Question

Suppose a star with mass 30 M_SUN  and radius 50R_SUN. It is rotating at equatorial rotational speed of 200 km s^-1. For simplicity, consider the star as a rigid body with constant density. Suddenly, this star loses 10% of its mass due to a strong stellar wind, and
then readjusts its radius to be 50 R_SUN again. Estimate the equatorial rotation speed after
the wind and readjustment for the following cases.

(a) The wind is only from the polar region.
(b) The wind is only from the equatorial region.
(c) The mass flux of the stellar wind is spherically symmetric.

Answer 1

Here,
Star mass before stellar wind
Star radius before stellar wind
Star speed at equator before stellar wind
Star radius after stellar wind
Star speed at equator after stellar wind

Due to stellar wind, the star loses its mass of

Therefore, the star mass after mass loss due to stellar wind:

According to conservation of angular momentum, the angular momentum of star before stellar wind and the angular momentum of star after stellar wind:

Therefore, after the stellar wind the equatorial rotation speed is 2000 km/h.

Solution of (a):

The effects due to stellar wind at polar region is negligible because at the polar region, the length of arm, radius of the circle of rotation is very small. As you go from pole to equator, the radius of the circle of rotation is increases and as your go from equator to pole, radius of the circle of rotation is decreases.

Since, star has a constant density, the mass loss will occur uniformly and for this reason after the stellar wind the equatorial rotation speed is 2000 km/h if the stellar wind is only at the polar region.

Solution of (b):

Since, star has a constant density, the mass loss will occur uniformly and for this reason after the stellar wind the equatorial rotation speed is 2000 km/h if the stellar wind is only at the equatorial region.

Solution of (c):

Since, star has a constant density, the mass loss will occur uniformly and for this reason after the stellar wind the equatorial rotation speed is 2000 km/h if the stellar wind is only is spherically symmetric.