clouds of gas and dust, also known as nebulae. We have already encountered special kinds of such nebulae: planetary nebulae, supernova remnants and nova shells.

What is a binary star?

As it turns out, the majority of stars are members of binary systems, or even multiple systems. The term binary in the stellar context was coined in 1802 by William Herschel only a few years after he introduced the term planetary nebula, as mentioned in Section 9.7. The first telescopic discovery of a double star, Mizar, is attributed to Giambattista Riccioli in 1650, just 41 years after Galileo's first telescope. Other stellar pairs were found by the mid-eighteenth century, but little effort was devoted at the time to their study.

A binary system consists of two stars revolving around their common centre of mass, as shown in Figure 11.1, and is defined by three parameters: the masses of its member stars and the distance d between their centres. The distance is not necessarily constant in time; it may vary periodically or change secularly. The masses, too, may change in the course of time. So perhaps a better characterization should be: initial masses and separation, and current age. Each parameter spans a wide range of values and their combinations are innumerable. In most cases, however, the members are so far apart that their individual structures and evolutionary courses are barely affected; they are thus no different from single stars, except that their dynamics as point masses is more complicated.

Binary stars are born together as a bound system; in principle, a star may capture another, in the presence of a third body, into a bound (negative energy) state, but the chances for that to happen are small even in a dense star cluster.

Having answered the two basic questions posed at the the end of Chapter 2, our present task is to combine the knowledge acquired so far into a general picture of the evolution of stars. We recall that the timescale of stellar evolution is set by the (slow) rate of consumption of the nuclear fuel. Now, the rate of nuclear burning increases with density and rises steeply with temperature, and the structure equations of a star show that both the temperature and the density decrease from the centre outward. We may therefore conclude that the evolution of a star will be led by the the central region (the core), with the outer parts lagging behind it. Changes in composition first occur in the core, and as the core is gradually depleted of each nuclear fuel, the evolution of the star progresses.

Thus insight may be gained into the evolutionary course of a star by considering the changes that occur at its centre. To obtain a simplified picture of stellar evolution, we shall characterize a star by its central conditions and follow the change of these conditions with time. We have seen that besides the composition, the temperature and density are the only properties required in order to determine any other physical quantity. If we denote the central temperature by Tc and the central density by ρc , the state of a star is defined at any given time t by a pair of values: Tc (t) and ρc (t). Consider now a diagram whose axes are temperature and density.

It is now a decade since the publication of the first edition of this book. Despite the large number of research papers devoted to the subject during this period of time, the basic principles and their applications that are addressed in the book remain valid and hence the original text has been mostly left unchanged. And yet a major development did occur soon after the book first appeared in print: the ‘solar neutrino problem’ that had puzzled physicists and astrophysicists for almost four decades finally found its solution, which indeed necessitated new physics. However, the new physics belongs to the theory of elementary particles, which must now account for neutrino masses, rather than to the theory of stars. Also worth mentioning is a major recent discovery that finally provides support to the theory proposed about four decades ago regarding the end of very massive stars in powerful supernova explosions triggered by pair-production instability: SN2006gy, the first observed candidate for such a mechanism. Thus the section on solar neutrinos is now complete and that on supernovae expanded.

Stellar evolution calculations have made great progress in recent years, following the rapid development of computational means: increasingly faster CPUs and greater memory volumes. Nevertheless, I have made use of new results only when they provide better illustration for points raised in text. For the most part, old results are still valid and this long-term validity is worth emphasizing; the theory of stellar structure and evolution, with all its complexity, is a well-established physical theory.