2018年IOAA理论第9题-射电星系

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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), t_i, as follows:

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

where T_sys 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 f_ν = 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, t_i?

(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 (ν_obs) 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 v_obs 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_obs. 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?