Key Concepts:
* Gravitational Waves: The primary driver of orbital decay in such systems is the emission of gravitational waves. These waves carry energy and angular momentum away from the system, causing the orbits to shrink.
* Quadrupole Moment: The strength of gravitational wave emission is directly related to the system's quadrupole moment, which depends on the masses of the stars and the separation between them.
* General Relativity: General relativity is crucial for accurately modeling the gravitational wave emission and the evolution of the orbit.
Simplified Equation (Approximation):
A very simplified approximation of the orbital decay timescale (T) can be obtained using the following equation:
```
T ≈ (5/256) * (c^5) * (G^-3) * (M^-5) * (a^4)
```
where:
* c is the speed of light
* G is the gravitational constant
* M is the total mass of the binary system (2 * 1.4 solar masses in this case)
* a is the orbital semi-major axis (approximately equal to the radius in your case, 60 km).
Important Caveats:
* Approximation: This equation is a rough approximation and doesn't account for the full complexity of the system, including relativistic effects and the non-circular nature of the orbit.
* Precession: The orbit of a binary neutron star system is not perfectly circular but precesses due to general relativistic effects.
* Numerical Simulations: For accurate modeling of the orbital decay, numerical simulations are often employed using specialized software that incorporates general relativity and other relevant physical processes.
Further Considerations:
* Chirp Signal: As the orbits decay, the frequency of gravitational waves emitted increases, resulting in a characteristic "chirp" signal that astronomers are trying to detect.
* Merger: Eventually, the neutron stars will merge, releasing an enormous burst of gravitational waves and electromagnetic radiation.
In Summary:
While a simple equation can provide a rough estimate, the orbital decay of a binary neutron star system is a complex phenomenon best described through sophisticated numerical simulations that consider the full range of relativistic effects.
