USAAAO 2024, I кръг — Задача 2
USAAAO 2024 - First Round · 10 февруари 2024 г.
Problem writers
Wesley Andrade, Abhay Bestrapalli, Austin Chen, Justin Chen, Ved Gund, Hagan Hensley, Sandesh Kalantre, Evan Kim, David Lee, Joe McCarty, Arjun Patel, Sahil Pontula, Tara Rezaei, Raul Teixeira, Leo Yao, David Zhang
Условие
Abhay looks at the light curves for two main sequence stars A and B, which you can assume are blackbodies. A has its peak at a frequency two times as high as that of B. By looking at the depth of spectral lines, Abhay can also determine that A has higher metallicity than B. Abhay makes the following statements:
P: A has higher absolute magnitude than B.
Q: A is older than B.
Which of the following is true?
(a) P and Q are true.
(b) P and Q are false.
(c) P is true and Q is false.
(d) P is false and Q is true.
(e) We don’t have sufficient information for one or more of these statements.
Отговори
- B
Решение
Solution:
A has a peak at a higher frequency/lower wavelength, thus it has a higher temperature by Wien’s law. Thus, by Stefan Boltzmann’s law we can say A has higher intensity. This will means a lower absolute magnitude.
A has higher metallicity, thus it is younger (newer stars are able to use metals created in supernovae, and thus have higher metallic content).
P and Q are both false.
Answer: B
Оригинал в Архива: usaaao_first_exam_2024-3.pdf · официални решения: usaaao_first_exam_2024_solutions-1.pdf