USAAAO 2026, I кръг — Задача 22

USAAAO 2026 - First Round · 9 февруари 2026 г.

Problem writers

Problem writers: Srihari (Hari) Balaji, Vincent Bian, Ferdinand, Hagan Hensley, Elizabeth Lee, Joe McCarty, Lucas Pinheiro, Feodor Yevtushenko

Условие

Use the following information for Questions 21, 22, and 23. Consider the following graph, which shows the mean orbital velocity of stars around a galaxy’s center as a function of distance from the center. The graph also shows the expected orbital velocities (dashed line) from observations of visible matter. The discrepancy between the observed and expected values is assumed to be due to invisible dark matter.

Galaxy rotation curve drawn over a photo of a spiral galaxy: Velocity (km s⁻¹) axis with ticks 50 and 100, Distance (light years) axis with ticks 10,000, 20,000, 30,000 and 40,000; yellow points with error bars labelled “Observations from starlight” at small radii, blue points labelled “Observations from 21 cm hydrogen” at large radii, a white solid curve through them rising and then slowly increasing, a green dot-dash line labelled “Low-radius best fit” near the origin, and a grey dashed curve labelled “Expected from the visible disk” peaking near 60 km/s and then declining.

Now, for larger values of rr, the discrepancy between the observed and expected rotation curves begins to appear more significant. Assume that the expected rotation curve (dashed gray) curve is calculated off the distribution of all baryonic (“standard”) matter, while the observed rotation curve (solid white) is due to the combination of baryonic matter and dark matter. Within a radius of r=40,000r = 40,000 ly from the galactic center, and according to the graph, which of the following is closest to the ratio between the dark matter mass and the baryonic matter mass enclosed?

(a) 2

(b) 5

(c) 10

(d) 25

(e) 50

Отговори

Решение

Оригинал в Архива: usaaao_first_exam_2026.pdf · официални решения: usaaao_first_exam_solutions_2026.pdf