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Thread: Dark Matter In spiral galaxy VS Elliptical Galaxy

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    Dark Matter In spiral galaxy VS Elliptical Galaxy

    I wonder why dark matter is mainly concentrated in spiral galaxy.
    Why not in elliptical galaxy?

    Let's look at M87

    https://en.wikipedia.org/wiki/Messier_87
    "The total mass of M87 may be 200 times that of the Milky Way."
    "The core contains a supermassive black hole that weighs billions of times the Sun's mass: estimates have ranged from (3.5 0.8) 109 M☉[61] to (6.6 0.4) 109 M☉,"
    "A rotating disk of ionized gas surrounds the black hole, and is roughly perpendicular to the relativistic jet. The disk rotates at velocities of up to roughly 1,000 km/s,"
    "M87's elliptical shape is maintained by the random orbital motions of its constituent stars, in contrast to the more orderly rotational motions found in a spiral galaxy such as the Milky Way."
    "M87 has an abnormally large population of globular clusters. A 2006 survey out to an angular distance of 25′ from the core estimates that there are 12,000 800 globular clusters in orbit around M87,[78] compared to 150–200 in and around the Milky Way. The clusters are similar in size distribution to those of the Milky Way, most having an effective radius of 1 to 6 parsecs. "
    " M87's elliptical shape is maintained by the random orbital motions of its constituent stars, in contrast to the more orderly rotational motions found in a spiral galaxy such as the Milky Way.[59]"

    So, M87 is very massive. (200 Times the Milky way)
    It has a heavier SMBH (comparing with the Milky way)
    It also has a compact disc (close to the center) which orbits at 1000K/s (almost 4 times faster than the average orbital speed in the Milky way.

    However,
    When it comes to its orbital stars velocities (after the compact disc, and if I understand it correctly) the velocity meets the Newton law.
    "M87's elliptical shape is maintained by the random orbital motions of its constituent stars, in contrast to the more orderly rotational motions found in a spiral galaxy such as the Milky Way."
    Therefore, there is no rotation curve problem.
    Hence, there is no need to call the dark matter for help.

    I wonder why is it?
    Why dark matter concentrates mainly at spiral galaxy?
    Why there is no high dark matter in elliptical galaxy?
    Last edited by Dave Lee; 2018-May-30 at 03:25 PM.

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    Quote Originally Posted by Dave Lee View Post
    I wonder why dark matter is mainly concentrated in spiral galaxy.
    Why not in elliptical galaxy?

    Let's look at M87

    https://en.wikipedia.org/wiki/Messier_87
    "The total mass of M87 may be 200 times that of the Milky Way."
    "The core contains a supermassive black hole that weighs billions of times the Sun's mass: estimates have ranged from (3.5 0.8) 109 M☉[61] to (6.6 0.4) 109 M☉,"
    "A rotating disk of ionized gas surrounds the black hole, and is roughly perpendicular to the relativistic jet. The disk rotates at velocities of up to roughly 1,000 km/s,"
    "M87's elliptical shape is maintained by the random orbital motions of its constituent stars, in contrast to the more orderly rotational motions found in a spiral galaxy such as the Milky Way."
    "M87 has an abnormally large population of globular clusters. A 2006 survey out to an angular distance of 25′ from the core estimates that there are 12,000 800 globular clusters in orbit around M87,[78] compared to 150200 in and around the Milky Way. The clusters are similar in size distribution to those of the Milky Way, most having an effective radius of 1 to 6 parsecs. "
    " M87's elliptical shape is maintained by the random orbital motions of its constituent stars, in contrast to the more orderly rotational motions found in a spiral galaxy such as the Milky Way.[59]"

    So, M87 is very massive. (200 Times the Milky way)
    It has a heavier SMBH (comparing with the Milky way)
    It also has a compact disc (close to the center) which orbits at 1000K/s (almost 4 times faster than the average orbital speed in the Milky way.

    However,
    When it comes to its orbital stars velocities (after the compact disc, and if I understand it correctly) the velocity meets the Newton law.
    "M87's elliptical shape is maintained by the random orbital motions of its constituent stars, in contrast to the more orderly rotational motions found in a spiral galaxy such as the Milky Way."
    Therefore, there is no rotation curve problem.
    Hence, there is no need to call the dark matter for help.

    I wonder why is it?
    Why dark matter concentrates mainly at spiral galaxy?
    Why there is no high dark matter in elliptical galaxy?
    That Wiki article is incomplete. It states that stars are a minority of the total estimated mass, but it does not give the corresponding information about the amount of interstellar gas. Thus, on the basis of this article, we cannot tell how much of the remaining mass is gas and how much is dark matter.

    The random orientations of the stellar orbits are not a valid basis for inferring a lack of dark matter. We would need the average velocities of the stars at various distances from the center, and the article does not provide that information.

    These Wiki articles on astronomical topics are usually pretty good, but this one is disappointing for the aforementioned reasons.

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    In a casual skim through of that article, I see it explicitly notes (at least) twice that stars make up only 1/6th of the mass of M87.

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    Quote Originally Posted by Dave Lee View Post
    However,
    When it comes to its orbital stars velocities (after the compact disc, and if I understand it correctly) the velocity meets the Newton law.
    "M87's elliptical shape is maintained by the random orbital motions of its constituent stars, in contrast to the more orderly rotational motions found in a spiral galaxy such as the Milky Way."
    Therefore, there is no rotation curve problem.
    Hence, there is no need to call the dark matter for help.
    This statement is inaccurate. It's sometimes more challenging to measure the orbital velocity of stars in an elliptical galaxy than in a spiral. Since the orbits are less orderly, you usually have to look at a velocity dispersion rather than being able to directly compare one side's velocity to that of the other side. But you can still study their kinematics, and find the same thing as in spiral galaxies: the visible stars and gas are embedded within a sphere of dark matter which generally extends well beyond the visible matter and has a much greater overall mass. Here's a paper that analyzes the dark matter content of M87 specifically, where they "run a large set of axisymmetric, orbit-based dynamical models and find clear evidence for a massive dark matter halo". From their data (fig. 13), looking at the region bounded by the visible stars in the galaxy itself, dark matter accounts for about 60% of the mass, and looking at the region bounded by M87's globular clusters, dark matter accounts for about 80% of the mass.
    Conserve energy. Commute with the Hamiltonian.

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    Quote Originally Posted by Dave Lee View Post
    I wonder why dark matter is mainly concentrated in spiral galaxy.
    Why not in elliptical galaxy?
    That is not correct. Dark matter interacts gravitationally so all galaxies have dark matter simply because they have mass. The difference between spiral and elliptical galaxies is that we can measure rotation curves in spiral galaxies and so we have a lot more data on their dark matter content. For elliptical galaxies there are other techniques, e.g. see the perhaps outdated Dark matter in elliptical galaxies, Dark Matter in Elliptical Galaxies (2011), etc.

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    Quote Originally Posted by Grey View Post
    This statement is inaccurate. It's sometimes more challenging to measure the orbital velocity of stars in an elliptical galaxy than in a spiral. Since the orbits are less orderly, you usually have to look at a velocity dispersion rather than being able to directly compare one side's velocity to that of the other side. But you can still study their kinematics, and find the same thing as in spiral galaxies: the visible stars and gas are embedded within a sphere of dark matter which generally extends well beyond the visible matter and has a much greater overall mass. Here's a paper that analyzes the dark matter content of M87 specifically, where they "run a large set of axisymmetric, orbit-based dynamical models and find clear evidence for a massive dark matter halo". From their data (fig. 13), looking at the region bounded by the visible stars in the galaxy itself, dark matter accounts for about 60% of the mass, and looking at the region bounded by M87's globular clusters, dark matter accounts for about 80% of the mass.

    Thanks

    I'm quite confused.
    What is the real data and how do they extract the dark matter for M87?


    Quote Originally Posted by Reality Check View Post
    That is not correct. Dark matter interacts gravitationally so all galaxies have dark matter simply because they have mass. The difference between spiral and elliptical galaxies is that we can measure rotation curves in spiral galaxies and so we have a lot more data on their dark matter content. For elliptical galaxies there are other techniques, e.g. see the perhaps outdated Dark matter in elliptical galaxies, Dark Matter in Elliptical Galaxies (2011), etc.
    In this article

    https://arxiv.org/pdf/1101.1957.pdf

    Pg 22, fig 7, we see a nice velocity dispersion at any radius from 300 to 340 Km/s.
    However, we already know that the disc orbits at 1000 Km/s.
    So, how can we explain this contradiction?

    In any case, in the following article it is stated that the rotation curve is used ONLY in small elliptical galaxies:
    https://ned.ipac.caltech.edu/level5/...er/node11.html

    "b) A small fraction of elliptical galaxies are surrounded by a ring of neutral hydrogen, for instance, NGC 1052, NGC 4278 and NGC 5128. In these cases, the determination of a dark matter halo is very similar to its determination in spiral galaxies, from the rotation curve."

    In all the big elliptical galaxies (including M87), they are using:

    "There are basically three methods for specifically estimating the mass of an elliptical galaxy:
    a) From the stellar velocity dispersion.
    b) From the neutral gas velocities found in the outermost region, in certain galaxies.
    c) From the X-ray corona surrounding all elliptical.
    There also exist complementary methods, using observations of ionized gas in the central parts, globular clusters, gravitational lensing, theoretical considerations about the bar instability and the chemical evolution."

    It is stated:

    "Existing SAURON data (R ≤ 13′′), and globular cluster kinematic data covering 145′′ ≤ R ≤ 554′′ complete the kinematic coverage to R = 47 kpc (∼ 5 Re). At this radial distance the logarithmic dark halo comprises 85.3 +2.5 −2.4% of the total enclosed mass of 5.7 +1.3 −0.9 1012 M⊙ making M87 one of the most massive galaxies in the local universe. "

    So, what do they really use?
    Is it the orbital rotation curve of stars or the kinematic energy of Globular clusters?
    If they are using globular clusters, than where is all the relevant data on those globular clusters? Why only one?

  7. #7
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    Quote Originally Posted by Dave Lee
    Pg 22, fig 7, we see a nice velocity dispersion at any radius from 300 to 340 Km/s.
    However, we already know that the disc orbits at 1000 Km/s.
    So, how can we explain this contradiction?
    There is no contradiction. That disc is a local feature less than a light year from the supermassive black hole. Out where we are looking at that dispersion, tens and even hundreds of thousands of lightyears out, the effect of the black hole is very small compared with that of the great mass of stuff that is enclosed at large distances from the center. Welcome to the Shell Theorem.

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    Quote Originally Posted by Hornblower View Post
    There is no contradiction. That disc is a local feature less than a light year from the supermassive black hole. Out where we are looking at that dispersion, tens and even hundreds of thousands of lightyears out, the effect of the black hole is very small compared with that of the great mass of stuff that is enclosed at large distances from the center. Welcome to the Shell Theorem.
    The shell theorem applies for spherically-symmetrical objects, but the general concept is still meaningful.
    Depending on whom you ask, everything is relative.

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    Quote Originally Posted by mkline55 View Post
    The shell theorem applies for spherically-symmetrical objects, but the general concept is still meaningful.
    Yes indeed, and M87 is near enough to being spherical that the shell theorem gives us a very good approximation of its gravitational action. The accretion disk in close to the black hole is a sizzling radiation generator, but it is virtually a point mass for figuring the gravitational signature in outlying parts of the galaxy.

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    Quote Originally Posted by Dave Lee View Post
    In this article ...
    Galaxy Kinematics with VIRUS-P: The Dark Matter Halo of M87
    There is seems no contradiction. FIG 7: "The first 4 moments of the Gauss-Hermite expansion of the 88 VIRUS-P LOSVDs. The filled diamonds show the data at different angular bins." and the curves and data agree..

    What they actually use is in the paper you cited.
    Last edited by Reality Check; 2018-Jun-01 at 01:08 AM.

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    Quote Originally Posted by Dave Lee View Post
    I wonder why dark matter is mainly concentrated in spiral galaxy.
    Why not in elliptical galaxy?

    Let's look at M87....
    Anecdotal evidence is not normally very helpful.

    I believe, however, that spirals generally have more dark matter than ellipticals. Is the reason really unknown? My guess is that ellipticals are older and produced by collisions of smaller galaxies. It seems like such collisions can disperse the dark matter into intergalactic space, more than newer spirals. Perhaps.
    Everyone is entitled to his own opinion, but not his own facts.

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    Quote Originally Posted by Cougar View Post
    Anecdotal evidence is not normally very helpful.

    I believe, however, that spirals generally have more dark matter than ellipticals. Is the reason really unknown? My guess is that ellipticals are older and produced by collisions of smaller galaxies. It seems like such collisions can disperse the dark matter into intergalactic space, more than newer spirals. Perhaps.
    My educated guess is different. In a collision I would expect the dark matter to behave in much the same way as the stars. The individual particles fly by each other with little if any interaction other than gravitational. When two galaxies collide, some stars are flung far and wide while the others, in accordance with conservation of total momentum, settle down in a merged galaxy. I see no reason to expect the dark matter particles to do otherwise.

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    Quote Originally Posted by Hornblower View Post
    There is no contradiction. That disc is a local feature less than a light year from the supermassive black hole. Out where we are looking at that dispersion, tens and even hundreds of thousands of lightyears out, the effect of the black hole is very small compared with that of the great mass of stuff that is enclosed at large distances from the center. Welcome to the Shell Theorem.
    Thanks

    Let me focus on: Welcome to the Shell Theorem - for dark matter.

    So, if I understand it correctly:
    As we increase the radius of the star orbital cycle around the center of the galaxy, we also increase the volume of the sphere for the dark matter.

    Let's look again at Pg 22, fig 7.
    https://arxiv.org/pdf/1101.1957.pdf

    We see that the velocity at radius of 5 arcsec is 310 Km/s at 10 arcsec - 300 Km/s and at 20 arcsec -320 Km/s.

    Now, lets start by assuming that the dark density is constant in the whole galaxy and monitor the impact of that issue:

    With regards to the velocity - and based on Newton law:

    V = Ref to (1/R ^ 2)

    Hence, if the velocity at 5 arcsec is 310 Km/s, the calculated velocity at 10 arcsec is:

    V (10 arcsec) = V (5 arcsec) / (10/5) ^2 = 310 / 2 ^ 2 = 310 / 4 = 77.5 km/s

    V (20 arcsec) = V (5 arcsec) / (20/5) ^2 = 310 / 4 ^ 2 = 310 / 16 = 19.4 km/s

    So, those are the velocities which we are expecting to get based on Newton law (without adding the impact of the Shell Theorem) .

    Now, let's see how the increasing of the radius should increase the expected total mass of the dark matter in the sphere (let's also assume that the impact of the normal matter is neglected with regards to the dark matter).

    So, the total dark matter in a given radius is:

    V' = Volume

    V' (at R) = 3.14 * 4 * R ^3 / 3 = Ref to R ^3.

    Hence:

    V' (10 arcc sec) = V' (5 arcsec) x (10/5) ^ 3 = V' (5 arcsec) x (10/5) ^ 3 = V' (5 arcsec) x 2 ^ 3 =V' (5 arcsec) x 8

    However, as the total dark mass is

    M (dark matter in a sphere) = Ref to Volume

    Hence:

    Total Dark matter mass (M) in the sphere = Ref to R ^ 3.

    Than

    M (10 arcc sec) = M (5 arcsec) x (10/5) ^ 3 = M (5 arcsec) x 2 ^ 3 =M (5 arcsec) x 8

    M (20 arcc sec) = M (5 arcsec) x (20/5) ^ 3 = M (5 arcsec) x 4 ^ 3 =M (5 arcsec) x 64

    However, the impact of the velocity is as follow:

    V (velocity) = ref to mass = Ref to Volume = Ref to (R^3)

    conclusion:

    As we increase the radius:
    The velocity due to Newton law should decrease by 1/R^2
    However, The velocity due to Volume (or total dark mass) should increase by R ^3.

    Hence:

    Vc = Combined Velocity due to dark mass and Newton law

    Vc 2 = V1 * (R2/R1) ^ 3 / R2/R1 ^ 2 = V1 R2/R1

    So, at Radius (R2) the combined velocity (Vc 2) should be based on the velocity at radius (R1) divide by Radius (R2)

    This by definition can't give us a constant velocity.

    Based on our example:

    Vc (10 arcsec) due to total dark matter in a sphere + Newton law = V (5arcsec) * R(10arcsec) / R(5arcsec) = 310 x 10/5 = 620 Km/s
    Vc (20 arcsec) due to total dark matter in a sphere + Newton law = V (5arcsec) * R(20arcsec) / R(5arcsec) = 310 x 20/5 = 1240 Km/s

    Now we come to the main issue:

    So, we take a function which is ref to 1/(R2/R1)^ 2 (due to Newton law), and try to fix it by a function which is ref ro (R2/R1)^ 3 (dark matter - assuming fixed density).

    It is clear that we won't get a constant (more or less) outcome from that.
    How can we fix it?
    The only solution (im my opinion) is by using a density of the dark matter which is ref to R1/R2 in the galaxy:

    So, let's call the dark matter density D.

    Now D (at radius R2) should be = D (at radius R1) * R1 /R2.

    If we do so, we get a constant velocity.

    My personal conclusion:

    We take a function which is ref to 1/(R2/R1)^ 2 (due to Newton law), fix it by a function which is ref ro (R2/R1)^ 3 (dark matter) and fix it by a function which is ref to (R1/R2) (dark matter density)

    Wow!
    Is it real?

    Do you see any error in my calculation/understanding?
    Last edited by Dave Lee; 2018-Jun-01 at 12:01 PM.

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    Quote Originally Posted by Dave Lee View Post
    Now, lets start by assuming that the dark density is constant in the whole galaxy and monitor the impact of that issue:
    ...
    Do you see any error in my calculation/understanding?
    It isn't constant. High alpha Einasto profiles can be close to constant for small radii, but in general DM profiles vary with radius.
    https://en.wikipedia.org/wiki/Navarr...3White_profile
    https://en.wikipedia.org/wiki/Einasto_profile

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    Quote Originally Posted by Dave Lee View Post
    I'm quite confused.
    What is the real data and how do they extract the dark matter for M87?
    It kind of seems like you've mostly answered your own question.


    Quote Originally Posted by Dave Lee View Post
    In any case, in the following article it is stated that the rotation curve is used ONLY in small elliptical galaxies:
    https://ned.ipac.caltech.edu/level5/...er/node11.html

    "b) A small fraction of elliptical galaxies are surrounded by a ring of neutral hydrogen, for instance, NGC 1052, NGC 4278 and NGC 5128. In these cases, the determination of a dark matter halo is very similar to its determination in spiral galaxies, from the rotation curve."

    In all the big elliptical galaxies (including M87), they are using:

    "There are basically three methods for specifically estimating the mass of an elliptical galaxy:
    a) From the stellar velocity dispersion.
    b) From the neutral gas velocities found in the outermost region, in certain galaxies.
    c) From the X-ray corona surrounding all elliptical.
    There also exist complementary methods, using observations of ionized gas in the central parts, globular clusters, gravitational lensing, theoretical considerations about the bar instability and the chemical evolution."

    ...

    So, what do they really use?
    Is it the orbital rotation curve of stars or the kinematic energy of Globular clusters?
    They use all of the above methods, wherever possible. In cases where there's a ring of rotating gas, they can use the rotation curve just like they would for a spiral. For most, they use the velocity dispersion. But they also try to use globular cluster velocities when possible, in addition to the velocity dispersion. By using more than one method, they have a way to double check their results. Also, the velocity dispersion values are only useful for calculating the mass within the visible portion of the galaxy itself (since you're using the stars in the galaxy), while the globular cluster data can be used to constrain the amount of mass beyond the visible stars in the galaxy.
    Conserve energy. Commute with the Hamiltonian.

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    Quote Originally Posted by Shaula View Post
    It isn't constant.
    Thanks

    I hope that you agree with the outcome of my calculation that in order to compensate the impact of Newton law which is based on 1/ (R2/R1) ^ 2 and the dark matter volume which is based on (R2/R1) ^ 3 we must assume that the dark matter density "isn't constant".

    It is also fully clear to me why:
    "High alpha Einasto profiles can be close to constant for small radii" - As the impact of the Normal mass is quite high at small radius.
    "but in general DM profiles vary with radius" - As I have already proved.

    However, I have found that the dark mass density is based on = (R1/R2).
    If I can do it, why our scientists try to solve this problem by using so complicated equations as we see in examples which you have offered?
    At the end of the day, the outcome is the same: A dark matter solution for the orbital rotation curve problem in the galaxy.
    Do you agree with that?
    Last edited by Dave Lee; 2018-Jun-01 at 04:22 PM.

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    From post 13:
    Quote Originally Posted by Dave Lee
    Now, lets start by assuming that the dark density is constant in the whole galaxy and monitor the impact of that issue:
    Let's stop right here. The astronomers do not start by assuming any given distribution of matter, dark or otherwise. They calculate the enclosed mass at any given radius from the observed orbital velocities, on the basis of Newton's formula for a spherically symmetrical system. In the outer regions this mass is usually much greater than the amount indicated by the stars and gas they can observe directly. The reputed dark matter makes up the remainder. We get a flat velocity curve when the total density tapers off with increasing radius and makes the enclosed mass proportional to the radius.

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    Quote Originally Posted by Dave Lee View Post
    I hope that you agree with the outcome of my calculation that in order to compensate the impact of Newton law which is based on 1/ (R2/R1) ^ 2 and the dark matter volume which is based on (R2/R1) ^ 3 we must assume that the dark matter density "isn't constant".
    Pretty sure no one has ever made that assumption. Your toy model makes a number of questionable assumptions you'd need to treat separately to get anything close to reality. So I'm not sure you have proven anything, and if you have you have proven something that was assumed anyway. If it helps you, great, but it doesn't add much to the DM field.

    Quote Originally Posted by Dave Lee View Post
    It is also fully clear to me why:
    "High alpha Einasto profiles can be close to constant for small radii" - As the impact of the Normal mass is quite high at small radius.
    Um, you miss the point. The alpha value is a tuning parameter that describes the DM density. I mentioned the high alpha case because it is the only version of the various available DM profiles that come close to having a constant density of DM anywhere on the curve.

    Quote Originally Posted by Dave Lee View Post
    However, I have found that the dark mass density is based on = (R1/R2).
    If I can do it, why our scientists try to solve this problem by using so complicated equations as we see in examples which you have offered?
    At the end of the day, the outcome is the same: A dark matter solution for the orbital rotation curve problem in the galaxy.
    Do you agree with that?
    The would be because their forms match observation. The NFW profile is also the profile you get from simulating DM. Not from rotation curves - but from the known or expected properties of it. So it is a nice validation that we might be getting a chunk of the physics right.

    Your toy model has a number of reasons why I don't see it as replacing these 'complicated equations'. First off velocity isn't constant. It varies at small R and has an inflexion in it. Neither of these properties are present in your model. Your model also becomes undefined at R2 = 0. It breaks down when R1 = 0. So it doesn't really fit observations. If you tune it until it does you'll end up with something with a similar form to the profiles linked.

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    Thanks Shaula

    Let me start with your following reply:

    Quote Originally Posted by Shaula View Post
    Your model also becomes undefined at R2 = 0. It breaks down when R1 = 0. So it doesn't really fit observations. If you tune it until it does you'll end up with something with a similar form to the profiles linked.
    This case in not relevant by definition:
    At very small radius the impact of the dark matter is almost neglected comparing to the Normal matter.
    So, R1 must be big enough to start the impact of the dark matter.
    R2 is bigger than R1 by definition.
    Therefore, the assumption of R1 =0 or R2 = 0 is just unrealistic.

    After that, let me summerize the simple formula for the dark matter density in order to get a flat velocity curve:

    N(1-2) : Newton effect on the velocity - due to change location/radius from R1 to R2.

    N(1-2) = 1/ (R2/R1) ^ 2

    M(1-2) : Dark mass effect on the Velocity - due to change location/radius from R1 to R2.

    D(1-2) : Dark mass density - due to change location/radius from R1 to R2.

    V'(1-2) : Dark matter Volume in a shpere - due to change location/radius from R1 to R2.

    V'(1-2) = (R2/R1) ^ 3

    Hence:

    M(1-2) = V'(1-2) * D(1-2)

    However, in order to get a flat velocity curve, we must set the following:

    N(1-2) * M(1-2) = 1

    1/ (R2/R1) ^ 2 * (R2/R1) ^ 3 * D(1-2) = 1

    Hence

    D(1-2) = R1/R2

    Quote Originally Posted by Shaula View Post
    The alpha value is a tuning parameter that describes the DM density.I mentioned the high alpha case because it is the only version of the various available DM profiles that come close to having a constant density of DM anywhere on the curve.

    The would be because their forms match observation. The NFW profile is also the profile you get from simulating DM. Not from rotation curves - but from the known or expected properties of it. So it is a nice validation that we might be getting a chunk of the physics right.

    So, if I understand you correctly -

    For each galaxy in the Universe, you first must use observation

    After the observation you need to set a very complicated calculation in order to find the most acurate formula out of the several formulas which you have for dark matter.
    However, there are about 400 Billion galaxies in the Universe. Most of them are spiral galaxies.
    So, how can you make this complicated work for each one of them?
    Even if you find a formula, what is the accurate fit level?
    Is it 99% or could it be 70% or less?
    What is the chance that at least for some of them none of the available dark matter formulas could set the requested fit?

    Quote Originally Posted by Shaula View Post
    Your toy model has a number of reasons why I don't see it as replacing these 'complicated equations'. First off velocity isn't constant. It varies at small R and has an inflexion in it. Neither of these properties are present in your model.
    Yes, I fully agree with you that in reality the velocity varies at small R and has an inflexion in it.
    I also agree that they aren't presented in my model.
    Technically, I could add it to the formula.
    However, I have found a simple solution for a very complex one.
    In this example the velocity was 310 km/s +/- 10

    Hence, the error level is

    10/310 = 0.032

    Which means an accuracy fit of
    100% * (1- 0.032) = 96.8%

    So, even if it is correct by only 96.8%, it still gives a fairly good solution.

    Hence, what do we prefer:
    To set an observation for each galaxy in the Universe, set complicated calculations in order to chose the preferable dark matter formula, and find at the end that our accuracy fit might be less than 80%.
    Or
    Take a simple formula to all the relevant galaxies and have accuracy fit of 96.8%?
    Last edited by Dave Lee; 2018-Jun-02 at 04:29 AM.

  20. #20
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    Quote Originally Posted by Dave Lee View Post
    Hence, what do we prefer:
    To set an observation for each galaxy in the Universe, set complicated calculations in order to chose the preferable dark matter formula, and find at the end that our accuracy fit might be less than 80%.
    Or
    Take a simple formula to all the relevant galaxies and find accuracy fit of 96.8%?
    Your idea requires that you observe the value of rotation curve in order to work it out at another radius. It requires just as much observational data required as the DM profiles. Your idea is not 97% accurate as it only works for a section of the rotation curve of some galaxies.

    So you have a choice between a model that takes into account the physics, that can be justified on kinematic grounds, that works for all radii, that can tested by methods other than orbital speeds (lensing and cluster dynamics, for example) and can be used in models of galactic evolution. Or a rule of thumb that works for a part of the rotation curve for some galaxies but can't be used for much else.

    Also there are currently estimated to be 2 trillion galaxies in the observable universe. Most of these are small, diffuse galaxies, not spirals. >70% of galaxies we see are spiral but that is a selection effect due to their star formation (and hence brightness).

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    Quote Originally Posted by Shaula View Post
    Your idea requires that you observe the value of rotation curve in order to work it out at another radius. It requires just as much observational data required as the DM profiles. Your idea is not 97% accurate as it only works for a section of the rotation curve of some galaxies.

    So you have a choice between a model that takes into account the physics, that can be justified on kinematic grounds, that works for all radii, that can tested by methods other than orbital speeds (lensing and cluster dynamics, for example) and can be used in models of galactic evolution. Or a rule of thumb that works for a part of the rotation curve for some galaxies but can't be used for much else.

    Also there are currently estimated to be 2 trillion galaxies in the observable universe. Most of these are small, diffuse galaxies, not spirals. >70% of galaxies we see are spiral but that is a selection effect due to their star formation (and hence brightness).
    Thanks

    So why can't we add this simple dark mass formula/model to all the current available formulas/models that we have?
    So, instead of using n formulas we will have n+ 1 formulas.
    Each scientist can chose the preferable solution for his study case.

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    Quote Originally Posted by Dave Lee View Post
    So why can't we add this simple dark mass formula/model to all the current available formulas/models that we have?
    So, instead of using n formulas we will have n+ 1 formulas.
    Each scientist can chose the preferable solution for his study case.
    Because is isn't particularly useful?

    All you are doing, essentially, is replicating very early estimates of the DM distribution in a more complex notation and description. These profiles were ones that were superseded by the current ones because they were not good enough for the job, generally. If you need a simple profile use the pseudo-isothermal halo one.

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    Quote Originally Posted by Shaula View Post
    Because is isn't particularly useful?

    All you are doing, essentially, is replicating very early estimates of the DM distribution in a more complex notation and description. These profiles were ones that were superseded by the current ones because they were not good enough for the job, generally. If you need a simple profile use the pseudo-isothermal halo one.
    With regards to the pseudo-isothermal halo:

    https://arxiv.org/abs/astro-ph/0201352

    "The whole sample is also well fitted by a pseudo-isothermal dark halo with a core, but the size of the core is rather small (for 70% of the sample the core size is less than 2 kpc).
    Thus we conclude that the profile of dark matter is steep (r−1 or steeper) down to this radius; large dark matter cores..."

    Wow
    This is similar to my conclusion:

    I have stated that

    D(1-2) = R1/R2

    In reality, as R2 is greater than R1 we should write it as:

    D(1-2) = 1 / (R2/R1)

    Amazing.

    In any case, in the article it is also stated:

    "We study a large set of high spatial resolution optical rotation curves of galaxies with the goal of determining the model parameters for a disk embedded within a CDM halo that we model either with a NFW profile or pseudo-isothermal profile. We show that parameter degeneracies present in lower resolution data are lifted at these higher resolutions. 34% of the galaxies do not have a meaningful fit when using the NFW profile and 32% when using the pseudoisothermal profile, however only 14% do not have a meaningful fit in either model."

    Therefore, it is clear that the dark matter fit is quite low as I have expected.
    So, how many dark matter models do we have in total?

    Actually, I assume that based on my model we might find a fit for over than 90% of the galaxies.
    If you wish, just give me the rotation curve of any galaxy and I'm ready set the calculation.
    Last edited by Dave Lee; 2018-Jun-02 at 06:08 AM.

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