What does the Chandrasekhar boundary (or line, i'm not sure about it) means?
It's the limit of how massive a white dwarf star can be, and it's about 1 1/2 the mass of our Sun. Anything more massive than that will keep collapsing to form a Black Hole. This is not to say that a star twice as massive as the Sun will become a black hole, since it will blow off most of its mass before collapsing. But any star that still has more than Chandrasekhar Limit of its mass remaining when it collapses will just keep collapsing.
To be more specific, the Chandrasekhar limit is the mass of the largest possible white dwarf star, which is a particular type of star that is supported against gravitational collapse by electron degeneracy pressure. Electron degeneracy pressure is a sort of pressure due to the inability of electrons to occupy the same quantum states -- you may have heard of this as the "Pauli exclusion principle."
A white dwarf of more than the Chandrasekhar mass does not necessarily become a black hole -- it may collapse a bit further and become a neutron star, an even more peculiar object supported by a stronger form of degeneracy pressure due to neutrons.
The upper mass limit for a neutron star is not very firm at this time. Estimates range anywhere from 2 to as much a 3 solar masses. I did some checking and was somewhat surprised to find it does not appear any neutron stars discovered to date have been measured to be much heavier than the lower limit of about 1.4 solar masses.
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