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The Physics of Crystallization in
a Dense Coulomb Plasma from
Globular Cluster
White Dwarf Stars
Don Winget
Department of Astronomy and McDonald Observatory
University of Texas
and
Department of Physcis UFRGS Brasil
S.O. Kepler, Pierre Bergeron, Mike Montgomery,
Fabi Campos, Leo Girardi, Kurtis Williams
OUTLINE
I.
Historical & Astrophysical Context
Quantum mechanics, cosmochronology and the
equation of state (EoS) of matter
II. What We Can Learn From the Disk
Obstacles remain, even after 20 years
III. White Dwarf Physics from Globular Clusters
Overcoming obstacles with globular clusters
OUTLINE
I.
Historical & Astrophysical Context
Quantum mechanics, cosmochronology and the
equation of state (EoS) of matter
II. What We Can Learn From the Disk
Obstacles remain, even after 20 years
III. White Dwarf Physics from Globular Clusters
Overcoming obstacles with globular clusters
White Dwarf Stars: Eddington’s
“Impossible” Star
•1844: Bessel notices “wobble” in Sirius’ position
•1862: Alvan Clark directly observes a faint companion
Sirius B
White Dwarf Stars: Eddington’s
“Impossible” Star
•Dark companion is hot and compact, roughly the size
of Earth and the mass of the Sun
•Interior, even if made of the smallest atoms, must be
ionized
•“ … to cool the star must expand and do work against
gravity …” Eddington.
•Heisenberg uncertainty principle and Pauli exclustion
principle to the rescue – Fowler 1926
•Chandrasekhar (1931) limit
•Mestel (1952) Theory: develops understanding of
decoupled mechanical and thermal properties:
ions  electrons
White Dwarf Flavors
White Dwarf Stars:
•Endpoint of evolution for most stars
•Homogeneous
–Narrow mass distribution
–Chemically pure layers
•Uncomplicated
–Structure
–Composition
–Evolution dominated by cooling:
(oldest=coldest)
They Shed Their Complexity!
… and why are they interesting?
• Representative (and personal)
– 98% of all stars, including our sun, will become one
– Archeological history of star formation in our galaxy
=> White Dwarf Cosmochronology
• A way to find Solar Systems dynamically like ours
• Exploration of Extreme physics
– Matter at extreme densities and temperatures
• 60% of the mass of the Sun compressed into star
the size of the Earth
– Chance to study important and exotic physical processes:
plasmon neutrinos, search for dark matter in the form of axions ,
and study the physics of crystallization …
White Dwarf Cosmoshronology
•Observations: finding the
coolest white dwarf stars in a
population
–Thin disk
–Open clusters
–Thick disk
–Halo
Calculate the ages of the coolest white
dwarf stars:
White dwarf cosmochronology
• Critical theoretical uncertainties for
dating the coolest WDs
– Outer layers
• Convection, degeneracy, and radiative opacity
control throttle
– Interiors
• Neutrino emission in the hot stars
• Crystallization and phase separation in coolest
• Compare with observed distribution, and
repeat the cycle…
Hot pre-white dwarf
model
cool white dwarf
model
Various physical
processes
thought to occur
in WDs as they
cool
The DB
“Gap”
OUTLINE
I.
Historical & Astrophysical Context
Quantum mechanics, cosmochronology and the
equation of state (EoS) of matter
II. What We Can Learn From the Disk
Obstacles remain, even after 20 years
III. White Dwarf Physics from Globular Clusters
Overcoming obstacles with globular clusters
The Disk Luminosity Function
Fontaine, Brassard, & Bergeron (2001)
DeGennaro et al. (2008) Disk LF
3358 new SDSS WDs (with spectra)
shows
the
lower
portion
of
Going
after the
cool WDs:left
Mukremin
Kilic ….
the reduced proper motion
diagram from SDSS Data
Release 2.
HET Spectra of Cool White Dwarf Stars
The Disk vs M4: Globular clusters are
older than the disk ….
Hansen & Liebert (2003)
OUTLINE
I.
Historical & Astrophysical Context
Quantum mechanics, cosmochronology and the
equation of state (EoS) of matter
II. What We Can Learn From the Disk
Obstacles remain, even after 20 years
III. White Dwarf Physics from Globular Clusters
Overcoming obstacles with globular clusters
White Dwarf Stars in Clusters
• Explore white dwarf cooling ages as
compared to main sequence isochrone ages
• Open clusters help in establishing
constraints on disk age
• Older open clusters sample critical physics
of white dwarf cooling
• Minimize problems with birthrates
• Globular Clusters: Finally, we can isolate
masses and explore the physics!
NGC 6397
NGC 6397 with HST AC
Comparing
Theoretical
models:
new(er)
opacities,
interior EOS and
atmospheric
boundary
conditions
Hansen & Liebert
(2003)
Fontaine 2001 models and Winget et al. 2008 models
0.5 Msun
Conclusions from model comparisons
• Mass – radius is consistent for all groups
– EoS improvements ( Chabrier et al. 2000 over Lamb
& Van Horn 1975 for interiors and Saumon
Chabrier & Van Horn 1993 over Fontaine , Graboske
& Van Horn 1977 for the envelope) do not produce
(presently) observable differences in the models.
– Improved atmospheric surface boundary condition
is not as important as has been claimed in the
literature … it produces no observable differences
until bolometric luminosities below the largest
magnitude globular cluster stars
HST
Observations
Hansen et al.
2007
point sources
only
Fixing the WD
evolutionary
tracks in the
CMD by
simultaneously
fitting the
main sequence
and the WDs
gives Z, (m-M)
and E
Data: proper motion screened sample from Richer et al. 2008, AJ, 135,2131
What advantages do we have
over the disk population?
• The cooling sequences are “pinned” to the CMD by the main
sequence and white dwarfs fitted together – sliding is not allowed.
• If we ignore the observational errors, the CMD location of a star
uniquely determines its mass and radius: setting the mechanical
properties of the white dwarf determined independently of the
thermal.
• The mass range is very narrow.
• Ages provide some independent information … The terminus
white dwarfs aren’t as old as you think!
Oops … the CIA hook is in the wrong place!
Luminosity Function for NGC 6397 proper motion screened WD sample
Richer et al. 2008 (proper motion)
Hansen et. Al. 2007
Richer et al. 2008 completeness
What physics might be relevant near
the peak of theLuminosity Function
(the “clump” in the CMD)?
• Convective Coupling: The surface convection
zone reaches the degeneracy boundary,
reducing the insulation of the envelope
• Crystallization: Ions crystallize with attendant
latent heat and phase separation expected
from theory
Fontaine, Brassard & Bergeron (2001)
Crystallization Visuallization
a cartoon by M.H. Montgomery
Ratio of Coulomb Energy to Ion
Thermal Energy
What is the expected value of Gamma at crystallization?
(OCP)
= 176 (Potekhin & Chabrier 2000, DeWitt et al.
2001, Horowitz, Berry & Brown 2007)
(MIX)= 230 - 260 (Horowitz, Berry & Brown 2007)
This is at the frontier of (brute force) molecular dynamics
Ratio of Coulomb Energy to Ion
Thermal Energy
What is the value of Gamma at and near the “clump” in
the observed CMD, or equivalently, the value of Gamma
at and before (rise) the peak of the Luminosity
Function?
log rho = 6.32 log T = 6.40
… nearly independent of composition!
(peak) = 194 (carbon) = 313 (oxygen)
(rise) = 182 (carbon) = 291 (oxygen)
Richer et al. 2008 completeness
Conclusions from NGC 6397
•
•
•
•
Confirm that crystallization occurs
Confirm that Debye cooling occurs
We can measure the Gamma of crystallization
Low metallicity clusters may not produce
significant O in cores of some of the 0.5Msun
stars … or Brown and collaborators are right
and Gamma = 230 - 260
• We find the first empirical evidence that Van
Horn’s 1968 prediction is correct:
Crystallization is a first order phase transition
The End
Thank you