Download Incredible Shrinking Stars

Incredible Shrinking Stars
Outline
1. White Dwarfs
* Approx. size of Earth
* Carbon, oxygen composition
* Mass limit: 1.4 Msun
* High density!
* Ultimate fate: continuous cooling
2. Neutron Stars
* Final state of core in some high-mass stars
* Compostion: neutrons
* Diameter: a few km
* Mass: 1 - 2 Msun
* Living on a neutron star
> Your weight is enormous
> Marshmallows become dangerously explosive
* Neutron stars should be rapidly spinning
* Neutron stars should have strong magnetic fields
* Pulsars: rotating neutron stars
> Radiate preferentially from magnetic poles
> Crab Nebula pulsar
> Pulsar sounds
3. Black Holes
* Core mass > 3 Msun ==> black hole results
* Gravity is geometry: space(time) is curved
> Light is affected by gravity
> Black hole: infinitely deep puncture in space(time)
* Schwarzchild black hole
> Singularity
> Event horizon
> Schwarzchild radius (Rs): Rs = 3M
> Escape velocities
* Falling into a black hole
* Time slows near a black hole
* Detecting black holes
> High mass, dark object in binary system
> Lots of x-ray emission
Questions
1. What is a white dwarf? What is a typical radius and mass of a white dwarf? What kind of
pressure keeps a white dwarf inflated against the inward pull of gravity?
2. What is the Chandrasekhar limit?
3. Why should neutron stars have very high rates of spin?
4. What are neutron stars made of? What is the typical diameter of a neutron star? Why is the
density of a neutron star so high relative to ordinary matter (for example, the material in the chair
you are sitting on)?
5. The pulsed light from a pulsar is produced in what manner? Do you suppose the pulsed light
is the only light radiated by the pulsar? Explain.
6. Should all neutron stars be observed as pulsars? Explain.
7. An astronomer observes a binary star system in which the spectrum lines of only one star (a
bright B-type main sequence star) can be observed, yet that star is moving with an orbit speed
that would indicate that a second star with mass at least 8 times the mass of the sun must be
present. What might the astronomer conclude about the identity of the unseen star? Explain.
8. How are orbits explained in terms of Einstein's gravity?
9. What is the significance of the event horizon of a black hole?
10. What would happen to someone falling into a black hole?
11. If the Sun suddenly became a black hole, how would Earth's orbit be affected?
Answers
1. A white dwarf is what remains of the core of a low-mass star that has come to the end of its
core nuclear burning life. Typical radius: 1 Earth radius. White dwarfs are kept inflated by
"electron crowding" (electron degeneracy) pressure.
2. This is the maximum mass of any white dwarf: 1.4 Msun.
3. A neutron star results from the collapse of the core of a high-mass star. When the core of a
high-mass star reaches the point where nuclear fusion terminates (i.e., when it is composed of
iron), it collapses suddenly. One of the results of this collapse is a neutron star. Neutron stars
are very small (about 10 km across) - much
smaller than the stellar core. The stellar core was rotating (because it was part of a rotating star).
When the core collapses, the rotation is concentrated (sort of) in the neutron. Consequently, tbe
neutron star ends up spinning very rapidly
4. The interior of a neutron star consists of neutrons. A typical neutron star has diameter 10 km.
The atomic particles which comprise a neutron star (neutrons) are about as close to each other as
are the particles in an atomic nucleus. Ordinary matter consists of atoms which contain nuclei,
but the vast majority of the space of any atom is mainly empty (except for a few light electrons).
Here's an analogy: If the nucleus is a golf ball, then an atom takes up as much volume as Beaver
Stadium. So, as most ordinary matter consists of atoms, most ordinary matter is empty space.
Not so in a neutron star, where almost all of the space is taken up by neutrons.
5. The pulsed light originates near the the magnetic poles of the neutron star. The neutron star is
highly magnetized. Rotating this magnetic field creates a strong electric field (the inside of a
wire connecting a lamp to an electric outlet contains an electric field). The electric field drives
electrons along the magnetic field lines of the neutron stars. As the electrons move, they are
accelerated (the magnetic field is curved); because they are accelerated, they radiate
electromagnetic waves. Because field lines bunch-up near the magnetic poles, the radiation is
most pronounced near the poles. Thus the poles become bright 'hotspots.' These spots behave
much like the lamps in a rotating lighthouse; you tend to see a beam only when it's pointed at
you (or very nearly at you). So, light originating near the magnetic poles appears pulsed. Some
of the light produced by a neutron star is not pulsed. Neutron stars (especially when they're
young) are very hot. So, they radiate light from their hot surfaces. However, very few neutron
stars are detected because they're hot; nearly all are found only because of the distinctive pulsed
radiation.
6. Not all neutron stars should be observable as pulsars. For one thing, pulsars slow down as
they age, because the energy of rotation is dissipated in creating the 'lighthouse' beams.
Eventually, the pulse becomes very weak. In addition, we don't even expect to see fresh, young
pulsars because, in order for us to see the pulsed beams, they must be pointed at us! There's no
reason why all pulsars in the universe should be oriented in such a way that their beams point
toward Earth.
7. The astronomer ought to conclude that the unseen companion is a black hole. A completely
unseen object this massive can only be a black hole. Other candidates (e.g., white dwarfs and
neutron stars) simply can't be this massive.
8. Orbits result when an object (like a planet) moves within the curved space of another object
(like the Sun).
9. At the event horizon, escape from a black hole becomes impossible as the escape speed at the
event horizon is equal to the speed of light.
10. An individual falling into a black hole is both stretched and squeezed. Stretching results
from the different amount of gravititational force pulling on your feet and
your head due to the black hole. This difference in force (called a tide) results in a stretch. You
are squeezed because you are actually moving toward a geometrical point (the singularity).
11. Assuming the Sun collapsed rapidly and uniformly, nothing would happen to Earth's orbit.
Earth would persist in its current nearly circular orbit in perpetuity.