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]

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:):P

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) (http://www.fishpond.com.au/Books/Science/Astronomy_Space/9780691130279/?cf=3&rid=1250525813&i=3&keywords=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 (http://www.fishpond.com.au/Books/Science/Astronomy_Space/9780691025650/?cf=3&rid=1250525813&i=1&keywords=astrophysics+). Also very good.

[CraigS]

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]

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/Astr222/Galaxies/Spiral/spiral.html

http://nedwww.ipac.caltech.edu/level5/ESSAYS/Carlberg/carlberg.html

[CraigS]

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 !!
:):P
but, then again, ... I might just try ...:question:

[renormalised]

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

[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]

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]

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]

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]

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:):P

Not that anyone would notice:)

[renormalised]

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]

Yep....High Energy Astrophysics (http://www.fishpond.com.au/Books/Science/Physics2/9780691140292/?cf=3&rid=1808286496&i=11&keywords=astrophysics), Introduction to Modern Astrophysics (http://www.fishpond.com.au/Books/Science/Physics2/9780805304022/?cf=3&rid=1808286496&i=8&keywords=astrophysics),
Active Galactic Nuclei: From the Central Black Hole to the Galactic Environment (http://www.fishpond.com.au/Books/Science/Astronomy_Space/9780691011516/?cf=3&rid=1808286496&i=18&keywords=astrophysics). 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]

"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]

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]

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]

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]

Something else you might like to consider here...

http://en.wikipedia.org/wiki/Modified_Newtonian_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 (http://arxiv.org/abs/astro-ph/9802174), 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.

[CraigS]

Yep. From Ned Wright's site .. (Mr CMBR):

"Aguirre, Schaye & Quataert (2001) find that while MOND works well on galaxy scales, it fails for Lyman alpha clouds and clusters of galaxies. The basic problem with MOND on cluster scales is that a point mass in MOND gives the observed isothermal profile in clusters, but most of the mass in clusters is due to a diffuse cloud of hot gas. Thus the observed gas density profile generates a gravity field under MOND that is not consistent with the observed gas temperature and density profile. Sanders (2002), written by a long time supporter of MOND, recognizes this problem and finds that dark matter is needed in clusters even under MOND.

A long standing problem with MOND was that it did not have a relativistic version. Bekenstein & Sanders (2005) have proposed a solution to this problem. But Zhao et al. (2005) find that this model requires different values for the universal constant ao in different gravitationally lensing clusters of galaxies, so the problem of not having a consistent relativistic version of MOND remains."




No worries, there !



Yep. I go with disease outbreaks .. but who knows ? (or cares, for that matter .. don't know why they threw that into a good paper !).

Coming back to the paper though, what they've done is use everyday plain old vanilla physics to explain lots of astro observations with no need for anything else. They also makes the point that upon deeper consideration of the complex mechanics that's going on in the arms, (which they believe most scientists have skipped over), there are rational explanations for what we see. I like the approach. A 'middle-of-the-road' approach using unsensational conventionality.

Very worthwhile reading, but never worthwhile holding it up as "The Truth".
;)
Cheers

[renormalised]

I think there's a lot more work to be done on how spiral arms form and how all the factors which go into their formation and maintenance are related and work together. Spiral density waves are only part of the equation.

[CraigS]

Yep. And I think that's what they're implying as well (except for spiral density wave part of what you mention). They talk about the errors in current data:

"Unfortunately, the existing error factors in determining rotational speeds in galaxies, or in our own Galaxy, are great enough as to not even provide us whether the galaxy rotation velocity curve increases, decreases, or stays constant with increasing distance from the center. This situation seems to be true for all the data that appears to yet be available.
...
The data regarding the rotation of our own Galaxy also has many unavoidable large error factors, which again can be interpreted as supporting any of the general concepts. The individual motions of each of the stars are often large enough to mask the effects of localized differential rotation."

And then about Density Wave Theories (back to where we started):

"The currently popular density-wave concepts do not adequately explain several things. There seems no provision for keeping most of the component stars from quickly escaping along the Z-axis. The universal logarithmic curvature/convexity seen in the shape of spiral arms would not be a consequence of any (planar) density wave concept. In addition, no one seems to have considered that an incoming planar gravity wave would have had to have come from some initial direction, and there would therefore NOT be any "spiral pattern" of a shock or density wave at all, but instead, a rather planar wave, which would pass through the region of a galaxy, allegedly causing starbursts. There is no conceivable way that would cause a pattern of stars "lighting up" that were ALWAYS in a spiral pattern! And a generally symmetric one at that! So the common claims of a fairly uniform actual (but invisible) distribution of a disk mass, with the alleged density waves causing localized ignition, cannot be causing spiral arm patterns. In addition, many existing theories do not seem to properly consider Keplerian considerations as they describe them."

The wording escapes me a bit in the last para but I get their drift (no pun intended). Very interesting...

Cheers

[renormalised]

I wouldn't necessarily agree with their determination they've made about rotation curves. There are errors there, but not that fundamental that they can't determine an overall pattern to the rotation curves in galaxies. When they measure the rotation curves of galaxies, they don't take it off the movements of the individual stars, they measure the curves for the whole mass of the galaxies. They measure the rotation curves using the Doppler shift of emission lines (across the EM spectrum) from gases such as CO, neutral hydrogen etc. These are generally in large concentrations scattered within the galaxy, but are associated with the spiral arms in particular. Trying to determine the rotation curve from individual stars would be nigh on impossible and would give you all sorts of answers to start with. What they also tend to forget is that the stars that form in the spiral arms are generally moving rather slowly w.r.t. to rest of the arm's contents when they're born. Most of the stars that delineate spiral arms are large and don't last all that long in any case. They do move with respect to the z axis of the galaxy, but not very far in their lifetimes. It's the smaller stars, like the sun, that get scattered all over the place by gravitational interactions. You get exceptions, like M67 (http://messier.obspm.fr/m/m067.html), but the only reason why it's lasted as long as it has (about 4-5 billion years (http://adsabs.harvard.edu/cgi-bin/bib_query?1993A%26AS...98..477M)) is it's on the outer edges of the galaxy (in terms of its distance above the galactic plane) and has not been unduly affected by it's surroundings. Most OC's only last a few hundred million years at the very most before they get torn apart by gravitational interactions with the surroundings as well as their internal dynamics.

Then about the density waves....what is this insistence on them being planar. Spiral density waves occur when you get rotation of a gas/dust cloud where pockets of that gas/dust develop an over density due to the average velocities of the particles in those regions becoming lower than the average for the cloud. The planar nature of the wave would only be assumed in the direction perpendicular to its direction of travel....the z axis. The density waves are basically like a shock wave....a "wall" if you will. They don't sit coplanar with the spiral arms, if they did they wouldn't produce any stars or compress the gases. There'd be no spiral arms. Their direction of travel is coplanar, but their shock geometry isn't. The wavefront is perpendicular to the long axis of the arms (that which runs along the arms). All waves, including the spiral density waves themselves come from some initial direction. They're assuming a wave coming from an external source, by the sounds of their interpretation. Spiral density waves are driven internally, once the initial internal conditions are met to act as the seed for the over density. They've also seem to have forgotten that once the wave has been established, it's the movement of material in and out of the wave, not the other way around, that creates the spiral patterns. The wave moves, but at a velocity much slower than the overall rotation of the galaxies contents. Once it sets up it maintains the spiral pattern and that's all, it doesn't race out to sweep up material to form stars etc, and then deposits them into a spiral arm. Remember, these phenomena are just over densities in the general bulk of the galaxies, not some solid wall of material that has built up in one place and remains there. The contents of the arms are free to move on in whatever direction they happen to be moving....the identity of the contents is not immutable and it changes constantly through time. In the end, the reason why most existing theories don't consider Keplerian factors is that the observations thus far have ruled them out, for the most part. The bulk of the material within spiral galaxies doesn't obey Keplerian orbital mechanics in general. If it did, it would show in the observations.

[CraigS]

I think they're saying that the mass density distribution across the arm tends to effect the acceleration of any matter moving transversely. Until better mass density info is available, this data must be considered to have a high error factor.



Because of the slowness of the movements over time ? (Timescale issue here ?). Also there'd be a huge amount of data to gather and process which so far, doesn't appear to have been attempted.



Yep. And they go on to do some basic calcs using our Sun as an example, in order to quantify the accelerations (order of magnitude stuff), along the various axes. Conclusion is a sinusoidal, variable acceleration resulting in oscillation transversely across the arm. "The Intra-Arm gravitational effects are strong enough to enable Arm Stability and Persistence. In fact, they are strong enough to enable Arm-genesis."



Ok. I'm not sure why, either...



I think because of the net transverse accelerations, they say that the material tends to hang around (oscillating about the transverse axis) and thereby forms the arm (see my above comment).



Ok. It must remain there for a while though, otherwise we wouldn't see a spiral arm at all, (courtesy of the persistence of the material)? Eventually, it gets flung out ... and goes on its merry way.



I think they're challenging their fellow scientists from the premise that the Keplarian/Newtonian physics may not have been followed thru, in sufficient detail, in order for them to justify dismissing it altogether. (Ie: they've never seen this considered in any papers). And I think they lead the reader to the conclusion that perhaps the observations are explainable, upon deeper deliberations of the modelling.

Interesting !

Cheers

[renormalised]

I'll have to get back to you on this, I'm right in the middle of writing up the first part of my latest assignment!!!:)

Maybe Steven or someone else familiar with the theory as well, might explain where I was coming from and what I was trying to say.

As I mentioned in a previous post, there's more to spiral arms than just density waves and the intra-arm gravitational effects will play a part in their formation and maintenance, no doubt.

Don't be mistaken that large scale survey of galactic rotation haven't been carried out. They have....

http://arxiv.org/find/all/1/all:+AND+rotation+AND+spiral+galaxy/0/1/0/all/0/1

[CraigS]

Having read a fair bit on the debate about rotation curves. Just for the record I'll go forward assuming the following from a definitions perspective, (unless anyone howls me down):

i) the Rotation Curves (RCs) of the most luminous spirals decline at large Radius (R), they are typically also not dominated by Dark Matter (DM) at these radii (by definition);

ii) similarly, dwarf galaxies have rising RCs at large R (not flat). This is still a problem, and also the dwarfs, typically, are not spirals;

iii) the actual OBSERVED RCs that are deemed to be DM dominated, and decline, seem to be very rare. So while it may not be precisely correct (in detail), it would seem in general, that a flat RC still approximately describes the behavior of the observed mass distributions of spiral galaxies at large radii.

... just for the record.

Cheers & Rgds.

[renormalised]

Do you have any examples of the RC's of these galaxies with declining curves. Can you post them here, if you do.

No, the dwarfs are mostly elliptical. It appears that these galaxies maybe DM dominated, in a big way (>10:1 DM:matter ratios)

[CraigS]

Carl;
Not wanting to tie you up, I'll try & explain as best I can. I think this 'debate' is all about nomenclature and wording. The declining Radius they refer to doesn't mean that the Galaxy RCs obey Keplarian mechanics. This is why I qualified my last post using the phrase 'from a definitions perspective'. They're also using the term 'decline' to describe parts of the curves (as distinct from the entire curve). The paper is:

"The mass distribution in early-type disk galaxies: declining rotation curves and correlations with optical properties"
E. Noordermeer,1,2⋆ J. M. van der Hulst,1 R. Sancisi,1,3 R. S. Swaters4 and
T. S. van Albada, 2007:
http://arxiv.org/pdf/astro-ph/0701731v1

"It is important to note that we have not found any rotation curve which declines in Keplerian fashion. In fact, all rotation curves flatten out in the outer regions. Early type disk galaxies, despite appearing dominated by luminous matter in the central parts, must also contain large amounts of dark matter to explain the shape of the rotation curves in the outer regions."

However, as a partial "quicky answer" to your request (it'll take me some time to come up with all the 'declining' names & categories), as an example, apparently the two galaxies with the most strongly 'declining' rotation curves are NGC 2683 and NGC 3521. (According to Casertano & van Gorkom).

The dwarf spiral galaxy NGC 5907 also apparently has 'declining' velocity from about 4 arcmins out (see attachment). As you can see, it still looks pretty flat but apparently, the 'decline' shouldn't be ignored by the dark matter theorists.

Cheers
PS: I've now attached the table which is the key to reading the RCs and the RCs themselves. These came from the Noordermeer paper I mention above. There is some interesting discussion at the end of the paper on each individual galaxy RC (see the paper). The "Conclusions" section is also very interesting. Unfortunately, NGC 2683 and NGC 3521 are the subject of a previous paper (in 1991, I think) and I don't seem to be able to find it, yet). Cheers

[renormalised]

You won't be tying me up today....for some reason I woke up tired and I've been off all day, so it's a little hard to get motivated to do any work!!!.

Interesting curve...a little unusual in that it gradual increases and then slowly drops away, but I'd like to know what the curve is like out around 50-80kpc, out in the halo regions. I have a suspicion it'll flatten out. What that curve says is that most of the galaxy's mass seems to be contained within the inner 15kpc and mostly outside of the core of the galaxy. Outside of there, the dark matter probably isn't so prevalent or it's distributed unevenly in the halo around the galaxy. Wonder how you'd go modeling an elliptical/lensed shaped halo of dark matter to the curve??

[CraigS]

M33's RC rises between 5 and 10 kpc !! (See attached).

PS: Other curves now attached in my previous post. Cheers.
also ..
"In this paper, we have derived rotation curves for a sample of 19 early-type disk galaxies (S0− – Sab) spanning almost 2 decades in optical luminosity. The majority of the galaxies are luminous, with MB < −20. The rotation curves were derived from a combination of Hi synthesis observations and long-slit optical spectroscopy of the ionised gas and probe the rotational velocities and mass distributions on scales ranging from 100 pc to 100 kpc. Almost all of the rotation curves share a number of properties, which appear to be typical for this type of galaxies."
...
"At larger radii, most rotation curves decline, with the asymptotic rotation velocity typically 10 – 20% lower than the maximum. The strength of the decline is coupled to the luminosity of the galaxy, more luminous galaxies having on average more strongly declining rotation curves, in agreement with Casertano & van Gorkom (1991)."

[renormalised]

Looking at M33's RC, there's going to be a reasonably massive halo surrounding the galaxy. That's why you're getting the increase in the RC between 5-10kpc looking like it does. Much more mass lies outside the inner 5kpc than is residing within it. M33 doesn't have much of nucleus...it is classed Scd, so the central hole is most likely a pitiful little thing compared to most holes in large spirals.

[CraigS]

"Professional astronomers (including myself) do use non-singular isothermal spheres and "pseudo" isothermal spheres for the DM component of mass models precisely because they asymptote to be flat. Typically they do fit RCs better than some cosmologically based models like the NFW profile. That being said, I do agree with you that RCs have a variety of shapes, and I believe that your work with Persic on showing that RC shape correlates with luminosity or Vmax is a very important constraint on what is happening. However, being able to trace the DM distributions beyond the radius where they behave like isothermal spheres remains a largely unreached goal in astrophysics."
(From the Facebook site).

I gather from the above that anything other than an isothermal sphere is an "unreached goal in astrophysics" ...?

Cheers

[renormalised]

They're unreached because no one has done much of anything on them. It's much easier to model a nice spherical component to DM simply because the mass distribution is much easier to map and study. Start getting into ellipses, lenses and other non spherical DM distribution and you have added complications of odd velocity vectors, curves not quite matching the expected luminosity and/or Vmax parameters of the galaxies, non flat curves etc etc. That's why I asked that original question...whether somebody has taken the math and figured out the geometry of the DM distribution around some of these galaxies, other than spherical halos.

[CraigS]

So, I feel a need to wrap up this thread. I'll try to summarise:

i) Density Waves are a wavelike phenomenon that creates an over density in the material of a galactic disk. The material within the disks can be moving slower or faster than the harmonic standing waves observed in the material. Material passing in and out of standing waves gets compressed and forms spiral arms.

ii) The 'frame dragging' effect is only a localised phenomenon around the vicinity of a typical central Supermassive Black Hole (SMBH), and despite the very large mass of some central holes, the spacetime gradient for a SMBH is actually rather small (because its effect is spread over the large horizon). 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. In general, on the scale of a galaxy and its arms, the frame dragging effects can be ignored.

iii) There are some papers suggesting modified Netwonian and Keplarian mechanics (MOND) could explain movements within the arm structure and its formation. These theories haven't yet been confirmed by direct observations. What's more, these observations (& others such as Cosmic Microwave Background Radiation measurements), actually lead away from MOND theory models and towards the conclusion that other mechanisms may be at play (ie: Dark Matter Halos outside the visible bits of the galaxies);

iv) Closer analysis of Galaxy Rotation curves for thousands of galaxies has been done based on a combination of Hi synthesis observations and long-slit optical spectroscopy of the ionised gas between radii from 10pc to 100kpc. The results show variations in the velocity of rotation of the galaxies, at different radii from the centre, some go up, some go down, some are flat. Which implies that dark matter is not necessarily distributed evenly both within a specific galaxy type, or, certainly, across different galaxy types (of different luminosities, central bulges and hence mass distributions).

v) Current research, based on observations, is attempting to characterise the 'shape' of the dark matter halos (suggested by non accordance with Newtonian/Keplarian mechanics). It appears that some scientists may skim over the significance of the non-flat galaxy Rotation Curves, which may hold other clues as to the nature of Dark Matter distributions throughout the Universe.

vi) Some scientist are re-examining Einstein's spacetime Relativity equations, decoupling space and time, resulting in a more mainstream theoretical explanation which reduces our dependence on the 'Darkness' constructs.

The above is an attempt at creating a straw-man of understanding, (mostly for my benefit but it may help others, too).

It is entirely open to RATification and modification as more info becomes available.

Cheers
PS: Yep .. all this is to avoid 'going back to school'. After all, as we get older, we can take some short-cuts, can't we ? :)

[renormalised]

Good summary...I think the reason why some scientist maybe skimming over "non flat" rotation curves is that they don't want to have to do any work on really stressful calculation that maybe needed to model "out of shape" DM distributions:)