I have zero knowledge about astronomy (I often mistake it with astrology) so my question might be a bit naïve. But what are the limits for stars to be stable? I guess you can't up or downscale our sun to any size without changing its properties. So I am wondering what are sizes where stars still work like our sun. Lets take our sun's radius as reference for the scale. What range of scaling factors is viable to obtain stars with similar properties that could support earth-like planets?
The lowest possible mass for a star is about 8% of our Sun’s mass. Below this, the temperature and pressure at the core are not sufficient to sustain nuclear fusion (which is what defines a star) and the object is a large gas giant (like a large version of the planet Jupiter) known as a brown dwarf.
Excluding black holes, a small number of stars are known with masses between 150 and 250 times that of our Sun. However, the first stars in the very early universe are thought to have been up to 300 times as massive as the Sun. A star that was more massive than this would rapidly lose mass due to its intense solar wind.
The range of values for the radius of stars is even wider. White dwarf stars, which are very dense, can be less than 1% of the radius of the Sun. Red giant stars can be over 1,000 times as large as the Sun.
Very small and very large stars tend to be unstable and are unlikely to have Earth-like planets in orbit around them. However, there is considerable debate over exactly how large or small a star with Earth-like planets can be - for more details see this Wikipedia article on circumstellar habitable zones.