mtot

mtot is a common notation used in physics and astronomy to denote the total mass of a system. It is not a fixed physical constant; rather, it is a variable symbol that can take different meanings depending on context. In many works, mtot is distinguished from component masses such as Mstar (stellar mass), Mgas (gas mass), and Mdm (dark matter mass). In extended objects mtot is often a function of radius, written as Mtot(r), representing the cumulative mass enclosed within a sphere of radius r.

In galaxies and galaxy clusters, Mtot(r) is used to model rotation curves and gravitational lensing, providing a measure of the mass needed to account for observed kinematics and lensing effects. In planetary systems and binary stars, mtot is typically the sum of the masses of the orbiting bodies, for example Mtot = M1 + M2 in a two-body system. The concept also appears in simulations and analytical models of mass profiles, where Mtot serves as the governing quantity in gravitational forces and potential.

Measurement and estimation of mtot rely on multiple approaches. Dynamical methods use observed velocities and velocity dispersions to infer the gravitational mass, often incorporating the distribution of luminous matter. Gravitational lensing provides a mass estimate independent of the nature of the matter. Photometric methods combine luminosity with mass-to-light ratios to estimate the stellar component, which is then combined with other mass components to obtain mtot. Care must be taken to specify which components are included and the spatial dependence, especially in radii-dependent cases.

Common units for mtot are solar masses (Msun) or kilograms. Clear definitions and consistent conventions are essential when comparing mtot across studies or implementing it in simulations. See also Mstar, Mgas, Mdm, and Mhalo.