TODAY - Black Holes & Relativity (Chap 22) R Special ...neffj.people.cofc.edu/ASTR130/Notes/lec21.pdf1! Lec 21: 27 March 2012 ASTR 130 - Introductory Astronomy II (Chapter 22)! Last

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Lec 21: 27 March 2012 ASTR 130 - Introductory Astronomy II (Chapter 22) Last Time - Neutron Stars & Pulsars (Chap 21)

TODAY - Black Holes & Relativity (Chap 22) •  Special Relativity •  General Relativity •  Black Holes

THURSDAY - Milky Way (Chap. 23) •  there will be a pre-quiz!

Escape Velocity vesc = (2 G M / r)1/2

= c when...

Rs = 2GM/c2 “Schwarzschild Radius”

Mass RS corpse size 1 M 3 km white dwarf ~8000 km 3 M 9 km neutron star < 30 km

RS ~ r for 3 M neutron star, so star disappears within its own “event horizon” Also, gravity exceeds neutron pressure, so star..??..

Newtonian Gravity and Light

•  Fg = G M1M2/R2 and F = ma – but photons have no mass!

•  Clear prediction: Gravity should not attract light, change its direction of travel, etc.

•  But it does! 1919 solar eclipse...

Classical (“newtonian”) Mechanics •  time moves one way, at same rate everywhere •  space is 3-dimensional and uniform

–  length measures change in uniform space

•  Newton’s Laws of Motion give simple description of how things move through space for all time under the influence of forces. –  includes orbits (Keplers’ Laws) – mass measures inertia and relates force to

acceleration –  forces always occur in oppositely-directed pairs

Special Relativity Assumption: Laws of physics should be the same everywhere in the universe.

•  Consequences: –  speed of light is same observed any time, any place –  time slows, length contracts, and mass increases if

there is relative motion between observer and event Lorentz factors γ=(1-v2/c2)1/2

very tiny unless v is close to c

– E = γmc2 (m=γm0; “rest mass” = m0c2)

relative motion changes measured velocity

but not with light!

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if relative motion, measured

length is shorter (in direction of travel)

time is longer

mass is greater

relative motion is all that matters; doesn’t matter if one “observer” thinks he’s sitting still (they both do!)

General Relativity Equivalence between force and acceleration

–  not just a proportional relationship F=ma –  gravity and acceleration are indistinguishable

•  Consequences: –  space is warped by mass –  time is slowed by mass

•  low mass -> low gravity -> GR = Newtonian •  low speed -> SR = Newtonian •  How can we test, visualize, and quantify this?

General Relativity Equivalence between force and acceleration

–  not just a proportional relationship F=ma –  gravity and acceleration are indistinguishable

•  Consequences: –  space is warped by mass –  time is slowed by mass

•  low mass -> low gravity -> GR = Newtonian •  low speed -> SR = Newtonian

•  How can we test, visualize, and quantify this?

Observational Tests of General Relativity

1.  Solar Eclipse

2.  Advance of Mercury’s perihelion

1919 – Solar Eclipse Test of General Relativity

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3. Clock speeds vary with altitude (left)

4. gravitational redshift of light from massive objects (right)

Time for a DEMO...

strong gravity bends paths of light leaving star

5. gravity can work like a lens!

Black Holes

•  nothing can escape from within event horizon •  laws of physics break down at singularity •  black hole still has mass, charge, rotation

what’s really going on here?

impossible to say!

Can We Observe Black Holes? •  not directly, since even light cannot escape •  probably not by blocking light from behind,

because they are so small •  but maybe by gravitational lensing •  Best bet: Binary Systems

–  normal star orbiting black hole; orbital motion – matter accretes onto black hole through accretion disk –  x-ray emission from disk

Note: NOT COSMIC VACUUM CLEANERS!

Close Binaries and Stellar Evolution

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NOVA

If accretion rate just right, it will accrete an atmosphere, which then detonates. Then the process starts all over.

If rate is slow, enough material can build up to 1.4 Msun Type Ia S.N.!

X-RAY BURSTER

Same phenomenon, but on neutron star.

Much shorter timescales!

We can detect black holes in binary systems by

1.  orbital motion of companion

2.  emission from accretion disk and jets

3.  catastrophic events