In a binary system containing one neutron star and an ordinary companion star, the companion star has some of its matter ripped away in a specific area due to the intense gravitational pull of the nearby neutron star. This can sometimes form an accretion disk....

My question is, in cases such as these, how come the matter from the companion star is pulled away from an isolated area? Why doesn't the entire star collide with the neutron star if its gravitational pull is so intense? Does angular momentum play a role here, and if so, wouldn't the angular momentum prevent any matter from becoming part of the accretion process?

I would imagine that with angular momentum and gravity acting upon the same body, the companion star would continue to orbit the neutron star with the same pattern we see in our solar system and galaxy- that is, as our moon orbits the earth and our planets orbit the sun. I just don't understand how such an intense gravitational pull would only affect a small area of the entire star, causing it to fall into the neutron star....

the matter nearest to the neutron star, i.e. the periferal matter of the comp. star placed in the ecliptic plain should be most willing to betray its mother star and change sides, where is the problem ?

You are right that angular momentum preservation hinders the stars involved to fall into one another rightaway ( as allways in all similar situations). The angular momentum also hinders the flow-over-matter of the "sun" to fall just like that in the neutron star. So that gives rise to the forming of this accreation disc. In this disc part of the matter can give off angular momentum to neighbouring lumps of matter and so gradualy home in on the NS. Angular momentum exchange should be driven by probably very strong tidal forces and turbulencis in the disc. Also radiation could be a means for the rotating matter to loose some angular momentum.
Note also, that NSs have exeedingly strong magnetic fields which surely will play a dominant (if hard to understand) role here and gravitation may also allready relativistic...
So I don't truly understand.... but surely angular momentum conservation is the main cause for this disc building in the first place !

timeless,
You may be misinterpreting illustrations in the popular media. For extremely close binaries, when one of the stars is a compact object (white dwarf, neutron star or black hole) the companion star can fill its "Roche lobe", especially if it is a main sequence star trying to evolve to the red giant stage. When the companion star fills the Roche lobe, material flows through the equal gravity point toward the compact object. Angular momentum forces the material to spiral into an accretion disk.

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Everything gets pulled from one area because of tidal forces. Same reason that we have tides here on earth. The side of the star facing the neutron star will feel the gravitational pull more then the side facing away. This difference will tear gas off the side of the star facing the neutron star.

triclon,
yes of course, the big companion must surely be in a tidal lock...