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By using only the electromagnetic signature of a star, could a star be distinguished with reliable accuracy from any other star?
To elaborate a little, say we have a collection of about 200,000 stars. By using EM spectrum alone (and any means of analysis, such as spectral analysis), and by tagging each star with its corresponding EM signature, could there be similarities too close to fail a distinction between any two or more stars?

Now, of course, I know that such a thing is possible. I'm not asking whether it is possible. I just want to know the odds of such a lack of distinction, considering all the factors of stellar evolution. It's either in the ballpark or not.

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  • $\begingroup$ I don't understand. You ask if two stars could be indistinguishable. Then you say that you know that any two stars are distinguishable. Then you ask what are the odds of two stars not being distinguishable. Then you ask for an estimation of something ("in the ballpark"). The question is confused and unclear. $\endgroup$ – James K Dec 23 '17 at 22:48
  • $\begingroup$ @JamesK Given enough time, virtually anything should hypothetically possible. That is what I meant by "such a thing is possible." The ballpark I mention is the reliability factor. Is the distinction between two stellar spectra accurate and this reliable? Where reliability breaks down, so does distinction. By including the last paragraph, I was simply trying to remove any obvious answers such as the answer I made in the first sentence of this comment. Realistically, given real world circumstances, is such a similarity possible, or do factors involved in, say, stellar evolution, prevent it? $\endgroup$ – Brayden Fox Dec 23 '17 at 23:21
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    $\begingroup$ Given enough time, virtually anything should [be] hypothetically possible This is not how science works. Some things will remain impossible no matter how long you spend trying to do it. $\endgroup$ – StephenG Dec 24 '17 at 8:25
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The spectrum of a star is almost certainly a unique fingerprint. Even though stars are born in clusters, formed from the reasonably chemically homogeneous environment of a giant molecular cloud, there are likely to be small differences in their local environment. Furthermore their formation environments, and the stars themselves at later times, can be polluted by external events (e.g. nearby supernovae). Even if their chemical abundances were identical, their spectra would not be because of differences in their mass, rotation and hence their temperatures.

But, the differences between stars may be smaller than the measurement precision, rendering their spectra effectively indistinguishable.

To give any sort of definitive answer requires some definition of what types of stars are being observed, their temperature, gravity and chemical abundance dispersion, at what spectral resolution and with what signal to noise ratio in what waveband.

At the moment I would say this is impossible for any star in our Galaxy. The differences in the spectra between one star and its most similar "twin" (the word might be appropriate here, as they were likely born in the same stellar nursery) are far smaller than we can distinguish with current data and techniques.

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Even the optical spectrum alone has lots of goodies.

In addition to chemical abundance, size, and other outer properties from emission and absorption lines you can get the rotational rate from a narrow line's doppler profile, and very careful spectroscopy information on vibrational modes of the star through spectral asteroseismology.

Also most stars are part of multiple-star systems, so spectroscopy from a distance will yield information on each star and so even if two different stars are barely differentiable, chances are that their companions won't be also! This also gives some potential additional differentiation from the relative velocities, but that depends on how long you observe and if you know the orientation.

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