Mass Function ○◂

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• Mass Function (f₍M₎≡P𝘰𝘳𝘣K₂³∕2πG=M₁sin³i∕₍1+q₎²) ○￩ ⮜

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Mass Function ○◂｜Definition｜1st｜20251119205401-00-⌔

Binary mass function - Wikipedia

Binary mass function

In astronomy, the binary mass function or simply mass function is a function that constrains the mass of the unseen component (typically a star or exoplanet) in a single-lined spectroscopic binary star or in a planetary system. It can be calculated from observable quantities only, namely the orbital period of the binary system, and the peak radial velocity of the observed star. The velocity of one binary component and the orbital period provide information on the separation and gravitational force between the two components, and hence on the masses of the components.

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Mass Function ○◂｜untitled_remarks｜1st｜20261011111750-00-●

Remillard & McClintock 2006 ┃ X-Ray Properties… ⚬𓂃

An observational quantity of special interest is the mass function, $f(M)\equiv P_{\mathrm{orb}}{K}_2^3/2\pi G=M_1{\sin }^{3}i/(1+q{)}^2$ (see Table 1, column 6). The observables on the left side of this equation are the orbital period $P_{\mathrm{orb}}$ and the half-amplitude of the velocity curve of the secondary $K_2$. On the right, the quantity of greatest interest is $M_1$, the mass of the BH primary (given in column 7); the other parameters are the orbital inclination angle $i$ and the mass ratio $q\equiv M_2/M_1$, where $M_2$ is the mass of the secondary. The value of $f(M)$ can be determined by simply measuring the radial velocity curve of the secondary star, and it corresponds to the absolute minimum allowable mass of the compact object.

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