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.

 

[Nate810]

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.

 

[quicknote]

As a scientist in the field of astrophysics, I can provide some insight into this question. First, let's define what a contact binary is. A contact binary is a binary star system in which the two stars are so close together that they share a common envelope of gas. This means that they are in physical contact with each other, with their surfaces touching.

Now, let's address the question of whether it is possible for two white dwarfs to form a contact binary. Based on the given information, it is not possible for two identical white dwarfs to form a contact binary. This is because the maximum mass of a white dwarf is about 1.4 solar masses (known as the Chandrasekhar limit), and the combined mass of two white dwarfs would exceed this limit, resulting in a supernova explosion.

However, it is possible for a white dwarf and a neutron star to form a contact binary. This is because the neutron star is significantly more massive than the white dwarf, and its strong gravitational pull can compress the white dwarf to a size small enough to form a contact binary.

As for the energy calculations you have done, it is important to note that the equations you have used are simplified versions and do not take into account the complexities of binary systems. The energy of a binary system is not solely determined by the masses and velocities of the two objects, but also by their separation and orbital dynamics. Therefore, it is not accurate to solely rely on these equations to determine the possibility of a contact binary.

In conclusion, while a contact binary from two identical white dwarfs is not possible, a contact binary between a white dwarf and a neutron star is possible under certain conditions. Further research and observations are needed to fully understand the dynamics of binary systems and the formation of contact binaries.