Volume Vs Mass - Kepler 7b

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  • #1
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Or, just how big can a gas giant get?

I read this article recently:

http://www.bbc.co.uk/news/science-environment-24348024

In it, Kepler 7b's clouds are 'directly' mapped for the first time. The planet itself is said to have an overall mass roughly that of polystyrene. Bearing in mind that for a long time Jupiter has been posited as roughly how voluminous a planet can get before it gains mass rather than volume if it gets any more massive, is this world proving to be the exception to that 'rule', and what does it say about just how much more voluminous a world could potentially get? Will we discover much larger, more voluminous worlds than Kepler 7b?
 

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  • #2
D H
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Kepler 7b is a hot Jupiter. It's naturally going to be more voluminous than would be a cold gas giant of equal mass.
 
  • #3
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True, but my question was just how big could a gas giant get. I suppose I need to add that the local conditions might need to be defined too, if they can have a significant effect.
 
  • #4
Chronos
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The minimum mass for deuterium fusion is about 13 Jupiter masses. This limits the maximum mass of an extrasolar planet before it is considered a brown dwarf. At around 75 Jupiter masses, a brown dwarf is capable of hydrogen fusion. It is then considered a red dwarf star.
 
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That's big by mass, not big by volume which is what the thread is about.
 
  • #6
Drakkith
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In it, Kepler 7b's clouds are 'directly' mapped for the first time. The planet itself is said to have an overall mass roughly that of polystyrene. Bearing in mind that for a long time Jupiter has been posited as roughly how voluminous a planet can get before it gains mass rather than volume if it gets any more massive, is this world proving to be the exception to that 'rule', and what does it say about just how much more voluminous a world could potentially get?

Adding more mass to Jupiter would not increase its volume. This is because the added mass would increase the pressure inside the planet and the overall effect would be that the planet contracts. However, we're missing a key component here if you want to compare different planets. Temperature. A planet like Kepler 7b is MUCH hotter than Jupiter is. Remember that Jupiter is almost entirely hydrogen and helium. Gasses. A volume of gas expands when heated up. So if we heated Jupiter up to Kepler 7b's temperature it would grow to a larger volume.
 
  • #7
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So temperature could be considered the local condition affecting Kepler-7b. How much volume expansion of the gasses can the temperature cause? What is likely to be the maximum volume of gas giant before the temperature can't push out the gasses any more?

I'm also presuming, with such temperatures, that such low density, high volume worlds are likely to be short lived due to whatever fuels the heat burning up?
 
  • #8
Drakkith
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So temperature could be considered the local condition affecting Kepler-7b. How much volume expansion of the gasses can the temperature cause? What is likely to be the maximum volume of gas giant before the temperature can't push out the gasses any more?

No idea.

I'm also presuming, with such temperatures, that such low density, high volume worlds are likely to be short lived due to whatever fuels the heat burning up?


What do you mean? What fuels and why would the planet disappear?
 
  • #9
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What do you mean? What fuels and why would the planet disappear?

I didn't mean 'disappear'. I suppose 'short lived' was a poor choice of words on my part.

I mean that the heat that is keeping the gases expanded, if coming from inside the planet, must be being generated by something and I'm presuming it's an internal process rather than an external one coming from an orbited star. That heat would have to have a fuel, and that would eventually deplete to the point that the heat generated would no longer be enough to keep the gases expanded. At that point, the gases would cool and contract, meaning the planet would no longer be a low density voluminous one, and become more like Jupiter as a higher density, smaller volume gas giant.
 
  • #10
Bandersnatch
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The heat is actually coming mostly from the star. Hot Jupiters are so hot not because of some special processes of energy production in their interiors, but because they orbit their stars in very tight orbits. Like balloons of hot air heated by the fire of a burner, they swell up.

The largest exoplanets so far discovered, TrES-4b and WASP-12b are approximately 1.7 times the size(radius) of Jupiter, with something like 0.9 and 1.4 of its mass respectively. They orbit their stars at between 5 and 2% of the Earth-Sun distance.
Check this paper's(http://arxiv.org/pdf/1103.3078.pdf) data(tables 5 and 7) for more precise values. There's also some discussion of why these are anomalous(i.e., current models are inadequate), and references to other papers.
 
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  • #11
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OK, that explains a lot, thanks! :)
 
  • #12
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One other consideration is density, which is the object's mass divided by the object's volume. If you increase the mass to ~13 Jupiter masses, but keep the radius the same as Jupiter, then the density of the planet would be about the same as gold (17.31 g/cm3).

Brown dwarfs, as Chronos mentioned, are formed when a planet reaches ~13 Jupiter masses and begins to fuse deuterium, but that also implies ~13 Jupiter radius in order to have the same (or in Jupiter's case, slightly higher) density as deuterium (1.11 g/cm3).

A planet could potentially be much bigger than 13 Jupiter radius, and still be ~13 Jupiter masses, in which case it would not be dense enough to fuse deuterium, and therefore not considered a brown dwarf. Brown dwarfs are determined by when they start fusing deuterium, not by their mass or radius.

A planet that is 43.4 times the mass and radius of Saturn, for example, would not have sufficient density to begin deuterium fusion. Even though that planet would be 13 Jupiter masses, its volume is considerable more than 13 times the volume of Jupiter, and therefore has a much lower density.
 
  • #13
D H
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One other consideration is density, which is the object's mass divided by the object's volume. If you increase the mass to ~13 Jupiter masses, but keep the radius the same as Jupiter, then the density of the planet would be about the same as gold (17.31 g/cm3).
That's correct. Brown dwarfs are rather dense objects, and they get even more dense as they age and cool off, therefore shrinking. A rather old and very large brown dwarf can have a density of more than 200 g/cm3.

Brown dwarfs, as Chronos mentioned, are formed when a planet reaches ~13 Jupiter masses and begins to fuse deuterium, but that also implies ~13 Jupiter radius in order to have the same (or in Jupiter's case, slightly higher) density as deuterium (1.11 g/cm3).
That's incorrect. You are forgetting about gravitational effects. Gases does not have one density. Compress a gas and the density increases. Compress a gas a lot and the density increases a lot. Compress it even more and it becomes a solid. Even solids are compressible given enough pressure. For example, the iron in the Earth's core has a density 1.66 times that of iron at the Earth's surface. The Earth's gravity field is rather puny compared to that of Jupiter, which in turn is smaller than that of a brown dwarf.
 
  • #14
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Brown dwarfs, as Chronos mentioned, are formed when a planet reaches ~13 Jupiter masses and begins to fuse deuterium, but that also implies ~13 Jupiter radius in order to have the same (or in Jupiter's case, slightly higher) density as deuterium (1.11 g/cm3).

A planet could potentially be much bigger than 13 Jupiter radius, and still be ~13 Jupiter masses, in which case it would not be dense enough to fuse deuterium, and therefore not considered a brown dwarf. Brown dwarfs are determined by when they start fusing deuterium, not by their mass or radius.

A planet that is 43.4 times the mass and radius of Saturn, for example, would not have sufficient density to begin deuterium fusion. Even though that planet would be 13 Jupiter masses, its volume is considerable more than 13 times the volume of Jupiter, and therefore has a much lower density.
In addition to D H's post: don't mix volume and radius. Volume scales with the cubed radius, so 13 times the volume means just 2.35 times the radius.

There is no "minimal density" for fusion. Actually, the biggest and most luminous stars have a very low average density. It can be below the density our atmosphere (~1.3kg/m^3).
 
  • #15
D H
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In addition to D H's post: don't mix volume and radius. Volume scales with the cubed radius, so 13 times the volume means just 2.35 times the radius.
Brown dwarfs, especially older ones, are typically smaller than Jupiter. Young ones can be a tiny bit larger, but not much. Here's a nice plot from the scholarpedia article on brown dwarfs (http://www.scholarpedia.org/article/Brown_dwarfs):

544px-Segransan03.jpg


The black triangle near the lower right: That's Jupiter. The other labeled objects are red dwarfs. The dashed red curve is a model of objects at an age of 400 million years. The solid black curve, an age of five billion years. The low point on the black curve corresponds to density of over 200 g/cm3.
 
  • #16
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That's correct. Brown dwarfs are rather dense objects, and they get even more dense as they age and cool off, therefore shrinking. A rather old and very large brown dwarf can have a density of more than 200 g/cm3.
I have no doubt that is the case.

That's incorrect. You are forgetting about gravitational effects. Gases does not have one density. Compress a gas and the density increases. Compress a gas a lot and the density increases a lot. Compress it even more and it becomes a solid. Even solids are compressible given enough pressure.

Would not the gravitational effects be determined by the volume the mass is contained within? The less volume, the more the mass (gas in this case) is compressed.

Also, I did take into consideration the gravitational effects, which is why I concurred with Chronos that ~13 Jupiter masses is when the planet begins fusing deuterium and becomes a brown dwarf. If I did not take gravity into consideration then it would merely be a planet that is 13 times the mass of Jupiter, and not start fusing deuterium.

For example, the iron in the Earth's core has a density 1.66 times that of iron at the Earth's surface.
I was not aware of that.

The Earth's gravity field is rather puny compared to that of Jupiter, which in turn is smaller than that of a brown dwarf.
As far as mass is concerned, you are quite correct. Although, it may be possible for planet with ~13 Jupiter masses, and significantly denser (much more than 13 times Jupiter's density) to begin deuterium fusion while being much smaller than 13 Jupiter volumes.
 
  • #17
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Would not the gravitational effects be determined by the volume the mass is contained within? The less volume, the more the mass (gas in this case) is compressed.
That's not the order of effects - gravity compresses stuff until there is an equilibrium between pressure gradient and gravitational forces.

If I did not take gravity into consideration then it would merely be a planet that is 13 times the mass of Jupiter, and not start fusing deuterium.
Without gravity there would be no planets or stars at all.

As far as mass is concerned, you are quite correct. Although, it may be possible for planet with ~13 Jupiter masses, and significantly denser (much more than 13 times Jupiter's density) to begin deuterium fusion while being much smaller than 13 Jupiter volumes.
How would that object be stable? It would just expand until it is a regular planet.
 
  • #18
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In addition to D H's post: don't mix volume and radius. Volume scales with the cubed radius, so 13 times the volume means just 2.35 times the radius.
You are quite right, and I did notice my mistake in the last sentence of my post. Thanks for catching it.

There is no "minimal density" for fusion. Actually, the biggest and most luminous stars have a very low average density. It can be below the density our atmosphere (~1.3kg/m^3).
That seems contradictory. In order for fusion to occur, would you not need a large amount of mass in a very small volume?
 
  • #19
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The core density is relatively high (and pressure and temperature are really high), the density in the outer regions (>99.99% of the volume) is low, giving a low average density.
 
  • #20
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That's not the order of effects - gravity compresses stuff until there is an equilibrium between pressure gradient and gravitational forces.
Yes, I understand that. I did not mean to imply that gravity is determined by volume. Mass and density determine the gravitational effects, and that in turn determines the volume.

If there is insufficient mass, there will be no fusion, because gravity will not be able to compress the material sufficiently. However, if you could introduce more mass, then the effects of gravity increases, compressing the gas (reducing the volume) in the process, and thus increasing the density of the material.

Without gravity there would be no planets or stars at all.
Agreed.

How would that object be stable? It would just expand until it is a regular planet.
A ~13 Jupiter mass planet with a density of 2.156 g/cm3 would have a radius (not volume, I am paying closer attention) only twice that of Jupiter. Why would that be unstable? I do not understand.
 
  • #21
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The core density is relatively high (and pressure and temperature are really high), the density in the outer regions (>99.99% of the volume) is low, giving a low average density.
I was under the impression that density was calculated by dividing the mass of an object by its volume. While I do understand that it is merely a mean average density, I was not aware that density was also determined by the distance one was from the center of an object.

Could you please point me to someplace were I might find the equations for calculating this graduating density?

Thanks.
 
  • #22
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If there is insufficient mass, there will be no fusion, because gravity will not be able to compress the material sufficiently. However, if you could introduce more mass, then the effects of gravity increases, compressing the gas (reducing the volume) in the process, and thus increasing the density of the material.
That's what happens at ~13 Jupiter masses.

A ~13 Jupiter mass planet with a density of 2.156 g/cm3 would have a radius (not volume, I am paying closer attention) only twice that of Jupiter. Why would that be unstable? I do not understand.
Why do you think such an object would exist? It would have a volume similar to Jupiter, slowly fusioning deuterium.

I was not aware that density was also determined by the distance one was from the center of an object.
It is not "determined" by that, but density can depend on the position in the object. For stars, the density is mainly a function of the radius and decreases with increasing radius.
This is given by the hydrostatic equilibrium.
 

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