I How is Dark Matter distributed around our galaxy?

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Wikipedia describes the distribution of Dark Matter as a halo around our galaxy. Are there any laws or equations on the distribution of dark matter?
From what I have read, dark matter does not clump into stars, since it cannot radiate energy. It cannot be seen or directly observed. Does it repel itself? Does baryonic matter concentrate dark matter? Is its shape and distribution fixed relative to itself? Why would it distribute itself on the peripheries of our galaxy? It did not distribute itself to uphold Newton's Law of Universal Gravitation, yet it seems that it is used as such in arguments in some articles and books which I have read on the structures of galaxies.
For our galaxy, is MOND a simpler explanation? Can there be two models? (Similar to, light is both a particle and a wave.)
According to the LCDM Model, which most physicists support, an existing structure of dark matter was needed at our 380,000 year-old universe to accelerate the formation of large structures and galaxies. We know that dark matter must exist to explain the large scale structures in our universe.
 
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Many of your questions are quite basic and wold be resolved by a very modest amount of research. How about you do that and then you'll have fewer and better targeted questions
 

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Wikipedia describes the distribution of Dark Matter as a halo around our galaxy. Are there any laws or equations on the distribution of dark matter?
From what I have read, dark matter does not clump into stars, since it cannot radiate energy. It cannot be seen or directly observed. Does it repel itself? Does baryonic matter concentrate dark matter? Is its shape and distribution fixed relative to itself? Why would it distribute itself on the peripheries of our galaxy?
The problem here is that you are confusing the common usage idea of the word "halo" with its meaning in astronomy.
In common usage, the word "halo" brings up the image of a ring or torus shape*. In astronomy it represents a spherical volume. (So no, the DM halo is not confined to the peripheries of the galaxy.)

*And even this is a corruption of its original usage. In many older pieces of artwork showing religious figures with halos, that "ring" or circle around their head is meant to symbolize an overall aura or glow surrounding the figure's head and not an actual ring of light.
 
I have re-read the whole article on dark matter in Wikipedia.
Now, I do understand that dark matter is distributed in a spherical shape in our galaxy.
Is there a field equation for the distribution of black matter which predicts the acceleration gradient due to black matter?
Are the hypothesis of Black Matter and MOND mutually exclusive? Why is there a reluctance to allow both to describe different phenomena?
Do you have a better source of information on black matter, such as a physics paper on arXiv or a text book.
 
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Are the hypothesis of Black Matter and MOND mutually exclusive?
Probably but since we don't have a settled theory, it's impossible to say that there isn't some truth to both. I think the smart mony is on dark matter (NOT "black" matter) and not MOND.

Why is there a reluctance to allow both to describe different phenomena?
Elegance is admired in physics. If TWO theories are required to describe what appears to be a single phenomenon, that would not be elegant.
 
(Sorry for the slip on dark matter, I wrote black matter for the second time.)
There must be at least two theories involved:
1. It makes sense to assume that at the beginning, 380,000 years after the big bang, gravity wells of dark matter were required to initiate and accelerated the formation of galaxies and large scale structures from the uniform gas of baryonic matter. These structures could not have formed in the time of 13.8 billion years.
2. It is reasonable to assume that there is quantum gravity. All text books write about the need for a theory of quantum gravity. But we do not need to have a theory of quantum gravity to observe its effects. Newton stated his laws of universal gravity, force and inertia while wondering about "action at a distance." It is more than a coincidence that modified Newtonian dynamics and TeVeS accurately describe the motion of stars in extremely weak gravitational fields. There quantum gravity shows its secrets, if only we are willing to take its hints.
 

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