2018年IOAA理论第9题-射电星系 - 版本历史

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2019年7月24日 (三) 07:12 Quan787

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创建页面，内容为“{{需要解答}} ==英文题目== '''(T9) Radio Galaxy (25 points)''' An observer wants to use the Five-hundred-meter Aperture Spherical radio Telescope (FAST) in C…”

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{{需要解答}}
==英文题目==
'''(T9) Radio Galaxy (25 points)'''

An observer wants to use the Five-hundred-meter Aperture Spherical radio Telescope (FAST) in China to observe a radio galaxy at redshift of 𝑧 = 0.06. We assume that the radio source is compact compared to the beam size of the telescope at the observing frequencies, i.e., the source is point-like as seen through the telescope. To detect a point source with FAST, it must be sufficiently strong (bright) relative to the noise level (for single polarization observations), σ, which depends on the bandwidth, △ν, and the integration time (the radio astronomy equivalent of exposure time), ti, as follows:

<nowiki>$$\sigma=\frac{2k_B T_{sys}}{A_e\sqrt{t_i \Delta\nu}}$$</nowiki>

where Tsys is the system temperature (about 150 K in the frequency range of 0.28 GHz – 0.56 GHz and 25 K in the frequency range of 1.05 GHz – 1.45 GHz), and Ae = 4.6x104 m2 is the effective area of the telescope taking into account the total efficiency of the instrument. This radio galaxy has an observed continuum flux density of fν = 2.5 × 10−3 Jy at an observing frequency of 0.4 GHz. The bandwidth △ν for the continuum observation centered at 0.4 GHz is 2.8×108 Hz.

(a) In order to detect the continuum flux density at 0.4 GHz with a signal-to-noise ratio of 30 (a so-called
30σ detection), what is the required integration time, ti?

(b) We want to search for the neutral Hydrogen (HI) in the galaxy using 21cm absorption line. The HI 21cm
line, with rest frame frequency of 1.4204 GHz. Calculate the observed frequency (νobs) of the HI line for this
galaxy.

(c) The radio continuum emission from this galaxy can be described by a power law $$f_\nu\sim \nu^\alpha$$
, with a spectral index of α = −0.2. Calculate the continuum flux density at vobs for this galaxy.

(d) The line width of the HI 21cm absorption line is 90 km/s. Calculate the line width in Hz at the observing frequency of vobs. According to Figure 1, the HI 21cm line absorbs 4% of the continuum flux density (on average) over the line width of 90 kms-1
. In order to detect the absorption line at ≥3σ in three consecutive 30 kms-1 channels, what is the required integration time?

==中文翻译==

←上一版本		2019年7月27日 (六) 14:20的版本
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	(d) 中性氢（HI）21厘米的吸收线线宽为90 km/s。计算在观测频率处，以赫兹为单位的线宽。根据图1，中性氢21厘米谱线在90 kms<sup>-1</sup>的宽度上平均吸收了4%的连续谱。为了在三个连续的30 kms<sup>-1</sup>频道中以3σ探测到这条谱线，需要多少的积分时间？		(d) 中性氢（HI）21厘米的吸收线线宽为90 km/s。计算在观测频率处，以赫兹为单位的线宽。根据图1，中性氢21厘米谱线在90 kms<sup>-1</sup>的宽度上平均吸收了4%的连续谱。为了在三个连续的30 kms<sup>-1</sup>频道中以3σ探测到这条谱线，需要多少的积分时间？
		+
		+	[[分类:射电望远镜]]

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 (d) The line width of the HI 21cm absorption line is 90 km/s. Calculate the line width in Hz at the observing frequency of v<sub>obs</sub>. According to Figure 1, the HI 21cm line absorbs 4% of the continuum flux density (on average) over the line width of 90 kms<sup>-1</sup>. In order to detect the absorption line at ≥3σ in three consecutive 30 kms<sup>-1</sup> channels, what is the required integration time?
-[[文件:IOAA2018-T9.jpg|缩略图|Figure 1: Spectrum of the HI 21cm absorption relative to the continuum emission in the radio galaxy 图1： 中性氢21厘米吸收线相比于星系的连续谱辐射]]
+[[文件:IOAA2018-T9.jpg|缩略图|Figure 1: Spectrum of the HI 21cm absorption relative to the continuum emission in the radio galaxy / 图1： 中性氢21厘米吸收线相比于星系的连续谱辐射]]
 ==中文翻译==

@@ 第5行： / 第5行： @@
 An observer wants to use the Five-hundred-meter Aperture Spherical radio Telescope (FAST) in China to observe a radio galaxy at redshift of 𝑧 = 0.06. We assume that the radio source is compact compared to the beam size of the telescope at the observing frequencies, i.e., the source is point-like as seen through the telescope. To detect a point source with FAST, it must be sufficiently strong (bright) relative to the noise level (for single polarization observations), σ, which depends on the bandwidth, △ν, and the integration time (the radio astronomy equivalent of exposure time), t<sub>i</sub>, as follows:
-<nowiki>$$\sigma=\frac{2k_B T_{sys}}{A_e\sqrt{t_i \Delta\nu}}$$</nowiki>
+$$\sigma=\frac{2k_B T_{sys}}{A_e\sqrt{t_i \Delta\nu}}$$
-where T<sub>sys</sub> is the system temperature (about 150 K in the frequency range of 0.28 GHz – 0.56 GHz and 25 K in the frequency range of 1.05 GHz – 1.45 GHz), and Ae = 4.6x10<sup>4</sup> m<sup>2</sup> is the effective area of the telescope taking into account the total efficiency of the instrument. This radio galaxy has an observed continuum flux density of f<sub>ν</sub> = 2.5 × 10<sup>−3</sup> Jy at an observing frequency of 0.4 GHz. The bandwidth △ν for the continuum observation centered at 0.4 GHz is 2.8×10<sup>8</sup> Hz.
+where T<sub>sys</sub> is the system temperature (about 150 K in the frequency range of 0.28 GHz – 0.56 GHz and 25 K in the frequency range of 1.05 GHz – 1.45 GHz), and A<sub>e</sub> = 4.6x10<sup>4</sup> m<sup>2</sup> is the effective area of the telescope taking into account the total efficiency of the instrument.
 (a) In order to detect the continuum flux density at 0.4 GHz with a signal-to-noise ratio of 30 (a so-called
@@ 第19行： / 第21行： @@
 , with a spectral index of α = −0.2. Calculate the continuum flux density at v<sub>obs</sub> for this galaxy.
-(d) The line width of the HI 21cm absorption line is 90 km/s. Calculate the line width in Hz at the observing frequency of v<sub>obs</sub>. According to Figure 1, the HI 21cm line absorbs 4% of the continuum flux density (on average) over the line width of 90 kms<sup>-1</sup>
+(d) The line width of the HI 21cm absorption line is 90 km/s. Calculate the line width in Hz at the observing frequency of v<sub>obs</sub>. According to Figure 1, the HI 21cm line absorbs 4% of the continuum flux density (on average) over the line width of 90 kms<sup>-1</sup>. In order to detect the absorption line at ≥3σ in three consecutive 30 kms<sup>-1</sup> channels, what is the required integration time?
 . In order to detect the absorption line at ≥3σ in three consecutive 30 kms<sup>-1</sup> channels, what is the required integration time?
 ==中文翻译==