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 MechanismStart here

• Extreme conditions – Tc~8 x 109 K– Density ~ 1013 kg/m3

• Electrons are captured by nuclei and protons produced via photo-disintegration…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 photo-disintegration 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 r-process 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

Producing more massive nuclei that are either stable or unstable against the beta decay reaction

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/Pagel/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/cws/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 main-sequence

White Dwarfs

• http://en.wikipedia.org/wiki/White_dwarf

Classes of White Dwarfs

• DA White Dwarfs:– Pressure broadened Hydrogen

absorption lines in spectrum

– Largest group. About 2/3.

• DB White Dwarfs:– Hydrogen lines absent

– Helium absorption lines

– About 8% of sample

• DC White Dwarfs:– No lines. Only continuum devoid of

features

– About 14%

• DQ White Dwarfs:– Carbon features in spectra

• DZ White Dwarfs:– Evidence of metal lines

Central Conditions in White DwarfsThe 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 carbon-oxygen 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.

• 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

•Successful modeling of pulsating white dwarfs . Predicted DBV stars….

•Hydrogen partial ionization zone DAV•Helium partial ionization zone DB

Pulsating White Dwarfs

The Physics of Degenerate MatterThe Pauli Exclusion Principle and Electron Degeneracy

• What can support a white dwarf against the relentless pull of its own gravity???

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???

Energy Removed from system

Particles are forced into lower energy states

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 EnergyEven at T=0K there are fermions in

excited states.

The motion of these fermions

produces a Pressure.

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 maximum energy of any electron in a completely degenerate gas at T=0K is known as the Fermi Energy.

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!!!!