High School Mass transfer between neutron stars in a binary pair

[Andy DS]

TL;DR

Conservation of rotational momentum question

When we read about the mass transfer between neutron star pairs in a binary system, how is it that the one receiving the matter can increase its spin rate. Adding mass to a spinning object ought to slow due to conservation of momentum. Where does the energy come from?

 

[Drakkith]

It comes from the falling matter. The matter doesn't fall straight down, but comes spiraling in and hits at an angle and at a very, very high velocity. Thus the vector component of the velocity and momentum perpendicular to the neutron star's radius is significant.

 

[collinsmark]

There's a few aspects at play here. The big important one I'll hint at without actually giving away the answer.

Firstly, the overall angular momentum is conserved. Suppose you have two stars, A and B. Either of which can be a neutron star. In a simplified model, there are three (3) "sources" of angular momentum. There's the spinning of star A on its own, the spinning of star B on its own, and the orbital angular momentum of two stars as they orbit around each other. So even if you transfer mass from one to the other, the total angular momentum must remain constant (just be sure to add the angular momentum's together in vector form; remember angular momentum is a vector).

Now let's step back for a moment, and just concentrate on a single star (forget about the angular momentum of the other two "sources" for now). It's useful here to remember the ice-skater analogy. When an ice-skater pulls her hands in, decreasing her effective radius, her angular speed increases, right?

Now here's the tricky bit: What happens to a neutron star when mass is added to it. Does its radius increase or decrease? If you don't know, you may want to look this up. The answer may surprise you.

 

[Drakkith]

Now here's the tricky bit: What happens to a neutron star when mass is added to it. Does its radius increase or decrease? If you don't know, you may want to look this up. The answer may surprise you.

Ooh, I didn't know this either. I thought it was solely due to the matter falling onto the star.

 

[Andy DS]

Oh right, so it's the angular momentum of the whole system which is preserved which includes the co-orbital momentum.
Thanks I hadn't taken that into account.
And without looking it up I can imagine that the radius of the neutron star decreases with added mass as it would help to compress the object due to its immense gravity, thus helping it to spin-up.