Orbits

Orbits• Angular momentum

mass x velocity x lever arm

Conserved for isolated objects

Change requires torque: force x lever arm

Demo

Orbits• Kepler orbits:

Outer orbits have higher angular momentum

• Angular momentum “barrier”:

Say particle gets kick inward

⇒ smaller lever arm = faster velocity

faster velocity means more centrifugal force

⇒ Particle moves back out

• http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/kepler6.htm

Schwarzschild orbits• Angular momentum still conserved

• The only difference is close to BH:

Gravity stronger and stronger

⇒ Gravity can overwhelm angular momentum

• What are the possible orbits?

Circular orbits?

Ellipses?

“Plunging” orbits?

• http://www.fourmilab.ch/gravitation/orbits/

• What are the possible orbits?

Circular orbits: stable only outside 3 x RS

Ellipses: not closed

Hyperbolic orbits: With precession

“Plunging” orbits: orbits inside 3 x RS

Schwarzschild orbits

eventhorizon

“plunging region”

RS unstable stable

• What are the possible orbits?

Circular orbits: stable only outside 3 x RS

Ellipses: not closed

Hyperbolic orbits: With precession

“Plunging” orbits: orbits inside 3 x RS

Schwarzschild orbits

eventhorizon

“plunging region”

RS 3xRS

• Photon (=light) orbits:

Photon can be on unstable circular orbits at 1.5 x RS

Light bending: Green (hyperbolic) orbits

Multiple wraps are possible!

Schwarzschild orbits

eventhorizon

RS 1.5xRS

NOTE: this is not a real image!

Light bendingWhat the sky behind a black hole would look like

How to find black holes

How to find black holes• So far:

Black holes themselves should not emit light

Must be massive and/or really small

Orbits of surrounding objects must be perturbed

How to find black holes• Strategy #1 for finding black holes:

Look for objects whose trajectory is perturbed by a massive dark object

How to find black holes• Strategy #1 for finding black holes:

Look for objects whose trajectory is perturbed by a massive dark object

Measure the mass using Kepler’s laws

“Measure” radius (must be smaller than orbit)

The Galactic center• 17 years of observation:

Stars orbit a dark object

Mass: 3.6 million suns (“supermassive”)

Radius < size of earth orbit

Black hole!

Genzel et al. 2005

The Galactic center• A very dim object

only ~ 100 solar luminosities

“Blackest black hole” known to date!

One of the best cases for existence of black holes

Genzel et al. 2005

hidden inside this bright clump (not from black hole)

NASA / Chandra public image archive

The Galactic center

Other galactic centers...

• ...also host “supermassive black holes”

• More massive galaxies host more massive black holes...

• This method is hard!

• Have to know where to look

• Takes a long time

• Have to resolve stars (only nearby galaxies)

Black hole formation• Knowing where black holes come from could

help us find them...

• Slight complication:

We don’t know where “supermassive” black holes come from

We do know how to make “small” black holes...