2019年IOAA理论第3题-银河系与M87中心的超大质量黑洞

英文题目

3. The supermassive black hole in the centre of Milky Way Galaxy and M87 (10 p)

The first image of a black hole was constructed recently by the international team of the Event Horizon Telescope (EHT). The imaged area surrounds the supermassive black hole in the centre of the galaxy M87. The observations resulting in the final image were carried out at a wavelength 𝜆 = 1.3 mm where the interstellar extinction is not prohibitively large.

a) How large an instrument would be needed to resolve the shadow (in effect the photon capture radius, which is three times the size of event horizon) of a supermassive black hole in the centre of a galaxy? Express the result as a function of the distance 𝑑 and the mass 𝑀 of the black hole. (6 p)

b) Give the size of the instrument in units of Earth radius for i. the supermassive black hole in the centre of M87, (1 p)

$$d_{BH-M87}=5.5*10^7ly$$ , $$M_{BH-M87}=6.5*10^9M_☉$$

ii. and Sgr A*, the supermassive black hole of our own galaxy, Milky Way. (1 p)

$$d_{SgrA^*}=8.5kpc$$ , $$M_{SgrA^*}=3.6*10^6M_☉$$

c) What type of technology is needed for the development of such an instrument? Mark the letter of your answer with × on the answer sheet. (2 p)

(A) Gravitational lensing by dark matter

(B) Interferometry with an array of radio telescopes

(C) Photon deceleration in a dense environment

(D) Reducing the effect of incoming wavefront distortions

(E) Neutrino focusing with strong electromagnetic fields

中文题目

3.银河系中心超大质量黑洞与M87（10分）

最近，事件视界望远镜（EHT）的国际团队制作了第一张黑洞图像。成像区域围绕着M87星系中心的超大质量黑洞。产生最终图像的观测是在波长为1.3毫米的地方进行的，那里的星际消光并不是非常大。

a）需要多大的仪器才能分辨银河系中心超大质量黑洞的阴影（实际上是光子捕获半径，是视界大小的三倍）？将结果表示为黑洞的距离和质量的函数。（6分）

b）以地球半径为单位给出仪器的尺寸，i.M87中心的超大质量黑洞，（1分）

直径-M87=5.5*10^7ly，直径-M87=6.5*10^9M*

二。以及Sgr A*，我们银河系中的超大质量黑洞。（1分）

dSgrA∗=8.5kpc，MSgrA∗=3.6∗106M☉

c）开发这种仪器需要哪种技术？在答题纸上用*标出你的答案。（2分）

（A）暗物质的引力透镜效应

（B）用射电望远镜阵列进行干涉测量

（C）密集环境中的光子减速

（D）减少来自入射波前畸变的影响

（E）用强电磁场聚焦中微子