Astrophysics - Can there be a contact binary from white dwarfs

[jaidon]

Question:

A typical white dwarf has a mass of 1 solar mass and a radius of 10 thousand km. A typical neutron star has a mass of 1.5 solar masses and a radius of 30km. Given that there's a natural speed limit in Nature, namely the speed of light, is it possible to have a contact binary consisting of two white dwarfs (each identical to one another in size and mass)? Same question for two neutron stars.

I was thinking about:

E= (1/2) (mu) (v^2) - GM (mu) /r

I used this with v= speed of light and came up with positive numbers for each set of binaries.

However, considering E= -GM (mu) /2a one would expect the total energy to be negative.


Am I completely wrong in what I have done which leads me to say that no, neither binary is possible because E is not negative?

Any help would be greatly appreciated. Thanks.

 

[member 553083]

Answer:It is theoretically possible to have a contact binary consisting of two white dwarfs or two neutron stars, as long as the total energy of the system is negative. This can be calculated using the equation E= -GM (mu) /2a, where G is the gravitational constant, M is the mass of the stars in the binary, mu is the reduced mass and a is the semi-major axis of the binary. In this case, the reduced mass for a binary system of two identical stars is equal to the mass of one star, and the semi-major axis is equal to half the distance between the stars. Using these values, you can calculate the total energy of the system, which must be negative for the binary to be stable.