astro-init - 用户贡献 [zh-cn]

2017年IOAA理论第11题-本星系群的质量

2019-09-08T08:46:54Z

Fjllrven Hu：

== 英文原题 ==
'''Mass of the Local Group''' [50 marks]

The dynamics of M31 (Andromeda) and the Milky Way (MW) can be used to estimate the total mass of the Local Group (LG). The basic idea is that galaxies currently in a binary system were at approximately the same point in space shortly after the Big Bang. To a reasonable approximation, the mass of the local group is dominated by the masses of the MW and M31. Via Doppler shifts of the spectral lines, it was found that M31 is moving towards the MW with a speed of 118 km·s−1. This may be surprising, given that most galaxies are moving away from each other with the general Hubble flow. The fact that M31 is moving towards the MW is presumably because their mutual gravitational attraction has eventually reversed their initial velocities. In principle, if the pair of galaxies is well-represented by isolated point masses, their total mass may be determined by measuring their separation, relative velocity and the time since the universe began. [https://ui.adsabs.harvard.edu/abs/1959ApJ...130..705K/abstract Kahn and Woltjer (1959)] used this argument to estimate the mass in the LG.

In this problem we will follow this argument through our calculation as follows.

== 中文题目 ==
'''本星系群的质量''' [50 分]

M31（仙女座星系）以及银河系之间的动力学过程可以用来估算整个本星系群的质量。可以做个这样的基本假设：现存星系对里的两个星系在宇宙大爆炸后没多久，大致都在相同的位置上。为了合理估算整个本星系群的质量，这里还得假设本星系群总质量绝大部分都是由 M31 和银河系贡献出来的。通过谱线测量出的多普勒红移，可看出 M31 现在正以 118 km·s−1 朝银河系运动。也许你会比较惊讶，毕竟通常而言星系会因为哈勃流导致相互远离。但实际上 M31 正朝向银河系运动也不是不可能，因为（星系群里）引力的相互作用的效果（本动速度）要高于哈勃流（退行速度）带来的效果。把星系对中的俩星系视为俩质点，它们总质量就能通过两者间距离、相对运动速度以及宇宙年龄来得出。 [https://ui.adsabs.harvard.edu/abs/1959ApJ...130..705K/abstract Kahn & Woltjer (1959)] 就是这样计算本星系群质量的。

请顺着该思路计算本星系群的质量。

== 题目解答 ==

2017年IOAA理论第7题-外星生命

2019-09-08T08:41:55Z

Fjllrven Hu：/* 中文翻译 */

{{需要解答}}

IOAA赛场上通常是使用英文回答问题，所以建议各位用英文回答本题

=英文原题=
'''(T7) Life on Other Planets [20 marks]'''

One place to search for life is on planets orbiting main sequence stars. A good starting point is the planets that have an Earth-like temperature range and a small temperature fluctuation. Assume that for a main sequence star, the relation between the luminosity ''L'' and the mass ''M'' is given by

''L ∝ M3.5''

You may assume that the total energy ''E'' released over the lifetime of the star is proportional to the mass M of the star. For the Sun, it will have a main sequence lifetime of about 10 billion years. The stellar spectral types are given in the table below. Assume that the spectral subclasses of stars (0-9) are assigned on a scale that is linear in log M .
{| class="wikitable"
|+
|Spectral Class
|O5V
|B0V
|A0V
|F0V
|G0V
|K0V
|M0V
|-
|Mass（''M''⊙）
|60
|17.5
|2.9
|1.6
|1.05
|0.79
|0.51
|}

a) If it takes at least 4×109 years for an intelligent life form to evolve, what is the spectral type (accurate to the subclass level) of the most massive star in the main sequence around which astronomers should look for intelligent life? [6]

b) Assume that the target planet has the same emissivity ''ε'' and albedo ''a'' as the Earth. In order to have the same temperature as the Earth, express the distance ''d'', in au, of the planet to its parent main sequence star, of mass ''M''. [6]

c) The existence of a planet around a star can be shown by the variation in the radial velocity of the star about the star-planet system centre of mass. If the smallest Doppler shift in the wavelength detectable by the observer is (Δ''λ'' / ''λ'') =10-10 , calculate the lowest mass of such a planet in b), in units of Earth masses, that can be detected by this method, around the main sequence star in a). [8]

=中文翻译=
'''外星生命'''

寻找地外生命的一个基本思路就是从围绕主序星公转的系外行星下手。最好是从那些和地球气温相似，且温差变化较小的行星开始找起。对于任意主序星，它的光度 L 和质量 M 满足：

''L ∝ M3.5。''

假定恒星在主序阶段辐射出的总能量 E 与它的质量 M 成正比。以太阳为例，它在主序阶段时长为100亿年。下表给出了不同光谱型的恒星质量。假设恒星同一光谱型中的每一亚级（数字）用 logM 的线性关系来分割：

{| class="wikitable"
|光谱型
|O5V
|B0V
|A0V
|F0V
|G0V
|K0V
|M0V
|-
|质量（''M''⊙）
|60
|17.5
|2.9
|1.6
|1.05
|0.79
|0.51
|}

（a）如果一颗行星进化出智慧生命至少需要40亿年的话，那么天文学家应该着重搜寻哪些光谱型的恒星？（光谱型应精确到具体的子类）

（b）假设目标行星的辐射率 ε 和反照率 a 与地球相同。如果该行星的温度和地球相近，请以天文单位 au 为单位，列出该行星到其质量为 M 的母恒星的距离 d 的表达式。

（c）如果一颗恒星周围有一颗行星围绕它转动，恒星的视向速度就会发生微小的变化。如果观测者能探测到的最小多普勒位移是(Δ''λ'' / ''λ'') =10-10，请计算围绕（a）问中这类光谱型的恒星绕转的（b）问中这类行星的最小质量，以地球质量为单位。

（（a）问的题目有一些问题。实际上答案给出来的确实是一个范围，但是确是临界情况——也就是什么光谱型的恒星恰好满足这40亿年的条件）

2017年IOAA理论第7题-外星生命

2019-09-08T08:39:45Z

Fjllrven Hu：机翻味道太浓了。

{{需要解答}}

IOAA赛场上通常是使用英文回答问题，所以建议各位用英文回答本题

=英文原题=
'''(T7) Life on Other Planets [20 marks]'''

One place to search for life is on planets orbiting main sequence stars. A good starting point is the planets that have an Earth-like temperature range and a small temperature fluctuation. Assume that for a main sequence star, the relation between the luminosity ''L'' and the mass ''M'' is given by

''L ∝ M3.5''

You may assume that the total energy ''E'' released over the lifetime of the star is proportional to the mass M of the star. For the Sun, it will have a main sequence lifetime of about 10 billion years. The stellar spectral types are given in the table below. Assume that the spectral subclasses of stars (0-9) are assigned on a scale that is linear in log M .
{| class="wikitable"
|+
|Spectral Class
|O5V
|B0V
|A0V
|F0V
|G0V
|K0V
|M0V
|-
|Mass（''M''⊙）
|60
|17.5
|2.9
|1.6
|1.05
|0.79
|0.51
|}

a) If it takes at least 4×109 years for an intelligent life form to evolve, what is the spectral type (accurate to the subclass level) of the most massive star in the main sequence around which astronomers should look for intelligent life? [6]

b) Assume that the target planet has the same emissivity ''ε'' and albedo ''a'' as the Earth. In order to have the same temperature as the Earth, express the distance ''d'', in au, of the planet to its parent main sequence star, of mass ''M''. [6]

c) The existence of a planet around a star can be shown by the variation in the radial velocity of the star about the star-planet system centre of mass. If the smallest Doppler shift in the wavelength detectable by the observer is (Δ''λ'' / ''λ'') =10-10 , calculate the lowest mass of such a planet in b), in units of Earth masses, that can be detected by this method, around the main sequence star in a). [8]

=中文翻译=
'''外星生命'''

寻找地外生命的一个基本思路就是从围绕主序星公转的系外行星下手。最好是从那些和地球气温相似，且温差变化较小的行星开始找起。对于任意主序星，它的光度 L 和质量 M 满足：

''L ∝ M3.5。''

假定恒星在主序阶段辐射出的总能量 E 与它的质量 M 成正比。以太阳为例，它在主序阶段时长为100亿年。下表给出了不同光谱型的恒星质量。假设恒星同一光谱型中的每一个小级（数字）用 logM 的线性关系来分割：

{| class="wikitable"
|光谱型
|O5V
|B0V
|A0V
|F0V
|G0V
|K0V
|M0V
|-
|质量（''M''⊙）
|60
|17.5
|2.9
|1.6
|1.05
|0.79
|0.51
|}

（a）如果一颗行星进化出智慧生命至少需要40亿年的话，那么天文学家应该着重搜寻哪些光谱型的恒星？（光谱型应精确到具体的子类）

（b）假设目标行星的辐射率 ε 和反照率 a 与地球相同。如果该行星的温度和地球相近，请以天文单位 au 为单位，列出该行星到其质量为 M 的母恒星的距离 d 的表达式。

（c）如果一颗恒星周围有一颗行星围绕它转动，恒星的视向速度就会发生微小的变化。如果观测者能探测到的最小多普勒位移是(Δ''λ'' / ''λ'') =10-10，请计算围绕（a）问中这类光谱型的恒星绕转的（b）问中这类行星的最小质量，以地球质量为单位。

（（a）问的题目有一些问题。实际上答案给出来的确实是一个范围，但是确是临界情况——也就是什么光谱型的恒星恰好满足这40亿年的条件）

2017年IOAA理论第11题-本星系群的质量

2019-09-08T08:22:17Z

Fjllrven Hu：

2017年IOAA理论第11题-本星系群的质量

2019-09-08T08:20:08Z

Fjllrven Hu：/* 英文原题 */

== 英文原题 ==
'''Mass of the Local Group''' [50 marks]

The dynamics of M31 (Andromeda) and the Milky Way (MW) can be used to estimate the total mass of the Local Group (LG). The basic idea is that galaxies currently in a binary system were at approximately the same point in space shortly after the Big Bang. To a reasonable approximation, the mass of the local group is dominated by the masses of the MW and M31. Via Doppler shifts of the spectral lines, it was found that M31 is moving towards the MW with a speed of 118 km·s−1. This may be surprising, given that most galaxies are moving away from each other with the general Hubble flow. The fact that M31 is moving towards the MW is presumably because their mutual gravitational attraction has eventually reversed their initial velocities. In principle, if the pair of galaxies is well-represented by isolated point masses, their total mass may be determined by measuring their separation, relative velocity and the time since the universe began. [https://ui.adsabs.harvard.edu/abs/1959ApJ...130..705K/abstract Kahn and Woltjer (1959)] used this argument to estimate the mass in the LG.

In this problem we will follow this argument through our calculation as follows.

== 中文题目 ==
'''本星系群的质量''' [50 分]

M31（仙女座星系）以及银河系之间的动力学过程可以用来估算整个本星系群的质量。可以做个这样的基本假设：现存星系对里的两个星系在宇宙大爆炸后没多久，大致都在相同的位置上。为了合理估算整个本星系群的质量，这里还得假设本星系群总质量绝大部分都是由 M31 和银河系贡献出来的。通过谱线测量出的多普勒红移，可看出 M31 现在正以 118 km·s−1 朝银河系运动。也许你会比较惊讶，毕竟通常而言星系会因为哈勃流导致相互远离。但实际上 M31 正朝向银河系运动也不是不可能，因为（星系群里）引力的相互作用的效果（本动速度）要高于哈勃流（退行速度）带来的效果。把星系对中的俩星系视为俩质点，它们总质量就能通过两者间距离、相对运动速度以及宇宙年龄来得出。 Kahn 和 Woltjer (1959) 就是这样计算本星系群质量的。

请顺着该思路计算本星系群的质量。

2017年IOAA理论第11题-本星系群的质量

2019-09-08T08:15:48Z

Fjllrven Hu：

== 英文原题 ==
'''Mass of the Local Group''' [50 marks]

The dynamics of M31 (Andromeda) and the Milky Way (MW) can be used to estimate the total mass of the Local Group (LG). The basic idea is that galaxies currently in a binary system were at approximately the same point in space shortly after the Big Bang. To a reasonable approximation, the mass of the local group is dominated by the masses of the MW and M31. Via Doppler shifts of the spectral lines, it was found that M31 is moving towards the MW with a speed of 118 km·s−1. This may be surprising, given that most galaxies are moving away from each other with the general Hubble flow. The fact that M31 is moving towards the MW is presumably because their mutual gravitational attraction has eventually reversed their initial velocities. In principle, if the pair of galaxies is well-represented by isolated point masses, their total mass may be determined by measuring their separation, relative velocity and the time since the universe began. Kahn and Woltjer (1959) used this argument to estimate the mass in the LG.

In this problem we will follow this argument through our calculation as follows.

== 中文题目 ==
'''本星系群的质量''' [50 分]

M31（仙女座星系）以及银河系之间的动力学过程可以用来估算整个本星系群的质量。可以做个这样的基本假设：现存星系对里的两个星系在宇宙大爆炸后没多久，大致都在相同的位置上。为了合理估算整个本星系群的质量，这里还得假设本星系群总质量绝大部分都是由 M31 和银河系贡献出来的。通过谱线测量出的多普勒红移，可看出 M31 现在正以 118 km·s−1 朝银河系运动。也许你会比较惊讶，毕竟通常而言星系会因为哈勃流导致相互远离。但实际上 M31 正朝向银河系运动也不是不可能，因为（星系群里）引力的相互作用的效果（本动速度）要高于哈勃流（退行速度）带来的效果。把星系对中的俩星系视为俩质点，它们总质量就能通过两者间距离、相对运动速度以及宇宙年龄来得出。 Kahn 和 Woltjer (1959) 就是这样计算本星系群质量的。

请顺着该思路计算本星系群的质量。

2017年IOAA理论第9题-星系物质外流

2019-09-08T07:49:52Z

Fjllrven Hu：/* 解答 */

=='''英文原题'''==
Galactic Outflow [20 marks]

[https://ui.adsabs.harvard.edu/abs/2004ApJ...608..768C/abstract Cannon et al. (2004)] conducted an HI observation of a disk starburst galaxy, [https://ned.ipac.caltech.edu/byname?objname=2MASX%20J08382309%2B6507160&hconst=67.8&omegam=0.308&omegav=0.692&wmap=4&corr_z=1 IRAS 0833+6517 (IRAS 08339+6517)], with the Very Large Array (VLA). The galaxy is located at a distance of 80.2 Mpc <ref>[https://ui.adsabs.harvard.edu/abs/2014A%26A...566A..38O/abstract Physical properties and evolutionary state of the Lyman alpha emitting starburst galaxy IRAS 08339+6517], Table 1.</ref> with an approximate inclination angle of 23 degrees. According to the HI velocity map, IRAS 0833+6517 appears to be undergoing regular rotation with an observed radial velocity of the HI gas of roughly 5850 km/s at a distance of 7.8 kpc from the centre (the left panel of the figure below).

Gas outflow from IRAS 0833+6517 is traced by using the blueshifted interstellar absorption lines observed against the backlight of the stellar continuum (the right panel of the figure). Assuming that this galaxy is gravitationally stable and all the stars are moving in circular orbits,

a) Determine the rotational velocity ($$v_{rot}$$) of IRAS 0833+6517 at the observed radius of HI gas. [5]

b) Calculate the escape velocity for a test particle in the gas outflow at the radius of 7.8 kpc. [9]

c) Determine if the outflowing gas can escape from the galaxy at this radius by considering the velocity offset of the C II（λ1335） absorption line, which is already corrected for the cosmological recessional velocity. (The central rest-frame wavelength of the CII absorption line is 1335 Å.) (YES / NO) [6]
[[文件:Image.png|居中|缩略图|400x400像素]]
 

=='''中文题目'''==
星系物质外流（20分）

[https://ui.adsabs.harvard.edu/abs/2004ApJ...608..768C/abstract Cannon et al. (2004)] 对一个星暴盘星系（IRAS 0833+6517）用甚大天线阵（VLA）来探测中性氢（HI）的分布。该星系距离我们 80.2 Mpc远，盘面倾角约 23 度。根据中性氢的速度分布可看出 IRAS 0833+6517 绕中心旋转，在离星系中心的 7.8 kpc 的某一点观测到的视向速度为 5850 km/s （如左图所示）。

IRAS 0833+6517 的气体外流情况可以根据背景恒星连续谱上星际吸收线的蓝移程度来判定（如右图所示）。这里假设该星系是稳定的自引力体系且所有的成员恒星都以圆轨道绕转星系中心，

a）通过中性氢分布，计算 IRAS 0833+6517 在被观测过的某个点的旋转速度（$$v_{rot}$$）。（5分）

b）在离星系中心 7.8 kpc 远的地方，如果一个粒子要外流，其逃逸速度多少？（9分）

c）通过 C II（λ1335）吸收线所反映出来的速度偏差（横坐标已用宇宙学红移改正），请问在这个半径上向外流的气体是否能流出星系？（6分）

=='''解答'''==
a) IRAS 0833+6517的距离已经给定（80.2 Mpc），根据哈勃公式：

<center> $$v_{gal} = H_{0}D$$ </center>

其中，[[哈勃常数]]：$$H_{0}$$ = 67.8 km⋅ s−1 ⋅ Mpc−1

这样就能得出星系自身的退行速度：$$v_{gal}$$ = 67.8 km⋅ s−1 ⋅ Mpc−1 $$\times$$ 80.2 Mpc = 5437.56 km s−1

由于在星系盘上的某处测量的速度值为：$$v_{rad}$$ = 5850 km⋅ s−1，该星系的盘面倾角为：i = 23 $$^{\circ}$$

则根据视向速度的叠加：$$v_{rad} = v_{gal} + v_{rot}\cdot{\sin}i$$

可得出：

<center> $$\displaystyle v_{rot} = \frac{v_{rad} - v_{gal}}{{\sin}i} = \frac{5850 - 5437.56}{0.39}$$ km⋅ s−1 $$=$$ 1057.54 km⋅ s−1 </center>

b) 根据向心加速度的公式：

<center> $$\displaystyle \frac{v_{rot}^{2}}{r} = \frac{G \cdot M(r)}{r^{2}} $$ </center>

可得出：

<center> $$\displaystyle M(r) = \frac{v_{rot}^{2} \cdot r}{G} \sim 4.0 \times 10^{42} $$ kg </center>

然后，这里假设 7.8 kpc 以外的外盘对星系质量的贡献极小（原答案直接套用维里定律）：

<center> $$\displaystyle \frac{1}{2}v_{esc}^{2} = \int^{+\infty}_{r} \frac{G \cdot M(r)}{R^{2}}dR = \frac{G \cdot M(r)}{r} $$</center>

就能算出：

<center> $$\displaystyle v_{esc} = \sqrt{\frac{2G \cdot M(r)}{r}} = $$ 1492 km⋅ s−1 </center>

c) 第三题中 CII 吸收线的波长位于 1335 Å, 而实际光谱中，扣除掉哈勃流后，能从图中看见显著的吸收线蓝移，这个蓝移就是外流气体造成的结果：

<center> $$\displaystyle \frac{\Delta \lambda}{\lambda} = \frac{\Delta v}{c}$$ </center>

如果吸收坑对应中心波长取 1332 Å的话：

<center> $$\displaystyle \Delta v = 3 \times 10^{5}$$ km⋅ s−1 $$\displaystyle \frac{1332-1335}{1335} = -674.2$$ km⋅ s−1 </center>

并没有超过逃逸速度（$$v_{esc}$$），因此气体流不出去。

=='''拓展'''==

<references />

2017年IOAA理论第9题-星系物质外流

2019-09-08T07:44:44Z

Fjllrven Hu：/* 解答 */

=='''英文原题'''==
Galactic Outflow [20 marks]

[https://ui.adsabs.harvard.edu/abs/2004ApJ...608..768C/abstract Cannon et al. (2004)] conducted an HI observation of a disk starburst galaxy, [https://ned.ipac.caltech.edu/byname?objname=2MASX%20J08382309%2B6507160&hconst=67.8&omegam=0.308&omegav=0.692&wmap=4&corr_z=1 IRAS 0833+6517 (IRAS 08339+6517)], with the Very Large Array (VLA). The galaxy is located at a distance of 80.2 Mpc <ref>[https://ui.adsabs.harvard.edu/abs/2014A%26A...566A..38O/abstract Physical properties and evolutionary state of the Lyman alpha emitting starburst galaxy IRAS 08339+6517], Table 1.</ref> with an approximate inclination angle of 23 degrees. According to the HI velocity map, IRAS 0833+6517 appears to be undergoing regular rotation with an observed radial velocity of the HI gas of roughly 5850 km/s at a distance of 7.8 kpc from the centre (the left panel of the figure below).

Gas outflow from IRAS 0833+6517 is traced by using the blueshifted interstellar absorption lines observed against the backlight of the stellar continuum (the right panel of the figure). Assuming that this galaxy is gravitationally stable and all the stars are moving in circular orbits,

a) Determine the rotational velocity ($$v_{rot}$$) of IRAS 0833+6517 at the observed radius of HI gas. [5]

b) Calculate the escape velocity for a test particle in the gas outflow at the radius of 7.8 kpc. [9]

c) Determine if the outflowing gas can escape from the galaxy at this radius by considering the velocity offset of the C II（λ1335） absorption line, which is already corrected for the cosmological recessional velocity. (The central rest-frame wavelength of the CII absorption line is 1335 Å.) (YES / NO) [6]
[[文件:Image.png|居中|缩略图|400x400像素]]
 

=='''中文题目'''==
星系物质外流（20分）

[https://ui.adsabs.harvard.edu/abs/2004ApJ...608..768C/abstract Cannon et al. (2004)] 对一个星暴盘星系（IRAS 0833+6517）用甚大天线阵（VLA）来探测中性氢（HI）的分布。该星系距离我们 80.2 Mpc远，盘面倾角约 23 度。根据中性氢的速度分布可看出 IRAS 0833+6517 绕中心旋转，在离星系中心的 7.8 kpc 的某一点观测到的视向速度为 5850 km/s （如左图所示）。

IRAS 0833+6517 的气体外流情况可以根据背景恒星连续谱上星际吸收线的蓝移程度来判定（如右图所示）。这里假设该星系是稳定的自引力体系且所有的成员恒星都以圆轨道绕转星系中心，

a）通过中性氢分布，计算 IRAS 0833+6517 在被观测过的某个点的旋转速度（$$v_{rot}$$）。（5分）

b）在离星系中心 7.8 kpc 远的地方，如果一个粒子要外流，其逃逸速度多少？（9分）

c）通过 C II（λ1335）吸收线所反映出来的速度偏差（横坐标已用宇宙学红移改正），请问在这个半径上向外流的气体是否能流出星系？（6分）

=='''解答'''==
a) IRAS 0833+6517的距离已经给定（80.2 Mpc），根据哈勃公式：

<center> $$v_{gal} = H_{0}D$$ </center>

其中，[[哈勃常数]]：$$H_{0}$$ = 67.8 km⋅ s−1 ⋅ Mpc−1

这样就能得出星系自身的退行速度：$$v_{gal}$$ = 67.8 km⋅ s−1 ⋅ Mpc−1 $$\times$$ 80.2 Mpc = 5437.56 km s−1

由于在星系盘上的某处测量的速度值为：$$v_{rad}$$ = 5850 km⋅ s−1，该星系的盘面倾角为：i = 23 $$^{\circ}$$

则根据视向速度的叠加：$$v_{rad} = v_{gal} + v_{rot}\cdot{\sin}i$$

可得出：

<center> $$\displaystyle v_{rot} = \frac{v_{rad} - v_{gal}}{{\sin}i} = \frac{5850 - 5437.56}{0.39}$$ km⋅ s−1 $$=$$ 1057.54 km⋅ s−1 </center>

b) 根据向心加速度的公式：

<center> $$\displaystyle \frac{v_{rot}^{2}}{r} = \frac{G \cdot M(r)}{r^{2}} $$ </center>

可得出：

<center> $$\displaystyle M(r) = \frac{v_{rot}^{2} \cdot r}{G} \sim 4.0 \times 10^{42} $$ kg </center>

然后，这里假设 7.8 kpc 以外的外盘对星系质量的贡献极小（原答案直接套用维里定律）：

<center> $$\displaystyle \frac{1}{2}v_{esc}^{2} = \int^{+\infty}_{r} \frac{G \cdot M(r)}{R^{2}}dR = \frac{G \cdot M(r)}{r} $$</center>

就能算出：

<center> $$\displaystyle v_{esc} = \sqrt{\frac{2G \cdot M(r)}{r}} = $$ 1492 km⋅ s−1 </center>

c) 第三题中 CII 吸收线的波长位于 1335 Å, 而实际光谱中，扣除掉哈勃流后，能从图中看见显著的吸收线蓝移，这个蓝移就是外流气体造成的结果：

<center> $$\displaystyle \frac{\Delta \lambda}{\lambda} = \frac{\Delta v}{c}$$ </center>

如果吸收坑对应中心波长取 1332 Å的话：

<center> $$\displaystyle \Delta v = 3 \times 10^{5}$$ km⋅ s−1 $$\frac{1332-1335}{1335} = -674.2$$ km⋅ s−1 </center>

并没有超过逃逸速度（$$v_{esc}$$），因此气体流不出去

=='''拓展'''==

<references />

用户:Fjllrven Hu

2019-09-07T13:14:01Z

Fjllrven Hu：创建页面，内容为“这是一个该死的用户页面。”

这是一个该死的用户页面。

2017年IOAA理论第9题-星系物质外流

2019-09-07T13:09:25Z

Fjllrven Hu：/* 解答 */

=='''英文原题'''==
Galactic Outflow [20 marks]

[https://ui.adsabs.harvard.edu/abs/2004ApJ...608..768C/abstract Cannon et al. (2004)] conducted an HI observation of a disk starburst galaxy, [https://ned.ipac.caltech.edu/byname?objname=2MASX%20J08382309%2B6507160&hconst=67.8&omegam=0.308&omegav=0.692&wmap=4&corr_z=1 IRAS 0833+6517 (IRAS 08339+6517)], with the Very Large Array (VLA). The galaxy is located at a distance of 80.2 Mpc <ref>[https://ui.adsabs.harvard.edu/abs/2014A%26A...566A..38O/abstract Physical properties and evolutionary state of the Lyman alpha emitting starburst galaxy IRAS 08339+6517], Table 1.</ref> with an approximate inclination angle of 23 degrees. According to the HI velocity map, IRAS 0833+6517 appears to be undergoing regular rotation with an observed radial velocity of the HI gas of roughly 5850 km/s at a distance of 7.8 kpc from the centre (the left panel of the figure below).

Gas outflow from IRAS 0833+6517 is traced by using the blueshifted interstellar absorption lines observed against the backlight of the stellar continuum (the right panel of the figure). Assuming that this galaxy is gravitationally stable and all the stars are moving in circular orbits,

a) Determine the rotational velocity ($$v_{rot}$$) of IRAS 0833+6517 at the observed radius of HI gas. [5]

b) Calculate the escape velocity for a test particle in the gas outflow at the radius of 7.8 kpc. [9]

c) Determine if the outflowing gas can escape from the galaxy at this radius by considering the velocity offset of the C II（λ1335） absorption line, which is already corrected for the cosmological recessional velocity. (The central rest-frame wavelength of the CII absorption line is 1335 Å.) (YES / NO) [6]
[[文件:Image.png|居中|缩略图|400x400像素]]
 

=='''中文题目'''==
星系物质外流（20分）

[https://ui.adsabs.harvard.edu/abs/2004ApJ...608..768C/abstract Cannon et al. (2004)] 对一个星暴盘星系（IRAS 0833+6517）用甚大天线阵（VLA）来探测中性氢（HI）的分布。该星系距离我们 80.2 Mpc远，盘面倾角约 23 度。根据中性氢的速度分布可看出 IRAS 0833+6517 绕中心旋转，在离星系中心的 7.8 kpc 的某一点观测到的视向速度为 5850 km/s （如左图所示）。

IRAS 0833+6517 的气体外流情况可以根据背景恒星连续谱上星际吸收线的蓝移程度来判定（如右图所示）。这里假设该星系是稳定的自引力体系且所有的成员恒星都以圆轨道绕转星系中心，

a）通过中性氢分布，计算 IRAS 0833+6517 在被观测过的某个点的旋转速度（$$v_{rot}$$）。（5分）

b）在离星系中心 7.8 kpc 远的地方，如果一个粒子要外流，其逃逸速度多少？（9分）

c）通过 C II（λ1335）吸收线所反映出来的速度偏差（横坐标已用宇宙学红移改正），请问在这个半径上向外流的气体是否能流出星系？（6分）

=='''解答'''==
a) IRAS 0833+6517的距离已经给定（80.2 Mpc），根据哈勃公式：

<center> $$v_{gal} = H_{0}D$$ </center>

其中，[[哈勃常数]]：$$H_{0}$$ = 67.8 km⋅ s−1 ⋅ Mpc−1

这样就能得出星系自身的退行速度：$$v_{gal}$$ = 67.8 km⋅ s−1 ⋅ Mpc−1 $$\times$$ 80.2 Mpc = 5437.56 km s−1

由于在星系盘上的某处测量的速度值为：$$v_{rad}$$ = 5850 km⋅ s−1，该星系的盘面倾角为：i = 23 $$^{\circ}$$

则根据视向速度的叠加：$$v_{rad} = v_{gal} + v_{rot}\cdot{\sin}i$$

可得出：

<center> $$\displaystyle v_{rot} = \frac{v_{rad} - v_{gal}}{{\sin}i} = \frac{5850 - 5437.56}{0.39}$$ km⋅ s−1 $$=$$ 1057.54 km⋅ s−1 </center>

b) 根据向心加速度的公式：

<center> $$\displaystyle \frac{v_{rot}^{2}}{r} = \frac{G \cdot M(r)}{r^{2}} $$ </center>

可得出：

<center> $$\displaystyle M(r) = \frac{v_{rot}^{2} \cdot r}{G} \sim 4.0 \times 10^{42} $$ kg </center>

然后，这里假设 7.8 kpc 以外的外盘对星系质量的贡献极小（原答案就直接套用维里定律了）：

<center> $$\displaystyle \frac{1}{2}v_{esc}^{2} = \int^{+\infty}_{r} \frac{G \cdot M(r)}{R^{2}}dR = \frac{G \cdot M(r)}{r} $$</center>

就能算出：

<center> $$\displaystyle v_{esc} = \sqrt{\frac{2G \cdot M(r)}{r}} = $$ 1492 km⋅ s−1 </center>

c) 第三题中 CII 吸收线的波长位于 1335 埃, 而实际光谱中，扣除掉哈勃流后，能从图中看见显著的吸收线蓝移，这个蓝移就是外流气体造成的结果：

<center> $$\displaystyle \frac{\Delta \lambda}{\lambda} = \frac{\Delta v}{c}$$ </center>

如果吸收坑的谷值对应波长取 1332 埃的话：

<center> $$\displaystyle \Delta v = 3 \times 10^{5}$$ km⋅ s−1 $$\frac{1332-1335}{1335} = -674.2$$ km⋅ s−1 </center>

并没有超过逃逸速度（$$v_{esc}$$），因此气体流不出去

=='''拓展'''==

<references />

2017年IOAA理论第9题-星系物质外流

2019-09-07T12:40:40Z

Fjllrven Hu：/* 解答 */

=='''英文原题'''==
Galactic Outflow [20 marks]

[https://ui.adsabs.harvard.edu/abs/2004ApJ...608..768C/abstract Cannon et al. (2004)] conducted an HI observation of a disk starburst galaxy, [https://ned.ipac.caltech.edu/byname?objname=2MASX%20J08382309%2B6507160&hconst=67.8&omegam=0.308&omegav=0.692&wmap=4&corr_z=1 IRAS 0833+6517 (IRAS 08339+6517)], with the Very Large Array (VLA). The galaxy is located at a distance of 80.2 Mpc <ref>[https://ui.adsabs.harvard.edu/abs/2014A%26A...566A..38O/abstract Physical properties and evolutionary state of the Lyman alpha emitting starburst galaxy IRAS 08339+6517], Table 1.</ref> with an approximate inclination angle of 23 degrees. According to the HI velocity map, IRAS 0833+6517 appears to be undergoing regular rotation with an observed radial velocity of the HI gas of roughly 5850 km/s at a distance of 7.8 kpc from the centre (the left panel of the figure below).

Gas outflow from IRAS 0833+6517 is traced by using the blueshifted interstellar absorption lines observed against the backlight of the stellar continuum (the right panel of the figure). Assuming that this galaxy is gravitationally stable and all the stars are moving in circular orbits,

a) Determine the rotational velocity ($$v_{rot}$$) of IRAS 0833+6517 at the observed radius of HI gas. [5]

b) Calculate the escape velocity for a test particle in the gas outflow at the radius of 7.8 kpc. [9]

c) Determine if the outflowing gas can escape from the galaxy at this radius by considering the velocity offset of the C II（λ1335） absorption line, which is already corrected for the cosmological recessional velocity. (The central rest-frame wavelength of the CII absorption line is 1335 Å.) (YES / NO) [6]
[[文件:Image.png|居中|缩略图|400x400像素]]
 

=='''中文题目'''==
星系物质外流（20分）

[https://ui.adsabs.harvard.edu/abs/2004ApJ...608..768C/abstract Cannon et al. (2004)] 对一个星暴盘星系（IRAS 0833+6517）用甚大天线阵（VLA）来探测中性氢（HI）的分布。该星系距离我们 80.2 Mpc远，盘面倾角约 23 度。根据中性氢的速度分布可看出 IRAS 0833+6517 绕中心旋转，在离星系中心的 7.8 kpc 的某一点观测到的视向速度为 5850 km/s （如左图所示）。

IRAS 0833+6517 的气体外流情况可以根据背景恒星连续谱上星际吸收线的蓝移程度来判定（如右图所示）。这里假设该星系是稳定的自引力体系且所有的成员恒星都以圆轨道绕转星系中心，

a）通过中性氢分布，计算 IRAS 0833+6517 在被观测过的某个点的旋转速度（$$v_{rot}$$）。（5分）

b）在离星系中心 7.8 kpc 远的地方，如果一个粒子要外流，其逃逸速度多少？（9分）

c）通过 C II（λ1335）吸收线所反映出来的速度偏差（横坐标已用宇宙学红移改正），请问在这个半径上向外流的气体是否能流出星系？（6分）

=='''解答'''==
a) IRAS 0833+6517的距离已经给定（80.2 Mpc），根据哈勃公式：

<center> $$v_{gal} = H_{0}D$$ </center>

其中，[[哈勃常数]]：$$H_{0}$$ = 67.8 km⋅ s−1 ⋅ Mpc−1

这样就能得出星系自身的退行速度：$$v_{gal}$$ = 67.8 km⋅ s−1 ⋅ Mpc−1 $$\times$$ 80.2 Mpc = 5437.56 km s−1

由于在星系盘上的某处测量的速度值为：$$v_{rad}$$ = 5850 km⋅ s−1，该星系的盘面倾角为：i = 23 $$^{\circ}$$

则根据视向速度的叠加：$$v_{rad} = v_{gal} + v_{rot}\cdot{\sin}i$$

可得出：

<center> $$\displaystyle v_{rot} = \frac{v_{rad} - v_{gal}}{{\sin}i} = \frac{5850 - 5437.56}{0.39}$$ km⋅ s−1 $$=$$ 1057.54 km⋅ s−1 </center>

b) 根据向心加速度的公式：

<center> $$\displaystyle \frac{v^{2}}{r} = \frac{G \cdot M(r)}{r^{2}}$$ </center>

可得出：

<center> $$\displaystyle M(r) = \frac{v^{2} \cdot r}{G} \sim 4.0 \times 10^{42} $$ kg </center>

=='''拓展'''==

<references />

2017年IOAA理论第9题-星系物质外流

2019-09-07T12:28:02Z

Fjllrven Hu：/* 解答 */

2017年IOAA理论第9题-星系物质外流

2019-09-07T12:13:33Z

Fjllrven Hu：/* 中文题目 */

2017年IOAA理论第9题-星系物质外流

2019-09-07T12:10:52Z

Fjllrven Hu：

2017年IOAA理论第9题-星系物质外流

2019-09-07T12:07:08Z

Fjllrven Hu：/* 解答 */

2017年IOAA理论第9题-星系物质外流

2019-09-07T11:45:36Z

Fjllrven Hu：

2017年IOAA理论第9题-星系物质外流

2019-09-07T11:31:49Z

Fjllrven Hu：

2017年IOAA理论第9题-星系物质外流

2019-09-07T11:17:41Z

Fjllrven Hu：

=='''英文原题'''==
Galactic Outflow [20 marks]

[https://ui.adsabs.harvard.edu/abs/2004ApJ...608..768C/abstract Cannon et al. (2004)] conducted an HI observation of a disk starburst galaxy, IRAS 0833+6517, with the Very Large Array (VLA). The galaxy is located at a distance of 80.2 Mpc with an approximate inclination angle of 23 degrees. According to the HI velocity map, IRAS 0833+6517 appears to be undergoing regular rotation with an observed radial velocity of the HI gas of roughly 5850 km/s at a distance of 7.8 kpc from the centre (the left panel of the figure below).

Gas outflow from IRAS 0833+6517 is traced by using the blueshifted interstellar absorption lines observed against the backlight of the stellar continuum (the right panel of the figure). Assuming that this galaxy is gravitationally stable and all the stars are moving in circular orbits,

a) Determine the rotational velocity ($$v_{rot}$$) of IRAS 0833+6517 at the observed radius of HI gas. [5]

b) Calculate the escape velocity for a test particle in the gas outflow at the radius of 7.8 kpc. [9]

c) Determine if the outflowing gas can escape from the galaxy at this radius by considering the velocity offset of the C II（λ1335） absorption line, which is already corrected for the cosmological recessional velocity. (The central rest-frame wavelength of the CII absorption line is 1335 Å.) (YES / NO) [6]
[[文件:Image.png|居中|缩略图|400x400像素]]
 

=='''中文题目'''==
星系物质外流（20分）

[https://ui.adsabs.harvard.edu/abs/2004ApJ...608..768C/abstract Cannon et al. (2004)] 对一个星暴盘星系（IRAS 0833+6517）用甚大天线阵（VLA）来探测中性氢（HI）的分布。该星系距离我们 80.2 Mpc远，盘面倾角约 23 度。根据中性氢的速度分布可看出 IRAS 0833+6517 绕中心旋转，在离星系中心的 7.8 kpc 的某一点观测到的视向速度为 5850 km/s （如左图所示）。

IRAS 0833+6517 的气体外流情况可以根据背景恒星连续谱上星际吸收线的蓝移程度来判定（如右图所示）。这里假设该星系是稳定的自引力体系且所有的成员恒星都以圆轨道绕转星系中心，

a）通过中性氢分布，计算 IRAS 0833+6517 在被观测过的某个点的旋转速度($$v_{rot}$$)

b）在离星系中心 7.8 kpc 远的地方，如果一个粒子要外流，其逃逸速度多少？

c）通过 C II（λ1335）吸收线所反映出来的速度偏差（横坐标已用宇宙学红移改正），请问在这个半径上向外流的气体是否能流出星系？

=='''解答'''==

2017年IOAA理论第9题-星系物质外流

2019-09-07T11:05:18Z

Fjllrven Hu：

=='''英文原题'''==
Galactic Outflow [20 marks]

Cannon et al. (2004) conducted an HI observation of a disk starburst galaxy, IRAS 0833+6517, with the Very Large Array (VLA). The galaxy is located at a distance of 80.2 Mpc with an approximate inclination angle of 23 degrees. According to the HI velocity map, IRAS 0833+6517 appears to be undergoing regular rotation with an observed radial velocity of the HI gas of roughly 5850 km/s at a distance of 7.8 kpc from the centre (the left panel of the figure below).

Gas outflow from IRAS 0833+6517 is traced by using the blueshifted interstellar absorption lines observed against the backlight of the stellar continuum (the right panel of the figure). Assuming that this galaxy is gravitationally stable and all the stars are moving in circular orbits,

a) Determine the rotational velocity ($$v_{rot}$$) of IRAS 0833+6517 at the observed radius of HI gas. [5]

b) Calculate the escape velocity for a test particle in the gas outflow at the radius of 7.8 kpc. [9]

c) Determine if the outflowing gas can escape from the galaxy at this radius by considering the velocity offset of the C II（λ1335） absorption line, which is already corrected for the cosmological recessional velocity. (The central rest-frame wavelength of the CII absorption line is 1335 Å.) (YES / NO) [6]
[[文件:Image.png|居中|缩略图|400x400像素]]
 

=='''中文题目'''==
星系物质外流（20分）

Cannon et al.(2004) 对一个星暴盘星系（IRAS 0833+6517）用甚大天线阵（VLA）来探测中性氢（HI）的分布。该星系距离我们 80.2 Mpc远，盘面倾角约 23 度。根据中性氢的速度分布可看出 IRAS 0833+6517 绕中心旋转，在离星系中心的 7.8 kpc 的某一点观测到的视向速度为 5850 km/s （如左图所示）。

IRAS 0833+6517 的气体外流情况可以根据背景恒星连续谱上星际吸收线的蓝移程度来判定（如右图所示）。这里假设该星系是稳定的自引力体系且所有的成员恒星都以圆轨道绕转星系中心，

a）通过中性氢分布，计算 IRAS 0833+6517 在被观测过的某个点的旋转速度($$v_{rot}$$)

b）在离星系中心 7.8 kpc 远的地方，如果一个粒子要外流，其逃逸速度多少？

c）通过 C II（λ1335）吸收线所反映出来的速度偏差（横坐标已用宇宙学红移改正），请问在这个半径上向外流的气体是否能流出星系？

=='''解答'''==

2017年IOAA理论第9题-星系物质外流

2019-09-07T11:02:23Z

Fjllrven Hu：

=='''英文原题'''==
Galactic Outflow [20 marks]

Cannon et al. (2004) conducted an HI observation of a disk starburst galaxy, IRAS 0833+6517, with the Very Large Array (VLA). The galaxy is located at a distance of 80.2 Mpc with an approximate inclination angle of 23 degrees. According to the HI velocity map, IRAS 0833+6517 appears to be undergoing regular rotation with an observed radial velocity of the HI gas of roughly 5850 $$km/s$$ at a distance of 7.8 kpc from the centre (the left panel of the figure below).

Gas outflow from IRAS 0833+6517 is traced by using the blueshifted interstellar absorption lines observed against the backlight of the stellar continuum (the right panel of the figure). Assuming that this galaxy is gravitationally stable and all the stars are moving in circular orbits,

a) Determine the rotational velocity ($$v_{rot}$$) of IRAS 0833+6517 at the observed radius of HI gas. [5]

b) Calculate the escape velocity for a test particle in the gas outflow at the radius of 7.8 kpc. [9]

c) Determine if the outflowing gas can escape from the galaxy at this radius by considering the velocity offset of the C II（λ1335） absorption line, which is already corrected for the cosmological recessional velocity. (The central rest-frame wavelength of the CII absorption line is 1335 Å.) (YES / NO) [6]
[[文件:Image.png|居中|缩略图|400x400像素]]
 

=='''中文题目'''==
星系物质外流（20分）

Cannon et al.(2004) 对一个星暴盘星系（IRAS 0833+6517）用甚大天线阵（VLA）来探测中性氢（HI）的分布。该星系距离我们 80.2 Mpc远，盘面倾角约 23 度。根据中性氢的速度分布可看出 IRAS 0833+6517 绕中心旋转，在离星系中心的 7.8 kpc 的某一点观测到的视向速度为 5850 $$km/s$$ （如左图所示）。

IRAS 0833+6517 的气体外流情况可以根据背景恒星连续谱上星际吸收线的蓝移程度来判定（如右图所示）。这里假设该星系是稳定的自引力体系且所有的成员恒星都以圆轨道绕转星系中心，

a）通过中性氢分布，计算 IRAS 0833+6517 在被观测过的某个点的旋转速度($$v_{rot}$$)

b）在离星系中心 7.8 kpc 远的地方，如果一个粒子要外流，其逃逸速度多少？

c）通过 C II（λ1335）吸收线所反映出来的速度偏差（横坐标已用宇宙学红移改正），请问在这个半径上向外流的气体是否能流出星系？

=='''解答'''==

2017年IOAA理论第9题-星系物质外流

2019-09-07T08:32:20Z

Fjllrven Hu：

=='''英文原题'''==
Galactic Outflow [20 marks]

Cannon et al. (2004) conducted an HI observation of a disk starburst galaxy, IRAS 0833+6517, with the Very Large Array (VLA). The galaxy is located at a distance of 80.2 Mpc with an approximate inclination angle of 23 degrees. According to the HI velocity map, IRAS 0833+6517 appears to be undergoing regular rotation with an observed radial velocity of the HI gas of roughly 5850 $$km s^{-1}$$ at a distance of 7.8 kpc from the centre (the left panel of the figure below).

Gas outflow from IRAS 0833+6517 is traced by using the blueshifted interstellar absorption lines observed against the backlight of the stellar continuum (the right panel of the figure). Assuming that this galaxy is gravitationally stable and all the stars are moving in circular orbits,

a) Determine the rotational velocity ($$v_{rot}$$) of IRAS 0833+6517 at the observed radius of HI gas. [5]

b) Calculate the escape velocity for a test particle in the gas outflow at the radius of 7.8 kpc. [9]

c) Determine if the outflowing gas can escape from the galaxy at this radius by considering the velocity offset of the C II（λ1335） absorption line, which is already corrected for the cosmological recessional velocity. (The central rest-frame wavelength of the CII absorption line is 1335 Å.) (YES / NO) [6]
[[文件:Image.png|居中|缩略图|400x400像素]]
 

==中文题目==
星系物质外流（20分）

Cannon et al.(2004) 对一个星暴盘星系（IRAS 0833+6517）用甚大天线阵（VLA）来探测中性氢（HI）的分布。该星系距离我们 80.2 Mpc远，盘面倾角约 23 度。根据中性氢的速度分布可看出 IRAS 0833+6517 绕中心旋转，在离星系中心的 7.8 kpc 的某一点观测到的视向速度为 5850 $$km s^{-1}$$ （如左图所示）。

IRAS 0833+6517 的气体外流情况可以根据背景恒星连续谱上星际吸收线的蓝移程度来判定（如右图所示）。这里假设该星系是稳定的自引力体系且所有的成员恒星都以圆轨道绕转星系中心，

a）通过中性氢分布，计算 IRAS 0833+6517 在被观测过的某个点的旋转速度($$v_{rot}$$)

b）在离星系中心 7.8 kpc 远的地方，如果一个粒子要外流，其逃逸速度多少？

c）通过 C II（λ1335）吸收线所反映出来的速度偏差（横坐标的红移已改正），请问在这个半径上向外流的气体是否能流出星系？

==解答==
==中文题目==