IOAA 2022, Теория — Задача 3. Expanding ring nebula
International Olympiad on Astronomy and Astrophysics 2022 Georgia — Theoretical Competition · 16 август 2022 г. · 10 т.
Условие
A planetary nebula, located from the Earth, has the shape of a perfect circular ring with an inner radius of and an outer radius of . Its luminosity is powered by the UV radiation from the white dwarf remnant at the center of the nebula. From other observations, we know that 2000 years ago the inner radius of the nebula was and outer radius was . We believe that throughout these 2000 years the evolution of the nebula obeys a free expansion scenario, so gravity is negligible and the expansion velocity remains constant with time. Assume that all material in the planetary nebula was ejected at the same instant, but different gas particles have different velocities.
(a) Estimate the range of velocities of the gas particles [4 т.]
(b) Is the assumption of free expansion justified? Write YES or NO alongside appropriate calculations. [3 т.]
(c) If this planetary nebula is bright enough, would an astronaut aboard the International Space Station be able to resolve the thickness of the shell clearly? Write YES or NO alongside with necessary calculations. [3 т.]
Отговори
(a) from to
(b) YES
(c) YES
A diameter suffices.
Решение
(a) The distance traveled by the gas particles of inner and outer radius can be calculated as follows:
(b) At the inner edge, escape velocity from the white dwarf can be maximal (- Chandrasekhar limit)
Since , the no-gravity scenario can be applied. YES 1.0
(c)
Hence YES 1.0
Оригинал в Архива: Theory Problems.pdf · официални решения: Theory Solutions.pdf