Outline

1. Neutron Stars
2. Black Holes

Terms to Know

1. Neutron Stars

It turns out there may be an intermediate step. As you compress the material (made of densely-packed electrons and atomic nuclei) further, you will eventually force the electrons to merge with protons and form neutrons. The neutrons will be packed together almost touching, with densities approaching the densities in atomic nuclei. A neutron star is essentially one gigantic atomic nucleus, with very few protons and very many neutrons. Neutron stars are supported by neutron degeneracy pressure, similar to electron degeneracy pressure but at much much higher density.

The major properties of neutron stars predicted by theory include:

• masses up to about 3 M_Sun
• densities of around 2 x 10¹⁴ g/cm³; one sugarcube would weigh the same as all of the 6 billion humans on Earth
• radii of around 10 km
• very fast rotation (think of a figure skater with arms pulled in tight)
• very strong magnetic fields

The theoretical prediction of the existence of neutron stars received a big boost with the discovery of pulsars in 1967. Pulsars are objects that blink very fast in the radio (or optical) -- up to almost 1000 times per second. They are naturally explained by spinning neutron stars with a beam of radiation that sweeps past the observer every rotation, like a lighthouse beacon. Pulsars are often -- but not always -- observed in supernova remnants.

So the whole theory hangs together: one probable end for massive stars (M>7 M_Sun) after the red giant phase is a supernova that leaves behind a neutron star core at the center of the remnant. If the remaining core has a mass of more than about 3 M_Sun, however, even neutron degeneracy pressure can't support the crushing weight of material, and gravity finally wins...

2. Black Holes

1. What is a black hole?

   A black hole is any collection of matter that is so dense that even light cannot escape its gravitational field. Note that black holes don't have to be massive -- just dense!

   How dense? Any mass M packed into a radius smaller than r=2GM/c² is a black hole. That radius is called the Schwarzschild radius after the scientist who first calculated it, and that location around the black hole is called the event horizon.

   The idea is that as an object gets smaller and smaller, you can get closer and closer to its center, so the force of gravity (which goes as 1/r²) becomes stronger and stronger. As a result, to escape the object's gravity, you would need to travel at a higher and higher speed to avoid being pulled back to the surface. The speed at which you can just barely escape from the surface is called the escape velocity. (For example, at the Earth's surface, escape velocity is about 11 km/s -- which is how fast spaceships need to go to make it to the Moon or beyond.) A black hole is an object with an escape velocity equal to or greater than the speed of light.

   Examples:
   
   

   Object	Mass	Schwarzschild Radius
   Human	7.5x104grams	10-23 cm (less than a trillionth of a wavelength of green light)
   Earth	6x1027 grams	0.9 cm
   Sun	2x1023 grams	3 km
   Massive Star	2x1024 grams	30 km
   Milky Way	2x1034 grams	.01 pc -- less than distance to Alpha Cen

   So if you could cram the entire Earth into a golfball, it would be dense enough to constitute a black hole.

   Note that the mass of Earth as it is now and the mass of Earth compressed to the size of a golfball would be the same; only the density would be different. At golfball size, the Earth would be small enough that you could get very, very close to the center of gravity, rather than being stuck far away, as we are now at the Earth's surface (r=6,000 km).
   
   

2. What happens near a black hole?

   Because black holes are small enough to let you get close to them and fall under the influence of extraordinarily strong gravitational forces, funny things start to happen.

   Space itself gets distorted and curved very near a black hole's event horizon. Since light travels through space -- like a ball rolling on a rubber sheet with a big weight on it -- light can get bent by the strong gravitational field near a black hole. If the light gets too close -- within the Schwarzschild radius -- it gets sucked in, never to reappear. No information is available to the outside world on any events happening within the event horizon.

   If you were to fall head first into a 5 solar mass black hole, you would be ripped apart by tidal forces (stronger pull on head than on feet, so your head would be pulled off) long before you reached the event horizon. Meanwhile, as your friends watched you, you'd seem to fall slower and slower until finally you seemed to hang frozen in time. You, on the other hand, would experience (if you could survive the tidal forces, which you couldn't) a tremendous acceleration, but time would seem to behave normally. As the matter of our bodies accelerated towards the event horizon, it would heat up tremendously from the distortion, and would start to shine brightly in X-rays.
   
   

3. Where do black holes occur, and how do they form?
   
   
   • Dead stars: when massive stars (M>6 M_Sun) run out of fuel and collapse, then explode in a supernova, the core may be left behind as a black hole. Typical mass of the black hole would be a few solar masses.

     White dwarfs can also become neutron stars and then black holes if a nearby star in a close binary pair dumps enough gas onto its surface to make it collapse gravitationally.
     
     

   • Galaxy centers: There is mounting evidence that massive black holes -- millions of solar masses or more -- exist in the centers of many galaxies, including perhaps our own Milky Way. The black holes may have formed first from primordial ultra-dense lumps of gas or early massive stars, before the galaxies assembled around them, or they may be the result of billions of years of gas and stars spiraling in towards the galactic nuclei.
   
   
   
4. What is the evidence for their existence?
   
   
   • Fast motions in active galactic nuclei (AGN: quasars, radio galaxies)
   • Huge luminosity of AGN in tiny radius (brighter than whole galaxy, but from volume the size of the solar system)
   • Large masses of X-ray binary companion stars in the Milky Way

Lectures

Table of Contents

Astro 100