Estimate the angular speed of a neutron star in the following way.Consider a sta

Question

Estimate the angular speed of a neutron star in the following way.Consider a star 1.5 times as massive as the Sun, rotating on itsaxis about once per year. (this is quite a slow rate of rotation -our Sun rotates about once per month.) Assume the start to haveabout the same radius as the Sun (7 x 105km) and to berelatively uniform in density. If angular momentum is conserved inthe collapse, what will be the final angular velocity? Is this ofthe right order of magnitude for a neutron star? What errors aremade in this estimate and how do they affect the final result?

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Explanation / Answer

Calculate the density d1 of the pre-collapse star asmass/volume. (m = 1.5*1.99E30 kg, r is given) Then look up the density d2 of a neutron star. Calculate volume ratio V2/V1 = d1/d2 Ang. momentum H = Iw, where I is moment of inertia and w is angularrate. From conservation of ang. momentum I1w1 = I2w2. We need to findI2/I1 to calculate w2/w1. I is proportional to mr^2 and r is proportional to (V2/V1)^(1/3),thus I2/I1 = V2/V1^(2/3) From this you can calculate w2/w1 = I1/I2. The most obvious error sources are (1) the estimated density of aneutron star and (2) the assumption in this analysis that thedensity distribution is the same in both versions of thestar. The latter means we assume I = kmr^2 where k is the same for bothstates. If the ratio of central to outer density differs in the twostates, then the value of I will be more like that of a hollowsphere (larger k) for one state and more like that of a point mass(smaller k) for the other. k = 0.4 for an ideal solid sphere.

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