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antoniseb
2011-Dec-07, 07:02 PM
I'm being lazy here, I know I could calculate it myself...

How many times more massive would Jupiter need to be for its own light to be brighter than the sunlight reflected off of it (in the optical part of the spectrum) ? Assume that at 4.6 billion years, it is already old enough that the heat of formation is no longer a factor, and that if it were a Lithium star, the Lithium is long gone.

chornedsnorkack
2011-Dec-07, 07:45 PM
I'm being lazy here, I know I could calculate it myself...

I am impressed.

Jupiter reflects about 250 millions times less light than Sun emits.

For a brown dwarf, what is emitted is the blue tail of the spectrum. Even the red dwarf Proxima Centauri has bolometric correction of about 36 times smaller visible light fraction than Sun. Incidentally it means that quiet Proxima should match the luminosity of Jupiter at opposition at about 450 AU.

Now, a brown dwarf is not necessarily black! Say it has clouds which are opaque to near infrared (where the peak emission should be) but translucent in visible red. Then the peak of spectrum would be emitted from cloudtops at their temperature, but the lower and hotter regions would be emitting bluer visible red light glowing through - thus the spectrum would have strong blueward tail compared to a black body. Or the opposite, clouds might cut off the blue end of spectrum.

Do you have sufficient details as to the specific chemistry of brown dwarfs at various temperatures and their resulting albedos and colours in emitted and reflected lights so as to spot the correct temperature and thus mass?

antoniseb
2011-Dec-07, 08:05 PM
I am impressed....
Don't be impressed. I meant I could calculate it sufficiently close that I was satisfied... not that I could calculate it precisely.

Do you have sufficient details as to the specific chemistry of brown dwarfs at various temperatures and their resulting albedos and colours in emitted and reflected lights so as to spot the correct temperature and thus mass?
I was going to make the rash assumption of an albedo between 50% and 90%, and as to emitted light, assume a thin photosphere, i.e. not much blue tail. ... The bolemtric answer is how much mass before the fusion engine is cranking out 1.6x1024ergs per second? ... but since many more of those ergs would be in the IR for an M8, we'd need some kind of correction factor.

SamCashion
2011-Dec-07, 08:34 PM
How many times more massive would Jupiter need to be for its own light to be brighter than the sunlight reflected off of it (in the optical part of the spectrum) ?

Wait, wait 0_o Jupiter produces its own light???

glappkaeft
2011-Dec-07, 08:42 PM
Wait, wait 0_o Jupiter produces its own light???

It's not that wierd, you do too (and anything above 0K).

PraedSt
2011-Dec-07, 09:05 PM
I had a rough stab at this, so probably not what you're looking for antoniseb. But anyway:

Apparent mag of Sun: -27; Apparent mag of Jupiter: -2.
So using the apparent magnitude formula, the Sun is ~ 9*109 brighter than Jupiter.
Allowing for the approx 10 AU return trip, Jupiter's luminosity is ~ 1*10-8 that of the Sun.

Then, using the mass-luminosity relationship for main sequence stars, you find that Jupiter should be 1/100 the mass of the Sun. So seeing as Jupiter is 1/1000 the mass of the Sun, it needs to be 10 times bigger.

chornedsnorkack
2011-Dec-07, 09:37 PM
Then, using the mass-luminosity relationship for main sequence stars
Which does not hold for brown dwarfs.

Anyway, inching closer.

A simple estimate will show that Proxima, absolute magnitude +15,37, would at Jupiterīs orbit be about magnitude -13, or about as bright as full Moon. Would look pretty around ecliptic, like the contrast seeing the different colours and surface luminosities in conjunction....

So, we are looking for something with absolute visual magnitude +25. But has anything like this ever been seen?

Surprisingly, there is. DENIS-P J0255-4700 is seen in visible light - magnitude +22,92. It turns out to be about 16 lightyears away - which is about a million AU.
At 4,2 AU like Jupiter at opposition, this would mean about -4. So, a brown dwarf only slightly cooler than DENIS J0255-4700 would be as bright as Jupiter.

J0255-4700 is classified as L8. However, its temperature has variously been quoted as 1400 or 1700 K. Its mass has been guessed at 60 Jupiter masses, but obviously depends on unknown age.

Thus, what you are looking for is a body around L8...L9, around 1300...1600 K. What should the mass be, at solar age?

antoniseb
2011-Dec-07, 09:46 PM
... Thus, what you are looking for is a body around L8...L9, around 1300...1600 K. What should the mass be, at solar age?
I may be wrong assuming this, but I'm thinking that DENIS J0255-4700 is probably a hot young object - maybe still fusing Lithium. I can only imagine that the mass for a Jupiter-aged object would have to be more to give that much light. Do you know more about it?

WayneFrancis
2011-Dec-08, 12:14 AM
Wait, wait 0_o Jupiter produces its own light???

Yup! ...so does the Earth, Mars, asteroids, you, me, the little spider crawling across my desk...heck my desk does too.

It is just infra-red light and it isn't produced from fusion but just the fact that we are at a temperature > absolute 0.

PraedSt
2011-Dec-08, 09:44 AM
Maybe I misunderstood the question. I thought we were talking about red dwarfs.

Anyway, I can't see how an old brown dwarf can give off enough light to match Jupiter. Unless you're talking about the whole spectrum, in which case Jupiter already does that I think.

glappkaeft
2011-Dec-08, 04:53 PM
Yup! ...so does the Earth, Mars, asteroids, you, me, the little spider crawling across my desk...heck my desk does too.

It is just infra-red light and it isn't produced from fusion but just the fact that we are at a temperature > absolute 0.

It's not just infra-red light, there is a small, although addmitedly very much so, visual component as well. In fact even the sun outputs more IR than visual light.

chornedsnorkack
2011-Dec-08, 05:02 PM
Maybe I misunderstood the question. I thought we were talking about red dwarfs.

Anyway, I can't see how an old brown dwarf can give off enough light to match Jupiter. Unless you're talking about the whole spectrum, in which case Jupiter already does that I think.

Yes, that is a question.

From the brown dwarf cooling curves, what is the temperature of a maximum mass brown dwarf (70...75 Jupiter masses) at solar age?

antoniseb
2011-Dec-08, 05:36 PM
Yes, that is a question.

From the brown dwarf cooling curves, what is the temperature of a maximum mass brown dwarf (70...75 Jupiter masses) at solar age?

Almost... What is the temperature of the outermost opaque-to-NIR-and-Optical-photons layer of such a BD, and I suspect that you can carry that up into the 80 JM range before the optical light surpasses the reflected Sunlight on such an old dwarf star.

EDG
2011-Dec-11, 01:21 AM
From the brown dwarf cooling curves, what is the temperature of a maximum mass brown dwarf (70...75 Jupiter masses) at solar age?

A 70 MJ Brown Dwarf at 4.6 Ga should have an effective temperature of 1258K, Luminosity of 0.0000134 Sols, surface gravity of 2720.12 m/sē, and radius of 57,385 km.

(according to a spreadsheet I made using the formulas in The Theory of Brown Dwarfs and Extrasolar Giant Planets, Burrows et al., Reviews of Modern Physics, volume 73, 719-765 (2001).)

antoniseb
2011-Dec-11, 01:26 AM
A 70 MJ Brown Dwarf at 4.6 Ga should have a... Luminosity of 0.0000134 Sols...

I'm assuming that is the bolometric luminosity. What would it be in white light?

whimsyfree
2011-Dec-11, 02:29 AM
Any red dwarf would be much brighter than Jupiter. If you're talking about brown dwarfs then it's a matter of studying cooling curves, which are probably very unreliable due to uncertainties about the atmospheric chemistry of brown dwarfs. I don't think it's possible answer the question with any precision.

antoniseb
2011-Dec-11, 02:37 AM
Any red dwarf would be much brighter than Jupiter....

You could be right... There is some amount of fusion that would give an old dwarf exactly as much visible light as Jupiter reflects. Whether that is a an M9.9 or something dimmer is hard to say, though in vernacular we tend to think of a "brown dwarf" as a star that does no fusion whatsoever, and only radiates based on gravitational energy as the star compresses.

chornedsnorkack
2011-Dec-11, 05:56 AM
Young brown dwarfs can have unsustained thermonuclear fusion of deuterium, lithium and protium. Unsustained because when the contraction slows down, loss of core heat by conduction exceeds production of fusion heat, so the core cools and thermonuclear fusion slows down further. There would be the background level of pycnonuclear fusion, but that is tiny.

In a young population of stars, red dwarfs and young brown dwarfs are close in temperature and luminosity and therefore undistinguishable. In an old population, however, a gap should open - minimum mass red dwarfs stabilize at a luminosity necessary to sustain core fusion, whereas maximum mass brown dwarfs keep cooling.

What is the observed position of that gap in the oldest populations (i. e. globular clusters)?

And this means that from a known temperature in the gap, a maximum age can be found for a dwarf of otherwise unknown mass.

whimsyfree
2011-Dec-11, 08:00 AM
You could be right... There is some amount of fusion that would give an old dwarf exactly as much visible light as Jupiter reflects. Whether that is a an M9.9 or something dimmer is hard to say, though in vernacular we tend to think of a "brown dwarf" as a star that does no fusion whatsoever, and only radiates based on gravitational energy as the star compresses.

I thought the latest true stars were M7.

antoniseb
2011-Dec-11, 12:48 PM
... What is the observed position of that gap in the oldest populations (i. e. globular clusters)? ...
Excellent idea! That sounds like a job for the 30+ meter telescopes, or perhaps the JWST. I don't think we have *any* observations of BDs in GCs yet, aside, perhaps from hot jupiters, which don't really work for this discussion.


I thought the latest true stars were M7.
I highlighted the expression 'true stars' because I don't think that has a meaning. As I mentioned in the OP, and as chornedsnorkack reminds us, we have stars which convert Lithium, and Deuterium briefly, and that no matter how small you get there is random fusion, spallation, and perhaps pycnonuclear fusion going on. Further, the isotope distribution in the core can affect how the lowest pressure and temperature allowed there while still producing *some* fusion, and the element distribution of the outer layers can affect what photons are released, and hence what M-number we give it.

So I'm not specifically arguing that you are wrong about M7. I'm saying that the boundary between "true star" and "untrue star" (to coin a term) is a poorly defined one at the moment.

glappkaeft
2011-Dec-11, 02:04 PM
IIRC from a talk given by a local astronomer the general consensus is that true stars fuse hydrogen and brown dwarfs don't. This works well for models but with observations the problem is that the many of the indicators can be less than helpful. For instance the presence of lithium, BD should have lithium - stars shouldn't, isn't as clear cut as we would like because young stars still have some lithium and high mass brown dwarfs manage to fuse some of it before they cool too much.