Plausibility of a cosmic flashbulb

Pendorain, admiral of the illustrious Tenth Fleet, had gathered its fleet near the Xzlicyan Pulsar to nurse its wounds. Battle against the hated Andecklin was not going well. The fleet was using the intense, modulating magnetic fields of the pulsar to induct power for repairs. But navigation was offline and most of the sensors were down — so nobody knew when the EM stream from the pulsar swept past all the ships. Navigational shields absorbed the brunt of the stream (except for the destroyer Hendi, which was destroyed, which is what destroyers do, but not normally to themselves) and repairs continued....

Some 40 million years later, astronomer Zhāng Ai just happened to be looking at ULX-1 in NGC 5907 at the right time to see something amazing... a snapshot of what's obviously the first real evidence of artificial construction ever seen by Humanity.

Question: Can the EM stream from a pulsar (or similar astronomical coolness) be bright enough to create a "flash bulb" effect that, if we (miraculously) are looking at the right place at the right time, could illuminate a fleet of space ships that, in size and mass, are similar to a U.S. aircraft carrier group?

• Please assume the reflectivity along the entire EM spectrum of an aircraft carrier. I'm not in a position to postulate what an advanced-tech alien fleet may or may not be able to do.

• I understand that today's data-gathering abilities might not have the resolution to see a fleet, especially at the distance used in my backstory statement. But work with me on that one. It's only a matter of time. Otherwise, please assume real-life technology.

There are two thing to consider here: Resolution and intensity.

The angular resolution of a telescope - effectively, the smallest angular scale it can probe - is approximately $$\theta\approx\frac{\lambda}{D}$$ where $$\lambda$$ is the wavelength of light and $$D$$ is the diameter of the dish - or, in the case of an interferometer, the size of the longest baseline. Let's consider two reasonably representative wavelengths: In the x-ray band, $$\lambda\approx1.2\times10^{-10}$$ meters, corresponding to the energy $$E=10\;\text{keV}$$, and in the radio band, $$\lambda\approx0.75$$ meters, corresponding to the frequency $$\nu=400\;\text{MHz}$$.

If we're observing a fleet on a scale of, say, one hundred kilometers or so (an order of magnitude larger than the pulsar) at a distance of 40 million light-years, we'd need an angular resolution of $$\theta=\frac{100\;\text{km}}{40\;\text{million light-years}}\approx2.6\times10^{-19}\;\text{radians}$$ Achieving this resolution at x-ray wavelengths would require an interferometer roughly 300,000 kilometers across; achieving it at radio wavelengths would require telescopes 300 light-years apart. The calculation is a fairly naïve one, but the point is, discerning structure at that distance is impossible in the radio regime. In x-rays, it might be possible; 300,000 km is just under the distance between Earth and the Moon. Therefore, building x-ray telescopes on the Moon and in a close Earth orbit (to avoid absorption by the atmosphere) might be feasible.

As for intensity - well, pulsars tend to be brighter in x-rays than at radio wavelengths. For rotation-powered pulsars, the ratio of spin-down energy to luminosity in x-rays is usually several orders of magnitude higher than in radio. With x-ray luminosities of maybe $$\sim10^{34}\;\text{erg s}^{-1}$$, they're certainly not faint. In addition, NGC 5907 ULX-1 is actively accreting matter, which provides orders of magnitude more energy, at around $$L_x\sim5\times10^{40}\;\text{erg s}^{-1}\approx1.3\times10^7L_{\odot}$$ at peak (Walton et al. 2016). Therefore, were we to observe all of the x-ray emission from the source, it wouldn't be hard to detect at peak.

The question, then, is what fraction of its x-rays would be reflected by the fleet - and that's more difficult to answer. I suspect it would be low; you wouldn't want more ships than necessary near an x-ray source of any kind. Therefore, it's likely that only a few individual ships (probably much smaller than one hundred kilometers) will be close enough to the pulsar to reflect much of its x-rays. I don't have numbers for this, so I'm just handwaving, but my gut tells me that the reflected x-rays would be drowned out by the intense direct x-ray emission from the pulsar itself.

I'll quote Arthur C. Clarke here:

If an elderly but distinguished scientist says that something is possible, he is almost certainly right; but if he says that it is impossible, he is very probably wrong.

NGC 5907 is about 50 million light years away from Earth. For comparison, M87 is 53 million light years away. In 2019 Katie Bouman took a picture of M87's central black hole, the first ever image to show an event horizon. To take that picture, she needed to coordinate radio telescopes around the world so they would all together function as a "single camera".

In the future we might just be able to use multiple x-ray telescopes to do about the same thing. Consider Zeiss Ikon's comment on this answer:

An X-ray telescope would need to be less than a billionth the size of the Event Horizon Telescope to have the same resolution -- a couple meters aperture is more than enough. Step up to Subaru (an interferometric pair on Mauna Kea) effective aperture (a couple hundred meter, as I recall), and you're approaching the resolution to make useful images of an object like a ULX pulsar. Of course, it would have to be in space, since the atmosphere blocks almost all X-rays.

• An X-ray telescope would need to be less than a billionth the size of the Event Horizon Telescope to have the same resolution -- a couple meters aperture is more than enough. Step up to Subaru (an interferometric pair on Mauna Kea) effective aperture (a couple hundred meter, as I recall), and you're approaching the resolution to make useful images of an object like a ULX pulsar. Of course, it would have to be in space, since the atmosphere blocks almost all X-rays. – Zeiss Ikon Dec 30 '20 at 19:47