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How strong would have to be nuclear explosion on exo-planet that orbits some other star for it to be detectable outside of that system.
Or it would be impossible due to amount of radiation coming from that star?
Could the angle at which radiation would go out of that system be indicator, or light interference would make it impossible?

Update: Atmospheric nuclear explosions produce a unique signature, often called a "double-humped curve": a short and intense flash lasting around 1 millisecond, followed by a second much more prolonged and less intense emission of light taking a fraction of a second to several seconds to build up. The effect occurs because the surface of the early fireball is quickly overtaken by the expanding atmospheric shock wave composed of ionised gas. Although it emits a considerable amount of light itself it is opaque and prevents the far brighter fireball from shining through. As the shock wave expands, it cools down becoming more transparent allowing the much hotter and brighter fireball to become visible again.

No single natural phenomenon is known to produce this signature.

Could this be used to identify or "double-humped curve" would be of no help in space due to radio pollution, of many double humped curves produced by stars?

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Having already offered an answer to the pre-update question, I think the OP is looking for something a bit different. This requires knowing the waveband for the signal we'd be looking for, and what the potential starlight background would look like. But it might be a bit more interesting than the basic luminosity calculation. M dwarfs presumably aren't bright in gamma-rays... –  Warrick Jul 5 at 20:01

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To calibrate our expectations, consider the largest nuclear weapon ever detonated, the Tsar Bomba. It's yield was at most about $58$ megatons TNT equivalent, or about $2.43\times10^{24}$ erg. Now, let's consider a smallish star, something like Gliese 581, which is reasonably nearby, small and faint, and has a planetary system (of some sort: the number of planets is debated). It has a luminosity of $0.013$ times solar, which is roughly $5\times10^{31}$ erg.s$^{-1}$.

In other words, the luminosity of Gliese 581b is about 20 million Tsar Bombas per second. This says nothing, however, about in what waveband the emission occurs, but I think the energetic argument is quite strong... (i.e. maybe if the nuclear bomb peaks in gamma-rays you could separate it from the starlight, but I don't know about our detection capabilities or the gamma-ray emission from the star).

But, what about bigger things? Like an asteroid similar to the one that killed the dinosaurs? It's yield was 100 teratons of TNT equivalent, or about one-twelfth of Gliese 581's per second luminosity. Which might sound hopeful, but I suspect it took many seconds for that energy to come out, in which case it'd still be washed about by the starlight.

It turns out stars are quite bright in absolute terms!

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Thank you very much for your answer and comment, they are of great help. You are absolutely right I am looking for any method that could identify nuclear explosion and would like apologize that content of question is somewhat different compared to the title. –  LIUFA Jul 6 at 8:43

This would ultimately be more a problem of signal processing than physics. The situation is detecting a signal at a very low signal to noise ratio. At the broadband level, the noise (starlight) is several orders of magnitude more intense than the signal (the explosion).

The only hope would be some sort of spectral technique , taking advantage of spectral filtering to enhance the signal to noise ratio in some region of the electromagnetic spectrum where the explosion has characteristic detectable features. One would have to examine the spectral features of both the star and the explosion to determine what band (visible, x-ray, gamma etc.) would be best to attempt.

Still, I'd expect the signal to noise ratio to still be fractional, and there are fundamental statistical limits on detectability at very low signal to noise ratio. Plus the sensitivity of the detection system in whatever regime this was attempted (whether it be visible light, X-ray, gamma) would need to be taken into account.

Without doing the calculation I can't say it would be impossible, but intuitively it seems at best very very difficult.

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