In article ,
Joseph Lazio writes:
Kirkpatrick (2005) summarizes various cooling curves from other
authors. There is some uncertainty, due to our lack of understanding
of dust and cloud formation in the atmospheres of these objects.
Nonetheless, from his curves, I estimate that a T dwarf with a
temperature of about 1000 K and an age of about 1 Gyr is expected to
have a temperature of order 500 K at an age of about 4.5 Gyr.

I got slightly higher, maybe 600 K, but there's a lot of uncertainty.
According to Sterzik et al. (2005), there's also a lot of uncertainty
about the actual effective temperatures of both components of epsilon
Indi B.

Let's see. In the discovery observations, the combined system has an
infrared J-band magnitude of approximately 12. That's at a distance
of 3.6 pc. Move it about 500 times closer (to a distance of about
1500 AU). That means that it should become about 13.5 magnitudes
brighter. Its apparent J-band magnitude would be approximately -1.5.

Indeed.

Ah, but these calculations are for eps Ind Ba at its current
temperature. Suppose we consider a similar object but with a
temperature that is a factor of 2 lower, consistent with the notion
that it is 4.5 Gyr old. A factor of 2 in temperature should
correspond to a factor of 16 in luminosity which would be 3
magnitudes. So our hypothetical Sun Ba would be expected to have a
J-band magnitude of 1.5.

While the luminosity drops by a factor of 16, the drop in flux
density is larger at shorter wavelengths. For 500 K, J band is well
on the Wien side of the Planck curve, and the actual drop is more
like 12 magnitudes. That makes a "4 Gyr eps Indi Ba" at 1500 AU
about magnitude J=10.5.

Things are a lot better at K, where the aging drop is only about
7 mag. And at 12 microns, the drop is only about 1.6 mag. The
actual 12-micron flux density is about 6 mJy for each component, so
either one even after aging would be around magnitude -4 at 12
microns. That would make it one of the brightest objects in the sky,
easily visible to IRAS unless located in the 5% of the sky IRAS
didn't survey.

There have been all-sky surveys in the J band (e.g., 2MASS). I think
there's little chance that they would have missed either a -1.5 or 1.5
magnitude object.

Right. A 1 Gyr "eps Indi Ba" would have been one of the brightest
objects in the original Two Micron Sky Survey unless its declination
was south of -33 degrees. At 4 Gyr, it would have been below the
survey limit but easily visible to 2MASS, which covered the whole
sky. The one limitation I can think of would be if the proper motion
is large, 2MASS data-processing might have rejected the object. I
don't know enough about the catalog construction to say whether this
is possible or not.

--
Steve Willner Phone 617-495-7123
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