PHYS3080 Final homework question

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The stellar velocity dispersion s and rotational velocities V of stars near the centre of M31, the Andromeda galaxy, measured along the nuclear major axis of the bulge are shown above (solid symbols). All velocities are in units of km s^-1. The distance of Andromeda is 770 kpc.

(i) Show that an angle of 0.2 arc seconds corresponds to a distance of 0.75 parsecs at Andromeda.

(ii) Use the top part of the Figure to estimate the central radial velocity dispersion s of Andromeda.

(iii) Calculate the virial mass within 0.2 arc seconds of the centre of Andromeda in units of M_¤.

(iv)Why does this result suggest there is a black hole in the centre of Andromeda?

(v) Now, using the rotation curve in the lower part of the figure above, show that the mass within one arc second of the centre of Andromeda is approximately 1.7 ´ 10⁷ M_¤.

Compare these two mass estimates. Can you explain any differences?