IOAA 2016, theory — Задача 6. Cepheid Pulsations

Theoretical Examination · 10 т.

Условие

The star $\beta$-Doradus is a Cepheid variable star with a pulsation period of 9.84 days. We make a simplifying assumption that the star is brightest when it is most contracted (radius being $R_1$) and it is faintest when it is most expanded (radius being $R_2$). For simplicity, assume that the star maintains its spherical shape and behaves as a perfect black body at every instant during the entire cycle. The bolometric magnitude of the star varies from 3.46 to 4.08. From Doppler measurements, we know that during pulsation the stellar surface expands or contracts at an average radial speed of 12.8 km s$^{-1}$. Over the period of pulsation, the peak of thermal radiation (intrinsic) of the star varies from 531.0 nm to 649.1 nm.

T6.1 Find the ratio of radii of the star in its most contracted and most expanded states ($R_1/R_2$). [7 т.]

T6.2 Find the radii of the star (in metres) in its most contracted and most expanded states ($R_1$ and $R_2$). [3 т.]

T6.3 Calculate the flux of the star, $F_2$, when it is in its most expanded state. [5 т.]

T6.4 Find the distance to the star, $D_{\mathrm{star}}$, in parsecs. [5 т.]

Решение

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Оригинал в Архива: theory-qp.pdf · официални решения: theory_sol.pdf