Final answer:
To constrain mass, size, and luminosities of active regions in astronomy, observational data, such as X-ray variability in quasars, is combined with theoretical models, which relate mass to gravitational effects and stellar evolution. Observations in the X-ray band suggest quasars have masses that can only be confined by a black hole. Additionally, the relationship between mass and luminosity in stars provides insights into their physical properties and lifetimes.
Step-by-step explanation:
To constrain the mass, size, and luminosities of active regions, such as those surrounding quasars or in stellar systems, a mixture of observational astrophysics and theoretical models is used. For instance, variations in the X-ray band suggest that quasars emit more energetic radiation from a very small region, likely indicating that the mass of the accretion disk is confined to a space possibly just a few times larger than the black hole's event horizon. This supports the idea that quasars have a substantial mass, which can only be confined by a black hole. Additionally, by understanding that each mass in a two-body system like a planet and a sun describes a conic section with the system's center of mass at the focus, we can derive relationships to determine their masses and the sizes of their paths. Understanding stellar properties is also aided by comparing a star's mass and luminosity to that of the Sun, which serves as a basic unit of measurement. Lastly, massive stars, identified by their position on the Hertzsprung-Russell diagram at the upper left, are known to have short lifetimes due to their high core pressure and temperature, which lead to rapid hydrogen fusion. These stars burn through their hydrogen at an incredible rate, making them extremely luminous as a result of this intense fusion process.