why are there upper and lower limits to the masses luminosities and sizes of stars
Main sequence The observed upper limit for a main-sequence star is 120–200 M☉.[36] The theoretical explanation for this limit is that stars above this mass can not radiate energy fast enough to remain stable, so any additional mass will be ejected in a series of pulsations until the star reaches a stable limit.[37] The lower limit for sustained proton–proton nuclear fusion is about 0.08 M☉ or 80 times the mass of Jupiter.[33] Below this threshold are sub-stellar objects that can not sustain hydrogen fusion, known as brown dwarfs.[38]
Cepheid variable A strong direct relationship between a Cepheid variable's luminosity and pulsation period[1][2] established Cepheids as important indicators of cosmic benchmarks for scaling galactic and extragalactic distances.[3][4][5][6] This robust characteristic of classical Cepheids was discovered in 1908 by Henrietta Swan Leavitt after studying thousands of variable stars in the Magellanic Clouds.[7] This discovery allows one to know the true luminosity of a Cepheid by simply observing its pulsation period. This in turn allows one to determine the distance to the star, by comparing its known luminosity to its observed brightness.