Why is GR not Required to Model Galactic Rotation?

[mjc]

Can anyone enlighten me in why it is regarded as unnecessary to invoke GR when modelling galactic rotations - good ol' Newtonian mechanics apparently being fine for the task?

I have a fuzzy memory of reading this somewhere - and maybe that memory is just plain wrong.

Is it true - and is it readily explainable?

I would have thought that if one were to look at the plane of rotation of a distant galaxy the forces of gravity affecting any particular point include the forces from masses that have long since moved on and are visually (from observer's point of view) somewhere else now.

I'm completely out of my depth - but would imagine that would cause spiraling arms to be seen (but I also vaguely remember reading that the spiraling is due to something else).

Mark C.

[CraigS]

Hi Mark;
Good question. I'll defer to Carl or Steven on this one for the best answer ...but a quick answer (from me) is that GR is still relevant and is underpinned by Newtonian mechanics. I did a couple of threads on spirals recently:

http://www.iceinspace.com.au/forum/showthread.php?t=64705
and;
http://www.iceinspace.com.au/forum/showthread.php?t=64837

I try to summarise the long conversations at the end so I hope there's a quick answer at the ends of the threads for you.

Also, just because masses drift away from each other in a galaxy, doesn't mean that gravity field strength 'disappears'. It remains and diminishes with distance squared. The influence of other masses drifting into the spiral arms then adds another influence.

Gotta go.

Cheers
PS: The answer to your question is also "its a scale thing". GR is used over larger distances eg: intergalactic distances. Not so much influence in intra-galaxy distances.

[sjastro]

There are a number of reasons.

Astrophysicists are particularly interested in the rotation curves of stars well away from the galactic centre, where Keplers third law breaks down and subsequently spawned the theory of dark matter.

In this environment galaxy rotations involve slow moving stars, in low gravitational potentials well removed from the influence of supermassive black holes at the centre. Under these conditions it allows the use of Newtonian physics which is an excellent approximation for GR.

The other point is that GR is way too difficult to use.:D

Newtonian physics allows galaxy gravitation to be modelled as a "spherical shell". In this shell of radius r, all the mass is concentrated at the centre as a point. Inside the radius, the gravity is zero, outside the radius the point mass exerts a gravitational force.
Outside the radius Kepler's third law should hold, that is the velocity of a star is inversely proportional to the square root of the radius (or distance between the star and point mass.)

Measurements on outlying stars that exist outside "the shell" reveal that the velocity of the stars remains "flat" and does not drop off as predicted by Kepler's third law.

Regards

Steven

[CraigS]

Er ... close to flat.
Some galaxy rotation curves go up slightly, some go down slightly, some are flat. None obey Kepler's third law - which results in more unchartered water.
http://www.iceinspace.com.au/forum/s...ad.php?t=64705

Cheers

[higginsdj]

Excuse a stupid question, but what is GR?

[sjastro]

GR=General relativity.

Regards

Steven

[sjastro]

That may be true but the spherical shell model is based on a flat rotation curve past a given value of r.

This allows the mass/light ratio to be calculated for a galaxy which is an indirect measurement for the amount dark matter.
http://en.wikipedia.org/wiki/Mass_to_light_ratio

Regards

Steven

[CraigS]

Ok. So does this mean that if one were to change the model to another shape (eg: an ellipse) and whilst the mass/light ratio calculation would er ... 'get ugly', the apparent non-flat rotation curves feature might get explained, for those galaxies exhibiting this feature ?

Does that make sense ?

Cheers

[sjastro]

The mass to light ratio is only an average value. For flat curves this average is accurate where ever the curve is flat. For non flat curves you can measure the mass to light ratio in different areas of the rotation curve above a particular value of r.

Probably the flatter the curve the more even distribution of DM.

Regards

Steven

[mjc]

Thanks all for the replies - very helpful - I followed up with some reading in wikipedia on density waves and found that fascinating. The Light to Mass Ratio is new to me so thanks for that also.

Cheers
Mark C.