by neufer » Wed Jun 03, 2009 7:24 pm
Qev wrote:bhrobards wrote:Please explain how this makes sense. Two objects are approximateley the same size. The compositions of the objects is similar. The hot one is ten times the mass of the small cool one. With gravity and the ideal gas law we have a problem.
Bear in mind that, ignoring gravity and assuming both of these objects have the same density, a sphere ten times more massive is going to have only about double the radius. Gravity's effect on density is simply going to reduce that even further. There's even a good example of this sitting in our own solar system; Jupiter is three times more massive than Saturn, and yet is only about 25% larger in terms of radius. Then there's always the extreme cases, like neutron stars, where the greater the mass, the smaller the radius.
Obviously, heating from stellar fusion is going to counteract this trend once the object is massive enough to initiate it. So I would assume that VB10 is in fact larger in diameter than its planet, but probably not by a huge amount. The paper linked to from the APOD page simply states that both objects are ~0.1 times the radius of the Sun, which gives some wiggle-room for one to be larger than the other, while still being 'the same size' on astronomical scales.
Perhaps, some familiarity with "
the missing link" here might help:
http://en.wikipedia.org/wiki/Brown_dwarf wrote:
<<Brown dwarfs are sub-stellar objects with a mass below that necessary to maintain hydrogen-burning nuclear fusion reactions in their cores, as do stars on the main sequence, but which have fully convective surfaces and interiors, with no chemical differentiation by depth. Brown dwarfs occupy the mass range between that of large gas giant planets and the lowest mass stars; this upper limit is between 75 and 80 Jupiter masses (MJ). Currently there is some debate as to what criterion to use to define the separation between a brown dwarf from a giant planet at very low brown dwarf masses (~13 MJ ), and whether brown dwarfs are required to have experienced fusion at some point in their history. In any event, brown dwarfs heavier than 13 MJ do fuse deuterium and those above ~65 MJ also fuse lithium. The only planets known to orbit brown dwarfs are 2M1207b and MOA-2007-BLG-192Lb.
A remarkable property of brown dwarfs is that they are all roughly the same radius as Jupiter. At the high end of their mass range (60-90 Jupiter masses), the volume of a brown dwarf is governed primarily by electron degeneracy pressure, as it is in white dwarfs; at the low end of the range (1-10 Jupiter masses), their volume is governed primarily by Coulomb pressure, as it is in planets. The net result is that the radii of brown dwarfs vary by only 10-15% over the range of possible masses. This can make distinguishing them from planets difficult.
In addition, many brown dwarfs undergo no fusion; those at the low end of the mass range (under 13 Jupiter masses) are never hot enough to fuse even deuterium, and even those at the high end of the mass range (over 60 Jupiter masses) cool quickly enough that they no longer undergo fusion after some time on the order of 10 million years. However, there are other ways to distinguish dwarfs from planets:
Density is a clear giveaway. Brown dwarfs are all about the same radius; so anything that size with over 10 Jupiter masses is unlikely to be a planet.
X-ray and infrared spectra are telltale signs. Some brown dwarfs emit X-rays; and all "warm" dwarfs continue to glow tellingly in the red and infrared spectra until they cool to planet like temperatures (under 1000 K).
Some astronomers believe that there is in fact no actual black-and-white line separating light brown dwarfs from heavy planets, and that rather there is a continuum. For example, Jupiter and Saturn are both made out of primarily hydrogen and helium, like the Sun. Saturn is nearly as large as Jupiter, despite having only 30% the mass. Three of the giants in our solar system (Jupiter, Saturn, and Neptune) emit more heat than they receive from the Sun. And all four giant planets have their own "planetary systems" -- their moons. In addition, it has been found that both planets and brown dwarfs can have eccentric orbits.
Currently, the International Astronomical Union considers objects with masses above the limiting mass for thermonuclear fusion of deuterium (currently calculated to be 13 Jupiter masses for objects of solar metallicity) to be a brown dwarf, whereas those objects under that mass (and orbiting stars or stellar remnants) are considered planets.>>
[quote="Qev"][quote="bhrobards"]Please explain how this makes sense. Two objects are approximateley the same size. The compositions of the objects is similar. The hot one is ten times the mass of the small cool one. With gravity and the ideal gas law we have a problem.[/quote]
Bear in mind that, ignoring gravity and assuming both of these objects have the same density, a sphere ten times more massive is going to have only about double the radius. Gravity's effect on density is simply going to reduce that even further. There's even a good example of this sitting in our own solar system; Jupiter is three times more massive than Saturn, and yet is only about 25% larger in terms of radius. Then there's always the extreme cases, like neutron stars, where the greater the mass, the smaller the radius.
Obviously, heating from stellar fusion is going to counteract this trend once the object is massive enough to initiate it. So I would assume that VB10 is in fact larger in diameter than its planet, but probably not by a huge amount. The paper linked to from the APOD page simply states that both objects are ~0.1 times the radius of the Sun, which gives some wiggle-room for one to be larger than the other, while still being 'the same size' on astronomical scales. :)[/quote]
Perhaps, some familiarity with "[b]the missing link[/b]" here might help:
[quote=" http://en.wikipedia.org/wiki/Brown_dwarf"]
<<Brown dwarfs are sub-stellar objects with a mass below that necessary to maintain hydrogen-burning nuclear fusion reactions in their cores, as do stars on the main sequence, but which have fully convective surfaces and interiors, with no chemical differentiation by depth. Brown dwarfs occupy the mass range between that of large gas giant planets and the lowest mass stars; this upper limit is between 75 and 80 Jupiter masses (MJ). Currently there is some debate as to what criterion to use to define the separation between a brown dwarf from a giant planet at very low brown dwarf masses (~13 MJ ), and whether brown dwarfs are required to have experienced fusion at some point in their history. In any event, brown dwarfs heavier than 13 MJ do fuse deuterium and those above ~65 MJ also fuse lithium. The only planets known to orbit brown dwarfs are 2M1207b and MOA-2007-BLG-192Lb.
[b]A remarkable property of brown dwarfs is that they are all roughly the same radius as Jupiter. At the high end of their mass range (60-90 Jupiter masses), the volume of a brown dwarf is governed primarily by electron degeneracy pressure, as it is in white dwarfs;[/b] at the low end of the range (1-10 Jupiter masses), their volume is governed primarily by Coulomb pressure, as it is in planets. The net result is that the radii of brown dwarfs vary by only 10-15% over the range of possible masses. This can make distinguishing them from planets difficult.
In addition, many brown dwarfs undergo no fusion; those at the low end of the mass range (under 13 Jupiter masses) are never hot enough to fuse even deuterium, and even those at the high end of the mass range (over 60 Jupiter masses) cool quickly enough that they no longer undergo fusion after some time on the order of 10 million years. However, there are other ways to distinguish dwarfs from planets:
Density is a clear giveaway. Brown dwarfs are all about the same radius; so anything that size with over 10 Jupiter masses is unlikely to be a planet.
X-ray and infrared spectra are telltale signs. Some brown dwarfs emit X-rays; and all "warm" dwarfs continue to glow tellingly in the red and infrared spectra until they cool to planet like temperatures (under 1000 K).
Some astronomers believe that there is in fact no actual black-and-white line separating light brown dwarfs from heavy planets, and that rather there is a continuum. For example, Jupiter and Saturn are both made out of primarily hydrogen and helium, like the Sun. Saturn is nearly as large as Jupiter, despite having only 30% the mass. Three of the giants in our solar system (Jupiter, Saturn, and Neptune) emit more heat than they receive from the Sun. And all four giant planets have their own "planetary systems" -- their moons. In addition, it has been found that both planets and brown dwarfs can have eccentric orbits.
Currently, the International Astronomical Union considers objects with masses above the limiting mass for thermonuclear fusion of deuterium (currently calculated to be 13 Jupiter masses for objects of solar metallicity) to be a brown dwarf, whereas those objects under that mass (and orbiting stars or stellar remnants) are considered planets.>>[/quote]