The Physics of White Dwarf Stars

Denis J SullivanVictoria University of Wellington

October 18, 2011

White dwarf & pulsating WD brief history

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■ 1915 Astronomers: identify white dwarfs (WDs) as unusual.

White dwarf & pulsating WD brief history

2 / 28

■ 1915 Astronomers: identify white dwarfs (WDs) as unusual.

■ ∼1925 Schrodinger, Heisenberg, Pauli, . . . quantum mechanics (QM)developed.

White dwarf & pulsating WD brief history

2 / 28

■ 1915 Astronomers: identify white dwarfs (WDs) as unusual.

■ ∼1925 Schrodinger, Heisenberg, Pauli, . . . quantum mechanics (QM)developed.

■ 1926 Fowler: uses QM to develop a WD theory –electron degeneracy pressure prevents gravitational collapse.

White dwarf & pulsating WD brief history

2 / 28

■ 1915 Astronomers: identify white dwarfs (WDs) as unusual.

■ ∼1925 Schrodinger, Heisenberg, Pauli, . . . quantum mechanics (QM)developed.

■ 1926 Fowler: uses QM to develop a WD theory –electron degeneracy pressure prevents gravitational collapse.

■ 1932 Chandrasekhar: combines special relativity (SR) with QM toobtain a WD theory that predicts a maximum mass (∼ 1.4M⊙ )Eddington not impressed.

White dwarf & pulsating WD brief history

2 / 28

■ 1915 Astronomers: identify white dwarfs (WDs) as unusual.

■ ∼1925 Schrodinger, Heisenberg, Pauli, . . . quantum mechanics (QM)developed.

■ 1926 Fowler: uses QM to develop a WD theory –electron degeneracy pressure prevents gravitational collapse.

■ 1932 Chandrasekhar: combines special relativity (SR) with QM toobtain a WD theory that predicts a maximum mass (∼ 1.4M⊙ )Eddington not impressed.

■ 1964 Landolt accidentally discovers first pulsating WD (DAV,HLTau 76) – periodic variations ∼ 12.5 minutes in a potential WD fluxstandard (Landolt, ApJ, 1968).

White dwarf & pulsating WD brief history

2 / 28

■ 1915 Astronomers: identify white dwarfs (WDs) as unusual.

■ ∼1925 Schrodinger, Heisenberg, Pauli, . . . quantum mechanics (QM)developed.

■ 1926 Fowler: uses QM to develop a WD theory –electron degeneracy pressure prevents gravitational collapse.

■ 1932 Chandrasekhar: combines special relativity (SR) with QM toobtain a WD theory that predicts a maximum mass (∼ 1.4M⊙ )Eddington not impressed.

■ 1964 Landolt accidentally discovers first pulsating WD (DAV,HLTau 76) – periodic variations ∼ 12.5 minutes in a potential WD fluxstandard (Landolt, ApJ, 1968).

■ 1970+ WD pulsations explained by gravity modes driven bymechanism in partial ionization H atmosphere.Note: more common pressure modes have periods: ∼ seconds

t ∼ t ∼1

√ ∼ seconds for WD

WD History (continued)

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■ 1979 First DOV degenerate pulsator discovered (PG1159−035).(McGraw et al.) – explained by driving mechanism in partial ionized Cand O layers.

WD History (continued)

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■ 1979 First DOV degenerate pulsator discovered (PG1159−035).(McGraw et al.) – explained by driving mechanism in partial ionized Cand O layers.

■ 1982 First helium atmosphere WD pulsator discovered (GD358),following theoretical prediction of pulsation driving in He partialionization zone (Winget et al.)

WD History (continued)

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■ 1979 First DOV degenerate pulsator discovered (PG1159−035).(McGraw et al.) – explained by driving mechanism in partial ionized Cand O layers.

■ 1982 First helium atmosphere WD pulsator discovered (GD358),following theoretical prediction of pulsation driving in He partialionization zone (Winget et al.)

■ 1985 Period change due to secular cooling measured from multi-sitephotometry on PG 1159 (Winget et al. 1985).

WD History (continued)

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■ 1979 First DOV degenerate pulsator discovered (PG1159−035).(McGraw et al.) – explained by driving mechanism in partial ionized Cand O layers.

■ 1982 First helium atmosphere WD pulsator discovered (GD358),following theoretical prediction of pulsation driving in He partialionization zone (Winget et al.)

■ 1985 Period change due to secular cooling measured from multi-sitephotometry on PG 1159 (Winget et al. 1985).

■ 1990 WET: the Whole Earth Telescope (Nather et al., ApJ 361)

WD History (continued)

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■ 1979 First DOV degenerate pulsator discovered (PG1159−035).(McGraw et al.) – explained by driving mechanism in partial ionized Cand O layers.

■ 1982 First helium atmosphere WD pulsator discovered (GD358),following theoretical prediction of pulsation driving in He partialionization zone (Winget et al.)

■ 1985 Period change due to secular cooling measured from multi-sitephotometry on PG 1159 (Winget et al. 1985).

■ 1990 WET: the Whole Earth Telescope (Nather et al., ApJ 361)

■ 1991 WET observations of PG 1159−035 (Winget et al., ApJ 378)

WD History (continued)

3 / 28

■ 1979 First DOV degenerate pulsator discovered (PG1159−035).(McGraw et al.) – explained by driving mechanism in partial ionized Cand O layers.

■ 1982 First helium atmosphere WD pulsator discovered (GD358),following theoretical prediction of pulsation driving in He partialionization zone (Winget et al.)

■ 1985 Period change due to secular cooling measured from multi-sitephotometry on PG 1159 (Winget et al. 1985).

■ 1990 WET: the Whole Earth Telescope (Nather et al., ApJ 361)

■ 1991 WET observations of PG 1159−035 (Winget et al., ApJ 378)

■ 1994 WET observations of GD 358 (Winget et al., ApJ 430)

WD History (continued)

3 / 28

■ 1979 First DOV degenerate pulsator discovered (PG1159−035).(McGraw et al.) – explained by driving mechanism in partial ionized Cand O layers.

■ 1982 First helium atmosphere WD pulsator discovered (GD358),following theoretical prediction of pulsation driving in He partialionization zone (Winget et al.)

■ 1985 Period change due to secular cooling measured from multi-sitephotometry on PG 1159 (Winget et al. 1985).

■ 1990 WET: the Whole Earth Telescope (Nather et al., ApJ 361)

■ 1991 WET observations of PG 1159−035 (Winget et al., ApJ 378)

■ 1994 WET observations of GD 358 (Winget et al., ApJ 430)

■ WET continues . . . . . .

WD relative size

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Stellar structure equations

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Mechanical structure - P (r), ρ(r),m(r)

dP

dr= −ρ(r)g(r) ; g(r) =

Gm(r)

r2; m(r) =

∫

r

0

ρ(r)4πr2dr

Thermal structure - T (r), L(r), . . .

dT

dr= (· · · ) ;

dL

dr= (· · · )

Common stellar P(r),ρ(r),T(r) profiles

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WD Mechanical Structure

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■ WD support mechanism dominated by electron degeneracy pressure,which is essentially independent of temperature −→ depends on density

WD Mechanical Structure

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■ WD support mechanism dominated by electron degeneracy pressure,which is essentially independent of temperature −→ depends on density

■ Hence in a WD, mechanical structure decoupled from thermal structure

WD Mechanical Structure

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■ WD support mechanism dominated by electron degeneracy pressure,which is essentially independent of temperature −→ depends on density

■ Hence in a WD, mechanical structure decoupled from thermal structure

■ Nonrelativistic (NR) electron gas

n ∝ p3F ; P =1

3vp −→ P ∝ P 5

F −→ P ∝ ρ5

3

■ Extremely relativistic (ER) electron gas

n ∝ p3F ; P =1

3cp −→ P ∝ P 4

F −→ P ∝ ρ4

3

Simple WD mechanical model

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The following relatively simple differential equation describing x(r)(which is the electron momentum at the [local] fermi surface) quite accuratelycharacterises the density and pressure profiles of WDs.

d2u

dz2+

2

z

du

dz+

(

u2 −1

x2c + 1

)3

2

= 0

where

u =

(

x2 + 1

x2c + 1

)

1

2

and x =pF(r)

mec

Solve numerically for x(r):

x(r) −→ ρ(r), P (r)

Simple WD mechanical model

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Behaviour of increasingly relativistic particles

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WD density & temperature profiles

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WD Radius vs Mass

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WD Radius vs Mass

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White dwarf spectroscopy (Magellan 6.5m)

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EC20058 (He atm.) and flux standard (H atm.)

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White dwarf time-series photometry

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A WD light curve (MtJohn 1-m)

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WD light curve (Magellan 6.5-m telescope (Chile)

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Two different WD light curves

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A white dwarf with nonsinusoidal pulse shapes

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A white dwarf with nonsinusoidal pulse shapes

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WET (mult-site) time-series light curves

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WET xcov15 DFT, Sullivan et al., MNRAS (2008)

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Nonradial pulsations: spherical harmonics

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Asteroseismology and white dwarf physics

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■ Core chemical composition - stellar nuclear reaction ashes

dominated by 12C and 16O.

■ Core crystallization

■ Convection zone studies

■ Neutrino cooling mechanism

White dwarf cooling models - neutrino cooling

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Plasmon neutrino processes − Feynman diagrams

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Neutrino physics in hot WD plasmas

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■ Basically, neutrinos produced by e− e+ annihilation

■ But where do the positrons come from?

■ Even at WD core temperatures, not enough energy forreal e−,e+ pairs

■ However, plenty of short duration (real) virtual e−,e+ pairs createdcourtesy energy-time uncertainty principle

■ But, these pairs recombine with probability 0.99999 . . .

■ However, this probability is not 1, and there is a ∼ 1 in 10−19 chance offorming neutrino-antineutrino pairs via W±, Z0 exchange/creationprocesses (the electroweak connection).

■ Given the ν mass is ∼ zero, energy conservation permits formation of atwo ν final state from a ∼ KeV photon, but momentum conservationrequires more than a photon in initial state

■ Possible other particles: nuclei, many particles −→ plasmons (this is thedominant mechanism)