Question

Measurements of many extragalactic sources have shown that they typically have brightness temperatures of TB = 1011 K and S = 1 Jy. Approximately what size telescope is needed to resolve these sources? How does that compare with the VLBA?

Answer 1

Answer on Question 55063, Physics / Astronomy | Astrophysics

Question:

Measurements of many extragalactic sources have shown that they typically have brightness temperatures of TB = 1011 K and S = 1 Jy. Approximately what size telescope is needed to resolve these sources? How does that compare with the VLBA?

Solution:

$$S_v = I_v \Omega = \frac{2 k T_b}{\lambda^2} \times \frac{\pi \theta^2 s}{4}$$

Where $\theta_s$ is the source angular diameter. If $\theta_s \approx \theta_{FWHM} \approx \frac{\lambda}{D}$, then:

$$\frac{\lambda^2}{D^2} = \frac{2 \lambda^2 S_v}{\pi k T_b} \Rightarrow D = \left(\frac{\pi k T_b}{2 S_v}\right)^{\frac{1}{2}} = 1.5 \times 10^7 \, \text{m} \approx D_{\oplus} = 1.3 \times 10^7 \, \text{m}$$

So the Earth is just big enough for ground-based telescopes to image and resolve the brightest compact synchrotron sources!

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