The Fate of Massive Stars
• Core-Collapse
Supernovae
• Gamma Ray Bursts
• Cosmic Rays
Midterm 2 Computer problem
Choose m=2.0 instead of m=3.0 if you like on problem 6.0
Core Collapse Supernova Mechanism
Start here
•
•
•
Extreme conditions
– Tc~8 x 109 K
– Density ~ 1013 kg/m3
Electrons are captured by nuclei and
protons produced via photodisintegration…Electron Degeneracy
pressure greatly reduced
Energy loss by neutrinos produced in
reactions such as
•
Neutrino luminosity ~ 3.1 x 10 38 W (photon
luminosity ~ 4.4 x 1031 W for 20 M)
•
Most of the core’s support in the form of
electron degeneracy pressure is suddenly
gone….the “floor drops out”!!!
•Core begins to collapse extremely
rapidly
•In the inner portion of the core the
collpase is homologous and the
velocity of the collapse is proportional
to the distance away from the center
•At the radius where the velocity
excceeds the local sound speed the
inner core decouples from the now
supersonic outer core
•The outer core is left behind and
nearly in free-fall
•Speeds can reach almost 70,000
km/s in the outer core
•Within about one second a volume
about the size of the earth has
collapsed down to a radius of 50 km!!!!
Core Collapse Supernova Mechanism
•
•
•
•
•
•
•
•
•
Homologous collapse of inner core continues until
density exceeds about 8 x 10 17 kg/m3 (roughly 3
times the density of an tomic nucleus !!!!)
The nuclear material that makes up the inner core
stiffens because the strong force (normally atractive)
suddenly becomes “repulsive” as a a consequence
of the Pauli exclusion principle.
The inner core rebounds as a result sending
pressure waves outward into the infalling material
from the outer core. Shock waves move outward
when the wave velocity exceeds the sound speed
As the shock wave encounters the outer falling iron
core. The high temperatures induce further photodisintegration robbing the shock of most of its energy
(for every 0.1 M of Iron --> shock loses 1.7 x 10 44
J.
Shock stalls becoming nearly stationary (accretion
shock)
A neutrinosphere develops below the shock.
Neutrinos produced from photo-disintegration and
electron capture
Overlying material is so dense that not even
neutrinos can easily escape---> Neutrino heating just
behind the shock!!!
This allows the shock to resume its march towards
the surface….If this does not happen quickly enough
the initially outflowing material will fall back to the
core …no explosion!!!
Complicated modeling business….
•Assuming this model is correct..
•The shock will drive the envelope
and the remaining nuclear processed
material in front of it…
•The total kinetic energy in the
expanding material is ~ 1044 J
•When the material becomes optically
thin at a radius of about 100AU …a
tremendous optical display
results!!!!…1042 J in photons
•A peak luminosity of 1036 W (109 L)
Core Collapse Supernova Mechanism
Core Collapse Supernova Mechanism
Stellar Remnants of a Core-Collpase Supernova
•
Neutron Star:
– Initial ZAMS mass < 25 M
– Supported by neutron
degeneracy pressure
•
Black-hole
– Initial ZAMS mass > 25 M
– Neutron degeneracy pressure is
not sufficient
Light Curves and the Radioactive Decay of the
Ejecta
•
Light curve is partially explained by
radioactive decay of radioactive
isotopes produced during supernova
explosion!!!!
Supernova 1987a
The Detection of Neutrinos from SN 1987A
•
•
•
•
•
Burst of Neutrinos detected at
several neutrino detectors on Feb 23
1987
Time span of about 12.5 seconds
about 3 hours before the arrival of
photons
Confirmation of core collapse model
of supernovae!!!!
Upper limit on neutrino mass of 16eV
Still searching for other signs of
compact object
Chemical Abundance Ratio of the Universe
• Supernovae explosions
deposit vast quantities of
material that has been
“cooked” in the “bowels”
of stars…
• Can check stellar models
against observed
abundance of elements
• Core collapse supernovae
are responsible for the
significant quantities of
Oxygen in the universe
• Production of heavier
elements occur via rprocess nucleosynthesis
during supernova
events!!!!
S-process and r-process nucleosynthesis
Easier for neutrons to react with high-Z nuclei due to lack of Coulomb repulsion
nuclear reactions with neutrons can proceed at low temperatures
X +n ®
X +g
A
A+1
Z
Z
Producing more massive nuclei that are either stable or unstable against the beta
decay reaction
A+1
Z
A+1
X ® Z+1
X + e- + n e + g
If beta decay half-life is short compared to timescale for neutron capture
This reaction process is called s-process reaction (for slow process)
If beta decay half-life is LONG compared to timescale for neutron capture
This results in neutron-rich nuclei through the r-process…need a supernova !!!
Origin of the elements
•
Need Supenovae for the production
of elements beyond iron
•
http://www.cosmic-origins.org/
•
http://ned.ipac.caltech.edu/level5/Pa
gel/Pagel1_2.html
Gamma Ray Bursts
• First observed by Vela
military satellites in the
1960’s. These satellites
were looking for gamma
rays produced in
terrestrial thermonuclear
explosions!!!
• By 1967 it was clear that
bursts of gamma rays
were being produced from
above!!!
• About once per
day…durations from 10
ms to 1000s
• Where are they from?
Gamma Ray Bursts
Distribution of GRB sources
Distribution of GRB sources
Two Classes of GRB
•
Long-soft
– Correlated with core-collapse
supernovae
•
Short-hard
– Neutron star mergers
Gamma Ray Bursts
Gamma Ray Bursts (short duration)
Gamma Ray Bursts (short duration)
Gamma Ray Bursts (long duration)
•
•
•
•
Peculiar supernova
explosions of massive stars.
Generated by a central
engine that is likely to be a
newborn black hole at the
heart of the dying star
Supernovae are all of
spectral type Ibc
core-collapse supernovae
http://cerncourier.com/cw
s/article/cern/41720
GRB models
http://www.astro.caltech.edu/palomar/exhibits/grb/short02.htm
Cosmic Rays
•
•
•
Cosmic rays of energies up to about
1015 eV are believed to be produced
in Supernova explosions
Fermi-theory of shock acceleration
Magnetic confinement of charged
particles …Larmor Radius
The Degenerate Remnants of Massive Stars I
•
•
•
The Discovery of Sirius B
White Dwarfs
The Physics of Degenerate Matter
The Discovery of Sirius B
•
Bessel noted that the path of Sirius
did not follow a straight line through
space…
•
He concluded that Sirius must be in
a Binary star system with an orbital
period of 50 years
Alvin Clark later “discovered” Sirius
B using his father’s new 18 inch
refractor in 1862
Properties
– LA=23.5 L
LB=0.03 L
– TA=9910K
TB=27,000K
– MA=2.3 L
MB=1.05 L
•
•
•Temperature and Luminosity of B
RB=0.008 R
•Sirius B is smaller than Earth with the
mass of the Sun!!!!
•Average density ~ 3.0 x 109 kg/m3
•Surface gravity ~ 4.6 x 106 m/s2
White Dwarfs
•
•
•
•
Class of Star that has approximately the
mass of the Sun in a size of the Earth
Actually come in all colors Temperatures
range from less than 5000K to more than
80,000K
Complete sample difficult to obtain
Occupy a region of the H-R diagram that
is roughly parallel to and below the mainsequence
White Dwarfs
•
http://en.wikipedia.org/wiki/White_dwarf
Classes of White Dwarfs
•
DA White Dwarfs:
–
–
•
DB White Dwarfs:
–
–
–
•
–
No lines. Only continuum devoid of
features
About 14%
DQ White Dwarfs:
–
•
Hydrogen lines absent
Helium absorption lines
About 8% of sample
DC White Dwarfs:
–
•
Pressure broadened Hydrogen
absorption lines in spectrum
Largest group. About 2/3.
Carbon features in spectra
DZ White Dwarfs:
–
Evidence of metal lines
Central Conditions in White Dwarfs
The birth of White Dwarfs
•
Central Pressure
About 1 million x > Sun
•
Central Temperature
•White Dwarfs are “manufactured” in
the cores of low-intermediate mass (<
8-9 M) near the ends of their lives on
the Asymptotic Giant Branch.
•Most white dwarfs consist completely
of ionized carbon and oxygen nuclei,
because any star with a helium core
mass M>0.5 M will undergo fusion.
•As the aging giant star expels its
surface layers, the core is exposed as
a white dwarf progenitor
•Hydrogen not present in appreciable
amounts below the surface layers of
white dwarf.
•Material at center must be incapable
of fusion at these densities and
temperatures
Spectra and Surface Composition
•
Exceptionally strong pull of the white
Dwarf’s gravity
•
Pull heavier nuclei below the surface
•
Vertical Stratification of Nuclei (in
about 100 years!!)
A thin layer of hydrogen rests on a
layer of helium on top of a carbonoxygen core.
•
•Explains hydrogen line spectrum of
DA white dwarfs
•Non-DA white dwarfs possibly
explained by either
•No hydrogen left to form a
surface layer
•Convective mixing between
helium and hydrogen layers
Pulsating White Dwarfs
•
White Dwarfs of T~12,000K lie within
the instability strip of the H-R
diagram.
•Successful modeling of pulsating white
dwarfs . Predicted DBV stars….
•Hydrogen partial ionization zone  DAV
•Helium partial ionization zone  DB
•
•
•
•
•
Pulsate with periods between 100
and 1000 s.
ZZ Ceti variable stars. Also known as
DAV or variable DA white dwarfs
The pulsation periods correspond to
non-radial g-modes that resonate
within the white dwarf’s surface
layers of hydrogen and helium.
Horizontal displacements --> little
change in radius.
Brightness variations (few tenths of
magnitude) due to temperature
variation
Pulsating White Dwarfs
The Physics of Degenerate Matter
The Pauli Exclusion Principle and Electron Degeneracy
•
What can support a white dwarf
against the relentless pull of its
own gravity???
Energy Removed from system
Particles are forced into lower energy
states
Electron Degeneracy Pressure
•
•
•
Pauli Exclusion Principle allows at
most one fermion in each quantum
state.
In a gas at STP only one of every
107 quantum states is occupied.
Pauli Exclusion Principle is
insignificant in this case.
What happens when T--> 0K???
Only one Fermion allowed in each
quantum state
All of the Particles can not crowd into
ground state
Fermions will fill up the lowest
available unoccupied state
The Fermi Energy
Even at T=0K there are fermions in
excited states.
The motion of these fermions
produces a Pressure.
The maximum energy of any electron
in a completely degenerate gas at
T=0K is known as the Fermi Energy.
At T=0K all of the lower energy states and none
of the higher energy states are occupied
Such a Fermion gas is said to be completely
degenerate
The Fermi Energy
The Fermi Energy
The Condition for Degeneracy
The Condition for Degeneracy
Degeneracy in the Sun’s Center as it Evolves
Electron Degeneracy Pressure
•
Estimate The Electron Degeneracy
Pressure by using two key ideas
– The Pauli Exclusion Principle
– Heisenberg’s Uncertainty
Principle
•
Making the unrealistic assumption
that all of the electrons have the
same momentum
•
In a completely degenerate electron
gas, the electrons are packed as
tightly as possible
For a uniform number density the
separation between neighboring
electrons is ne-1/3
•
Pauli exclusion principle
Electrons must maintain their identity as
separate particles. That means the
uncertainty in their positions can not be
larger than their separation, I.e
Electron Degeneracy Pressure
Electron Degeneracy Pressure
Electron Degeneracy Pressure is responsible for
maintaining hydrostatic equilibrium in a white
dwarf!!!!