Basic Concepts of modern science

[Strange]

Density wave theory -

 

Is it a proved theory or hypothesis?

 

 

Theories are never proved. Never.

 

As far as I know, all the evidence is currently consistent with density wave theory.

Edited March 12, 2015 by Strange

[ajb]

It's not good or bad.

I have no idea what astrophysicists think of this model. I have no idea how it has been tested and if what it predicts matches well with nature.

 

It's a proved theory or unproved.

It is a theory and theories are never proved. The question is only if they are 'good' or 'bad'.

 

In any case, I had an impression that math by itself is not an evidence.

It is true that the mathematics by itself is not enough to decide if a theory matches nature well or not.

[Mordred]

Density wave is currently considered the best fit to observation theory, no theory is ever 100%

[swansont]

 

It's not good or bad.

It's a proved theory or unproved.

 

No, really, it's not. Science doesn't deal in "proven", it deals in evidence that supports or contradicts, i.e. good vs bad.

 

I believe it's already been mentioned that any area of investigation that appends "theory" to the end probably isn't a theory. A better name might be density wave model, as part of a greater theory cosmology. But scientists understand what a theory is, and that there are multiple definitions of the word, so we get a bit lax in its use, without regard for people who might try and build arguments of equivocation upon it.

[David Levy]

 

No, really, it's not. Science doesn't deal in "proven", it deals in evidence that supports or contradicts, i.e. good vs bad.

 

I believe it's already been mentioned that any area of investigation that appends "theory" to the end probably isn't a theory. A better name might be density wave model, as part of a greater theory cosmology. But scientists understand what a theory is, and that there are multiple definitions of the word, so we get a bit lax in its use, without regard for people who might try and build arguments of equivocation upon it.

Thanks

I thought that an unproved theory is Hypothesis. Now we might have some other definitions: good theory, Bad theory and even modeling theory. Therefore, we should set one clear definition for any theory. Those definitions must be clear.

Density wave is currently considered the best fit to observation theory, no theory is ever 100%

 

With regards to the Density Wave Theory

It is stated: http://en.m.wikipedia.org/wiki/Density_wave_theor

"The theory has also been successfully applied to Saturn's rings"

They didn’t claim that it had been successfully applied to some sort of spiral galaxy.

Saturn ring isn't spiral galaxy. So what does it mean? Why the use it as some kind of approval? They must apply it on a spiral galaxy.

The "best fit" definition is not good enough. It actually gives us an indication that there might be some other alternative for this theory. For example:

http://www.astronomynotes.com/ismnotes/s8.htm

"Another popular theory uses the shock waves from supernova explosions to shape the spiral pattern."

If the "Density wave" is good theory, while the "shock waves" is a bad theory, then it must be clear by the definition

In anyway, those two theories should be under "unproved theory" definition. (Which means – Hypothesis)

[Mordred]

Density wave works for both Saturn's rings as well as galaxy rotation curves. In principle the influence and nature of how particles of various mass move are the same. Just different size scales.

 

I posted you dozens of articles and explainations on this topic before.

 

Yes there are always alternative explanations no theory however solid is without a competing theory. No matter how effective a theory is.

 

In density waves the majority of the competition is primarily fine tuning the metrics involved. Galaxy rotation curves have a huge variety of influences over an extremely long period of time so this is a natural consequence.

 

On something as complex as detailing the average movement of every particle from gas to stars over its entire history of development, it would be foolish to think a few formulas cover every possibility.

 

Wiki is not a final authority on any subject. If one wants a clear picture on what models or theories are considered " concordance". Ie the more effective and well recognized theories are. It's best to study the textbooks and dissertations written by professional physicists.

 

Every textbook on astronomy I own or ever read covers density wave, this includes the vast majority of any related papers I read on galaxy rotation curves, this is over a course of the last 20 years. (Though I myself am not an astronomer I've had plenty of experience helping other forum posters understand this topic on numerous forums).

 

Whenever I have seen rotation curves come up in questions on those forums, the professional astronomers on those forums answer with the density wave metrics.

 

No theory is 100% every theory has a margin of error regardless of how accurate. Every theory has room for improvement.

 

No theory is considered proved, so your proved,unproven classification is pointless. The correct classification is which theory is considered the most accurate to observational evidence.

 

Currently this is density wave theory in regards to both Saturn's rings as well as spiral galaxy rotation curves.

 

 

Here is a direct quote from one of the Astronomy textbooks I own. I'll have to free hand copy it in as its a hardcopy text. (Try not to make any mistakes)

 

This is from page 294 Ian Morrison's "Introductory to astronomy and Cosmology"

 

"In its life, our Sun has circled the galactic centre about 20 times

so why have the spiral arms not wound up? The solution is hinted at by a visual clue. Spiral arms seen in other galaxies stand out because they contain many bright blue stars remember a single very hot star can outshine 50 000 suns

like ours! However, very hot bright stars must be young as they have very short lives, so the spiral structure we see now is not that which would have been observed in the past. As Bertil Lindblad first suggested, it appears that the spiral arms are transitory and caused by a spiral density wave rotating round the

galactic centre a ripple that sweeps around the galaxy moving through the dust and gas. This compresses the gas as it passes and can trigger the collapse of

gas clouds so forming the massive blue stars that delineate the spiral arms. The young blue stars show us where the density wave has just passed through"

 

 

I own 6 Astronomy textbooks, they all include similar statements and refer to the density wave theory.

 

PS I have a huge collection of textbooks. I just bought Quarks and Leptons. Good book for entry level particle physics very informative.

 

My current collection is approaching 50 textbooks.

[David Levy]

No theory is 100% every theory has a margin of error regardless of how accurate. Every theory has room for improvement.

 

No theory is considered proved, so your proved,unproven classification is pointless. The correct classification is which theory is considered the most accurate to observational evidence.

There is no need for 100%. But there is a big difference between 0% and 100%.

The definition should highlight our confidence in this thesis.

For example, Newton gravity Theory is a proved theory, although it doesn't cover all the possibilities. In some cases the GR theory is needed (which could be considered as a subset of Newton theory). Therefore, although Newton theory doesn't cover all the cases by 100%, we know for sure that it is a proved theory. Hence, there is no need for alternative theory for Newton.

So, if we call Newton as a "Theory" and we know that this is a proved theory, we must find a different definition for any thesis which isn't fully confirmed yet.

It is quite confusing that we use the same definition for different confidence level of thesis. Hence, scientists should use a definition which must be correlated with their confidence level.

Density wave works for both Saturn's rings as well as galaxy rotation curves. In principle the influence and nature of how particles of various mass move are the same. Just different size scales.

 

I have used the density wave theory as an example for a proved or unproved thesis.

Therefore, I had no intention to dig in this specific issue.

However, there might be a difference between the influence and the nature of how various mass move at each system.

For example: Rotation velocity.

We know that the sun rotation velocity is high above the expected one from Newton law. Is it the same condition is Saturn ring? Actually, it should be quite easy for us to monitor the velocities of the main objects at this ring. If we could find that the velocities are significantly high and we see similar phenomenon as the rotation curve in spiral galaxy – then we can say clearly that we have some similarity.

But currently, I see significant different.

The structure of spiral galaxy is totally different from Saturn ring as follow:

Sections – In Saturn we see only two sections – Star and rings. In spiral galaxy there are three sections – Bulge, Arms and Hallo.

Mass Dispersion - In Saturn the main mass is located in Saturn, while is spiral galaxy most of the mass is located in the spiral arms.

Ring shape – In Saturn all the rings are very thin. In spiral galaxy, there are two sections – Thick arms (close to the center) and thin arms (further from the center).

I assume that there are more differences. But this is just a brief highlight of some of them.

With regards to the picture of the spiral section in Saturn

-Why we only see the spiral behavior in a very narrow band in one of the rings?

-How many pictures of this section do we have? Did we try to get pictures at different years and locations? (Just figure out what might be the impact if in the next picture we will not find this spiral phenomenon is Saturn ring.)

Edited March 13, 2015 by David Levy

[Mordred]

You can believe whatever you choose professional astrophysicists around the world use the rotation curve power law profile

 

This is due in part, to density wave but only in part.

 

[latex] v^2=\frac{GM_r}{r}[/latex]

 

The thing is you do not apply f=ma or Newton properly, you also have no understanding on the hydrodynamic equations.

 

if you want a good book read Elements of Astrophysics.

 

The detail you refuse to accept Is galaxy rotation curves is based on gas laws. Every particle not just stars. Star formation is due to gas.... where the highest density is located is where new stars form.

 

This is no different than Saturn which is dust that forms larger rocks.

I think your biggest problem is you don't think at all scales of partulates. Saturn's rings has particulates of dust that dust makes larger rocks as they combine.

 

Same as galaxies, plasma hydrogen, lithium etc etc, form to make stars so where the plasma is located is your star formation region.

 

What I find fustrating is that I posted professional papers for you to study, yet you keep missing the important details which I repeatably explain

 

 

I even show you an example such as the whirlpool (density wave) when you pull the plug in your sink full of water. Same principles, difference in the influence strengths due to different particulates and medium

Edited March 13, 2015 by Mordred

[David Levy]

O.K.

With 50 textbooks you should have full Knowledge about this theory.

Therefore, I have a simple request from you.

Let's assume that none of us (in this forum) has any idea about the density wave theory.

You have just found this great theory.

Let's assume that you have already presented your idea.

Now, you are requested by swansont to proof your theory.

Without a proof (based on this forum rolls) your idea will be moved to speculation or even to trash.

So please go a head and try to introduce your evidences.

Please - it is forbidden to use Elite Scientists name as evidence. However, you can use their evidences as yours.

Good Luck

Edited March 13, 2015 by David Levy

[Mordred]

Here is the problem I already did that in the other thread, I already explained if you have a force that has a rotation, it will affect different mass particles at different acceleration.

 

Force =mass*acceleration.

 

So Smaller dust will move faster than stars.

 

How simple can you get? Eventually the faster dust will catch up to the previous formed stars. Wow is that hard for you?

 

The above formula is simple it is the mass at each radius, it doesn't use a point center of mass. Rather it uses the accumulated mass as you go from the center of the galaxy outward.

Get a Newton scale, hook it up to different mass weights measure the amount of Newtons it takes to move different mass objects. Spiral arms is not Rigid body. Each particle is influenced separately. They all have different mass, therefore they have different velocities.

 

 

Here follow this N Body simulation, and explanation.

http://articles.beltoforion.de/article.php?a=spiral_galaxy_renderer&hl=en&s=idTheory#idTheory

 

That's really the crux of this thread, your upset your thread got locked, as you couldn't offer any supportive evidence or proper math.

You also refused to accept anything that disagrees with your model. Despite the numerous professional papers we showed you. Well just too bad,

 

You can either learn why the mainstream science supports the current models and theories and learn. Or you can keep deluding yourself.

The subject of this topic is not rotation curves your thread on that subject was locked.

 

Science follows the theory or model that best fits the data.

Take this formula

 

 

[latex] v^2=\frac{GM_r}{r}[/latex]

 

Which is your velocity of TEST particles (test particles have zero mass)

 

The numerator term is total mass of the enclosed radius.

 

So this is basically a radius evolving mass calc of

 

[latex]f=\frac{Gm}{r}[/latex]

 

Now if f=say 10^5 Newtons how much acceleration will it give a one solar mass as opposed to a 2 solar mass? Will they have the same acceleration?

 

Will hydrogen move faster or slower than helium? Use atomic weights now apply that to all the gas types in the interstellar medium.

 

Apply that to the different mass stars.

 

Get the picture ?

Then look at what elements make up what classifications of stars. There is your regions aka hydrogen vs helium lines etc.

Why do younger stars burn hotter than older stars. They are made up of heavier elements. Plus they burn up faster. That extra brightness illuminates the gas in the spiral arms making them highly visible.

That provides your power law to luminosity functions on rotation curves.

Edited March 13, 2015 by Mordred

[ajb]

For example, Newton gravity Theory is a proved theory, although it doesn't cover all the possibilities.

This is the wrong language. Newtonian gravity has been shown via observations and experiments to match nature to reasonable degree of accuracy for a large range of gravitational phenomena. Taking into account the range of phenomena that we would expect Newtonian gravity to hold well, we say that Newtonian gravity is a 'good theory'.

 

There are ranges of the parameters that we would not expect Newtonian gravity to hold well. For instance, for very fast moving objects or strong gravitational fields. This is better handled within general relativity; so general relativity is a 'good theory' for a wider range of phenomena. However, it too does not hold for all possible ranges of parameters, say the energy.

You have just found this great theory.

Let's assume that you have already presented your idea.

Now, you are requested by swansont to proof your theory.

In the context of theoretical physics a theory is a mathematical model. So first you must have one of those.

 

Secondly you must be able. at least in principle, to make calculations of things we could observe and measure. If your 'theory' fails here then we would have to conclude that you don't really have a theory.

 

Then, if you have made such calculations then they should be consistent with observations. If you predict phenomena that is just not seen then your theory will have to be called a 'bad theory'. You may be able to rescue it, or you may have to throw it away. The exception to that could be if you view your theory as a toy model, so something that captures some of the features of more realistic models but allows you to preform easier calculations.

 

Without a proof (based on this forum rolls) your idea will be moved to speculation or even to trash.

In all honesty, most of the ideas that end up in the speculations section are not even speculations as I would understand them. They tend to be more like a blend of 'word salad', 'fairy tales' and a basic misunderstanding of science.

 

So please go a head and try to introduce your evidences.

Please - it is forbidden to use Elite Scientists name as evidence. However, you can use their evidences as yours.

The point is one should not simply try to compare yourself with Galileo or Einstein or any other scientist. It just looks so quackish.

 

What one should do is point to published papers as evidence, if they do indeed add support to the theory.

 

That said, most of the speculations here fail at the 'high school level' and break the basic laws of physics taught to teenagers.

Edited March 13, 2015 by ajb

[swansont]

 

With regards to the Density Wave Theory

It is stated: http://en.m.wikipedia.org/wiki/Density_wave_theor

"The theory has also been successfully applied to Saturn's rings"

They didn’t claim that it had been successfully applied to some sort of spiral galaxy.

Saturn ring isn't spiral galaxy. So what does it mean? Why the use it as some kind of approval? They must apply it on a spiral galaxy.

 

 

Density waves occur in a number of situations. So it has been applied to galaxies, but it has also been applied to Saturn's rings, and we have direct measurements in that case, in that we've flown a probe there to make them. We can't do that for a galaxy, so we have to rely on other ways of confirming.

[David Levy]

That's really the crux of this thread, your upset your thread got locked, as you couldn't offer any supportive evidence or proper math.
You also refused to accept anything that disagrees with your model. Despite the numerous professional papers we showed you. Well just too bad,

You can either learn why the mainstream science supports the current models and theories and learn. Or you can keep deluding yourself.
The subject of this topic is not rotation curves your thread on that subject was locked.

Science follows the theory or model that best fits the data.

 

Let me start with the following example:

If someone tells his doctor that he has headache, he can't see well and he has some other problems. What it is expected from the doctor? Give his patient one medicine for each problem? Or find the correlations between all the problems?

Same issue with science;

Scientists are the doctors for the universe.

They have got an input of several phenomenons on the same body – spiral galaxy. They shouldn't try to find a medicine to each phenomenon. They must find the correlation between all of those phenomenons. Based on that, they might find the key to the Spiral galaxy enigma.

Somehow, our scientists decided that there is no correlation between all phenomenons in spiral galaxy. I'm quite sure that for doctors, this approch should be considered as a severe mistake.

In spiral galaxy there are several aspects:

Rotation curve, structure, shape, activity…

For example – I couldn't find any explanation for the structure of spiral galaxy. Why spiral galaxy has three sections (Bulge, Spiral arms, Hallo). Is there a rotation curve problem in all the sections? Why in each section there is different activity?

Never the less, our scientists decided to do the following:

The density wave theory – will be used for the shape of spiral arms.

The dark energy – will be used for the rotation curve velocity.

And all the other aspects of spiral galaxy should be ignored.

Somehow, they do not see the correlation between all the aspects.

 

 

Here is the problem I already did that in the other thread, I already explained if you have a force that has a rotation, it will affect different mass particles at different acceleration.

Force =mass*acceleration.

So Smaller dust will move faster than stars.

How simple can you get? Eventually the faster dust will catch up to the previous formed stars. Wow is that hard for you?

The above formula is simple it is the mass at each radius, it doesn't use a point center of mass. Rather it uses the accumulated mass as you go from the center of the galaxy outward.

 

In one hand you speak about smaller dust, while in the other hand you use it for stars. Are you sure that it's accepted? how this formula helps us with the stracture, shape, velocity.. of the spiral galaxy?

Get a Newton scale, hook it up to different mass weights measure the amount of Newtons it takes to move different mass objects. Spiral arms is not Rigid body. Each particle is influenced separately. They all have different mass, therefore they have different velocities.

 

Yes and no. If you ignore the major effect of spiral arm – than yes, it won't work. However, if you set Newton low on spiral arms – you will see how easy it fits. Based on this approach it should give an answer to all the aspects of spiral galaxy. There is no need to look for different "medicine" to each aspect. Just one and single source of explanation to everything!

 

Take this formula


[latex] v^2=\frac{GM_r}{r}[/latex]

Which is your velocity of TEST particles (test particles have zero mass)

The numerator term is total mass of the enclosed radius.

So this is basically a radius evolving mass calc of

[latex]f=\frac{Gm}{r}[/latex]

Now if f=say 10^5 Newtons how much acceleration will it give a one solar mass as opposed to a 2 solar mass? Will they have the same acceleration?

Will hydrogen move faster or slower than helium? Use atomic weights now apply that to all the gas types in the interstellar medium.

Apply that to the different mass stars.

Get the picture ?
Then look at what elements make up what classifications of stars. There is your regions aka hydrogen vs helium lines etc.

 

Somehow it seems that you mismatch between dust/particles/zero mass and real mass/stars. I'm not sure that it is feasible to use the same assumption for both.

 

In any case, in your explanation you have used three formulas. However, you didn't mention even one time the density wave theory. So, I'm not sure that those formulas can be considered as an evidence for the density wave theory. You didn't use any other real evidence to proof the theory. Remember – Math by itself is not evidence. I also couldn't see any real effect of those formulas on spiral galaxy. There is no clear math calculation for spiral structure, gravity power, velocity and so on.

Edited March 13, 2015 by David Levy

[Strange]

Same issue with science;

Scientists are the doctors for the universe.

They have got an input of several phenomenons on the same body – spiral galaxy. They shouldn't try to find a medicine to each phenomenon. They must find the correlation between all of those phenomenons. Based on that, they might find the key to the Spiral galaxy enigma.

 

I suspect you will be told not to bring up your own speculations here and take the thread off topic. However, I will just point out that the other thing scientists do is try and come up with a single hypothesis or theory that explains multiple things. So, for example, dark matter explains:

- Galaxy rotation curves

- The orbits of galaxy c;usters

- The variations in temperature of the CMB

- Gravitational lensing

- and several other things

 

And these all require dark matter as some form of matter, not the other possibilities such as modifying the laws of gravity.

[Mordred]

That's why I provided the other links in your other thread. Keep in mind I'm trying to keep the explanations simple and straight forward. To account for every aspect is usually several chapters in textbooks. In

" Essence of Astrophysics" they go through close to 30 related formulas.

 

The majority players being Jeans equations, Poisson, Euler, NFW, Einstein field equations, etc, these are simplified to the power law equation I posted. I'm certainly not going to post dozens of equations and relations when I can supply you references and links that show the details.

[David Levy]

 

I suspect you will be told not to bring up your own speculations here and take the thread off topic. However, I will just point out that the other thing scientists do is try and come up with a single hypothesis or theory that explains multiple things. So, for example, dark matter explains:

- Galaxy rotation curves

- The orbits of galaxy c;usters

- The variations in temperature of the CMB

- Gravitational lensing

- and several other things

 

And these all require dark matter as some form of matter, not the other possibilities such as modifying the laws of gravity.

Well, I do not offer a solution.

I just highlight that we must look on all aspects of spiral galaxy as one set.

If dark energy is using for the rotation curves, then we should consider its effect on the spiral arm shape. same issue with the density wave.

Edited March 13, 2015 by David Levy

[swansont]

Let me start with the following example:

If someone tells his doctor that he has headache, he can't see well and he has some other problems. What it is expected from the doctor? Give his patient one medicine for each problem? Or find the correlations between all the problems?

Same issue with science;

Scientists are the doctors for the universe.

Possibly. But it's not a given that they have a common treatment. Someone who was in a car crash can have a headache from a concussion, pain from internal bleeding and a broken leg. There is no single treatment for all of that.

 

So this is heavily context-dependent.

 

They have got an input of several phenomenons on the same body – spiral galaxy. They shouldn't try to find a medicine to each phenomenon. They must find the correlation between all of those phenomenons. Based on that, they might find the key to the Spiral galaxy enigma.

Somehow, our scientists decided that there is no correlation between all phenomenons in spiral galaxy. I'm quite sure that for doctors, this approch should be considered as a severe mistake.

The specifics are OT for this discussion, but you would have to do more than assert that this is true. And in doing so, confirm that it's not just a misunderstanding you have.

[Mordred]

Not all particles behave the same, charged particles behave different than uncharged, DM behaves different than baryonic. Then you have collisionless vs collission hydrodynamics, relaxation times etc.

 

Hydrodynamics is a complex field, so is thermodynamic temperature influences. These can be appropriated using the power laws.

[Strange]

I just highlight that we must look on all aspects of spiral galaxy as one set.

 

So, for example, the mass, distribution, velocity, age, size, type, etc. of all the stars; the mass, temperature and distribution of gas; the smaller satellite galaxies around; the history of collisions and mergers; etc?

 

Yes, they do look at all these things and more, and try to come up with models that explain all of them.

 

And, of course, there are other types of galaxies, such as elliptical galaxies, which also require dark matter to explain the velocity distribution of stars.

[Mordred]

The other details you need to include is the vector aspects of spin and how spin-spin interactions interfere with one another.

 

Yeah that formula looks easy, it's a good approximation only, the reality is far far from simple.

 

As it's a decent aspect here is Jeans instability and Jeans mass

http://en.m.wikipedia.org/wiki/Jeans_instability

http://m.iopscience.iop.org/0004-637X/507/1/226/fulltext/?providedHtml=38384.text.html

[Sensei]

What are the other cosmological theories which could be consider as Hypotheses?

 

1) gravitational waves

2) black hole evaporation, Hawking radiation

3) many related to black holes

 

You have list here

http://en.wikipedia.org/wiki/Category:Astronomical_hypotheses

[imatfaal]

 

1) gravitational waves

2) black hole evaporation, Hawking radiation

3) many related to black holes

 

You have list here

http://en.wikipedia.org/wiki/Category:Astronomical_hypotheses

 

I would quibble with gravitational waves as a hypothesis - I am not sure you can have GR without them. I would classify them as an as-yet untested but necessary corollary of a good theory. The prediction that bigbang inflation would necessarily give rise to gravitational waves - that is a hypothesis.

 

Hypotheses set out to explain an observation that does not currently fit with theory or expand knowledge beyond our present ideas.

[Klaynos]

Your doctor analogy fails on a few points. We don't get paid to consult members of the public (unless you want to pay my consultancy fees). You at not coming to is saying you've got a headache you've come to is with a headache saying that both of your legs have fallen off which is stopping you playing your guitar. When anyone points or you have both legs and are currently strumming away quite happily you refuse to accept.

[David Levy]

That's why I provided the other links in your other thread. Keep in mind I'm trying to keep the explanations simple and straight forward. To account for every aspect is usually several chapters in textbooks. In

" Essence of Astrophysics" they go through close to 30 related formulas.

 

The majority players being Jeans equations, Poisson, Euler, NFW, Einstein field equations, etc, these are simplified to the power law equation I posted. I'm certainly not going to post dozens of equations and relations when I can supply you references and links that show the details.

 

Thanks

One last issue with regards to spiral galaxy;

In all the articles which you have delivered, I couldn't find any information about the spiral galaxy structure.

Please advice how the science explains the different activity and rotation curve at each segment - Bulge, spiral arms and Hallo.

Edited March 13, 2015 by David Levy

[Mordred]

I really don't get you at all, I already provided all that information in 6 pages of posts. In all those posts you continously missed the terms

 

Energy density profile. This term is where the Navarro Frank White

 

this is the thread where we continously told you rotation curves follow density profiles. Not point mass from stars only.

 

http://www.scienceforums.net/topic/87496-newton-gravity-for-spiral-galaxy/

 

 

Those energy density profiles use in part the NFW profile.

 

The bulge itself has a different energy density profile than the disk. In some ways its the closest you get to modelling in terms of rigid body.

 

The disk is modelled as either thin or thick disk, some of those papers in the first link uses both methods, this is done as an isotherm

 

The halo is more uniform in distribution, the dark matter halo itself is usually considered a uniform develop and collionless. This is the specific section covered by

 

The NFW profile that's why that link states Dark matter profile.

 

http://en.m.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile

 

The regions were separately modelled on this link here

 

 

http://en.m.wikipedia.org/wiki/Galaxy_rotation_problem

 

note different formula for the bulge, disk and halo.

 

All this information was provided to you already.

 

Jeans instability and the virial theorem correlates the interstellar medium You can honestly Google each term yourself. I'm positive that if you Google the terms and terminology in all those links, you will come across hundreds of related papers.

 

pretty much all of them use

 

Energy density/mass density distributions this is your mass distributions.

 

The power law formula is an approximation of those other formulas

 

A short hand if you prefer instead of having to continuously recalculate

 

The separate density profiles in each region then combine them. Or go through the extensive NFW profile.

 

You keep looking for easy answers, news flash there isn't any...

 

We have formulas that help simplify things but how those formulas get developed involves dozens of formulas,

 

Power law formulas are always an approximation, they are typically used to save steps.

 

You have been provided the information, we have continously told you galaxy rotation curves are treated as a medium. The Interstellar medium, which is modelled as a Plasma/gas.

Here

 

http://www.google.ca/url?sa=t&source=web&cd=8&ved=0CDUQFjAH&url=http%3A%2F%2Fwww.ioa.s.u-tokyo.ac.jp%2F~sofue%2Fhtdocs%2F2013psss%2Fsofue2013psss.pdf&rct=j&q=galaxy%20rotation%20curve%20profiles%20pdf&ei=S8wDVb_sIsOdgwS4uIPgBw&usg=AFQjCNHOQ8f9k5pSmpGu5eSYpAQX4isv0Q&sig2=nxEIWgq67Gn664YkAVojpA&bvm=bv.88198703,d.eXY

 

this is a 54 page article. It has the density profiles.

 

That is the key term you kept missing, every article we posted uses that term. For a reason.

This symbol is vital to understand.

 

[latex]\rho[/latex]=energy|mass density

This symbol is vital to understand.

 

 

Some papers may use the below for spiral disk regions and NFW profiles

 

http://en.m.wikipedia.org/wiki/Singular_isothermal_sphere_profile

Here is a paper that discusses Jeans,NFW,virial theorem,density wave etc

 

http://www.google.ca/url?sa=t&source=web&cd=5&ved=0CCwQFjAE&url=https%3A%2F%2Fwikis.uit.tufts.edu%2Fconfluence%2Fdownload%2Fattachments%2F9440479%2Fchemouni_bach_GE_dec07.pdf%3Fversion%3D1&rct=j&q=singular%20isothermal%20sphere%20profile%20of%20spiral%20arms&ei=xNQDVaDFLsfwoATsxoCACQ&usg=AFQjCNGm931PDgYo5WOdtIksZVMLKqwVSQ&sig2=fa628v9sgDG0sloyufaLVg&bvm=bv.88198703,d.eXY

 

"Constructing basic galactic models"

That last article is similar to what you would find in astronomy and astrophysics textbooks on the subject

Edited March 14, 2015 by Mordred