1. History of White Dwarfs
Bessell (1844)
Proper motions of Sirius and Procyon wobble
Suggested they orbited “dark stars”
Alvan Clark (1862)
Found Sirius B at Northwestern’s Dearborn Observatory
Procyon B found in 1895 at Lick
Was it a star that had cooled and dimmed?
Spectrum of 40 Eri B observed – an A star!
It must be hot
Must have small radius to be so faint
The first “white dwarf”
Adams found Sirius B is also an A star in 1915
From luminosity, R~ 2 x Earth (actually ¾)
From orbit, about 1 solar mass
Density 105 x water (actually 106)

2. 20th Century History Eddington R. H. Fowler (1926)
Gas must be fully ionized so that nuclei could be compacted together
Conundrum – as the white dwarf cools, the atoms should recombine, but they can’t because the star can’t swell against gravity
R. H. Fowler (1926)
Recognized the role of degeneracy pressure in supporting the star
Chandrasekhar (1935)
Upper limit to mass supported by electron degeneracy pressure due to limit of velocity of light (1.4 solar masses)
Zwicky (1930’s) - Degenerate Neutron Stars
Schatzman (1958) – chemical diffusion in strong gravity (plus radiative levitation, winds and mass loss, convective mixing, accretion)
Greenstein and Trimble (1967) - Gravitational redshift
Hewish and Bell (1967) - Pulsars

3. Interiors in a Nutshell
Upper mass limit for white dwarf formation is somewhere between 5-9 solar masses – “Inside every red giant is a white dwarf waiting to get out” (Warner)
Most have C-O cores, most massive may have O-Ne cores
In hot, pre-white dwarfs, neutrinos dominate energy loss
When nuclear burning stops, photon cooling dominates
interior becomes strongly electron degenerate, mechanical and thermal states decouple, ions are a classical ideal gas
Ions eventually crystallize but we still have no empirical evidence for this
Crystallization releases latent heat and carbon and oxygen may undergo a phase separation on crystallization may also provide heat which would prolong cooling times
after crystallization, heat capacity drops, cooling times shorten
Interplay of gravitational settling of heavier species and turbulent energy transport (convection) may affect surface abundances
As the degeneracy boundary moves outward, it eventually halts the convection
At cool enough temperatures H2 forms, and possibly even He2

4. Masses of White Dwarfs Methodology
orbital solutions or binary stars
measurements of surface gravity (with a mass-radius relation)
model atmospheres with photometry, parallaxes
gravitational redshifts
asterseismology
<M> = 0.58 – 0.59 solar masses
About 1/6 of (presumed) single white dwarfs show radial velocity variations

5. White Dwarfs White Dwarfs – DO, DB, DA, DF, DG, DM, DC
Classifications NOT analogous to MS – reflect compositions, not temperature
DA – hydrogen lines (no other lines, pure H atmosphere)
DB – neutral He lines (no hydrogen at all, pure He)
DO – ionized He lines (no hydrogen at all, hotter DBs)
DC – continuous spectrum, no lines
DF, DG, DM (can’t discriminate DA or DB)
Heavier atoms sink in gravitational field
Above 15,000 K, 15% are non-DA, below 15,000 K, half are non-DA. How do the stars do that?
NO DB stars between 30,000 and 45,000 K

6. Surface Compositions DA (80% of WDs) and non-DA
Most WDs have pure or nearly pure H or He atmospheres
DAs found from hottest to coolest
Non-DAs start with hot stars
DOs for Teff > 45,000K with He II or He I and He II
DBs for Teff < 30,000 with He I only
DCs (featureless) for Teff < 11,000
NO He-rich WDs between 45,000 and 30,000K

7. Why the DB Gap?
Simple picture of parallel sequences of H and He-rich objects doesn’t work
Accelerated evolution of DBs between 45,000 and 30,000K doesn’t make sense
Change in ratio of DAs and DBs around 10-15,000K also hard to explain
Mean masses of DAs and DBs are the same
Theory of spectral evolution – Fontaine and Wesemael
All WDs have a common origin (PNN) with some hydrogen, upper limit of 10-4 solar masses to solar masses of hydrogen (recall that 10-4 is the limit where H burning stops)
Only about is needed to produce an optically thick H layer at the surface
Diffusion brings H to surface; by Teff=45,000 K, all WDs have hydrogen atmospheres, so there are no DBs
At 30,000 K, the formation of an He ionization zone creates turbulence which mixes the H with He, and leads to He stars (stars with more than H have too much H to form a sufficient convection zone, and they remain DAs)
Change in DA/non-DA ratio at 11,000 K results from onset of convection from H ionization zone, increases mixing, and more DBs appear
But this model doesn’t work

8. Spectral Evolution Model
What’s wrong with the spectral evolution model?
model suggests DAs should have a wide range of hydrogen layers, from 10-4 solar masses to solar masses of hydrogen
Asteroseismology results suggest all DAs have thick hydrogen layers
The model also predicts trace amounts of H in the hottest DB stars (just at the cool edge of the DB gap)
H was found with GHRS on HST but at a level way to low (<10-18 solar masses) to have ever permitted this DB to have been a DA in the DB gap
The WDs are fed by other sources than PNN
subdwarf O and B stars (whose origin is still not clear)
IBWDs (interacting-binary white dwarfs)
Both of these enter the cooling curve somewhere along the spectral sequence
Maybe the DBs come from the IBWDs, and all the DOs become DAs at 45,000 K (and stay that way)

9. Variable White Dwarfs
Asteroseismology with the Whole Earth Telescope (WET)
Determine masses, hydrogen masses, rotation rates, magnetic fields
ZZ Ceti Stars – extension of Cepheid instability strip
Hydrogen ionization zone below the photosphere
Temperature range from 10,500 to 13,000 K
Amplitudes of 0.01 to 0.3 mag
Periods of 3-20 minutes
DB pulsators from He ionization zone
T ~ 20,000K
PG 1159 stars – also pulsators
T ~ 130,000
Oxygen ionization zone drives pulsations
Periods of minutes

10. Rotation Measuring rotation rates (vsini)
shapes of hydrogen line cores
rotational variation of polarization in magnetic white dwarfs
asteroseismology
vsini measurements suggest rotation rates < 8-40 km/sec – very slow! (where does the angular momentum go?)
Periodic changes in polarization gives two groups, those with rotation periods of a few days, and those with periods >100 years
Asteroseismology also gives slow rates
Class Problem – What is the approximate rotational velocity of a star with a rotational period of 2 days? (assume we are observing it in its equatorial plane)

11. Why Is Slow Rotation a Problem?
Assume a solar rotation period of 30 days, conserve angular momentum, and estimate the rotation rate if the Sun were shrunk to the radius of the Earth...

12. Magnetic Fields Broadband circular polarization
detects fields > 50 MGauss
Circular spectropolarimetry
limits to 1-50 kG
Detected fields range from 3 kG to 1 GG
asteroseismology suggests fields of 1 kG
Magnetic fields detected at all temperatuers, but more and stronger fields in cool WDs (<16,000K)
Does a dynamo form when convection starts?
Oblique rotators again?

13. Neutron Star Oddities The non-pulsar neutron star (Geminga)
discovered from x-ray brightness
imaged by HST in 1998 (V~25)
distance <~400 pc (in front of IS cloud)
Teff > 106 K
Probably lots of these around
The Black Widow Pulsar
Eclipsing double, companion R=0.2 RSun, mass of 0.02 MSun
Mass transfer spins up pulsar
Pulsar is eroding away the companion
The Magnetar
Magnetic field of 1014 G
field cracked pulsar’s crust, producing gamma and x-ray burst
burst partially ionized the upper atmosphere of Earth
Quark Stars?

14. Ages from White Dwarfs Age of the disk – from the coolest WDs found
Liebert, Dahn, and Monet (1988, etc) used a sample from the Luyten Half-Second catalog
Oswalt from common proper motion binaries
Observational problems
completeness
undetected binaries
small sample statistics, especially for the coolest, faintest white dwarfs. Need larger samples!
Many remaining issues in WD cooling physics
C/O ratio in core, phase separation at crystallization
Settling of heavier species (22Ne, 56Fe)
depth of He layer
Age estimated around 10 Gyr
Age of the halo and globular clusters still to be done

15. Degenerate Binaries Novae
10 magnitudes or more increase in brightness over a day or two
Drop typically 3 mags in a month or two
Back to original brightness after a few years or decades
White dwarf – low mass main sequence binary
Began as wider binary, then common envelope evolution tightens the binary
Recurrent novae, dwarf novae
Symbiotic Stars – binary separation sufficient that stars don’t interact until companion becomes a giant
Spectrum is a cool star + hot accretion disk
Mass loss from giants feeds an accretion disk around the white dwarf
Nova-like eruptions – due to white dwarf mass accretion or to instabilities in the accretion disk
X-ray binaries – neutron star + companion

16. R Corona Borealis (and other) Stars
RCorBor Stars & Extreme Helium Stars
A to G-type supergiants
Occasionally dim by ~8 magnitudes
Recovery can take a year
Veiling by carbon dust from mass loss
Highly deficient in hydrogen
Helium dominates
Carbon greatly enriched
Cepheid-like pulsations
Heating by 30K per year, shrinking
Post-AGB stars?
Coalesced white dwarf binaries?

17. White Dwarf Merger Scenario
The camera aspect remains the same, but moves back to keep the star in shot as it expands. After the star reaches 0.1 solar radii, an octal is cut away to reveal the surviving disk and white dwarf core. The red caption (x) is a nominal time counter since merger. A rod of length initially 0.1 and later 1 solar radius is shown just in front of the star.