Introducing the Stars by Martin Beech

Author:Martin Beech
Language: eng
Format: epub
ISBN: 9783030117047
Publisher: Springer International Publishing

4.5 Back to Reality

Finding a solution to the equations of stellar structure for a given stellar mass and initial composition is all well and good, but the ultimate test of such solutions is their ability to describe what is actually observed. As discussed in Chap. 1, the key observations that require explanation are the HR diagram (where the temperature, radius and luminosity of star are displayed), the mass-luminosity relationship and the mass-radius relationship (recall Figs. 1.​9, and 1.​11). The ability of stellar models to fully describe the main sequence in the HR diagram will be addressed in the next chapter, and for the moment we concentrate on other features—specifically, a basic explanation of the mass-luminosity relationship will be developed. To achieve this goal, we return to the use of approximation methods, and with the appropriate warnings of Eddington, Hoyle and Lyttleton ringing in our ears (recall Sect. 3.​2.​1), the various structure equations will be brought together in order to yield a set of scaling-law relationships. We begin with Eq. (4.5), and boldly approximating the temperature gradient as T/R, the luminosity is expressed as

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