Telescope Resolution for AGN Accretion Disk

[wtaylor]

[SOLVED] Telescope Resolution

Homework Statement

An Active Galactic Nucleus (AGN) is fueled by gas and dust in a rotating
accretion disk that is streaming onto a supermassive black hole in the center of the
galaxy. These accretion disks are typically a few pc in diameter and are best detected
at long wavelengths (to penetrate the dusty envelopes of these galactic centres). One
of the nearest AGNs is 3.3x106 pc from Earth and is powered by an accretion disk
that is 2 pc in diameter.
a) What size telescope would you need to resolve this accretion
disk at a wavelength of 10 μm and also at 21cm?

Homework Equations

p(′′) = 1/D(pc)

θ (") = 2.5 × 10^5 λ/D

The Attempt at a Solution

The only way I can see to find this is to use the parallax equation to find the size of the accretion disk in " and then use the angular resolution formula to find the telescopes diameter using each wavelength. But I am not sure if this will work considering that seems like an improper use of the parallax formula. Could someone give me a hint as to whether I am going in the right direction?

 

[mgb_phys]

You don't need the paralax formula since the distance and diameter are both given in parsec. You just need to work out the angular extent and then use 1.22 lambda/D for the diffraction limit, at 10um telescopes are pretty much diffraction limited.

 

[wtaylor]

Awesome, got it. Thanks a lot.

 

[mgb_phys]

Carefull, the 1.22 factor is the half angle (ie the radius of the source)