Galaxy centre and rotation curve

[Shailesh Pincha]

What is the density of galactic centre? Thus what form of Kepler's law account for the galaxy rotation curve increasing near the galactic centre?

 

[Janus]

At the core, the density can be ~1600 stars/cubic light year. As far as the rotation curve near the center, I assume you are asking about why the orbital speeds increase with distance from the center in the region of the bulge. For this, you have to use Newton's laws of gravity instead of Kelper's laws. Kepler's laws work when the mass being orbited is fixed and unchanging. This is not the case for stars orbiting in the central bulge of the galaxy. For them, the mass they are orbiting is the mass of all the stars closer to the center then they are. Thus the further from the center they are, the larger the mass that is effecting their orbital speed. More mass means a larger speed. In the central bulge region this increase in the mass overrides the increase in distance which would tend to decrease orbital speed.

Once you get outside of the bulge, the star distribution changes to being disk-like rather than spherical, this decreases how much the mass increases with orbital distance, and the distance begins to have a stronger influence on the orbital speed. If the only mass of in the galaxy were due to that those parts of it we see, the orbital speed should begin to fall off with distance, The fact that they don't and tend to stay fairly constant and are higher than they should be for the visible mass we see indicates that there is mass there that we do not see and that its distribution does not match that of the visible matter.

 

[Shailesh Pincha]

At the core, the density can be ~1600 stars/cubic light year. As far as the rotation curve near the center, I assume you are asking about why the orbital speeds increase with distance from the center in the region of the bulge. For this, you have to use Newton's laws of gravity instead of Kelper's laws. Kepler's laws work when the mass being orbited is fixed and unchanging. This is not the case for stars orbiting in the central bulge of the galaxy. For them, the mass they are orbiting is the mass of all the stars closer to the center then they are. Thus the further from the center they are, the larger the mass that is effecting their orbital speed. More mass means a larger speed. In the central bulge region this increase in the mass overrides the increase in distance which would tend to decrease orbital speed.

Once you get outside of the bulge, the star distribution changes to being disk-like rather than spherical, this decreases how much the mass increases with orbital distance, and the distance begins to have a stronger influence on the orbital speed. If the only mass of in the galaxy were due to that those parts of it we see, the orbital speed should begin to fall off with distance, The fact that they don't and tend to stay fairly constant and are higher than they should be for the visible mass we see indicates that there is mass there that we do not see and that its distribution does not match that of the visible matter.

It's speculated that there exists Supermassive Black Holes at the centre of the galaxies. So wouldn't the mass density obtained by the value, 1600stars/light year, be too great compared to the calculated and assumed density of the SMBHs.