Could Jupiter Be a Failed Star?

[hexhunter]

The Sun's twin star?

a book I'm reading now, 'the history of nearly everything' by bill bryson says that some cosmologists, or whatever they are called, reckon that as most solar systems have dual stars, Jupiter might be a star which is not ionic or on fire, or whatever...

is this a common thought, or is it rare. what do you think?

 

[SpaceTiger]

Basically, the question here is whether Jupiter formed from aggregation of material in the protoplanetary disk or gravitational collapse (like the sun). There are still some mainstream theories advocating the gravitational collapse of Jupiter, but aggregation is definitely favored at the moment.

 

[chroot]

Jupiter has the same chemical composition as the Sun; it is thus, in a way of speaking, a miniature companion "star." On the other hand, it has only about a thousandth of the mass it would need to actually ignite nuclear fusion and become an actual star.

- Warren

 

[hexhunter]

but in dual-star systems one of the stars has a greater mass, right, this orbits the larger one, and am i wrong in saying that the stars swap mass, as to change which star orbits and which star has the most mass?

also, would it be possible for a liquid body out at space? we have gas giants, rocky planets and stars, so why no liquid ones, understandablyif it is too hot we'd get a gassey planet and if too cold we would get an icy planet, is it just never the right conditions and temperature?

 

[chroot]

but in dual-star systems one of the stars has a greater mass, right, this orbits the larger one, and am i wrong in saying that the stars swap mass, as to change which star orbits and which star has the most mass?

Binary systems with any combination of masses are possible. Stars rarely exchange matter unless they are extremely close together, and one is of much larger radius (not necessarily mass) than the other.

Both stars in a binary system orbit the common center-of-mass. Neither star orbits the other.

also, would it be possible for a liquid body out at space? we have gas giants, rocky planets and stars, so why no liquid ones, understandablyif it is too hot we'd get a gassey planet and if too cold we would get an icy planet, is it just never the right conditions and temperature?

A liquid surrounded by vacuum would have to have an enormous surface tension to remain liquid. Liquids generally vaporize under such conditions.

It is possible that Jupiter contains a core of liquid hydrogen, surrounded by a thick envelope of gas. It is not possible for a sphere of liquid, unattended by such an envelope, to remain liquid.

- Warren

 

[hexhunter]

thanks about that, i seem to have shifted my interests from sub-atomic particles to space, anyway, few more questions:

1) what is in the centre of the Milky Way that our Sun orbits?

2) are there any good sites or video's on the net which can help explain the topic to me in general?

thanks

 

[chroot]

thanks about that, i seem to have shifted my interests from sub-atomic particles to space, anyway, few more questions:

1) what is in the centre of the Milky Way that our Sun orbits?

There doesn't have to be a specific object at the center. All objects orbit the common center-of-mass. It happens that the center-of-mass of the galaxy is there, even if the space there were actually empty. The space is not empty, however; it appears there is actually a supermassive black hole.

- Warren

 

[tony873004]

...On the other hand, it has only about a thousandth of the mass it would need to actually ignite nuclear fusion and become an actual star...

I think its more like a hundreth the mass. Jupiter is about 1/1000 the mass of the Sun, but a star only needs about 8% of the mass of the sun to burn H.

...There doesn't have to be a specific object at the center...

I think there does. This is just my own thinking, not something I read somewhere, but playing around using n-body, I could never get a system to hold together unless one object was much more massive than the rest of the objects. I don't mean combined. Just that the most massive objects needs to be something like 10x as massive as the 2nd most massive object.

I imagine that this "one object" could be a binary object, which would leave room in the middle. But if another object ever gravitationally perturbed the binary and split it apart, the whole system would evaporate away.

Maybe there's a perfect spacing that permits a group of objects to orbit their common center of mass, without a massive primary member, but I haven't found it yet. If my thinking is correct, Globular Clusters probably have a massive black hole in them. But I've never read that anywhere. It just doesn't make sense to me how something like Globular Clusters could have the ages they have without a massive primary member holding them together. I get the impression that the stars are just randomly wandering about the cluster in their orbits. But maybe there is some order to it?

 

[JamesU]

1) what is in the centre of the Milky Way that our Sun orbits?

Isn't there a supermassive black hole?

 

[chroot]

I think its more like a hundreth the mass. Jupiter is about 1/1000 the mass of the Sun, but a star only needs about 8% of the mass of the sun to burn H.

Thank you for the correction; I confused my ratios. :D

I imagine that this "one object" could be a binary object, which would leave room in the middle. But if another object ever gravitationally perturbed the binary and split it apart, the whole system would evaporate away.

With stability issues considered, you're probably right -- there must be something in the center to make the system stable. I only belabored the point because it seemed that hexhunter was falling prey to the fallacy that "small objects orbit big objects," when in fact both objects actually orbit the center-of-mass.

- Warren

 

[SpaceTiger]

I think there does. This is just my own thinking, not something I read somewhere, but playing around using n-body, I could never get a system to hold together unless one object was much more massive than the rest of the objects. I don't mean combined. Just that the most massive objects needs to be something like 10x as massive as the 2nd most massive object.

None of these systems are stable for indefinite periods of time, including globular clusters, but the timescales for instability vary. Generally, we look at the "relaxation time" to determine how long it will take for a gravitationally bound system to change in a significant way. One parameterization of this is:

$$t_{relax}=0.34\frac{\sigma^3}{G^2m\rho ln\ \Lambda}$$

where $$\sigma$$ is the velocity dispersion, m is the mass of the individual stellar components, $$\rho$$ is the stellar mass density, and $$ln\ \Lambda$$ is the Coulomb logarithm (order unity).

Globular clusters have relaxation times ranging from 10⁸ to 10¹⁰ years and have been modeled to undergo core collapse in a few hundred relaxation times. From this, can you figure out why we don't see globular clusters with relaxation times less than about 10⁸ years?

For comparison, the relaxation time of the Milky Way is something like 10¹⁹ years!

 

[DaveC426913]

Originally Posted by chroot...There doesn't have to be a specific object at the center...

I think there does. This is just my own thinking, not something I read somewhere, but playing around using n-body, I could never get a system to hold together unless one object was much more massive than the rest of the objects.

Well, Pluto and Charon would have issue with that. Depending on who you ask, Charon is somewhere around 1/10th to 1/5th of its parent's mass.

Their common centre of rotation is somewhere in the intervening space between them.

 

[SpaceTiger]

Well, Pluto and Charon would have issue with that. Depending on who you ask, Charon is somewhere around 1/10th to 1/5th of its parent's mass.

I think he was implicitly assuming more than two bodies. Ideal two-body systems are completely stable, but things get troublesome when you have any more than that. Tony's statement probably isn't too far from true in these cases. Given that they're still exploring the stability of our solar system, I don't think anybody knows for sure.

 

[Chronos]

Good observation, ST. I think the supermassive BH at the center of MW answers some of those questions. My guess is it is even more massive than accused. And it appears possible there may be more than one of them in that neighborhood.

 

[SpaceTiger]

center of MW answers some of those questions. My guess is it is even more massive than accused.

Why do you say that? I thought the mass determination was pretty solid.

 

[turbo]

Globular clusters have relaxation times ranging from 10⁸ to 10¹⁰ years and have been modeled to undergo core collapse in a few hundred relaxation times. From this, can you figure out why we don't see globular clusters with relaxation times less than about 10⁸ years?

What will a globular cluster look like when it has undergone core collapse? Do we currently see such animals (remnants from those clusters that might have collapsed on the 10⁸ time scale?)

 

[hexhunter]

so the centre of gravity is between the two bodies, closest to the denser of the two or more bodies...

so is this why the sun moves, does this mean that Earth gets pulled around slightly by the moon, and does the Earth actually orbit around the sun between it and the moon?

 

[SpaceTiger]

What will a globular cluster look like when it has undergone core collapse? Do we currently see such animals (remnants from those clusters that might have collapsed on the 10⁸ time scale?)

Here is a nice paper on the subject.

Really, things are a bit more complicated than I said. In addition to core collapse, you have a process known as evaporation occurring on similar timescales. This is basically analogous to evaporation from an atmosphere, in which the high-velocity tail of the Maxwell-Boltzmann distribution is able to escape from the system.

Also, there is mass segregation, a process that tends to separate the more massive stars from the less massive stars. Why does that happen? Well, the clusters are trying to establish equapartition of energy (same basic deal as in a gas), so the massive stars will tend to end up with smaller velocities and sink towards the core. This can be observed, but it is difficult in practice.

There are many papers on these processes in ads and astro-ph, so I suggest a search if you're interested.

 

[SpaceTiger]

so the centre of gravity is between the two bodies, closest to the denser of the two or more bodies...

It's closer to the more massive of the two.

so is this why the sun moves

The sun moves about the galactic center due to the combined gravitational field of many stars, dark matter, gas, etc. The sun also wobbles a little bit as a result of gravitational interactions with the planets in the solar system. This is the wobble that many extrasolar planet searches look for.

does this mean that Earth gets pulled around slightly by the moon, and does the Earth actually orbit around the sun between it and the moon?

Three-body interactions are a bit more complicated, but the Earth does wobble in its orbit as a result of interactions with the moon.

 

[turbo]

Really, things are a bit more complicated than I said. In addition to core collapse, you have a process known as evaporation occurring on similar timescales. This is basically analogous to evaporation from an atmosphere, in which the high-velocity tail of the Maxwell-Boltzmann distribution is able to escape from the system.

Also, there is mass segregation, a process that tends to separate the more massive stars from the less massive stars. Why does that happen? Well, the clusters are trying to establish equapartition of energy (same basic deal as in a gas), so the massive stars will tend to end up with smaller velocities and sink towards the core. This can be observed, but it is difficult in practice.

There are many papers on these processes in ads and astro-ph, so I suggest a search if you're interested.

Complicated indeed! A search of CiteBase turned up numerous papers including this one:

http://citebase.eprints.org/cgi-bin/citations?id=oai%3AarXiv%2Eorg%3Aastro%2Dph%2F0406227

Many of the papers I found said that the presence of a large binary at the core of a dense cluster could provide the dynamics to disperse stars and prevent further collapse. This paper says that a large enough black hole can do the same thing. Maybe the figure in the paper you cited (20% of observed clusters exhibit collapsed cores) is indicative of the small (1 in 5) number of clusters that have not come to some sort of dynamical equilibrium, in which the perturbations caused by the BH or binary at the core balance the tendency toward collapse?

Intuitively, a tendency toward core collapse will accelerate the formation of binaries and/or increase the mass of a central BH in the core, which will then provide the perturbative effects that disperse the core stars - kind of a feedback mechanism to keep the cluster stable against collapse.

 

[SpaceTiger]

Many of the papers I found said that the presence of a large binary at the core of a dense cluster could provide the dynamics to disperse stars and prevent further collapse.

Absolutely, and this is basically what tony was saying. It's easier to stabilize many-body systems when you have a inordinately massive object at the center.

in which the perturbations caused by the BH or binary at the core balance the tendency toward collapse?

The popular explanation for the lack of extreme core collapse involves hard binaries, but one could certainly throw a black hole into the mix.

One still expects the evaporation process to occur, however. Unless the stars were in a very regular configuration (like the solar system), close encounters would scatter stars to velocities beyond the escape speed of the cluster.

 

[DaveC426913]

so the centre of gravity is between the two bodies, closest to the denser of the two or more bodies...

so is this why the sun moves, does this mean that Earth gets pulled around slightly by the moon, and does the Earth actually orbit around the sun between it and the moon?

Yup and yup!

The Earth orbits the Moon. Though I think the centre of rotation of the Earth-Moon system is very close to the centre of the Earth. I think it's only about 400 km from the centre of the Earth. It'll be in direct ratio to their masses. (Earth's weight divided Moon's weight) divided by the distance from Earth to Moon.

And yes, the Earth-Moon system can be considered a single fixed, rotating body as far as its revolution about the Sun.

 

[Janus]

Yup and yup!

The Earth orbits the Moon. Though I think the centre of rotation of the Earth-Moon system is very close to the centre of the Earth. I think it's only about 400 km from the centre of the Earth. It'll be in direct ratio to their masses. (Earth's weight divided Moon's weight) divided by the distance from Earth to Moon.

It works out to being close to an average of 4000 km from the center of the Earth or about 2378 km below the Earth's surface And it won't be a direct ratio of their masses but a ratio of the Moon's mass to sum of their masses multiplied by the Earth-Moon distance. A small correction when dealing with the Earth and Moon, but it becomes significant as the bodies involved become more equal in mass to each other.

I gave the distance from the center of the Earth as an average because, due the the eccentricity of the Moon's orbit, the Earth-Moon distance is not a constant. At maxiumum apogee it would be 4240 km and at minimum perigee: 3755 km, a variation of 485 km.

 

[SpaceTiger]

Yup and yup!

Let's be careful not to confuse. Hexhunter said that the COM would be closer to the denser of the two, when actually it's closer to the more massive one. I'm sure you knew that, I just want to make sure the point is clear to hexhunter. For an example of a situation in which what HH said is not the case, the Earth is actually more dense than the sun, but their center of mass is much, much closer to the sun.

 

[SpaceTiger]

It works out to being close to an average of 4000 km from the center of the Earth or about 2378 km below the Earth's surface And it won't be a direct ratio of their masses but a ratio of the Moon's mass to sum of their masses multiplied by the Earth-Moon distance.

I think at this point we'd be better off communicating in equations. The ratio of the distances to the COM in a two-body system are

$$\frac{a_1}{a_2}=\frac{m_2}{m_1}$$

where these are just the distances to the center of mass and masses of each body. This is equivalent to

$$\frac{a_1}{a}=\frac{\mu}{m_1}=\frac{m_2}{m_1+m_2}$$

where "a" is the total distance between the bodies and $$\mu$$ is the reduced mass. Depending on the interpretation of yours and Dave's words, you could both be right.

 

[Chronos]

I think you should square that.

 

[SpaceTiger]

I think you should square that.

I'm not sure what you're referring to, but I did notice a mistake in my definition of the reduced mass, so the edit is in place.

 

[Chronos]

Shouldn't upsilon be squared?

 

[SpaceTiger]

Shouldn't upsilon be squared?

You mean $$\mu$$ (mu)? If we define that as:

$$\mu=\frac{m_1m_2}{m_1+m_2}$$

then squaring it would give the wrong dimensions (it has dimensions of mass). If you substitute:

$$a=a_1+a_2$$

and the above equation for reduced mass, the two equations I gave are identical (you can derive one from the other).

 

[x8jason8x]

I would guess that no super massive BH exists in the center of our universe, as the theories go, our universe is continually expanding. I don't think that would be possible if even a medium size supernova occurred in our known universe, let alone a massive one in interstellar space. More likely, as already pointed out, there is probably an inordinately large body/bodies (like the sirius system) at the center?