# Does the sun have angular momentum?

That's pretty much it.

Is it perfectly spherical, or is it squashed like the Earth due to a rotation?
Is it rotating through an axis perpendicular to the plane of the solar system?

If yes, can we measure this using Doppler shift of spectral lines either side of the sun, or something like this?

Not homework, just something I randomly thought of. It seems that it has to have at least some sort of angular momentum, what are the chances all the cold gas that collapsed to form it had exactly zero net angular momentum, right?

Thanks,
Mike

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mgb_phys
Homework Helper
That's pretty much it.
Yes quite a lot of it

Is it perfectly spherical, or is it squashed like the Earth due to a rotation?
Rather more squashed, it rotates faster (in m/s) than the Earth and is rather less solid.
The rotation is a bit more complicated, because the sun is a gas the equator can rotate faster than the poles.

Is it rotating through an axis perpendicular to the plane of the solar system?
Yes, it's rotation came from the angular momentum of the same could that created the planets.

If yes, can we measure this using Doppler shift of spectral lines either side of the sun, or something like this?
Yes, an easier way is just to watch sunspots moving across the surface.

It seems that it has to have at least some sort of angular momentum, what are the chances all the cold gas that collapsed to form it had exactly zero net angular momentum, right?
Exactly

Ah, right, I bet there are all sorts of weird currents going on inside it, sounds really interesting. Would this sort of work come under plasma physics, or astrophysics?

mgb_phys
Homework Helper
Helioseismolgy
Although astronomers are mostly are interested in just the temperature profile into the centre because that tells you about the lifetime and origin of the star.
What happens near the surface is very complicated and it's difficult to get good data fro anything other than the nearest example

Thanks.. I have just tried a few literature searches on that, but haven't come up with anything. Do you know any keywords that I could use to find a few review articles on it?

Thanks very much,

Matterwave
Gold Member
The sun is rotating, as is in general most other stars. That's one reason Pulsars exist. The original star was rotating rather slowly, but when it contracted to ~10km in radius, conservation of angular momentum made them rotate extremely fast! On a side note, conservation of Magnetic field makes the magnetic fields on a neutron star impossibly strong. So strong, the magnetic field itself (not to mention gravity) would tear you (a human, relatively impervious to magnetic fields) to pieces.

Astronuc
Staff Emeritus
Thanks.. I have just tried a few literature searches on that, but haven't come up with anything. Do you know any keywords that I could use to find a few review articles on it?
helioseismology

http://soi.stanford.edu/results/heliowhat.html

There is plenty of literature on the physics of stars, or 'stellar astrophysics'

http://gong.nso.edu/info/helioseismology.html

http://solar-center.stanford.edu/heliopage.html

http://solarscience.msfc.nasa.gov/Helioseismology.shtml

http://www.mps.mpg.de/projects/seismo/NA4/

The Fundamentals of Stellar Astrophysics
George W. Collins, II

D H
Staff Emeritus
Yes quite a lot of it
Actually, not a lot of it. Almost all of the mass of the solar system is attributable to the Sun, but almost all of the angular momentum of the solar system is attributable to the planets' orbits about the Sun (particular, Jupiter). This is the "angular momentum problem". The current explanation of this discrepancy is the solar wind, and particularly, magnetic coupling between the Sun and the solar wind out to distances well beyond the radius of the Sun.

Actually, not a lot of it. Almost all of the mass of the solar system is attributable to the Sun, but almost all of the angular momentum of the solar system is attributable to the planets' orbits about the Sun (particular, Jupiter). This is the "angular momentum problem". The current explanation of this discrepancy is the solar wind, and particularly, magnetic coupling between the Sun and the solar wind out to distances well beyond the radius of the Sun.
Hello,

Why should the ratio of angular momentum to mass be the same for different objects?

I can vaguely see that it might make sense, but not clearly.

Thanks,

mgb_phys
Homework Helper
Actually, not a lot of it.
Not a lot of the whole Solar System's angular momentum is in the sun - after all its at the 'axle' but an object that weighs 10^30kg and spins once a month has pretty significant angular momentum!

mgb_phys
Homework Helper
Why should the ratio of angular momentum to mass be the same for different objects?
Its because of how you define angular momentum.

The ang,. momentum of the sun (assuming a solid sphere for simplicity) L = 2/5 m r^2 * ω
r = 7E8 m m=2E30 kg ω = 2pi/25days = 3e-6 rad/s

L = 2/5 * 2E30 * 7e8^2 * 3E-6 = 10^42 kgm^2/s

Jupiter is smaller but its moving a lot faster (like a weight on a string ) I = mr^2
But r = radius of Jupiters orbit = 800million km = 8E11m and m = 2e27kg
orbital period = 12years so ω = 2pi/ 3.7E8s = 1.7E-8

L = 2e27 * 8e11^2 * 1.7E-8 = 2 * 10^43 kgm^2/s

So Jupiter has 20x as much angular momentum (in its orbit around the sun) than the sun has.

D H
Staff Emeritus
The ang,. momentum of the sun (assuming a solid sphere for simplicity) ... So Jupiter has 20x as much angular momentum (in its orbit around the sun) than the sun has
With this simplifying assumption, that is. This simplifying assumption overstates the angular momentum of the Sun by a factor of 6.8 (I=0.059mr2; ref http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html). In other words, Jupiter has ~120 times as much angular momentum (in its orbit about the sun) than the Sun has about its axis.

This discrepancy between mass and angular momentum was (and remains) the biggest problem for the nebular hypothesis of star and planet formulation. One explanation is that protostars lose angular momentum because of coupling of the star's magnetic field with the solar wind coming from the star. Even though this was first proposed in the 1970s, this explanation remains in the realm of hypothetical as opposed to theoretical.

I can appreciate the r^2 means Jupiter has a load more than the sun, (I guess the correction is because mass near the surface of the sun is less dense and moves slower?) but that doesn't answer the question of why this is a problem.

does some conservation law get violated if most of the matter takes very little of the angular momentum when forming the solar system?

mgb_phys
Homework Helper
but that doesn't answer the question of why this is a problem.
Yes it's a conservation law problem.
If there was a gas cloud out to Jupiter which rotated at Jupiter's current speed and collapsed to form the sun then the angular momentum is conserved and so you would expect the sun to be spinning much faster.

Either the momentum was lost to turbulence and material that escaped the system, or the original cloud was slower sun's momentum later went into the planets by some coupling mechanism

Is question of magnetic coupling purely theoretical or is there some experimental evidence? In an experiment, what would one realistically look for as evidence of a source of such coupling, and would such a system decouple? I'm familiar with that process during solar events such as flares, but not at such a great range.

Final question... if materal was lost to turbulance would there be some kind of radiation (thermal maybe) footprint of friction that slowed such a massive body? Would that process have left marks in the makeup of our local system that have or could be found? I find this whole concept fascinating, and far more palatable than more exotic and unlikely events such as "dark flow" *scoffs*