Basic Astrophysics by Dan Maoz

By Dan Maoz

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8). Sometimes, one of the members may be too faint, or devoid of strong absorption lines, to be detectable in the combined spectrum, but its presence will still be revealed by the periodically changing Doppler shifts of the brighter star. In fact, this is the very method by which planets orbiting other stars have been discovered in recent years (see below). To see how binaries sometimes allow stellar mass determination, let us review some aspects of the Keplerian two-body problem, in which two masses orbit their common center of mass in elliptical trajectories.

Assume again i = 90◦ and find the radius of each star. Is the result still insensitive to the exact value of i? 46r . basicastro4 October 26, 2006 basicastro4 October 26, 2006 Chapter Three Stellar Physics In this chapter, we will obtain a physical understanding of main-sequence stars and of their properties, as outlined in the previous chapter. The Sun is the nearest and best-studied star, and its properties provide useful standards to which other stars can be compared. For reference, let us summarize the measured parameters of the Sun.

58) dL(r) = 4πr2 ρ(r) (r). 59) We can define four boundary conditions for these equations. 63) where M∗ is the total mass of the star. 65) = (ρ, T, composition). 66) P (ρ, T ) is usually called the equation of state. Each of these three functions will depend on the composition through the element abundances and the ionization states of each element in the gas. It is common in astronomy to parametrize the mass abundances of hydrogen, helium, and the heavier elements (the latter are often referred to collectively by the term “metals”) as ρH ρHe ρmetals X≡ , Y ≡ , Z≡ .

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