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nicolauslamsiu
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Can a extremely massive star ( eg. thousands solar masses) be formed?
Ken G said:They would encounter the Eddington limit, but that's only a limit on the luminosity given the mass, it's not a limit on the mass.
Ken G said:Actually, to be precise, the Eddington limit limits the luminosity given the mass, it won't make the star fly apart. It just makes the star adjust its internal structure so it doesn't blow itself apart-- it imposes a limit on the luminosity, it does not impose a limit on the mass. What does impose a limit on the maximum mass must have something to do with radiation pressure, that's true, but it's not well known, and it's not the Eddington limit. It should have something to do with how many metals are present, because they add to the opacity, but the Eddington limit does not refer to metals.
Ken G said:The adjustment is what happens in high-mass stars-- the internal temperature is not as high as it would be if the Eddington limit was not being approached. Let me explain.
The luminosity is set by the time it takes to dump the luminous energy content. The luminous energy content is proportional to temperature to the 4th power times radius cubed, and the time it takes to diffuse out (for Thomson opacity, let's say) is proportional to the radius times the optical depth. Put that all together, and the luminosity is proportional to the temperature to the fourth power and radius to the fourth power, divided by mass. Now the temperature and the radius are not independent, and if gas pressure dominates, then the temperature is proportional to the mass divided by the radius, that's called the "virial theorem." So you get that the luminosity is proportional to mass cubed, and the temperature and radius fall out, they don't matter. This isn't exactly right, because we took a constant opacity, but it's not bad as long as gas pressure dominates.
However, gas pressure cannot dominate for the high-mass stars, because if the luminosity continues to scale like mass cubed as mass increases, it will eventually push the star apart as you say. But that doesn't happen, because the star won't push itself apart, it will simply readjust its structure such that the luminosity does not scale like mass cubed any more. This happens when radiation pressure dominates over gas pressure, which changes the virial theorem to something completely different-- it makes it so that temperature to the fourth power (radiative energy density) is proportional to mass squared over radius to the fourth power (that's what energy density will be in the virial theorem). So when radiation pressure dominates, you get temperature is proportional to mass to the one half times radius to the minus 1, not mass over radius. This makes a huge difference-- now the luminosity scales like two less powers of mass, so it is proportional to mass not mass cubed, That's how the star avoids violating the Eddington limit, its internal temperature is not as high for a given mass and radius as it would be if it had to use gas pressure to balance gravity. Or if temperature and mass are regarded as given, then it is the radius that will be less than if gas pressure had to balance gravity. Smaller radius reduces the radiative diffusion rate, which reduces the luminosity and keeps it from violating the Eddington limit.
Massive stars form through the collapse of a large cloud of gas and dust, known as a molecular cloud. As the cloud contracts due to gravity, it heats up and forms a dense core. This core continues to grow and eventually becomes a massive star.
The main difference is the amount of material involved in the collapse. Massive stars form from much larger molecular clouds, which contain more gas and dust than the clouds that form smaller stars. This allows for a larger core to form, leading to a more massive star.
The formation of a massive star can take several million years. The exact time frame depends on the size and density of the molecular cloud, as well as the environment in which it is located.
The key stages include the initial collapse of the molecular cloud, the formation of a protostar, the accretion of material onto the protostar, and the eventual ignition of nuclear fusion in the core. This is followed by the star entering the main sequence stage and continuing to grow and evolve.
Yes, massive stars can form in isolation, but they are more commonly found in clusters or associations with other stars. This is because the formation of a massive star often triggers the formation of other stars in the surrounding gas and dust, leading to the formation of a star cluster.