Luminosity and Magnitude

[Evil Dr Ganymede]

I'm trying to figure out if anyone would be able to see one Brown Dwarf in the Epsilon Indi pair from a moon of the other one. So how does one figure out the magnitude of an BD that is about 66000 km in radius with a luminosity of 0.0000044 Sols, from a distance of about 2.2 AU? I suspect it wouldn't be visible from the other dwarf without a good telescope, right?
(would the illumination from Epsilon Indi at 1500 AU away light up the dwarf and make it visible?)

[Ynjevi]

Old brown dwarfs that have cooled down are pretty much invisible in visible light unless something light them up. But because they are still quite hot, they emit much infrared radiation which can be detected. 1500 AUs is quite a distance, and Epsilon Indi is much dimmer than the Sun (14.7% of Sun's luminosity), so it's hard to think it can make any difference.

[granthutchison]

From the quoted temperatures and bolometric magnitudes, I can at least estimate the visual magnitude using the blackbody curve. Turns out to be an absolute visual magnitude of ~27 for Ba and ~36 for Bb. At a separation of 2.65 AU, that means that Ba would be a bright red star around mag -2.4 from Bb, whereas Bb would be below the limit of visibility at 6.8 when seen from Ba. These things are pretty dim to look at: from up close, Ba's surface brightness is about the same as a piece of white paper seen by good artificial light; Bb is as bright as a bit of paper seen by moonlight.
Knowing that, we can say that Eps Ind A isn't going to make a very noticeable difference to the apparent brightness of these objects: at 1500AU it shines around magnitude -8.8, or a just a fortieth of the full moon, so it's only going to brighten Bb by a percent or so.

Grant

[Evil Dr Ganymede]

Wow, that's brighter than I expected actually. Thanks again, folks.

[granthutchison]

The problem with brown dwarfs is that only bolometric magnitudes are given, and there is a huge difference between their bolometric and visual magnitudes. (I'm guessing that they're visually so dim that no-one has actually measured a visual magnitude yet, but I'd be happy to be wrong.)
What I've been doing to get a handle on this is to take the blackbody spectrum for the given effective temperature as a rough approximation to the actual distribution of energy output, factoring in the sensitivity of the eye at various wavelengths, and so deriving a bolometric correction factor - a number you need to add to the quoted bolometric magnitude for a brown dwarf to derive its corresponding visual magnitude.
This might be useful to the world-builders out there, so here's a little table:

Code: Select all

Temp (K)          B.C. (mags)
2000              4.4
1800              5.4
1600              6.8
1400              8.5
1200              10.9
1000              14.4
800               19.6


Grant

[selden]

KELU-1 has a visual magnitude of 22.3 and a temperature below 1700 degrees C according to http://www.eso.org/outreach/press-rel/pr-1997/pr-07-97.html

[Evil Dr Ganymede]

This might be useful to the world-builders out there, so here's a little table:

*yoink*

Thanks, that'll come in most useful

Grant - Have you ever tried world-building yourself, out of curiosity?

[granthutchison]

KELU-1 has a visual magnitude of 22.3 and a temperature below 1700 degrees C according to http://www.eso.org/outreach/press-rel/pr-1997/pr-07-97.html

Thanks Selden - they've annoyingly not given the bolometric magnitude, which I need to check that my simpleminded blackbody approximation isn't too far off. I'll need to go hunting and see if it's quoted elsewhere ...

Grant - Have you ever tried world-building yourself, out of curiosity?

I do little bits and bobs to play with the maths and see what's possible, but nothing you could call world-building.

Grant