ASTRONOMY FUNDAMENTALS - Chapter 5, Exercise 1 Solution
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Determining a Collapsed Core's Fate from Its Mass

PROBLEM
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A collapsing stellar core has a measured mass of 1.8 solar masses.
Using the Chandrasekhar limit (~1.44 M_sun) and the
Tolman-Oppenheimer-Volkoff limit (~2-3 M_sun), determine what this core
will most likely become, and explain why.

SOLUTION
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Check the core's mass (1.8 M_sun) against each real threshold in order:

Step 1 - compare against the Chandrasekhar limit (~1.44 M_sun):
    1.8 M_sun > 1.44 M_sun
    The core exceeds the Chandrasekhar limit, so electron degeneracy
    pressure alone cannot hold it up as a stable white dwarf. It will
    continue collapsing past that stage.

Step 2 - compare against the Tolman-Oppenheimer-Volkoff limit
(~2-3 M_sun):
    1.8 M_sun < 2 M_sun (the lower end of the real TOV range)
    The core falls below the TOV limit, meaning neutron degeneracy
    pressure should be sufficient to halt the collapse at this stage.

ANSWER: This core will most likely become a NEUTRON STAR - too massive
to remain a stable white dwarf, but not massive enough to overwhelm
neutron degeneracy pressure and continue collapsing into a black hole.

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WHY THIS WORKS AS AN ANSWER

The chapter's own table lays out three real, ordered mass ranges, each
with a different physical force responsible for holding the collapsing
core up against its own gravity: electron degeneracy pressure below the
Chandrasekhar limit, neutron degeneracy pressure between the
Chandrasekhar limit and the TOV limit, and no known force above the TOV
limit. Answering this kind of question is a matter of checking the
given mass against each threshold, in order, to find which real
physical force is actually strong enough to stop the collapse at that
specific mass. At 1.8 solar masses, the core is too heavy for the first
stopping force but light enough for the second - placing it squarely in
the real neutron-star range.