History of White DwarfsHistory 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)

2020thth Century History Century History• Eddington

– 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

Interiors in a NutshellInteriors 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

Masses of White DwarfsMasses 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

White DwarfsWhite 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

Surface CompositionsSurface 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

Why the DB Gap?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 10-15 solar masses of hydrogen (recall that 10-4 is the limit where H burning stops)

– Only about 10-15 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 10-13 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

Spectral Evolution ModelSpectral 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 10-13 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)

Variable White DwarfsVariable 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

RotationRotation• 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 ratesClass 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)

Why Is Slow Rotation a Why Is Slow Rotation a Problem?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...

Magnetic FieldsMagnetic 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?

Neutron Star OdditiesNeutron 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?

Ages from White DwarfsAges 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

Degenerate BinariesDegenerate 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

R Corona Borealis (and other) R Corona Borealis (and other) StarsStars

• 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?

White Dwarf Merger White Dwarf Merger ScenarioScenario

• 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.