The Keffect

In general, the opacities increase with increasing metallicity. This is the case for the bound-free (see Equation (16.107) in Cox & Giuli (1969)) and free-free (see Equation (16.95) in Cox & Giuli (1969)) transitions. Using the well-known mass-luminosity relation L ¡.i4M3/k, where ¡x is the mean molecular mass, M the mass of the star, and k the opacity, one immediately deduces that the increase of the opacity produces a decrease of the luminosity. This can be seen in the left-hand part

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Figure 36.1. Left panel: zero-age main-sequence (ZAMS) locations in the HR diagram of M0, 3M0 and 20M0 star models for various metallicities. Models for Z = 0.1 are identified by triangles. Figure taken from Mowlavi et al. (1998b). Right panel: variations of the radius as a function of initial mass, for various metallicities on the ZAMS.

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Figure 36.1. Left panel: zero-age main-sequence (ZAMS) locations in the HR diagram of M0, 3M0 and 20M0 star models for various metallicities. Models for Z = 0.1 are identified by triangles. Figure taken from Mowlavi et al. (1998b). Right panel: variations of the radius as a function of initial mass, for various metallicities on the ZAMS.

of Figure 36.1 for the 3M0 and M0 stellar models and for metallicities inferior or equal to 0.04. At still higher metallicities the effect of ^ becomes more important than the opacity effect and the luminosity increases (see below).

In contrast, for massive stars free electron scattering is the main opacity source. This opacity depends only on X, with Ke — 0.20(1 + X), which is about constant at Z < 0.01 and decreases with Z at Z > 0.01. Thus at high Z the luminosity of the 20M0 model shown in the left-hand part of Figure 36.1 first remains nearly constant and then increases with the metallicity.

In the right-hand part of Figure 36.1 the variation of the radii on the zero-age main sequence (MS) for stars of various initial masses and metallicities is shown. We see that the radii increase with the metallicity. From the relation L = 4n R2a Tf and from the variation of L with Z one can deduce that, when the metallicity increases, the effective temperature decreases. For metallicities superior to about 0.04, the effective temperature and the luminosity both increase due to the ^-effect (see below).

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