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I found an article suggesting a supernova injected debris which helped nudge the formation of the Solar System 4.5 billion years ago.

I couldn't find a name for this hypothetical star/supernova after some research. Is there one? What is it?

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    $\begingroup$ There is none. Why would there? We call it "the supernova that injected $\rm Al^{26}$ into the young solar nebula". We have no other specifics than that, and that it probably happened in some birth cluster. Without specifics, naming it would seem silly. $\endgroup$ Jul 17 '18 at 12:00
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    $\begingroup$ The referenced site, space.com, is something I steer clear of. It has a key problem that is even worse than the chock-full of ads nature of that site (some of which want to infect my computer), even worse that space.com fails to distinguish between woo, conjecture, and well-established science. My biggest gripe is that that site almost never provides links to their source material (most likely a press release from the institution for which one of the authors worked), or to scientific journal paper(s) that resulted from the work. $\endgroup$ Jul 17 '18 at 12:29
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    $\begingroup$ "The solar system" isn't much of a name. So I wouldn't be expecting too much here James. $\endgroup$ Jul 17 '18 at 12:39
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    $\begingroup$ Given the naming convention of the IAU, I suspect it may be called SN-4500000000A $\endgroup$
    – Beta Decay
    Jul 17 '18 at 14:28
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I couldn't find a name for this hypothetical star/nova after some research.

First off, the existence of this former object is hypothetical. Others working in this field have different hypotheses / conjectures; the science is far from settled. Secondly, if true, this star formed a supernova at the time the solar system was born and hence it no longer exists as a star. Thirdly, what's the point? Naming this hypothetical object would add zero credence to the hypothesis, and arguably would detract as being a bit premature.

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  • $\begingroup$ Excellent points! The main value a name would have is to make it easier for the authors' university's press office to hype the paper. (A lot of names serve no other purpose than this.) $\endgroup$
    – Mark Olson
    Jul 17 '18 at 13:58
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Names of stars can serve a variety of purposes. Let's look at the different names and designations of Betelgeuse, for example.

  • A star's colloquial name, for lack of a better word, is sometimes chosen to recognize past cultural value. In the case of Betelgeuse, this name is . . . Betelgeuse. In the case of the hypothetical star, though, there is no name from antiquity, as it was not around in antiquity.
  • A star's Bayer designation describes what constellation it is in and its apparent brightness. Betelgeuse appears to us as one of the brightest stars in Orion, so its Bayer designation is $\alpha$ Orionis. As we know nothing about the location or absolute magnitude of the hypothetical star (and heck, the constellations wouldn't have been the same 4.6 billion years ago), giving it a Bayer designation would be pointless.
  • The name of a star in various catalogs may be arbitrary or may tell you something about its current location in the sky (see for instance the Henry Draper Catalogue. However, as I said above, things change on astronomical timescales, and a star will wander from its celestial coordinates on timeframes of hundreds, thousands, or millions of years. And there's no point in assigning this star an arbitrary number.

Finally, as David Hammen said, the existence of this star is still very much hypothetical. Assuming that the paper he found is the right one (and I think it is), the authors don't claim to identify the supernova progenitor with any supernova remnant, location in the sky, or astronomical object. They simply attempt to support the supernova hypothesis with more modeling, something which itself isn't new in the context of this theory. It's certainly nowhere near compelling enough to name the hypothetical object, nor, I think, is the overall evidence for the theory.

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