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khí quyển sao p6

Mặt trời là không đồng đều sáng trên tất cả, nhưng nó là tối tăm đối với chi. Hiệu ứng này là phát âm ở cuối màu xanh của quang phổ và ít rõ ràng hơn màu đỏ. Một lý tốt đại diện thực nghiệm về hình thức của chi tối được cho bởi một phương trình cho cường độ cụ thể của mẫu | 1 CHAPTER 6 LIMB DARKENING 6.1 Introduction. The Empirical Limb-darkening The Sun is not equally bright all over but it is darkened towards the limb. The effect is more pronounced at the blue end of the spectrum and less pronounced at the red. A reasonably good empirical representation of the form of the limb darkening is given by an equation for the specific intensity of the form I r I 0 1 - u 1 6.1.1 V Here a is the radius of the solar disc r is radial distance from the centre of the disc and u is the limb darkening coefficient. This is often written in terms of 0 see figure VI.1 or of LI cos 0 6.1.2 I 0 I 0 1 - u 1 - cos0 I 0 1 - u 1 - L Whether written in the form of equation 6.1.1 or 6.1.2 I 0 is the specific intensity at the centre of the disc. The specific intensity at the limb where r a or 0 90o is I 0 1-u . The limb darkening coefficient can be written as u I centre - I limb I centre . Equation 6.1.1 is shown in graphical form in figure VI.2 for different values of the limb darkening coefficient. 2 -0.8 -0.6 -0.4 0.5 -0.2 0 0.2 r FIGURE VI.2 Equation 6.1.1 for six limb darkening coefficients from the lowest curve upwards u 1.0 0.8 0.6 0.4 0.2 and 0.0. The curve for the last of these no limb darkening is formed from three of the boundary lines. The curve for u 1 is a circle. The radius of the disc is taken to be 1 r 0 is the centre of the disc and r 1 is the limb. Limb-darkening is much greater in the violet and near ultraviolet than in the red. For example at a wavelength of 600 nm u 0.56 whereas at 320 nm u 0.95. A slightly better empirical representation of the limb darkening can be obtained with two parameters u and v I e I 0 1 - u 1 - cos e - v sin 2 e 6.1.3 Why is the Sun darkened towards the limb We may perhaps imagine that the surface of the Sun radiates like a black body with uniform lambertian radiance but it is surrounded by an absorbing atmosphere. Light from near the limb has to traverse a greater length of atmosphere than light from near the .