Compact Objects

Means......

1. White Dwarfs
2. Neutron Stars
3. Black Holes
4. SS433

Mass is the critical factor for "normal" stars: the other important parameter is density

ρ =  Mass =    M  
        Volume     4/3πr³

For comparison

• Water (by definition) ρ = 1
• Lead ρ ∼ 13
• Osmium ρ ∼ 22
• Air ρ ∼ .001
• Earth ρ ∼ 6
• Jupiter ρ ∼ 1
• Saturn ρ ∼ .7 (yes, it would float!)
• Sun ρ ∼ 1 (but about 150 at centre, much less at outside)

(these are old units: if you compare to a modern book, multiply all densities by 1000)

White dwarfs

As seen in planetary nebula: star with about the same mass as sun but size of earth (∼10000 km )

Density: ∼ 10⁶: ∼ 100,000 times as dense as lead.

This shows some in M4 (a rich globular cluster of stars). temperature very hot: T ∼ 50000°C: since they are small, they cool very slowly.

Credit: NASA, HST, WFPC 2, H. Richer (UBC)

e.g. Sirius B: probably the best studied;
"Found" by Herschel who noticed Sirius was "wobbling". Observed in 1862 by Alvan Clark: very hard to see since it is close to Sirius A but 1/10000 of the brightness, but mass ∼ 1.05 M_o

This implies a very small object: T =29500 K L ∼ 0.003 L₀. Radius= 1500 km ∼ 1/5 R of the earth. Since it is so hot, it is bright in X-rays: this shows Sirius B bright and a very dim Sirius A!

Two oddities:

• the Dogon people of West Africa have the legend that their ancestors came from a star that circled Sirius and one day they will come back.
• Both Greek and Chinese records describe Sirius as red: it may have changed in historical times

What Sirius might have looked like: NGC 3132 (the Eight Burst Nebula), a recently formed planetary nebula with a white dwarf and companion, will probably look like Sirius in 100000 years

Credit: Hubble Heritage Team (AURA/STScI /NASA)

Typically, R∼ 4000 km

Why are white dwarfs so dense? Not possible for a normal gas: in fact the star is supported by the "degeneracy" pressure of electrons, predicted by Chandreshekar in 1930

Neutron stars

Very regular radio pulses, period of 4 s ⇒ 2 ms Note that height of pulse is very irregular

All lie close to Milky Way (i.e. in plane of galaxy). Therefore must be related to stars

Best known is Crab. Known to be remnant from supernova in 1054 (seen by Chinese) Pulsar at centre has period of ∼ .03 s

Optical pulsing observed by TV or strobe
Pulses at all wavelengths, in synch.

ρ ∼ 1015:

Do we see all the pulsars?

No, because they would have to be oriented so that they point towards us. rotation period will slow down...

1. Neutron Star forms from supernova, P ∼ 1 ms
2. P ∼ 30 ms after 1000 years
   
3. P ∼ 5 s over 10⁵ years, also magnetic field may weaken, at which stage radio signal is too weak to be seen

Hence probably large number of radio-quiet neutron stars: essentially impossible to see.

Since neutron stars are so hot we see them in X-rays and γ-rays. This shows how a new satellite (GLAST) will see the sky: the brightest object is he Crab and the second brightest....... Geminga: a pulsar that had only been seen in γ-rays until it was identified as a very faint star

GLAST Gamma Ray Sky Simulation Credit: S. Digel (USRA/ LHEA/ GSFC), NASA

Black Holes

• Einstein
• Hawking?

• geologist?
• philosopher?
• astronomer?
• Seismologist?
• Polymath?

presented his ideas to the Royal Society in London in 1783. and astronomer Pierre Laplace, in 1795.

Escape Velocity

How hard would you need to throw something so that it never came back? energy is conserved: ,the gravitational potential energy of any object at a distance r is

P.E. = -GMm
               r 

G = 6.67x10^-11 is Newton's constant, M is the mass of the object from which you are launching, so for the earth is 6x10²⁴ kg and m is the mass of the object. Note P. E. = 0 at r=∞ . The kinetic energy is

K.E. = ½mv²

T.E. = P.E. + K.E. or

E = ½mv² - GMm
                      r

and at r= ∞, P.E. = 0, so want K.E. = 0 as well and Remember T.E. = P.E. + K.E. = 0

so for the earth:

• R = 6500 km ,
• M = 6x10²⁴
• so v = (2GM/R)^½ = 110000 m/s = 11 km/s

R = 2GM
         v²

R = 2GM         
         c²

This is the Schwarzchild radius ( black-hole radius) for any mass. For the earth it is ∼ 3mm

Statutory Warning:This is a fudge: you cannot treat light as a massive particle, nor can you handle a very strong gravitational field as if it were a weak one...... (there are actually two factors of 2 error which cancel out.....weren't we lucky!)

A black hole is the end product of star with > 10 M₀

But black holes are black:

as the bumper sticker says. So how do we see them?

If we are really lucky....(or unlucky) as a gap in the sky

Too Close to a Black Hole Credit & Copyright: Robert Nemiroff (MTU)

But more likely via the "accretion disk" which will have velocity ∼ c at inner edge, so temp well into X-rays

So want binary, with invisible heavy companion with M > 3M₀, emitting X-rays

Prime candidate is Cygnus X-1, which agrees with position of a massive blue star HD 226868

• Mass of primary star ∼ 20M₀
  
• Mass of invisible object M∼ 9M₀
  
• puts out 4x10³⁰ W in X-rays (i.e. 10⁴ L₀!!)

Other weird objects include Cyg X-3, Herc X-1 and

SS-433

SS-433 found as star with very unusual spectrum X-ray source discovered at same position Spectrum changes with 164 day cycle, corresponding to v ∼ 50000 km/s

This is something new! Narrow jets travelling at 1/5 speed of light are shot out of poles, probably formed by thick accretion disk around neutron star or black hole: "cosmic lawn sprinkler"