White Dwarf: The Quantum Mechanical Star (ch 39,40)

The Universe provides a laboratory for physics underconditions more extreme than any we could replicate onEarth.

New theory, Quantum Mechanics, under development while Universe already revealing its predicted, strange states of matter. Take the white dwarf, a star the size of the Earth, revealing quantum mechanics in action.

A wobble, a mystery.7.6”

1844-F. Bessel saw that Sirius, brightest star inSky (mag=-1.5) had a wave-like motion indicatingpossible, unseen companion

1862-telescope maker A. Clark resolves Sirius B,(18” refractor). Kepler’s law & distance fromCenter of mass, Sirius B ~ 1 solar mass, but 10 mags or 1010/2.5=10,000 times fainter than Sirius A Recall from H-R diagram (next slide) that stars that faint should be red and cool.

The Hertzsprung-Russell (H-R) Diagram

Modern, Local H-R diagram, 23,000 stars

Original: Russell 1914

“Absolute Magnitude” scale of luminosity:M=4.8-2.5 log L/L, soL2=100L1 M2=M1-5

Sirius A

A wobble, a mystery.7.6”

1844-F. Bessel saw that Sirius, brightest star inSky (mag=-1.5) had a wave-like motion indicatingpossible, unseen companion

1862-telescope maker A. Clark resolves Sirius B,(18” refractor). From Kepler’s law and distance fromCenter of mass, Sirius B ~ 1 solar mass, but 10 mags or 1010/2.5=10,000 times fainter than Sirius A !Recall from H-R diagram (next slide) that stars that faint were supposed to be red and cool.

1915-Walter Adams at Mt. Wilson gets spectrum:(Its not in his paper so lets look at an HSTSpectrum of Sirius B:

B-Sirius!!

Sirius-B should have been a cool, red M-type, what is it?

HST spectrum

Peak color=blue

Sirius Problem!

Sirius A

Sirius B

Sirius B is hot (25,000 k) and faint, and so was Eridani B!

Eridani B

Russell:”I was flabbergasted, baffled trying to make out what it meant”

And, if Sirius A and B had same temperature (surface flux), why was B 10,000 fainter? How could Sirius B be so faint?

Let’s compare the size of Sirius B to A:RB/ RA=(LB/ LA)1/2(TA/TB)2 and (TA/TB)2~1, LB/ LA=10-4,

so RB/ RA~10-2 Now RA=1.7 R, so RB=0.01R=104 km

So Sirius B has mass of the Sun but size of the Earth!

Density=2x1030 kg/(4/3 (104km)3)=500kg/cm3, 1000 lb in a sugar cube!styrofoam=0.03 gr/cm3, Water=1 gr/cm3, lead=11 gr/cm3, gold/uranium= 19 gr/cm3

What could a white dwarf be made of to be a 100,00 timesdenser than the densest known elements?! In 1914 unknown..

Luminosity = (Surface Area) x ( ) energy emitted

cm2 sec

L = 4R2 T4

Remember the Stefan-Boltzmann law:

White Dwarf, A Star The Size of the Earth!Sirius A B

Question

What would happen if held a pinch of white dwarfin your hand?

a) it would explode b) you would explodec) it would cut your hand

c), assuming a pinch is ~1/10th of a sugar cube, that’s~100 lb sitting on ~a millimeter of skin

How Did the White Dwarf Get So Small?The Incredible Shrinking Star

•Recall: star is held up by pressure generated by heat which balances gravity. •When the furnace goes out, gravity wins, star contracts. Might heat up again and radiate, but eventually star runs out of fuel and keeps shrinking…•A white dwarf becomes so compact (I.e., size of Earth, mass of Sun), so gravity at surface (and the support pressure needed) is ~10,000x the Sun’s!•So, what is holding the star up after it runs out of fuel for its fire?

1 M

1 M

What happenswhen a starruns out of fuel?

Quantum Mechanics to the Rescue!A white dwarf so dense, needs tremendous support pressure tokeep from being crushed by its own gravity (gas not hot enoughto supply it, and out of fuel anyway). How does it hold itself up?

By 1926 the new field of quantum mechanics gives a clue.

1. The Pauli Exclusion Principle (W. Pauli: 1924 empirical, 1925 Explained by QM).

No two electrons can occupy the same “quantum state” (location, speed, etc).

So electrons must “stack”, they cannot be jammed too close together.

This explains the filling of electron shells in chemistry and properties of the periodic table. QM works!

Uncertainty2. Heisenberg Uncertainty principle (1927): x=positional uncertainty, v=velocity uncertainty

x v>h, A particle’s location and speed cannot bothbe completely confined, there is a limit. So this sets the smallest possible spacing between electrons.i.e., x =h/v

Velocity

Position

e- e-

Let’s get together, where will you be at

8:00?

I can tellyou where I am going or where I am

now, but not both!

Degenerate Matter

•Gravity is crushing but free electrons cannot get closer than x ~h/v so they begin to stack into a super-dense state, the gaps in matter (usually 1 in 107 states filled) are gone! •Even cold, electrons forced to have large velocities because these are unoccupied states (if x small, v is big). The tighter its squeezed the more it pushes back! (The smaller it becomes, the harder to compress)•Stacking of positions and velocities provides pressure (like jumping jellybeans in a jar) without heat (not thermal pressure)! Called degeneracy pressure (pressure to be different, like anti-peer pressure!)

R. Fowler, 1926, Electron Degeneracy Pressureor How stuff moves and creates pressure even when its cold

In R. Fowler’s Own Words, “On Dense Matter” 1926:

We recognize now that matter can exist in such a dense state that the electrons are not bound in their ordinary atomic orbits but are free…there may come a time when a very curious state of affairs is set up…As the dense matter radiates its energy away…the absolutely final state is one in which there is only one possible configuration left …the star is analogous to one gigantic molecule.

Not only has Fowler explained what holds up WD, he haspointed to a way stars can gracefully die (not fire but ice)!

Retired Stars or What to do With the Stellar Corpse

•The degenerate electrons in a white dwarf are moving very fast but the laws of quantum mechanics prevent them from losing or conducting away energy. They provide the stiffness to hold up the white dwarf.

•Atomic nuclei (positive ions) are not degenerate at this density, they remain in classic, gas state. So they can and do lose energy.

•So white dwarfs can shine as the nuclei lose energy, slowly cool down, and turn black: Black dwarfs. Size remains the same. Like Earth-sized lumps of coal with the mass of the Sun.

Electron degeneracypressure is the like the scaffolding of a stellar corpse

Subrahmanyan Chandrasekhar

1910-1995

In 1930 Chandrasekhar was 19, traveling byboat to England and discovered an evenstranger consequence of Fowler’s theoryof dense (degenerate) matter.

The more massive such a star was (imagineadding matter teaspoon at a time or finding a heavier one) the smaller it became, until finally it disappeared!

Eddington ridiculed Chandra’s idea in 1935 at an RAS meeting,“there should be a law of nature to prevent a star fromBehaving in this absurd way!”. This unfortunately set backthe acceptance of Chandra’s work for ~20 years!(he won Nobel 1983)

Strange Matter

•If more matter placed on a white dwarf, gravity--pressure get out of balance, so star contracts, x gets smaller, v gets larger which increases pressure. Star gets back to equilibrium but at a smaller size now then before!•Can’t keep getting smaller as v approaches speed of light! At the speed of light (and a change to a relativistic formula).R0, density∞,MMCH. Thus, there is a maximum mass, the Chandrasekhar mass (limit).

Add more beansJarful gets smaller,beans move faster!

Chandrasekhar Limit

Degeneracy pressure allows small stars (like the Sun) that end their lives with M<1.4M to die gracefully, leave a corpse. (Bigger stars can’t get their electrons closer together and jiggle them faster than speed of light).

So what happens to stars much bigger than the Chandrasekhar limit when they run our of fuel? How do they hold their massive, bloated corpse up?

Chandrasekhar’sPrediction

WD Mass and Size

limit

Supernova!Remember Tyco, Kepler, and Galileo’s “guest star”? By 1930’s indications were that L~109xSun! SN in 1054 mag=-6, visible by day

In 1934 Baade and Zwicky suggested that these could be the death of stars too massive to use the “graceful exit” possible for stars below Chandrasekhar’s limit.

When a very massive star runs out of fuel it would be unable to hold back gravity by degeneracy pressure and implode smashing electrons and protons to make neutrons. The result: a neutron star (neutron degeneracy allows greater density), a solar mass just 10 miles across! Then the star would rebound and an explosion would result. Demo!

Alternatively, if you (or its companion) adds one more teaspoon of matter to a Chandrasekhar-mass white dwarf it might explode.

These sounded like crazy ideas, but then how else could you explain a supernova in 1934?

Bang! A star explodes…

1987: The galaxy next door

Supernovae

Poem lyrics of When I Heard The Learn'd Astronomer by Walt Whitman, 1900

When I heard the learn'd astronomer;When the proofs, the figures, were ranged in columns before me;When I was shown the charts and the diagrams, to add, divide,

andmeasure them;When I, sitting, heard the astronomer, where he lectured with muchapplause in the lecture-room,How soon, unaccountable, I became tired and

sick;Till rising and gliding out, I wander'd off by myself,In the mystical moist night-air, and from time to time,Look'd

up in perfect silence at the stars.

The stars are made of the same atoms as the earth. I usually pick one small topic like this to give a lecture on. Poets say science takes away from the beauty of the stars - mere gobs of gas atoms. Nothing is "mere." I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination - stuck on this carousel my little eye can catch one-million-year-old light. A vast pattern - of which I am a part - perhaps my stuff was belched from some forgotten star, as one is belching there. Or see them with the greater eye of Palomar, rushing all apart from some common starting point when they were perhaps all together. What is the pattern, or the meaning, or the "why?" It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined! Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?-Richard Feynman

Question:

Do you feel more like Whitman (A)

or Feyman (B)?