Question on Density Waves

[CraigS]

I find density waves, used as an explanation for the spiral arms in a Galaxy a curious phenomenon:
http://en.wikipedia.org/wiki/Density_wave_theory

" ..so, the gravitational attraction between stars can only maintain the spiral structure if the frequency at which a star passes through the arms is less than the epicyclic frequency, κ(R), of the star. This means that a long-lived spiral structure will only exist between the inner and outer Linblad resonance (ILR, OLR, respectively), which are defined as the radii such that: Ω(R) = Ωgp + κ / m and Ω(R) = Ωgp − κ / m, respectively. Past the OLR and within the ILR, the extra density in the spiral arms pulls more often than the epicyclic rate of the stars, and the stars are thus unable to react and move in such a way as to "reinforce the spiral density enhancement".

What's more, there is observational evidence (& predictions) supporting this theory. (Eg: Saturn's moon-on-ring interactions).

So in general, might one view the arms as the end result of the 'twisting' in spacetime caused by the stars' gravitational fields interacting with their inertial/centrifugal forces ?

Yet another 'spacetime' warping phenomenon ? ... I wonder ...

Cheers

[renormalised (Carl)]

It's not so much a warping phenomenon of spacetime as it's a wavelike phenomenon that creates an over density in the material within a disk of material. You can get standing waves (which is what occurs in galaxies) or moving waves which occur in substances like fluids (e.g. water). The material within the disks can be moving slower or faster than the waves, but where it encounters the wave it enters those conditions of over density and gets compressed. That's where you get your HII regions and OB associations forming. These generally hang around in the areas of over density because they don't last very long and so you get your spiral arm pattern forming. The rest of the materials within the galaxy rotate at whatever speed they will, depending on their distance from the centre and the other factors affecting their movement, but the wave essentially stays put...the spiral pattern doesn't rotate, or moves very little.

Just notice something cool....play that little video of the spiral arms in the galaxy on the right hand side of the page, then quickly look up at M81....you can see the optical illusion of its arms actually rotating

If you want a really good book about galaxies and about spiral density waves in galaxies, grab yourself a copy of this Galactic Dynamics (Princeton Series in Astrophysics). It is quite maths heavy but you'll just have to wade through it. It's an exceptionally good book and will explain what you need to know about galaxies.

Oh, and I forgot, this book too....Galactic Astronomy. Also very good.

[CraigS]

Originally Posted by renormalised

It's not so much a warping phenomenon of spacetime as it's a wavelike phenomenon that creates an over density in the material within a disk of material. You can get standing waves (which is what occurs in galaxies) or moving waves which occur in substances like fluids (e.g. water). The material within the disks can be moving slower or faster than the waves, but where it encounters the wave it enters those conditions of over density and gets compressed. That's where you get your HII regions and OB associations forming. These generally hang around in the areas of over density because they don't last very long and so you get your spiral arm pattern forming. The rest of the materials within the galaxy rotate at whatever speed they will, depending on their distance from the centre and the other factors affecting their movement, but the wave essentially stays put...the spiral pattern doesn't rotate, or moves very little.

Just notice something cool....play that little video of the spiral arms in the galaxy on the right hand side of the page, then quickly look up at M81....you can see the optical illusion of its arms actually rotating

Hmm..
Very interesting. If I start my thoughts from your starting premise: "The material within the disks can be moving slower or faster than the <harmonic standing> waves", then I think I get it.

Moving outwards along an arm, the rotational velocity must get slower, otherwise, there'd be a disc, rather than an arm, right ? That there is an arm at all, must be courtesy of some really 'elegant' harmonics. The mathematics describing it all must be a mathematician's playground. There must be fairly deterministic (linear ?) velocity relationships between two adjacent objects/particles which describe their alignment, which begins the pattern, which eventually builds the 'arm' structure.

Gravity must play a role however, 'cause we're talking about some big objects like stars, as well as smaller ones like dust and gas (?). And the inter-stellar velocities synching up to form the arm pattern implies some kind of resonance in the gravitational fields (?).

Perhaps I'll go one further, & this may be a quantum leap, but I'm also reminded of that bizarre hexagonal structure on the (North ?) pole of Saturn. I think the current thinking on that one is that it may be a standing wave pattern described by fluid dynamics around a polar region. Oh .. to understand fluid mechanics as well, eh ?

Fascinating stuff.

Cheers (& thanks for your reply).

[renormalised (Carl)]

You also get moving density waves in galaxies as well, something I forgot to mention.

These also do the same thing as material passing in and out of standing waves....gets compressed and forms spiral arms.

The spiral arms are actually all those OB associations and HII regions, along with the other dust and gas. They are just areas of over density...roughly 10-20% higher than the surrounding space. They travel a lot slower than the general rotation of the galaxy's contents and that's why the arms appear as they do.

Gravity does play a roll....it does all the jostling about of the stars and gas, starts the formation of the stars by collapsing the gas and dust clouds etc.

http://burro.cwru.edu/Academics/Astr...al/spiral.html

http://nedwww.ipac.caltech.edu/level.../carlberg.html

[CraigS]

Originally Posted by renormalised

You also get moving density waves in galaxies as well, something I forgot to mention.

These also do the same thing as material passing in and out of standing waves....gets compressed and forms spiral arms.

The spiral arms are actually all those OB associations and HII regions, along with the other dust and gas. They are just areas of over density...roughly 10-20% higher than the surrounding space. They travel a lot slower than the general rotation of the galaxy's contents and that's why the arms appear as they do.

Gravity does play a roll....it does all the jostling about of the stars and gas, starts the formation of the stars by collapsing the gas and dust clouds etc.

http://burro.cwru.edu/Academics/Astr...al/spiral.html

http://nedwww.ipac.caltech.edu/level.../carlberg.html

Thanks Carl. Absolutely amazing !

Just read thru both links for the first time. Will read them again a few more times to get it to sink in. The last paragraph on the second link, (a better paper), contains a nice 'bottom-line' summary:

"In the end a complete theoretical description of all the details of spiral patterns will involve a tremendous amount of complicated physics of stars, gas, magnetic fields, and gravity. A very good approximate description of spiral structures is a description of many stars moving about as described by Newton's dynamics and theory of gravity. Stars moving together in nearly circular orbits are strong amplifiers of regions of higher star density, and they create the visible trailing spirals that we observe."

Cheers
PS: If I purchased, read, assimilated and understood all of the text books you have pointed me at over the last few weeks, apart from being brain-dead, I'd be a starving, broke, all-knowing, fully indoctrinated, card carrying Cosmologist !! Can't have that now ! There's too many of those guys .... and their theories .. phooey !!

but, then again, ... I might just try ...

[renormalised (Carl)]

Haha....yep. Better of playing with meccano sets and building stuff. You make more money

[CraigS]

Ok. So coming back to my original 'twists in spacetime' fantasy, one could say that perhaps this fantasy could be dismissed as follows:

In a galaxy, phenomena such as Rotational Frame Dragging described by the Kerr Metric, the Penrose processes in the Ergosphere and Gravitomagnetic Effects are mainly localised to the rotating core, right ? (This is a scale question).

Wiki mentions that the Frame Dragging effect (for eg) is fairly weak, about 1 part in 10^12 so, I guess, just comparing the magnitude of this metric with the metric radius of a spiral arm, about 4.5 x 10^17 kms, (50k ly), something like Frame Dragging would only be localised to a bit over one part distance from the core and hence wouldn't play much/any of a role beyond that distance? (Is the logic right, here ?)

(I'm trying to get a feel for how much impact rotating galactic holes might have on the objects comprising the arms and thus, the rotation of the galaxy, due to their torque effects).

Cheers

[renormalised (Carl)]

So far you're on the money....the frame dragging effect is only a localised phenomenon around the vicinity of the central supermassive BH, and despite the very large mass of the hole, spacetime gradient for such a large hole is actually rather small (because of its size). If it were a smaller stellar mass hole, the frame dragging effects would be very pronounced (very steep and intense spacetime gradient), but even more localised. On the scale of a galaxy and its arms, the frame dragging can be ignored.

[CraigS]

Originally Posted by renormalised

despite the very large mass of the hole, spacetime gradient for such a large hole is actually rather small (because of its size). If it were a smaller stellar mass hole, the frame dragging effects would be very pronounced (very steep and intense spacetime gradient), but even more localised.

I read this, and the rationale for this concept, somewhere recently -a Susskind book, I think.
Interesting to note that at sometime in the early days, it probably started off small so, at that time, it must've also had a big effect on everything around it. Perhaps plain old Newtonian momentum has continued the dynamics into the present day and that's what we're seeing.

The question here would seem to be: How big an impact has this original state made, in comparison with other subsequent effects (eg: gravitational attraction between objects trailing & leading in the arms, collisions with other galaxies, etc). Yet another scale question, I think.

Interesting.

Cheers

[sjastro]

Originally Posted by renormalised

So far you're on the money....the frame dragging effect is only a localised phenomenon around the vicinity of the central supermassive BH, and despite the very large mass of the hole, spacetime gradient for such a large hole is actually rather small (because of its size). If it were a smaller stellar mass hole, the frame dragging effects would be very pronounced (very steep and intense spacetime gradient), but even more localised. On the scale of a galaxy and its arms, the frame dragging can be ignored.

The key is the radius of the erosphere and the event horizon which is a function of BH mass. Increasing BH mass increases the radii. The further the horizons are from the centre of the BH the less the effects of tidal forces and space-time curvature.

Supermassive BHs are pussycats, it's those small solar mass BHs one has to be very careful of.

Steven

[renormalised (Carl)]

Originally Posted by sjastro

The key is the radius of the erosphere and the event horizon which is a function of BH mass. Increasing BH mass increases the radii. The further the horizons are from the centre of the BH the less the effects of tidal forces and space-time curvature.

Supermassive BHs are pussycats, it's those small solar mass BHs one has to be very careful of.

Steven

Precisely...you could cross over the event horizon of a supermassive black hole and not even notice it. Try doing that on a 3 or 4 solar mass hole and see what happens

Instant "spaghettification" and conversion into gamma rays

Not that anyone would notice

[renormalised (Carl)]

Originally Posted by CraigS

I read this, and the rationale for this concept, somewhere recently -a Susskind book, I think.
Interesting to note that at sometime in the early days, it probably started off small so, at that time, it must've also had a big effect on everything around it. Perhaps plain old Newtonian momentum has continued the dynamics into the present day and that's what we're seeing.

The question here would seem to be: How big an impact has this original state made, in comparison with other subsequent effects (eg: gravitational attraction between objects trailing & leading in the arms, collisions with other galaxies, etc). Yet another scale question, I think.

Interesting.

Cheers

A small hole has a very high spacetime gradient, hence the tidal forces present are extremely large...the smaller the hole the greater the tidal forces, so despite it being far less massive than the whopper in the centre of a galaxy, a stellar mass hole has an event horizon which is very close to the centre of the hole (the centre of mass) and because of this the gravitational field, the spacetime curvature and the tidal forces are extreme in comparison.

It'd be like if you packed all of Jupiter's mass into a body the size of the Moon. Even though the subsequent body would still be much less massive than the Sun and much smaller physically, the gravitational field of that smaller object would be much more intense than the Sun's and the gravitational acceleration at its surface would be considerably higher.

[CraigS]

Yep - also the larger the mass, the colder the hole and the smaller the mass, the warmer the hole ..

At the risk of turning this thread into a black hole discussion .. it was meant to be about Density Waves ... hang on .. I started it !! .. so what the heck !! Here goes ...

The thing that bugs me about black holes is their lifecycle ... eg: what is their growth rate?, will they grow forever?, will they reproduce?, do they evaporate to zip (less than Planck size) & will this ever happen for a given BH?, etc, etc. There must be some really interesting things which could be discovered if one compares the quantity of ingested matter, as they grow, to the resulting increase in macro-scale gravitational field densities, ergosphere effects, frame dragging effects, etc ??

(Probably a difficult empirical measurement problem, at the moment - estimates might do here, but perhaps not a problem for theoretical physics?)

I suppose someone's already had a go at these ones (Hawking etc)- if so , I've just got more reading to do ! If not, think of all the things we could learn about - eg: as a minimum - the physical properties of atypical states of matter and their effects on macro-scale cosmology, the effects on objects as a result of gravitational waves across the galaxy as a result of BH growth (BH growing pains), etc, etc !

I guess its all in some textbook - Carl ??

Cheers

[renormalised (Carl)]

Yep....High Energy Astrophysics, Introduction to Modern Astrophysics,
Active Galactic Nuclei: From the Central Black Hole to the Galactic Environment. There's a start

There's an old saying to do with black holes..."A black hole has no hair", meaning theirs nothing a black hole has or radiates which can be easily detectable, apart from it's gravity.

However, a black hole not only has hair (Hawking....Hawking Radiation), but they do evaporate. Only for a stellar mass hole it takes on the order of 10^66 years to evaporate to the stage where it becomes unstable and explodes with the force of a billion H bombs

[CraigS]

Originally Posted by renormalised

Yep....High Energy Astrophysics, Introduction to Modern Astrophysics,
Active Galactic Nuclei: From the Central Black Hole to the Galactic Environment. There's a start

There's an old saying to do with black holes..."A black hole has no hair", meaning theirs nothing a black hole has or radiates which can be easily detectable, apart from it's gravity.

However, a black hole not only has hair (Hawking....Hawking Radiation), but they do evaporate. Only for a stellar mass hole it takes on the order of 10^66 years to evaporate to the stage where it becomes unstable and explodes with the force of a billion H bombs

"By the time it has reached Planck mass, its temperature will have risen to 10^32 degrees. The only time any place in the universe might have been anywhere near that temperature was at the beginning of the Big Bang."

... oops !! ... did we just explain "The Origin" ??

.. cool ... er ... HOT !

Cheers

[renormalised (Carl)]

Originally Posted by CraigS

"By the time it has reached Planck mass, its temperature will have risen to 10^32 degrees. The only time any place in the universe might have been anywhere near that temperature was at the beginning of the Big Bang."

... oops !! ... did we just explain "The Origin" ??

.. cool ... er ... HOT !

Cheers

Possibly. It's been suggested that the universe may have come from the remains of a black hole that was in another universe. Or from the matter that had been sucked into the singularity at its centre. Maybe that's how it happens, a black hole in some universe reaches Planck temp and size then flashes out of existence in its universe with a blast of gamma rays, but starts up another universe somewhere else because the conditions are so extreme at these stages that maybe matter and energy are created out of the quantum effects at these sizes and energies.

[CraigS]

Anyway .. back to the farm ..

From the Ray Carlberg paper Carl sent me:

"The fact that stars cannot interact as individuals immediately leads to a simple explanation of the fact that all spirals appear to be "trailing,'' that is, they lag the direction of rotation with increasing radius in the disk. The explanation is that gravitating systems attempt to increase their gravitational energy, or at least become more concentrated, if at all possible. For a disk of stars an increase in gravitational energy of the central region can only occur if the stars move closer to the center. To move stars inward requires that they lose angular momentum, which can be accomplished if there is a torque directed opposite to their direction of rotation. A trailing spiral pattern supplies just such a torque because the stars in the spiral wave near the center are pulled backward by the stars further out in the spiral. Consequently the central gravitational energy is increased at the expense of a decrease in the energy of stars further out in the disk."

So, this suggests (carefully) that each star in the arm interacts via their gravitational fields. We're talking about 'inter-stellar distances' here (further out in the arm .. not around the core). This in turn, means that say, the Earth, is within the gravitational field of say, Alpha Centauri (4.24 ly distant), and its tugging us via the grav. field interactions.

Perhaps implying inter-stellar gravitational attraction is 'the stretch' area of this Theory, (which is OK by me). I think from an Equivalence Principle point of view, the Earth is observed to be in an Accelerated Frame of Reference but that's as far as we know. The implied association with gravity seems to be a bit of a "leap" ?

Your thoughts ?

Cheers

[renormalised (Carl)]

http://mb-soft.com/public/galaxy.html

http://en.wikipedia.org/wiki/Galaxy_rotation_curve

I haven't read the papers yet, but has the gravity of all the matter surrounding each of the stars been taken into account?? The reason why is that it's not just stars interacting with other stars that is happening, but they're also under the influence of all the other material surrounding them....gas, dust etc. You also have to remember that the gravitational interaction between any two individual stars would be exceedingly small, given their distances of separation on average (at the Sun's distance, roughly 1 star/10ly). However, all these tiny tugs add up over time to change the orbit of the stars. Most of the gravitational interactions occurring with stars would be coming from the other materials that each star passes by in its orbit.

[CraigS]

Originally Posted by renormalised

http://mb-soft.com/public/galaxy.html

http://en.wikipedia.org/wiki/Galaxy_rotation_curve

I haven't read the papers yet, but has the gravity of all the matter surrounding each of the stars been taken into account?? The reason why is that it's not just stars interacting with other stars that is happening, but they're also under the influence of all the other material surrounding them....gas, dust etc. You also have to remember that the gravitational interaction between any two individual stars would be exceedingly small, given their distances of separation on average (at the Sun's distance, roughly 1 star/10ly). However, all these tiny tugs add up over time to change the orbit of the stars. Most of the gravitational interactions occurring with stars would be coming from the other materials that each star passes by in its orbit.

Your first link contains an excellent paper ! This guy is actually going back to Keplerian & Newtonian mechanics and comes up with a very realistic perspective on Dark Matter:

"There are claims that enormous amounts of invisible mass must exist, as in a giant massive halo around the galaxy, but such claims seem to never have contemplated where that mass would have to be! In some such theories, a super-massive halo is supposed to exist OUTSIDE the Galaxy, but Newton showed us that such external mass would have no gravitational effects interior to it.

In some such theories, a very massive torus of invisible material (dark matter, hidden matter, neutrinos) would have to exist around the rim of the Core, and additional peculiar distributions of that mass would have to exist, in order to cause the non-Keplerian fast revolving of the Spiral Arms.

The alleged distribution is often simply referred to as an invisible halo! Such a structure would not be stable or even meta-stable."
...
"The current premise seems to comply with standard physical laws and principles much better than the exotic explanations of heretofore unconfirmed missing mass, gravity waves, black holes and other hypotheses. It does NOT require any new or exotic explanation, but rather just points out a logical flaw in the previous logic attempting to explain the Galaxy's rotation and the durability of the Spiral Arms. A consequence of it is a less massive Galaxy, possibly implying a significantly smaller Universe."

"First Developed, Nov 1997, First Published on the Web: Aug 16, 1998
This subject presentation was last updated on Mon, 25 Jan 2010."

.... But I can't seem to find out who wrote it !!

Cheers

[renormalised (Carl)]

Something else you might like to consider here...

http://en.wikipedia.org/wiki/Modifie...onian_dynamics

http://arxiv.org/abs/1007.3444

http://arxiv.org/abs/1007.1278

http://arxiv.org/abs/1006.5037

http://arxiv.org/abs/1001.3876

http://arxiv.org/abs/1005.3537

http://arxiv.org/abs/1005.5442

http://arxiv.org/abs/1005.5456

http://arxiv.org/abs/1005.2964

http://arxiv.org/abs/1005.4629

http://arxiv.org/abs/1003.0684

I won't add anymore, but there are some 388 papers that are written about MOND (Modified Newtonian Dynamics). Whilst MOND is an interesting and possible alternative to the CDM theory there are still problems with it...especially when MOND is derived in terms of quantum gravity. So far attempts to derive MOND in this way have been unsuccessful. There is also some observational evidence with clusters of galaxies and a few other situations which MOND has not been able to model well, as yet. In fact, just like most of the others theories it's a work in progress. Whether it stands the test of time is a matter of more research and observation.

As for the first of the links I posted previously...I wouldn't take what it says as a given until it's been tested. Also remember that it has to explain the observational evidence better than current theory and have credible alternative processes and mechanisms. For instance, the Sun's oscillations about the central plane of the galaxy and mass extinction timings. Whilst there maybe some circumstantial evidence for a possible correlation between spiral arm crossings and large scale mass extinctions, the general background pattern and timing for extinctions does not fit the proposed timing for any dominant extraterrestrial cause. There are probably several factors both terrestrial and extraterrestrial which may induce extinction events...extreme climate changes, large scale volcanic activity (La Garita/Lake Toba/Yellowstone type events, as well as massive basalt province type of eruptions such as Siberian/Deccan Traps), asteroid impacts, close by gamma ray bursts (hypernovae explosions), disease pandemic outbreaks etc etc.