IOAA 2011, theory — Задача 2

Автор: Olympiads XYZ · транскрипция на официалните материали

Проверена срещу оригинала на 14.9.2026 от независим модел

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Съдържание

УсловиеРешение

Long theoretical questions

[Source note]

v3

Instructions

  1. You will receive in your envelope an English and native language version of the questions.

  2. You have 5 hours to solve 15 short (tasks 1-15) and 3 long tasks.

  3. You can use only the pen given on the desk.

  4. The solutions of each task should be written on the answer sheets, starting each question on a new page. Only the answer sheets will be assessed.

  5. You may use the blank sheets for additional working. These work sheets will not be assessed

  6. At the top of each page you should put down your code and task number.

  7. If solution exceeds one page, please number the pages for each task.

  8. Draw a box around your final answer.

  9. Numerical results should be given with appropriate number of significant digits with units.

  10. You should use SI or units commonly used in astronomy. Points will be deducted if there is a lack of units or inappropriate number of significant digits.

  11. At the end of test, all sheets of papers should be put into the envelope and left on the desk.

  12. In your solution please write down each step and partial result.

[Source note]

v3

[Source note]

Long theoretical questions (max 30 points each)

Условие

Within the field of a galaxy cluster at a redshift of z=0.500z = 0.500, a galaxy which looks like a normal elliptical is observed, with an apparent magnitude in the BB filter mB=20.40m_B = 20.40 mag.

The luminosity distance corresponding to a redshift of z=0.500z = 0.500 is dL=2754d_L = 2754 Mpc.

The spectral energy distribution (SED) of elliptical galaxies in the wavelength range 250 nm to 500 nm is adequately approximated by the formula:

Lλ(λ)∝λ4L_\lambda(\lambda) \propto \lambda^4

(i.e., the spectral density of the object's luminosity, known also as the monochromatic luminosity, is proportional to λ4\lambda^4.)

a) What is the absolute magnitude of this galaxy in the BB filter ?

b) Can it be a member of this cluster? (write YES or NO alongside your final calculation)

Hints: Try to establish a relation that describe the dependence of the spectral density of flux on distance for small wavelength interval. Normal elliptical galaxies have maximum absolute magnitude equal to -22 mag.

Решение

Внимание: Непълно решение

В предоставените източници няма официално решение.

Теми и трудност

Трудност: неоценена.

Галактики и космология · Светлина и астрономически измервания · Купове и тъмна материя · Галактики · Разширение на Вселената · Звездни величини · Поток и светимост · Определяне на разстояния · Спектри и спектрални линии

Оригинал в Архива: 2011_Long_Questions.pdf