Our local galaxy, with binaries of the same mass with a separation of no more than 1 AU. The densities are of no concern as long as the masses are similar.
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Unfortunately, I couldn't find a list for this, so using Space Engine (I couldn't find a better option), I found a few (almost) matches:
- LTT 1445 B and C, somewhat close to a match;
- Epsilon Indi B, much closer, if you accept brown dwarves;
- Kepler-444 B and C, almost a perfect match;
- HD 106906 AB, even better.
These are all just binaries within a ~326ly radius of Earth!
I should mention that Space Engine's parameters are likely at least 9 years out of date.
EDIT: as requested, https://spaceengine.org/
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$\begingroup$ This is a great start, thanks for the update. $\endgroup$ Apr 20 at 17:19
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$\begingroup$ Kepler 444 is a triple star system, as is LTT 1445. In the Keplar system the primary (A) is larger than two similar mass stars (B and C). The stars of HD106906 aren't resolved, so their masses are inferred from their spectrographic type (resulting in some uncertainty about mass) $\endgroup$– James KApr 20 at 21:22
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$\begingroup$ Epsilon Indi is a complex system with a pair of brown dwarfs with masses of about 66 and 53 times the mass of Jupiter in orbit around an orange dwarf (with much greater mass, about 75% that of the sun) $\endgroup$– James KApr 20 at 21:30
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1$\begingroup$ Maybe provide a link to "Space Engine", whatever that is? $\endgroup$ Apr 21 at 10:47