Dark Matter & Gravitational Effects on Galaxies

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Dark matter surrounds galaxies in a spherical formation, influencing their gravitational effects despite being located outside the visible mass. The density of dark matter increases towards the center of galaxies, permeating their structure and contributing to the observed non-Keplerian rotation. The relationship between dark matter distribution and rotational speed is complex, with theories suggesting that if dark matter's mass is proportional to the distance from the center, it could lead to uniform speeds. The Navarro-Frenk-White (NFW) profile is a key model in understanding dark matter's radial distribution. Tidal forces also play a significant role in the dynamics of galaxies.
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My understanding is that dark matter surrounds a galaxy in a spherical formation. What I don't understand this type of dark matter can explain the non-Kepplerian rotation of the galaxy. According to Gauss's law, in a spherical shell, only the mass inside the orbit of a body has a net gravitational force on the body. Why then would the dark matter surrounding the galaxy have any gravitational effect on the anything inside of it?
 
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It's the 'surround' part that may have got you confused.

In one sense, dark matter does 'surround' dwarf galaxies, many spirals, etc ... the dark matter is present in regions beyond those where stars are observed.

However, the density of the dark matter increases towards the centre of the galaxy (the radial profile is a topic of considerable debate, both observationally and theoretically), so dark matter also permeates the whole galaxy (as well as surrounding it).
 
Yes, I came to that conclusion. Thanks for confirming it. But I still don't know for sure how the dark matter causes the speed to be the same. A friend and I figured out that if the dark matter fills up the galaxy so that the mass at any point is proportional to r (distance from center), the speed will be the same. This probably isn't correct, so what is the real reason?
 
If you google on 'dark matter radial profile', you get lots of references which include the mysterious letters 'NFW'. They stand for Navarro, Frenk and White, who wrote a paper (in 1996?) deriving a class of radial profiles. It's quite fun dipping into some of the papers google serves up ... sorry that I don't have a good one to recommend as a place to start :eek:
 
Nereid said:
If you google on 'dark matter radial profile', you get lots of references which include the mysterious letters 'NFW'. They stand for Navarro, Frenk and White, who wrote a paper (in 1996?) deriving a class of radial profiles. It's quite fun dipping into some of the papers google serves up ... sorry that I don't have a good one to recommend as a place to start :eek:

Tidal forces is the short answer.
 

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