USAAAO 2016, II кръг — Задача 14. Long Problem 2

USAAAO Round 2 Qualification Exam 2016 · 37 т.

Указания

(Read completely before you begin)

This is the second round qualification test for the USAAAO team. The test is short answer, consisting of 12 short questions and 2 longer, multipart questions. Once you begin, you will have two and a half hours (150 minutes) to complete the test. You may use the provided table of constants and a scientific calculator. No other materials are permitted.

Please show all your work. Answers without work will not receive credit. You will need to write your solutions on a separate sheet. Please begin a new page for each question, and number your pages. Please write as clearly as possible. Your test will be scanned for grading, so make sure that your writing is dark enough to be legible once scanned.

When you are done, please have your teacher scan your work and send it to usioaateam@gmail.com. We prefer to receive your work as a single pdf, named lastname_firstname.pdf.

Good luck.

Условие

The energy density of blackbody radiation is given by $u = 4\sigma T^4/c$, where $\sigma$ is the Stefan-Boltzmann constant. Assuming the temperature of the CMB today is $T_{CMB} = 2.73K$ and the critical density today is $\rho_{crit} = 0.921 * 10^{-29} h_{70}^2 g cm^{-3}$.

a. What is the energy density of the CMB? What is the corresponding $\Omega_{CMB}$? [6 т.]

b. What are the typical photon energies of the CMB, and the corresponding number density of photons per $cm^3$? [6 т.]

c. Assuming $\Omega_{CMB} = 0.3$ what was the redshift $z_{eq}$ of the transition from the radiation dominated to the matter dominated universe? [7 т.]

d. Assuming the age of the universe at the epoch of decoupling to be 380,000 years, and knowing its redshift, estimate the ate at $z_{eq}$. You can assume the expansion laws appropriate for an $\Omega = 1$ universe. [8 т.]

e. How old was the universe at the time when the temperature was comparable to the temperature in the Solar core, $T_c = 1.5 * 10^7 K$? [5 т.]

f. What were typical photon energies then? [5 т.]

Решение

---

Оригинал в Архива: 2016_round_2_test.pdf