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Unit 12: Stellar Remnants: White
Dwarfs, Neutron Stars, and Black
Holes
Mr. Ross Brown
Brooklyn School for Law and
Technology
In this unit we will learn about:
• The types of objects left behind by stars after their nuclear
fuel has been consumed
• The characteristics of white dwarfs and why there is an
upper limit to their mass
• The characteristics of neutron stars
• Why pulsars rotate so rapidly
• How gravity can prevent an object from emitting any light,
creating a “black hole”
• The nature of the curvature at the edge of a black hole
• The differences in types of supernova that result in black
holes instead of neutron stars
• The methods of detecting black holes
What are the general properties of
White Dwarfs?
• White Dwarfs:
– Hot, compact stars. Mass of about our Sun but
radius of our Earth (about 1% of the Sun)
– Little surface area means they are dim, even
though hot
– Light not from burning fuel, as none is left
– Light from residual heat as they cool
– Temps range from 25,000K-4,000K
Homework #19
• 5 April 2016
• What is a neutron star?
What are the general properties of
White Dwarfs?
• 6 April 2016
• Do now: How can we measure the mass of a
white dwarf?
– Think about this, based on all you know at this
point in the year. Would you use luminosity, color,
temperature, etc? Really impress me with this
one.
What are the general properties of
White Dwarfs?
• After ejection of planetary nebula shell, the
core is what’s left. That’s our white dwarf
• Mainly C and O2, trace H and He on crust
• Cools rapidly (by universal standards)
• Eventually dies out, like an ember in a fire
• Becomes so dark referred to as a black dwarf
What are the general properties of
White Dwarfs?
What are the general properties of
White Dwarfs?
• Gravity
– Very compact, no fuel
– Still hydrostatic equilibrium, but not from fusion
– Limit to amount of electrons occupying a given
space
– If we increase mass, a white dwarf would shrink!
What are the general properties of
White Dwarfs?
• Degeneracy Pressure
– There’s a limit on number of electrons that can
occupy a given space
– Remember Ideal Gas Law:
• P=ρ*R**T
– In a white dwarf, as we add more mass, the gas
heats up but it DOES NOT raise pressure
– Thus, more mass would make it shrink due to
GRAVITY
What are the general properties of
White Dwarfs?
• Chandrasekar Limit
– 1931, Indian astrophysicist Subrahmanyan
Chandrasekhar (who was only age 21!)
– He later won the Nobel Prize
– The limit to how large a white dwarf can be before
it collapses is about 1.4 M☉
What are the general properties of
White Dwarfs?
• 7 April 2016
• Do now: How can you tell whether something
is moving toward or away from you by using
your eyes alone? Ears alone? Sense of touch
alone?
What are the general properties of
White Dwarfs?
What are the general properties of
White Dwarfs?
• Gravitational Redshift
– For light to escape a star, it must fight gravity
– Sort of like a ball rolling up a hill loses energy, the
light loses some energy (while still traveling at the
speed of light, which is a constant)
– Longer, stretched wavelengths correspond to red
What are the general properties of
White Dwarfs?
• In much the way we use luminosity and
temperature to measure a white dwarf’s
radius, we can use wavelength to measure it’s
mass.
Homework #19, part 2
• 7 April 2016
• Review your notes from the Fall semester.
Explain the concept of escape velocity (you
needn’t use math.)
What are the general properties of
Neutron Stars?
• 8 April 2016
• Do now: How do the different elements of an
atom (proton, neutron, electron) interact with
each other? Think in terms of their various
charges.
What are the general properties of
Neutron Stars?
• 1932, the neutron is discovered
• Astronomers surmised there must be Neutron
Stars produced by a massive star collapses
• Like the Chandrasekar Limit in white dwarfs,
there’s a limit to how large an iron core can be
What are the general properties of
Neutron Stars?
What are the general properties of
Neutron Stars?
• But there was no evidence of neutron stars, so
it remained just a theory for 30 years.
• 1967, astronomers noticed odd radio signals,
pulsing at a precise rate
– They call it “LGM-1”
– Ultimately, called these Pulsars
What are the general properties of
Neutron Stars?
• Period-density relation: the pulse rate
depends on the inverse of the square root of
the pulsar’s density
– The higher the density, the shorter the period (so
it’s faster)
What are the general properties of
Neutron Stars?
• The pulsation of a neutron star is caused by its
spin.
What are the general properties of
Neutron Stars?
• Conservation of Angular Momentum
– Affects objects spinning around an axis, like a top
or a figure skater
– L=mvr (mass, velocity, radius)