Its tricky to define the Sun's solar relatives after all as far as we can tell relatively massive "lower mass stars, i.e. F and G type main sequence stars, like our Sun only form in dense star formation clusters the type where very massive stars form something we have evidence to support in terms of the presence of fossilized chemical bonds from short lived radioisotopes from the Early solar system with different chemistry to their daughter products (basically elements in chemical bonds that the current element wouldn't form but which a radioisotope that decays into that element does suggesting that when the molecules in "primordial" asteroid, meteor and or cometary derived material formed the short lived radioisotope was present).
Yes, but yet there are "solar twins" that are surprisingly close in all features, including composition. This would allow a close spectral comparison.
Roughly 4% or 5% of the stars in the galaxy are G-type. If only 4% or 5% of those are G2, then there may be as many as 200M G2 stars out there. Maybe 1/3 of those can be observed, leaving maybe 50 million or so. Deduct from those the time frame, as you mentioned.
So, some may have very similar composition. Those that are similar (not very similar) are called solar analogs. The very similar are the "twins".
Given that the Sun likely has tens of thousands of siblings at least even though the vast majority of the remaining stars will be less massive K and M type main sequence stars which will naturally fail to meet the solar twin criteria there will still be a lot of G type stars that meet that criteria and because the chaotic inhomogeneous conditions in starbursts even stars from the Sun's birth cluster may vary considerably in chemical composition.
There was a report I read a while back, but I don't think I saved it, that explained that the no. of siblings might be between 1000 and 3000. The upper constraint was due to the claim that the outer planets would have encountered more orbital instability due to perturbations from the close neighbors.
The IMF (Initial Mass Function) seems to show about 60 stars out of 3000 that would have masses between 0.9 and 1.1. So, perhaps there are a few solar twins from our own original GMC.
Then of course you get to the issue of stellar migration since we have some evidence to suggest the Sun likely formed closer to the Galactic center than it is found now which isn't surprising given that stars are locked within an angular momentum constrained random walk of sorts which over time via stellar encounters and interactions with passing density waves tidal perturbations etc. which all can cause shifts in a star's orbit around the Milky Way. This makes it difficult to trace back the Sun yet alone any of its siblings to their place of origin as there have been nearly 5 billion years of jumbled mixing with the general disk population.
All good points. I do recall U of Texas, however, finding one sibling, though I don't recall its type.
I must admit I don't really understand the crux of their argument. There are over 25,000 lines in the solar spectra. How many must they match with another star? Can't they pick the ones that match the most evident atoms, say a certain iron ion, to get their verification? If the constant they wish to confirm is not constant, wouldn't it be seen in those dozen lines or so for one atom?