Rotation Curves and the Influence of Stellar Mass on Orbital Velocity

[frankinstein]

I've read a little about how rotation curves for galaxies are calulated and my question is since rotation curves of galaxies are calculated using the center mass of a galaxy from a star's orbit would the effect of stellar mass extending beyond the star's orbit that is directly behind the galaxtic center have a significant influence on a star's expected orbital velocity?

In other words the amount of mass outside a star's orbit is significant, so for any calculation for a star's orbital velocity some 70% to 90%, depending on how far out a star is from the galatic center, of the galaxiy's total mass is needed to make the calculation. Attached is a pic of what I'm thinking about.

Frank

 

[frankinstein]

I've update the pic so the area that I'm thinking about is clearer to see. In doing so I noticed that there is also substial mass outside of the triangle which is obviously dependant on how far out the star is from the galatic center. Are there any topological or vector field models for calulating the orbital velocity of stars?

The difference between using a average mass in calculating planetary velocities is that the masses of the planets are insignificant to the sun's mass but in a galaxy the center mass is not the only significant mass acting on a star. Am I wrong in this observation?

Frank

 

[Chronos]

Dark matter halos are generally believed to account for rotational curves. A less accepted explanation is MOND. The problem I see with MOND is it too requires some amount of Dark Matter to work. Occams Razor tends to rule out MOND, IMO.

 

[frankinstein]

Dark matter halos are generally believed to account for rotational curves. A less accepted explanation is MOND. The problem I see with MOND is it too requires some amount of Dark Matter to work. Occams Razor tends to rule out MOND, IMO.

But a doesn't dark matter theory require dark matter to distribute itself in rings within a galaxy? And if there really is dark matter wouldn't there be dark stars made of the stuff? Or even stars whose mass is not visibly enough to ignite but because of dark matter it does.

 

[Matterwave]

I am under the impression that you only consider the mass of the galaxy within the star's orbit because the effects of the mass outside the orbit more or less cancel each other out.

 

[Chronos]

Dark matter does not clump.

 

[Matterwave]

Considering we don't even know what Dark matter is, how would you know that it doesn't clump? If Dark Matter indeed interacts gravitationally, why would it not clump? Or are you saying dark matter only has a gravitational effect on baryonic matter, while itself remaining impervious to gravity...?

 

[Janus]

Considering we don't even know what Dark matter is, how would you know that it doesn't clump? If Dark Matter indeed interacts gravitationally, why would it not clump? Or are you saying dark matter only has a gravitational effect on baryonic matter, while itself remaining impervious to gravity...?

It doesn't clump in the way that "normal" matter does for the same reason it is "dark". It doesn't interact electromagnetically. It is this electromagnetic interaction that causes matter to "stick" together after a collision. This interaction allows the matter to shed the energy of the collision as electromagnetic radiation.

When two dark matter particles collide they tend to pass right through each other. They will deflect each other's paths, but they will keep going and not stick together.

They will lose some energy through gravitational radiation, but since this is much much weaker than electromagnetic radiation, it is not enough to cause enough clumping to from dark matter bodies of any significant size.

 

[Jolb]

Dark matter halos are generally believed to account for rotational curves. A less accepted explanation is MOND. The problem I see with MOND is it too requires some amount of Dark Matter to work. Occams Razor tends to rule out MOND, IMO.

MOND also requires we abandon conservation of momentum!

So in the proposed interpretation, the MOND formula does not conserve momentum. By the same token it does not conserve angular momentum, nor energy. Milgrom sidesteps the problem by stipulating that the MOND formula is only valid for test particles moving on a given background, e.g., stars moving in the collective gravitational field of a galaxy. We may inquire more generally, does the MOND formula, or some closely related one, represent a modification of inertia in test particle motion? To comply with the conservation laws we likely want the formula to arise from a Lagrangian. The kinetic part of the Lagrangian should give us the μ(|a|/a0) a part with whatever “corrections” are required. However, it is a theorem that no MOND-like dynamics exists that simultaneously has a Newtonian limit for a0 → 0 (all accelerations are large), is Galilei invariant, and is derivable from a local action [32]. (“Local” means that the relevant Lagrangian can be written as a single integral over volume.) This prohibition is even more stringent from a relativistic standpoint [33]. Accordingly Milgrom introduced a nonlocal action, i.e. one which is a functional of complete orbits, but cannot be reduced to an integral over a Lagrangian [32]. This approach does not quite reproduce formula (1) generically, but that formula is recovered for the special case of circular orbits.

http://arxiv.org/abs/astro-ph/0701848v2

 

[inflector]

When two dark matter particles collide they tend to pass right through each other. They will deflect each other's paths, but they will keep going and not stick together.

They will lose some energy through gravitational radiation, but since this is much much weaker than electromagnetic radiation, it is not enough to cause enough clumping to from dark matter bodies of any significant size.

If dark matter doesn't clump, then why is dark matter centered in galaxies at all instead of bouncing around very large orbits around and between galaxies? There seems to be some requirement that dark matter be concentrated near the galaxies themselves in order to account for the rotation curves. Or am I missing something?

 

[Jolb]

If dark matter doesn't clump, then why is dark matter centered in galaxies at all instead of bouncing around very large orbits around and between galaxies? There seems to be some requirement that dark matter be concentrated near the galaxies themselves in order to account for the rotation curves. Or am I missing something?

Because dark matter is matter, it is still attracted toward other matter gravitationally. However, dark matter doesn't "clump" and therefore it never creates a significant attractive field (gravitational potential well). Normal baryonic matter does clump and therefore it can create areas of more negative gravitational potential, where dark matter would naturally be attracted.

However, dark matter that starts at zero gravitational potential in an otherwise galaxy-filled (potential well-filled) universe would indeed never be bound to a single galaxy (assuming it doesn't interact via any other force--though it probably does interact via the weak force). Instead it would follow parabolic or hyperbolic orbits between galaxies. However, dark matter that starts in a gravitational potential well would be forever stuck in an orbit around its galaxy (again provided no weak interactions).

Thus the dark matter that we see accounting for the rotation curve of galaxies just happened to be there when the gravitational potential well formed, binding it forever to the galaxy. There just happened to be a LOT everywhere when the galaxies' potential wells formed.

 

[Wallace]

Sorry Jolb but you've got in bass-ackwards. It is dark matter which forms into collapsed halos which drive the formation of galaxies and clusters. The dark matter makes the gravitational potential wells and the gas follows along for the ride, forming into galaxies at the centre of the dark matter halos.

When we say 'dark matter doesn't clump' that is referring to very small scales, like the size of planets or stars. Dark matter interacts only gravitationally (so the theory goes) which prevents it from forming high density contrast objects like stars and planets. However dark matter most certainly forms into much larger objects with smooth radial density profiles. It is this formation into halos, driven by gravity, that drives the structure formation in the Universe. Without it the gas alone is far too diffuse to have ever collapsed into the galaxies that we see.

Edit: Note that we do have observational evidence about the lack of existence of 'compact dark matter', through experiments like MACHO.

 

[emc2cracker]

This is exactly why I subscribe to scalar vector tensor gravity theory. Not only is dark matter undetectable, but its mass is spread thin like butter unaffected by both gravity and electromagnetism apparently. If gravitational forces really affected dark matter one might expect to see a thicker coating if you will bunching even slightly towards the nearest biggest objects. Since it is spread out evenly and in a manner as to just hold the galaxy together I am assuming that eventually MOG or SVTG will take over the dark matter/energy theory. The biggest problem I have with MOND is it cannot account for gravitational lensing, and since its made up of the same principles as MOG.

So basically I am going to answer your initial question with a yes, in time I believe the dark matter model will be dismissed. But for now its here and it does the job.

 

[Chronos]

Good luck, have you seen the bullet cluster papers?

 

[emc2cracker]

Seen them.. yes I have.. read them? No honestly I am fresh into physics and wouldn't know what to do with the data anyway. However I have read all the critiscism related to MOG and the bullet cluster, and I have read Moffats newest paper that generaly does fit in with the data. There is much more work they have to do to cover every nook and crany though. You can get links to the papers and see moffat arguing with his cricis personaly here: http://cosmocoffee.info/viewtopic.php?t=656

 

[Wallace]

This is exactly why I subscribe to scalar vector tensor gravity theory. Not only is dark matter undetectable, but its mass is spread thin like butter unaffected by both gravity and electromagnetism apparently. If gravitational forces really affected dark matter one might expect to see a thicker coating if you will bunching even slightly towards the nearest biggest objects. Since it is spread out evenly and in a manner as to just hold the galaxy together I am assuming that eventually MOG or SVTG will take over the dark matter/energy theory. The biggest problem I have with MOND is it cannot account for gravitational lensing, and since its made up of the same principles as MOG.

I'm not sure where this strange idea of dark matter being 'unaffected' by gravity came from. I've seen this brought up in a few threads around here lately. Let's nip this in the bud. Have a look at the pics and movies from http://www.mpa-garching.mpg.de/galform/millennium/" . These are the results of simulations modelling dark matter only (the colour scheme is chosen to invoke the idea that galaxies form at the high dark matter density regions, hence they are brightly coloured). You'll see that there are large density contrasts in the distribution of dark matter that are nothing like your description above.

It is dark matter structures, which form due to gravity, that drive the formation of galaxies and galaxy clusters.

Note that weak and strong lensing statistics support the simulations, i.e. the kind of things you observe are what these simulations predict you'd observe.

As for Moffat's theory more generally, you're referencing some old discussions on cosmo coffee, and the point about cosmological models is that that we currently have many independant data sets and a theory must satisfy all of them simultaneously. You can't decide between DM and MOG based on the bullet cluster. Have a look for Wayne Hu's work (with collaborators) on the Parametrised Post Friedmann framework (PPF). This is a general approach to assessing modifications to GR against the full details of available data. You can recover MOG for instance by choosing a particular set of parameters in the PPF framework. So far there is no convincing case for any modified gravity model over LCDM, when all of the current data is used.

 

[emc2cracker]

Thank you for the link, that looks much different than simulations I have looked at. I always just assumed all the dark matter halos would appear similar plus I too have heard that cited by people smarter than I. I will not make that argument again.

And I do not dispute that for the moment LCDM fits better. But that's only because for every person running MOG simulations you have 100 lcdms running. I see very plainly the logic of holding onto LCDM, I also see very plainly other modified gravity theories deserve closer looks.

My link was in response to the question directed to me about MOG relating to the bullet cluster above, not as an overall justification of MOG for everywhere that's not what I was asked. There are however more recent discussions, and MOG is gaining more and more support every day. It is a good time to be studying the universe actually and I have a feeling the next decade or so will be filled with some amazing discoveries. But that's because of the debate, the charged atmosphere of everyone searching for the answer, it is a very good thing. There are always those that hold their opinions very dear to heart and do not handle this process with much grace, but its FAR more friendly and civil a community than political science! I get a headache everytime I watch the news that's why I look to the stars. ANd you know in another 100 years there will be a new set of people trying to prove new and better theories and it will go on and on hopefully until we colonize space and not destroy each other.

Sorry off topic there, but you get the point. Agree to disagree, no disrespect intended at all.

cheers

 

[Wallace]

And I do not dispute that for the moment LCDM fits better. But that's only because for every person running MOG simulations you have 100 lcdms running. I see very plainly the logic of holding onto LCDM, I also see very plainly other modified gravity theories deserve closer looks.

This is another misconception about how cosmology (or science in general) is done. There are not 'LCDM theorists' and 'MOG theorists' and there are not 'LCDM simulations' and 'MOG simulations'. There are cosmologists, and cosmologists tend to be interested in all possibilities, that's the point. There are not competing camps building evidence for 'their' model, with the LCDM camp containg most of the researchers.

There is plenty of work being done on general frameworks for modified gravity (of which MOG is just one example) and this work is being done by people who also investigate the LCDM model and who also look at dark energy models. If you look at the kind of work that people are doing on the next generation cosmology surveys, you will see that testing gravity, dark energy and dark matter theories lies at the heart of these efforts. No one would bother building a telescope or desinging a survey just to study LCDM. Look at the science cases for the following surveys/instruments: BOSS, BigBOSS, JDEM, EUCLID, PAN-STARRS, WIFMOS, HET-DEX. These are some of the planned 'dark energy' surveys, but you'll see that testing gravity is the major driver. The term 'dark energy' in this context really just means 'accelerated expansion' regardless of whether that is caused by a real energy source of a change to the way we view gravity.

Modified gravity is not a fringe dwelling enterprise being pursued by a minority, it is very much at the heart of mainstream cosmology. Running a 'LCDM simulation' helps investigate gravity, because if the results are inconsistant with observations then it points to gravity needing some tweaking. People running these simulations (such as the authors on the paper I linked to with the pics and movies) are very well aware of this, and know that modifications to gravity are a real possibility to be considered.

 

[emc2cracker]

So you are telling me that the motives are pure, seems to me that there are indeed camps though. I see rarely anyone posting papers for the other theories credit. But I am glad that there is competition, that is how we advance faster. The more passionate the people are the harder they work, if it was all purely unbiased I doubt we would have progressed so far in theory. But maybe you are right and I should not be questioning the thought patters and motives of those that work so hard, I will just say whatever they are I am glad they do it.

 

[Chronos]

I am aware of bullet cluster papers that take issue with dark matter. I respect your views and those of researchers who have toiled to find other explanations, I merely feel they have failed. The bullet cluster has presented a compelling case that drives a stake in the heart of alternative theories, IMO.

 

[Wallace]

So you are telling me that the motives are pure, seems to me that there are indeed camps though. I see rarely anyone posting papers for the other theories credit. But I am glad that there is competition, that is how we advance faster. The more passionate the people are the harder they work, if it was all purely unbiased I doubt we would have progressed so far in theory. But maybe you are right and I should not be questioning the thought patters and motives of those that work so hard, I will just say whatever they are I am glad they do it.

I'm not meaning to harp on you here, just trying to give a better understanding of the working of cosmology from the inside. You still have a fundamentally mistaken view of how things operate. It is not a matter of people in cosmology having 'pure' motives; there is simply nothing to gain by only focusing on one idea, which is why that's not how things are done. Cosmologists keep and open mind to multiple possibilities and theories precisely because of their own self interest, not in spite of it.

There is 'competition' between theories, but this does not represent a competition between theorists. You suggest that you don't see many people posting papers on 'other peoples' theories, but there are almost no theories in cosmology that are 'owned' by any individual or group. You seem to be stuck on one particular scalar-tensor theory put forward by one author, but as I've pointed out, this is just one particular form of modified gravity which is a generic approach that is being pursued, at some level, by the majority of current professional cosmologist. Nobody 'owns' modified gravity as a concept, it is something that is discussed at length by the whole community. On any given day there will be papers on this come out, check ArXiv on a daily basis to see this in action.

It's a mistake to view science in the way one might view say politics, in which groups settle upon a concept and then advocate for that. You'll be lead up many a blind alley if you try and grasp the sociology of science through that kind of lens. It is not as though 'LCDM theorists' sit around telling each other how right they are all day; at conferences etc the overwhelming view is skeptism about the current model. There are so many theoretical absurdities that people are desperate to find a more satisfactory explanation, but so far the Universe hasn't complied with our wishes...

 

[emc2cracker]

I am aware of bullet cluster papers that take issue with dark matter. I respect your views and those of researchers who have toiled to find other explanations, I merely feel they have failed. The bullet cluster has presented a compelling case that drives a stake in the heart of alternative theories, IMO.

I respect your opinion, and you have grounds to have it. But the way I see it its an open question. The only stake in the heart will be when someone actually detects dark matter and proves its existence.