[WBH] Brown Dwarf Aging

mando501

Mongoose
Yes, it's me again :LOL:

I'm working with some Brown Dwarfs, and I'm trying to wrap my head around aging. Well, with characteristics in general past Y5. How do you determine values for Y6 to Y9?

The chart on page 226 doesn't extend past Y5, which is fine if you're not aging the Brown Dwarf - the minimum mass the formula on the same page can generate is 0.013, which is the mass of a Y5 that is around 1 GYr old.

However, the age of a Brown Dwarf is generated using the Small Star formula, which will spit out a value between 2 and 14 GYrs, although the page 20 notes that 13.8 GYr is roughly the limit.
Option d in the enumerated list on page 226, under the table, suggests reducing the subclass by 1 subtype per GYr (2 if the mass is 0.05 or less).

A 14 GYr old brown dwarf with 0.5 mass (starting at T0) will age 26 subtypes, taking it well past Y9. That's an extreme example, and would probably be capped at Y9 or otherwise addressed as the person generating the star would see fit.

However, the issue is that there is a non-trivial chance of a Brown Dwarf aging past a Y5, and I'm unsure how to address that. Do the characteristics not change between Y5 and Y9? Should I try to interpolate based on the pattern of the rest of the table (which is decided non-liner)?

Am I missing something obvious?
 
I think, in the interim, I'll peg a theoretical Y10 (X0?) at a diameter of 0.09 and interpolate between 0.01 and 0.09 from Y5 to Y9. Keep the diameter constant at 0.10, and drop the temp by 50K per step. I've seen values floated of 80 K, 200 K, and 250 K as the theoretical minimum temp of a Y9. Dropping by 50K per step from Y5 to Y9 will end up with a temperature of 100 K. Alternatively, cut it in half (-25 K / step) ends up with 200 K at Y9.

I'd be interested to see if there's any other approach that makes sense, though.
 
I think, in the interim, I'll peg a theoretical Y10 (X0?) at a diameter of 0.09 and interpolate between 0.01 and 0.09 from Y5 to Y9. Keep the diameter constant at 0.10, and drop the temp by 50K per step. I've seen values floated of 80 K, 200 K, and 250 K as the theoretical minimum temp of a Y9. Dropping by 50K per step from Y5 to Y9 will end up with a temperature of 100 K. Alternatively, cut it in half (-25 K / step) ends up with 200 K at Y9.

I'd be interested to see if there's any other approach that makes sense, though.
Yeah, it does sort of fall of the chart for something that starts out small, doesn't it? Depending on the system, it could reach equilibrium, which for a lone brown dwarf, might be 10K or less - or ignore the brown dwarf recommendations altogether and try the Gas Giant Residual Heat formula on page 125 (and no I haven't tried it with something as big as a brown dwarf - I suspect the two methods will not converge.)

Or, do what you're suggesting and drop by 50K until you hit Y9 and then... hover and assume equilibrium by 100K - warmer if being warmed by a brighter object.
 
[...] or ignore the brown dwarf recommendations altogether and try the Gas Giant Residual Heat formula on page 125 (and no I haven't tried it with something as big as a brown dwarf - I suspect the two methods will not converge.) [...]
They do not, and the results are a little comical :LOL:
A 1 GYr old L0 at 0.08 solar masses ends up with a temp of ... 42.55 K
A 1 GYr old Y6 at ~0.013 solar mases ends up with a temp of about 27 K, which is a bit of a drop from the 300K of a Y5


Correction, I was using solar masses and the residual heat formula uses earth masses. Oops.
A 1 GYr old L0 at 0.08 solar masses (26,642 earth masses) ends up with a temp of 1,022K
A 1 GYr old Y6 at ~0.013 solar masses (~4,150 earth masses) ends up with a temp of about 642 K

Looks like the range starts too small and reduces too slow to match up with the Brown Dwarf characteristics chart in any meaningful way.

I think going with a 50K or 25K reduction is the way I'm going to go. It gets things in the ball park of the theoretical without getting real deep in to other factors such as presence of a hotter object nearby. I may open that can of worms later, but much later 😂
 
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They do not, and the results are a little comical :LOL:
A 1 GYr old L0 at 0.08 solar masses ends up with a temp of ... 42.55 K
A 1 GYr old Y6 at ~0.013 solar mases ends up with a temp of about 27 K, which is a bit of a drop from the 300K of a Y5


Correction, I was using solar masses and the residual heat formula uses earth masses. Oops.
A 1 GYr old L0 at 0.08 solar masses (26,642 earth masses) ends up with a temp of 1,022K
A 1 GYr old Y6 at ~0.013 solar masses (~4,150 earth masses) ends up with a temp of about 642 K

Looks like the range starts too small and reduces too slow to match up with the Brown Dwarf characteristics chart in any meaningful way.

I think going with a 50K or 25K reduction is the way I'm going to go. It gets things in the ball park of the theoretical without getting real deep in to other factors such as presence of a hotter object nearby. I may open that can of worms later, but much later 😂
Well, at least it wasn't as bad as I feared. In some sciences, order of magnitude is 'good enough'.
 
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