IAO 2017, Практически тур, Група β — Задача 7. Spectral observation on an interacting galaxy.

XXII International Astronomy Olympiad — Practical round, Group β · 10 т.

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Languages of the solutions. (For Practical and also for Observational rounds).

No text in any language is permitted to use in solutions. All the solution must be written using only drawing pictures, plotting graph, writing formulae, numerical values and standard international astronomy symbols (like ♂, ♎, α UMa, M31, 5ᵐ). Numerical values must be written using standard symbols but not symbols of National alphabet. Jury of the Practical round will not take into account any text in any language in solution.

For example, the names of constellations, written in English, Russian or any other language will be not taken into account (should be only UMa, Ori, etc.).

Some constants and formulae — archive reference

Archive reference sheet: Some constants and formulae, explicitly headed Round Theo, groups α and β. It is retained here as an attributed archive reference; it is not claimed to have been handed out during the practical round.

Quantity	Value
Speed of light in vacuum, $c$ (m/s)	299792458
Constant of gravitation, $G$ (N·m²/kg²)	$6.674\cdot10^{-11}$
Solar constant, $A$ (W/m²)	1367
Hubble parameter, $H_0$ (km/s/Mpc), mean value	68
Hubble parameter, diapason of values	50–100
Plank constant, $h$ (J·s)	$6.626\cdot10^{-34}$
Charge of electron, $e$ (C)	$1.602\cdot10^{-19}$
Mass of electron, $m_e$ (kg)	$9.109\cdot10^{-31}$
Proton-to-electron mass ratio	1836.15
Faraday constant, $F$ (C/mol)	96485
Magnetic constant, $\mu_0$ (H/m)	$1.257\cdot10^{-6}$
Universal gas constant, $R$ (J/mol/K)	8.314
Boltzmann constant, $k$ (J/K)	$1.381\cdot10^{-23}$
Stefan-Boltzmann constant, $\sigma$ (W/m²/K⁴)	$5.670\cdot10^{-8}$
Wien's displacement constant, $b$ (m·K)	0.002897
Laboratory wavelength of Hα (Å)	6562.81
Tropical year length, $T$ (days)	365.242199
Sidereal year length, $T$ (days)	365.25636
Anomalistic year length, $T$ (days)	365.259636
Nodal period of lunar orbit (years)	~18.6
Standard atmosphere (Pa)	101325
Visible light extinction by the terrestrial atmosphere in zenith (minimum)	19%, $0.23^{\mathrm m}$
Height of homogeneous atmosphere (m)	7991
Refractive index of water for 20°C, $n$	1.334
Moment of inertia of a solid ball	$I=\frac25MR^2$
Moment of inertia of sphere	$I=\frac23MR^2$
Volume of a ball	$V=\frac43\pi R^3$
Area of sphere	$S=4\pi R^2$
$\pi$	3.14159265
$e$	2.71828183
Golden ratio, $\varphi$	1.61803399

Условие

The low-resolution spectra of 15 different regions in an interacting galaxy Arp 86 were observed by Multi-Object Spectrograph (MOS) on the 2.16-m telescope of Xinglong Station near Beijing, National Astronomical Observatories of China. The data is analyzed by Zhou et al. (2014, RAA, 14, 1393). The measured fluxes of the [OIII], Hβ, [NII], Hα emission lines are shown in Table β7 (see separate sheet). The fluxes are in units of $10^{-16}\ \mathrm{erg/s/cm^2}$.

7.1 Plot the scatter diagram between $\log_{10}(\mathrm{[OIII]}/\mathrm{H}\beta)$ vs. $\log_{10}(\mathrm{[NII]}/\mathrm{H}\alpha)$ for regions in the galaxy. [2 т.]

7.2 Draw a dashed curve on the diagram for the diagnostic function:

given by Kauffmann et al. (2003, MNRAS, 346, 1055). If the point of a region in the diagram is above this curve, the region can be classified as “AGN” (Active Galactic Nuclei). Determine which regions can be classified as “AGN”, write the answer in form of «AGN = “Region ID” …». (“Region ID” are given in the 1st column of Table β7.) [2 т.]

7.3 In your answer book draw a table in form of the following example. Calculate the angular distance between each region to the center ($\alpha=23^h47^m04.8^s$, $\delta=+29^\circ29'00.6''$) of the galaxy (in units of arcsec). Calculate the luminosities of Hα ($L(\mathrm{H}\alpha)$) for each region (in units of erg/s), and then estimate the Star Formation Rate (SFR) for each region based on Hα luminosities, following the formula:

Calculate the metallicities (oxygen abundance in units of $\log_{10}(\mathrm{O/H})$) of interstellar medium (ISM) for each region, following the formula:

The redshift of Arp 86 is: 0.016.

[3 т.]

7.4 Plot the radial distribution of the $\log_{10}(\mathrm{O/H})$ of this galaxy. The radial distribution should be plotted as a scatter diagram: $\log_{10}(\mathrm{O/H})$ vs. $\beta$, where $\beta$ is angular distance to the center in arcsec. [2 т.]

7.5 Draw a straight dashed line on the scatter diagram of oxygen abundance ($\log_{10}(\mathrm{O/H})$) radial distribution to indicate the trend of the profile. If there is a linear relation between $\log_{10}(\mathrm{O/H})$ and $\beta$, i.e. as $\log_{10}(\mathrm{O/H})=A+B\times\beta$, estimate $B$ with a help of graphical method, write the answer in form of «$B=\ldots$». [1 т.]

Table for problem 7

Отговори

Решение

Теми и трудност

Трудност: неоценена.

Светлина и астрономически измервания · Галактики и космология · Екзопланети и среди · Спектри и спектрални линии · Активни галактики и квазари · Междузвездна среда

Предпоставки: Разширена олимпиадна подготовка

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Оригинал в Архива: betapract.pdf · официални решения: practsol.pdf · допълнителни данни: instructions.pdf · допълнителни данни: data.pdf · допълнителни данни: hrd.pdf