WI Epsilon Indi B in Solar System

"c" == chornedsnorkack writes:

c What would happen if Epsilon Indi B orbited Sun, not Epsilon Indi
c A?

c B is allegedly 1500 a. u. from A. Does someone know exactly how far
c in front of or behind A, and on which orbit?

I haven't found anything in a quick search, other than that it might
lie nearly in the plane of the sky (McCaughrean et al. 2004).

c Anyway, imagine Epsilon Indi B orbiting on a circular orbit 1500
c a. u. from Sun.

c Ba is allegedly 47 Jupiter masses and 1,3 milliards of years
c old. It is known to have temperature of about 1000 Celsius.

c Sun Ba at 4,5 milliards of years would be cooler... how much?

c In any case, it would radiate no visible light.

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.


c It is about the size of Jupiter (maximum cold mass!). At 50 times
c the distance to Pluto in perihelion, and roughly 60 times the
c diametre, it would be slightly wider. And it would receive 2500
c times less light... meaning that in reflected light of Sun, it
c would be 8,5 magnitudes dimmer. Much dimmer than Charon, Quaoar or
c Sedna, it would be invisible.

c Would anyone discover it as a modest source of infrared?

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 pc). That means that it should become about 13.5 magnitudes
brighter. Its apparent J-band magnitude would be approximately -1.5.


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.

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. (Missing a -1.5 magnitude object would be like
conducting a survey at visual wavelengths and not seeing Sirius.)

Also note that the source of its infrared radiation cannot be
reflection from eps Ind A. That star has a spectral type K4.5, so
while a bit redder than the Sun, it is also dimmer.


c Also, what about Bb? Epsilon Indi Bb is known to be about 600
c Celsius at the age of 1,3 milliards of years and allegedly 27
c Jupiter masses. Would an object older than this, at 4,5 milliards
c of years, be discovered in infrared?

Without running the numbers, I'd still expect a hypothetical Sun Bb,
similar to eps Ind Bb but older, to still be detectable easily.

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