White Dwarfs PHYS390 Astrophysics Professor Lee Carkner Lecture 17

Compact Objects   Their cores become compact objects   Neutron star  Black hole   Physically small and thus low luminosity  Can be responsible for bright outburst phenomena due to mass transfer

Sirius B  In 1844 Bessel determines Sirius is a 50 year binary via astrometry   In 1862 Alvan G. Clark finds Sirius B in a telescope test   In 1915 Walter Adams uses spectroscopy to get a surface temperature for Sirius B of K  Three times hotter than Sirius A

White Dwarf Properties  Mass ~  Luminosity ~ 0.03 L sun  Radius ~  Density ~ 3X10 9 kg/m 3  surface gravity ~ 5X10 6 m/s 2

Observing White Dwarfs  Spectra show strong pressure broadened H lines   Also produce very low energy X-rays

Classification  About 2/3 of white dwarfs are in the DA class   Strong gravity creates a density gradient   Only thin surface layer of H can exist   Other white dwarfs show no H lines or no lines at all  Stripped of H in giant phase?

Fermi Energy  A gas where all of the low energy states are filled is called degenerate   The maximum energy of a degenerate electron is called the Fermi energy (E F ) E F = (h 2 /8  2 m e )(3  2 n) 2/3  Where n is the number density of electrons

Degeneracy  The degree of degeneracy depends on temperature and density  T/  2/3 < 1261 K m 2 kg -2/3  The smaller the value of T/  2/3 the more degenerate the gas

Pressure  P = ((3  2 ) 2/3 /5)(h 2 /4  2 m e )[(Z/A)(  /m H )] 5/3  where Z is the number of protons and A is the number of nucleons (~0.5 for white dwarfs)   For relativistic electrons: P = ((3  2) 1/3 /4)(hc/2  )[(Z/A)(  /m H )] 4/3

Mass-Volume Relation   We find that Mass X Volume = constant   In order the support a greater mass, we need more electron degeneracy pressure which requires a greater density

Chandrasekhar Limit  As the radius goes to zero the mass goes to a maximum   Mass greater than Chandrasekhar limit cannot be supported by electron degeneracy

White Dwarf Binaries   If the second star is not a compact object and is close enough, it will transfer mass onto the white dwarf   Can produce an accretion disk and variability  Generally referred to as novae or cataclysmic variables

Dwarf Novae  Quiescent for months then get brighter for a week or two   Caused by an increase in mass flow through the accretion disk   Friction in the disk causes the disk to heat up   Dwarf novae are periodic, reoccurring every few months

Classical Novae  Very large brightness increase over a few days   Caused by build up of hydrogen on the surface of the white dwarf   The luminosity quickly exceeds the Eddington limit   Takes thousands of years to build back up

Type Ia Supernova  If enough mass falls onto a white dwarf that it exceeds the Chandrasekhar limit, it will collapse violently   Very bright (M=-19.3) with brightness well correlated to light curve 

Next Time  Read , 17.3  Homework: 16.10, 16.12, 16.14, 17.12