How big would a telescope have to be to get a good look at the nearest neutron star?

Question

It's my understanding of observational astronomy that the size of a telescope limits its effective angular resolution, which is why scientists needed to use radio telescopes all over the globe to look at the M87 black hole and Sagittarius A*.

For the sake of convenience, let's define a "good picture" as at least 100-by-100 pixels, and assume that all neutron stars have a diameter of 20 km. With this assumption, the nearest known neutron star is PSR J0108−1431, at 424 light years away. This gives our neutron star an angular diameter of $2.9\times10^{-13}$ degrees, so the image would need a resolution of $2.9\times10^{-15}$ degrees per pixel. How big would a telescope need to be to see this accurately?

Answer 1

The angular resolution is just $\sim \lambda/D$ (in radians), where $\lambda$ is the wavelength and $D$ is the telescope diameter (or the size of an interferometer). So plug in the numbers you like.

To resolve the optical emission (say $\lambda = 500$ nm) at the angular power you specify would require $ D =10^{10}$ m.

Details

A 20000 m diameter neutron star at a distance of 424 light years (= $4.01\times 10^{18}$ m), subtends an angle of $5\times 10^{-15}$ radians.

To resolve this into 100 pixels requires a resolution of $5\times 10^{-17}$ radians.

Then $D = \lambda/5\times 10^{-17} = 10^{10}$ m.

Edit:

As blademan9999 points out, one can show that the nearest (undiscovered) neutron star to Earth is likely an order of magnetude closer than this - see How far away is the nearest compact star remnant likely to be? If so, then a telescope of diameter $\sim 10^9$ m might resolve it. However, such a neutron star is likely to be old and very cold. Its surface brightness might be very low in which case it may not be a good target for telescopic observation.

Answer 2

Closest neutron star is RX J1856.5−3754, which is about 400 light-years from us. HOWEVER the Hubble did visibly spot a 200 lightyear distant otherwise known moving Bare neutron star streaking space. They flash the sky, producing that twinkle stars are known for. Here is a photograph of a neutron star taken by Hubble. Never the less any neutron star close enough to obtain detailed resolution images would be lethal.... Neutron stars produce so much radiation and magnetic fields they're potentially lethal at distances of a few lightyears.