Download White dwarfs

White dwarfs : historical remarks
-Sirius = binary system (Bessel, 1844)
-Mass of Sirius B : M = 0.94 M⊙ (1910)
-Temperature of Sirius B (“white”) : Teff = 8 000 K (Adams, 1914)
It leads R = 18 000 km, ρ = 7 104 g/cm3
(Moderne values : Teff = 24 000 K , R = 2000 km , ρ = 6 107 g/cm3 )
- Eddington 1926 : “we have a star of a mass about equal to the sun and a radius much less than
Uranus [...] it seems likely that the ordinary failure of the gas laws due to finite sizes of molecules will
occur at these high densities, and I do not suppose that the white dwarfs behave like perfect gas.”
White dwarfs : historical remarks
Sirius :
Original Herzsprung-Russell diagram (1914)
-Sirius A = the brightest star in the sky after the Sun
Bright
MacDonald Observatory
-Binary system (Bessel, 1844)
Blue
-Sirius B :
Chandra
40 Eri
Faint
Red
White dwarfs : historical remarks
- Fermi-Dirac statistics (Dirac, 1926)
- White dwarfs : gravity is balanced by the pressure of degenerate electrons (Fowler, 1926)
- Relativistic corrections to the EOS (Chandrasekhar, 1930)
It leads to a maximum mass Mmax ~ 1.4 M⊙
- Chandrasekhar 1934 : “the life history of a star of small mass must be essentially different from the
life history of a star of large mass. For a star of small mass the natural white-dwarf stage is an initial
step towards complete extinction. A star of large mass cannot pass into the white-dwarf stage and
one is left speculating on other possibilities.”
- A simple argument in favor of the Chandrasekhar mass MCh (Landau, 1932)
- Correction for general relativity (Kaplan, 1949)
- Realistic EOS (Schatzman 1956,1958 - Harrison & Wheeler 1958)
- Modern questions : stability, cooling, ...
White dwarfs : EOS
Degenerate fermions at T=0, i.e. T << TF
Fermi temperature :
White dwarfs : EOS
Non-relativistic and ultra-relativistic limits :
Shapiro & Teukolsky, chapitre 2
White dwarfs : realistic EOS
Polytropes
Polytropes
γ
n
xmax
(-x2y’)max
Radius and mass
R = 1.122×104 (ρc/106 g.cm-3)-1/6 (μe/2)-5/6 km
5/3
3/2
3.65375
2.71406
M = 0.4964 (ρc/106 g.cm-3)1/2 (μe/2)-5/2 M⊙
= 0.7011 (R/104 km)-3 (μe/2)-5 M⊙
R = 3.347×104 (ρc/106 g.cm-3)-1/3 (μe/2)-2/3 km
4/3
3
6.89685
2.01824
M = 1.457 (μe/2)2 M⊙
Mass / Radius / Central density of white dwarfs
Dashed line : polytropes 5/3 and 4/3
Solid line : E.O.S. of the perfect gas of degenerate electrons at T=0
Observations : the effective temperature
Spectral type :
- as for normal stars with a ‘D’ in front of O, B, A, ...
- 80% of white dwarfs : DA (neutral hydrogen, Balmer lines ; 6 000-30 000 K)
- 20% : DC (no line in the visible ; <11 000 K); DB (HeI; 11 000 - 28 000 K); DO (HeII; 45 000 - 120 000 K).
- Special types with heavy elements (DQ, DZ) : accretion from the ISM ?
Bergeron et al. 1992
Effective temperature :
- Model of the atmosphere of the white dwarf
- Bonus : an estimate of the surface gravity from the shape of Balmer lines
Koester et al 2001 (VLT; UVES)
Observations : the effective temperature
Observations : mass and radius
Mass
- Binaries (Kepler laws)
- Gravitational redshift : Δλ/λ~Ξ
Sirius B : Adams 1925 6.3×10-5 with Hα line
(modern value ~3×10-4 in good agreement with M/R)
- Asteroseismology (stellar pulsations)
Bergeron et al. 1992
Radius
- Parallax : we get L, and then R via Teff
Shapiro & Teukolsky, chapitre 2
Mass - radius
Shapiro & Teukolsky, chapitre 2
Mass - central density
Provencal et al. 1998
Mass - radius (Hipparcos)
Madej et al. 1994
Mass - radius (SDSS)
Madej et al. 1994
Mass distribution of white dwarfs (SDSS)
Shapiro & Teukolsky, chapitre 2
HR diagram
Prada 2002
Cooling of white dwarfs
Salaris et al. 1997
Cooling of white dwarfs