Cosmologist are puzzled by the small value of the cosmological constant. Why don't they accept my non-singular model of the universe based on the back-reaction of quantum fields.
Dark matter is still a mystery. It can have unknown type of self interaction apart from gravity. Such interactions influence shape of dark matter halo. Conversely, by studying shape of dark matter halo one can try to guess a form of self interaction.
Because they don't radiate to lose energy so there is a balance between their pressure and gravitational attraction.
Velocity of the Sun in an orbit w.r.t the galactic center is about 230 KM/S; therefore it is not falling inside galactic center. Similarly, dark matter (at local regions) should also not fall if it has a comparable speed. But you may look at specific studies on radial velocity distribution profile; for example https://link.aps.org/doi/10.1103/PhysRevLett.116.031301
Dr G Bothun,
Are there a reference, where those equations are found?
Apart for orbits, one may expect clock works in space with frequency locking. Are there such models, for example describing secondary light spots on a halo?
How can a planet stay in orbit if its gravity is acting to pull it to the center?
@Anwar Shiekh; There is a radially outward force for circular motion in Newtonian description. In Einstein's gravity space-time is dynamic; one needs to solve two-body problems in general relativity. In the (approximate) limit where mass of a planet can be neglected w.r.t the heavier object; space-time is curved by the influence of the heavier object only. Then the lighter object moves through the shortest path (geodesic) in space-time, you can call it an orbit. This approximation works very well when photons pass through the vicinity of a star, giving rise to an interesting phenomenon called "bending of light".
I was asking about the planets as an answer to why dark matter does not settle in. It was a rhetorical question.
Sounds like the same rhetorical question Newton asked himself (before writing Principia): the apple falls from the tree toward the Earth, but the Moon does not. Why not? See e.g. G. Bothun's answer(s), and/or I. Newton, Principia.
My bad; I should just have said 'it is in orbit, even if that orbit is highly elliptical'; it was not my intention of obfuscate the issue.
Apparently there is no need for assuming dark matter to explain observed orbiting velocities in disk galaxies, see reference below.
Many thanks for those who tried to answer my question. However, I consider this question to be of serious implication in negating the presence of dark matter. The reason is that observations from gravitational lensing is indicating that dark matter is present in the form of a "nearly" homogeneous and isotropic distribution. For this reason I cannot buy the argument of rotation and the resemblance with the case of the Moon. I feel that this is one of the basic challenging questions that rises suspicions about the presence of dark matter.
Dark matter does not exist at all its the misconception of studying laws of nature in a correct manner.....we are missing some logic in Newton's laws of motion...once we crack it we kick dark matter away...
Mohammed, the local evidence is that the velocity of rotation of the stars is at roughly constant velocity outside the core. If you assume that the dark matter halo for the galaxy is spherically symmetrical, then the shell theorem (or Birkhoff's Theorem applied to a thin shell) means that the velocity is determined only by the matter within the radius of the star. You can use that to solve for the dark matter density as a function of radius (the mass of the disc stars is smaller so can be ignored for a first approximation). If you do that, you will find it matches the profile predicted by the Virial Theorem. It is similar to that for globular clusters except that clusters include stars with a variety of masses, dark matter presumably consists of particles of the same mass.
https://en.wikipedia.org/wiki/Birkhoff%27s_theorem_(relativity)#Implications
https://en.wikipedia.org/wiki/Virial_theorem#In_astrophysics
Some people are suggesting MOND (Modified Newtonian Dynamics) as an alternative to dark-matter, namely a modification of gravity at large scales (beyond those over which it has been tested, which I believe is solar system scales).
MOND modifies Newtonian gravity at low acceleration values, regardless of scale. It has an adjustable parameter so can be tuned to fit galaxy stellar velocity curves and with different values of its "fundamental constant" can match most galaxy clusters.
However:
- It gives the (incorrect) Newtonian prediction for gravitational lensing
- It cannot explain dark matter ("ultra-diffuse") galaxies like Dragonfly 44, Segue 1 or Willman 1.
- It cannot explain why the universe is flat
- It cannot explain how galaxy structure evolved within the first billion years of the universe
- it cannot explain why stucture formation is bottom up rather than top down.
https://en.wikipedia.org/wiki/Dragonfly_44
https://en.wikipedia.org/wiki/Segue_1#Properties
https://en.wikipedia.org/wiki/Willman_1
It does not need to explain why the Universe is flat, as that is where Dark Energy plays a contributing role.
Dark energy plus normal matter is insufficient to give a flat universe, dark matter contributes about quarter of the total.
I agree with Mr Biswajoy, that it selfinteracts. Possibly it takes some time to materialize and the flatness may be since that requires less energy, or it is quantized with other pixels than that we consider space when light. But the large strings vertical on the blue sky are curved, if it was the same thing and not a cloud of similar shape, but grey, (shows not often.)
The halo is much larger than our galaxy and the average speed of the particles mean they just pass through regions as small as the Solar System without noticing.
Excellent question
The dark mater halo is full of primordial black holes, (see MNRAS reference). They have to be primordial because their mass ( as confirmed by the MACHO experiments) is between 0.5-1 solar mass. The minimum mass for as stellar black hole is 3 solar masses.
There is good evidence that these black hole were ejected early in galaxy formation by the super-massive black at the centre of the galaxy by a accelerated sling shot effect. That left the primordial black holes stranded in the galactic HALO.
https://www.researchgate.net/publication/269689929_Advances_in_Black_Hole_Physics_and_Dark_Matter_Modelling_of_the_Galactic_Halo
Article Advances in Black Hole Physics and Dark Matter Modelling of ...
The observable part of such, might be a decaying scalar, from some points of view.
@Lena/All
I would tend to agree. The primordial black holes tend to inter-react and some have formed binaries. Evidence for which was disregarded in the MACHO studies.
Michael, you misunderstood my reply, sorry if it wasn't clear enough.
They do interact gravitationally but their velocity is much higher than Solar System escape velocity because it is determined through the Virial Theorem by the mass of the whole galaxy. The temperature of the halo is of the order of 106K. As they fall into our system, their speed would increase and as the leave it would fall back to the mean interstellar value but the change if speed will be very small. Overall, the local effect on density is tiny.
MLS: No matter how fast, there will always be a finite number of particles with velocities below the escape velocity from our solar system.
That is true in interstellar space, but as they fall in, they gain speed. For initial speed vi, at any point x on their course, the speed will be
- vx2 = vi2 + ve2
where ve is the escape velocity from location x.
MLS: A call to M-B statistics is not special pleading.
I agree, it is quite reasonable, there must be some distribution of speeds.
MLS: A call to the Virial Theorem might be considered special pleading.
Not at all. first the Virial Theorem is directly applicable since we are talking about a hypothesis for dark matter of non-relativistic particles (since they are gravitationally bound into a halo) with equal mass interacting solely through gravity.
Second, if you take the observed constant velocity profile and calculate the required mass density profile, you get the same as is predicted by the Virial Theorem (other than the cusp region in the core where the spiral is "barred") so you can also treat it as a purely empirical observation.
MLS: I think it much more likely that astronomers are wrong yet again.
I think it more likely that you are wrong, we know some form of matter exists and that it doesn't interact with EM or matter directly, only through gravity. That implies something like a massive neutrino but of course there are many other possibilities.
http://math.ucr.edu/home/baez/virial.html
http://www.mathpages.com/home/kmath572/kmath572.htm
https://en.wikipedia.org/wiki/Virial_theorem#In_astrophysics
The conventional answer is that we know that there is roughly 6 times as much dark matter as there is visible. That is distributed in a halo with a Virial distribution which results in the constant velocity profile.
Use the simple Newtonian approach, the "centrifugal force " must equal the gravitational force of all the mass inside the radius. The shell theorem says mass at greater radius has no effect while that at lesser radius can be treated as a point mass at the centre. The rest is just algebra.
Then there is no dark matter, as your reasoning applies equally well to elliptical galaxies without dark matter.
What makes you think ellipticals don't have dark matter?
Your logic is flawed anyway, if spirals have dark matter and ellipticals don't, then dark matter does exist.
I beg to differ
GmM/r^2 = m v^2/r
does not say v = constant except for a very special mass distribution.
And your 'shell theorem' is only valid for spherical distributions, but let's take it as roughly valid for a galaxy.
AS: .. except for a very special mass distribution. ..
So calculate what that distribution would be. It's not hard, I did it as one of many questions in an on-line cosmology course I took a few years ago.
AS: And your 'shell theorem' is only valid for spherical distributions, but let's take it as roughly valid for a galaxy.
It is not valid for the visible matter that has the distribution of a thin disc, but it is valid for the dark matter halo outside the core region (where the velocity curve drops rapidly). The total dark matter is significantly larger than the visible component and much of the latter is concentrated towards the core and bar so in the disc region, the visible matter is at least an order of magnitude less than the dark matter.
OK, same question; why is the mass distribution such that the velocity curve is level?
Doesn't anyone like straightforward explanation by Thierry De Mees? See annexed paper.
In fact, I read: "We consider equal masses M0 ... in various concentric hollow spheres according to some function of R (it must not be linear)."
How do you get to M ~ r ? See also Fig.2 of annexed paper for mass distribution.
AW: OK, same question; why is the mass distribution such that the velocity curve is level?
Same answer as before, at the simplest level, it is due to the partition of energy and momentum in accordance with the Virial Theorem.
The visible matter disc, arms and central bar distort that somewhat and of course the VT applies in equilibrium but the relaxation time may be quite long since it can only work through gravitational interactions. There is also a currently unexplained aspect called the "cuspy halo problem" but to first order, that is the current thinking.
Real density curves can be approximated empirically by the NFW or Einasto profiles.
https://en.wikipedia.org/wiki/Cuspy_halo_problem
TDM: The main cause for the alleged dark matter invention is precisely the lack of Newtonian integration of masses in the disc of galaxies
That may be your "main cause" but for the scientific community it is the wide range of different indications that makes it convincing. For example can you explain the abundance of deuterium by a change to the equations for gravity? Dark matter can.
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