Problem sets 5 and 6 due this week. ASTR 1200 Announcements Problem sets 5 and 6 due this week. Third exam November 20 (next week) Website http://casa.colorado.edu/~wcash/APS1200/APS1200.html

A Newtonian Black Hole Energy Falling To Surface Kinetic Energy OR if v=c

Schwarzschild Radius Two errors cancel. This is the radius of the “Event Horizon” The event horizon is a true singularity in space-time. It is a place where time and space cease to exist.

Curved Space

Rubber Sheet Analogy

Properties - Basic Mass (Schwarzschild Black Hole) Electric Charge (doesn’t happen) Angular Momentum (Kerr Black Hole) No “Surface” Features No Magnetic Fields No Pulsing “No Hair”

Time Dilation As r approaches Rs dt gets longer and longer. When r reaches the event horizon, time stops. We know how to make a time machine with a forward switch only! Just fly to a black hole and orbit above the surface. But you can fall in really fast as viewed from outside.

http://www. space. com/27701-interstellar-movie-science-black-holes http://www.space.com/27701-interstellar-movie-science-black-holes.html

Hawking Radiation The vacuum makes pairs of electrons and positrons that pop into existence and then annihilate without any net effect. Above a black hole, one can get sucked in. The other annihilates above the surface to cause radiation. Since its close to the surface, the light gets redshifted escaping, but it carries energy with it!

Temperature Hawking derived that the temperature of a black hole is thermal. Energy for the radiation comes from the mass of the hole. The black hole shrinks with time. That’s a really long time unless the black hole is tiny. A 1kg black hole would last only 10-16s.

Artist’s impression of Cyg X-1 (NASA) 6M0 BH orbiting an O9 star. 2000pc away in Cygnus

The Milky Way Stars Beyond Counting

100 Billion Stars

Orbital Period Takes the Sun 200million years to orbit Milky Way. Sun is 4600 million years old. The Sun is 23 Galactic Years Old.

A Spiral Galaxy Like Milky Way

Milky Way – Edge-On

The Milky Way

Formation of Milky Way Analogous to formation of the Sun Start with big blob of gas Let it collapse Disk Stability Again

Globular Clusters Gas has friction and collapses to disk. Stars have huge momentum with small cross section. When a star forms it remains frozen in its initial orbit forever. Little knots of high density are first to form into stars. These are the globular clusters. They each contain a million stars. There are about 100 orbiting the Milky Way.

The Globular Cluster – M80