Binary mass function
The mass function is a crucial tool in astrophysics for estimating the masses of objects in binary systems when direct observation is impossible. It relates observable parameters like radial velocity, orbital period, and eccentricity to the masses of the components. The formula for the mass function is:
\[ f(M) = \frac{(M_2 \sin i)^3}{(M_1 + M_2)^2} \]
where \( M_1 \) and \( M_2 \) are the masses of the two objects, and \( i \) is the inclination angle. This function provides a lower limit on the mass of the unseen companion because the inclination angle is unknown.
- Key Points:
- Example: Proxima Centauri b
By measuring the star's radial velocity and period, astronomers used the mass function to determine the planet's minimum mass (~1.27 Earth masses). This involved calculating semi-amplitude \( K \), period \( P \), and considering possible inclinations.
The mass function is a versatile tool that bridges observable data with theoretical constraints, enabling discoveries in astrophysics even when direct measurements are impossible.