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500 450 400 350

500 450 400 350

Figure 11.10. Examples of absorption and emission lines in sketches by the spec-troscopist, Lawrence Aller. (a) Spectrum of star a Carinae (Canopus), a star of Type F0, not unlike our sun (Type G2), showing absorption lines. The vertical and horizontal scales are changed leftward of 500 nm. (b) Partial spectrum (390-400 nm) of n Carinae, a star of type known as a luminous blue variable (LBV) which underwent huge mass ejections in the 1840s. This spectrum shows many narrow emission lines (He I, Cr II, Fe II, Ne II, Ne III, etc.) which are emitted by fluorescence of ejected gas. Very broad absorption and emission features are due to ionized calcium. The latter are emitted by fluorescence of ejected gas. The narrow absorption lines are due to interstellar gas between us and n Carinae. [(a) Adapted from L. Aller, Atoms, Stars & Nebulae, 3rd Ed., 1991, p. 60, Cambridge University Press; (b) ibid.., p. 285; reprinted with permission of Cambridge University Press]

Figure 11.10. Examples of absorption and emission lines in sketches by the spec-troscopist, Lawrence Aller. (a) Spectrum of star a Carinae (Canopus), a star of Type F0, not unlike our sun (Type G2), showing absorption lines. The vertical and horizontal scales are changed leftward of 500 nm. (b) Partial spectrum (390-400 nm) of n Carinae, a star of type known as a luminous blue variable (LBV) which underwent huge mass ejections in the 1840s. This spectrum shows many narrow emission lines (He I, Cr II, Fe II, Ne II, Ne III, etc.) which are emitted by fluorescence of ejected gas. Very broad absorption and emission features are due to ionized calcium. The latter are emitted by fluorescence of ejected gas. The narrow absorption lines are due to interstellar gas between us and n Carinae. [(a) Adapted from L. Aller, Atoms, Stars & Nebulae, 3rd Ed., 1991, p. 60, Cambridge University Press; (b) ibid.., p. 285; reprinted with permission of Cambridge University Press]

Consider 1 m2 of the stellar surface and let it radiate as a perfect blackbody into all directions in the upper hemisphere. Integrate the spectrum over all frequencies and all directions, taking into account the projected area, cos 9, at angle 9 to obtain the total power radiated by the 1 m2. It turns out to be

where a is the Stefan-Boltzmann constant:

a = 2n 2k43 = 5-670 x 10-8 Wm-2 K-4 (Stefan-Boltzmann (11.26) 15 c h constant)

The calculated flux (25) is that which passes in one direction through a surface immersed in a blackbody cavity. The total flux (in both directions) through the surface would be zero. The flux (25) increases rapidly with temperature. A doubling of the temperature yields a power greater by a factor of 16.

Since the spectrum from a normal star approximates that of a blackbody, one can use (25) to estimate its luminosity in terms of its surface temperature T and radius R. The surface area of the spherical star is 4nR2 and its luminosity is L ~ 4nR2a T 4. The approximate equality indicates that the star does not emit as a perfect blackbody. In Section 9.4, we defined an effective temperature Teff (9.13) to yield the exact relation,

L = 4nR2aTe4ff (W; luminosity of (11.27)

spherical object)

The total power L radiated by a star thus varies as the fourth power of Teff and the second power of its radius R.

Models of normal stars tell us that the more massive stars are both larger and hotter. In a simple model, the luminosity increases extremely fast with temperature, approximately as L a Teff 5 for lower mass stars where the dominant fusion process is initiated by a proton-proton interaction, the p-p process. For the massive hotter stars where fusion interactions involving carbon, nitrogen and oxygen take place, the model indicates L a T13. A small rise of surface temperature signifies a huge increase in the output from the thermonuclear reactions that power the star.

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