WHITE DWARFS AND

CATACLYSMIC

VARIABLESEvan Bray

Astro 550

Outline

• Basic nature of white dwarfs

• Evolution of white dwarfs and age indicators

• Simple & advanced computational models

• Variable white dwarfs

• Formation and evolution of cataclysmic variables

Introduction

• White dwarfs are the final evolutionary stage of 97% of

stars

• Populations of white dwarfs give information about their

host systems

• Direct relation between cooling time and age

• Requires solid understanding of evolution

• >10,000 identified today with known 𝑇eff and log 𝑔

Introduction

• Many white dwarfs are undergoing pulsations

• Possible probes of structure?

• Potential applications have led to renewed interest in full

evolutionary models

• C/O core

• He-rich envelope of ~0.01 M⊙ at most

• H-rich atmosphere of ≤ 10−4 M⊙

• Thin outer layers control radiation

Introduction

• First discovered in 1914

• Independent test of high densities first done in 1925

• With the method of gravitational redshift on Sirius B

• Concluded ρ ~ 104 𝑔/𝑐𝑚3

• ρ ~ 106 𝑔/𝑐𝑚3

• R ∝ M-α

• Surface gravity ~4 orders or magnitudes higher than solar

Madej et al. 2004

Harris et al. 2006

Classification Schemes

• Similarly to main sequence, named for spectral features

• DA – Strong Balmer lines.

• DO – Strong He II lines.

• DB – Strong He I lines.

• DC – Very cool, few spectral features

• DQ - Molecular/atomic features of carbon

• DAZ, DBZ, DZ – Limited traces of metals

• PG 1159 – hot carbon-rich atmosphere

Te

mp

era

ture

Helium rich

Mixed

Hydrogen rich

Carbon

Evolution of a DO Dwarf

• Complex evolution between spectral types, as a function of

temperature.

• He II features disappear as He+ recombines into neutral helium

DO DB45,000 K

Evolution of a DO Dwarf

• Complex evolution between spectral types, as a function of

temperature.

• Fast gravitational settling (<108 years) means He has sunk

to the core

Evan Bray

DO DB30,000 K

DA

Evolution of a DO Dwarf

• Complex evolution between spectral types, as a function of

temperature.

• Convection begins to mix helium back up in the atmosphere.

• When T = ~11000 K, #DA ≈ #DB

Evan Bray

DO DB

30,000 – 11,000 K

DA DA/DB

Evolution of a DO Dwarf

• Complex evolution between spectral types, as a function of

temperature.

• Recall: DC -> Very cool, few spectral features

Evan Bray

DO DB5,000 K

DA DA/DB DC

Evolution of a DO Dwarf

• Complex evolution between spectral types, as a function of

temperature.

• At even cooler temperatures, Carbon gets dredged up from

the core.

• Other feature of cool dwarfs include Ca, Si, Na, Mg, Fe

Evan Bray

DO DB<5,000 K

DA DA/DB DC DQ/DAZ/DBZ/DZ

Zero Temperature Approximation

• Degenerate electrons => Fermi-Dirac distribution

• Chemical potential ≫ thermal energy

• Luminosity provided by thermal radiation

• In the limit of 𝜌 → ∞,𝑀 → 5.8/𝜇𝑒2

Improvements to Zero Temperature Model

• Must treat thermal and hydrostatic evolution together

• Thermal energy is not the only source of luminosity

• Dwarf cores are not isothermal

• Chemical composition changes with time

• Lets explore the findings of more advanced modeling

techniques….

Other Sources of Dwarf Luminosity

• Neutrino radiation

• Main cooling mechanism of young, hot dwarfs

• Gravitational contraction

• Young dwarfs can be 2x larger than the zero temperature radius

• Increases e- Fermi energy, adjusts dwarf structure

• Nuclear fusion

• Small, non-negligible contribution

• Tied to mass-loss history of progenitor in AGB phase

• Crystallization

• Cores of old dwarfs crystallizes, releasing latent heat

Variable White Dwarfs

• Study of stellar interiors through asteroseismology

• Pulsation frequencies provide information on:• Gravity

• Effective temperature

• Stellar mass

• Rotation profile

• Chemical composition

• Magnetic fields

• Convective zones

• Appear as optical and FUV variations of ≤0.3 magnitudes

DAVs (ZZ Ceti Stars)

• 10,500 K ≤ T ≤ 12,500 K

• 100 s ≤ P ≤ 1,200 s

• H-rich atmospheres

• Mean 𝑀𝐻

𝑀∗= 5 × 10−7

• Cooler stars contain more frequencies => richer

information

• Computational models study effects of diffusion of

elements at shell boundaries

DBVs (V777 Her stars)

• T ~ 25,000 K

• 100 s ≤ P ≤ 1,100 s

• He-rich atmosphere

• “Purity” of the instability strip?

• Even the smallest H abundance significantly affects

pulsations

GW Vir stars (variable PG 1159)

• 20,000 K ≤ T ≤ 35,000 K

• 300 s ≤ P ≤ 3,000 s

• Constrains mixing of layers in AGB

• Higher than usual mass-loss prevents gravitational

settling

• Direct relationship between period and mass

• Very little dependence on exact atmosphere abundances

Cataclysmic Variable Stars

Cataclysmic Variable Stars

• Typical rise time of ~1 day, followed by ~10 day decay

• Can increase by 3-5 magnitudes

• Most tend to be very close => little extinction

• Difficult to categorize until advent of UV/X-Ray astronomy

• Presence of either hard/soft portions of X-Ray spectra

• Allows the most detailed observation of accretion physics

• Broken down into Polars and Intermediate Polars

Example Light Curve

Seward & Charles 2010

Marsh 2001

Dwarf Nova Outbursts

• Mass-transfer model

• Variable rate at which mass is transferred from companion

• Don’t observe changes in the bright spot of accretion disk!

• Disc-instability model

• Sudden changes in disk structure

• Accretion disk dumps mass periodically onto dwarf

• Observed as differences in hardness of X-Ray spectra

Formation of CVs

• Wide binaries form in large star-forming

regions

• Higher mass star engulfs smaller star during

the red giant branch

• Exterior envelope lost to conserve angular

momentum

Seward & Charles 2010

Seward & Charles 2010

Evolution to Short Periods

• “Magnetic braking” causes orbital period to slowly

decrease

• At P ~ 3 hours, this mechanism shuts off

• Interference by dwarf magnetosphere?

• Donor star shrinks => mass transfer stops

• Gravitational radiation begins to dominate

• Mass transfer picks up again at P ~ 2 hours

Polars (AM Her systems)

• Strong magnetic fields

• 𝑃𝑟𝑜𝑡 = 𝑃𝑜𝑟𝑏

• First detected by Uhuru

• Accretion stream threaded onto magnetic field

• Emits hard/soft X-Rays at shock front, and cyclotron

radiation

• Emissions highly dependent on viewing angle!

Seward & Charles 2010

Intermediate Polars

• Slightly weaker magnetic fields

• 𝑃𝑟𝑜𝑡 > 𝑃𝑜𝑟𝑏• 30 s < 𝑃𝑟𝑜𝑡 < 1 hour

• Disk forms, matter threads onto magnetic field at small R

• Creates “curtain” around central dwarf

• Accretion happens over larger surface area

• => Fewer soft X-Rays

Watson 1985

Summary

• White dwarfs are reliable cosmic clocks and high density

laboratories

• Simple structures and evolutions

• Provides info about star-formation history and AGB evolution

• Pulsations make wonderful probes of stellar interior

• CVs are interacting binaries with many similarities to other

astrophysical objects

• Far more numerous than higher mass X-Ray binaries

• Accretion disk physics can be applied to far more energetic systems