Cepheid Variable Stars

• Most pulsating variable stars inhabit an instability strip on the H-R diagram.

• The most luminous ones are known as Cepheid variables. Pulsating Variable Stars

• The light curve of this pulsating variable star shows that its brightness alternately rises and falls over a 50-day period. Cepheid variable: Period – Luminosity relation 18. The Bizarre Stellar Graveyard

Now, my suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose.

J. B. S. Haldane (1892 – 1964) from Possible Worlds, 1927 Binding Energy per Nucleon Low mass stars die as Planetary nebula with White Dwarf at center

Ring Nebula

The collapsing core becomes a White Dwarf Thermal Pressure:

Depends on heat content.

Is the main form of pressure in most stars.

Degeneracy Pressure:

Particles can’t be in same state in same place.

Doesn’t depend on heat content. Non-relativistic Electron Degeneracy: White Dwarf Radius vs. Mass White Dwarfs • Degenerate matter obeys different laws of physics. • The more mass the star has, the smaller the star becomes! • increased gravity makes the star denser • greater density increases degeneracy pressure to balance gravity White Dwarfs and Novae

• If WD in close binary: – matter from giant star can "spill over" onto WD – Pressure, temp on WD surface ingnite H fusion • WD suddenly gets 100-10,000 times brighter. Novae

• Though this shell contains a tiny amount

of mass (0.0001 M)… • it can cause the white dwarf to brighten by 10 magnitudes (10,000 times) in a few days. Novae

• Because so little mass is lost during nova, explosion does not disrupt binary system. • Ignition of infalling Hydrogen can recur again with periods ranging from months to thousands of years.

the nova T Pyxidis viewed by Hubble Space Telescope Limit on White Dwarf Mass

• Chandra formulated laws of degenerate matter. – for this he won the Nobel Prize in Physics • Predicted gravity will overcome pressure of electron degeneracy if white dwarf has

mass > 1.4 M – energetic electrons that cause this pressure reach speed of light

Subrahmanyan Chandrasekhar Chandrasekhar Limit (1910-1995) Relativistic Electron Degeneracy: Chandrasekhar Mass White Dwarf Supernovae

• If accretion brings mass of WD above Chandrasekhar limit, electron degeneracy can no longer support star. – WD collapses • Collapse raises core temperature and runaway carbon fusion begins, which ultimately leads to explosion of star. • Such an exploding white dwarf is called a white dwarf supernova. White Dwarf Supernovae • Nova may reach absolute magnitude of –8 (ca. 100,000 Suns)… • White dwarf Supernova reach absolute mag of –19 (ca. 10 billion Suns). – all reach nearly same peak luminosity (abs mag) – white dwarf supernovae make good distance indicators – More luminous than Cepheid variable stars – so can be used to measure out to much greater distances than Cepheids • There are two types of supernova: – white dwarf: no prominent lines of hydrogen seen; white dwarfs thought to be origin. – massive star: contains prominent hydrogen lines; results from explosion of single star. Supernova Light Curves

(Type II)

(Type I) Supernova Explosion

• Core degeneracy pressure goes away because electrons combine with protons, making neutrons and neutrinos.

• Neutrons collapse to the center, forming a neutron star. Neutron Stars • …are the leftover cores from supernova explosions of massive stars

• If the core < 3 M, it will stop collapsing and be held up by neutron degeneracy pressure. • Neutron stars are very dense (1012 g/cm3 )

– 1.5 M with a diameter of 10 to 20 km • They rotate very rapidly: Period = 0.03 to 4 sec 13 • Their magnetic fields are 10 times stronger than Earth’s.

Chandra X-ray image of the neutron star left behind by a supernova observed in A.D. 386. The remnant is known as G11.2-0.3. White Dwarf – Neutron Star – Black Hole Pulsars

• In 1967, graduate student Jocelyn Bell and her advisor Anthony Hewish accidentally discovered a radio source in Vulpecula. • Sharp pulse that recurred every 1.3 sec. • They determined it was 300 pc away. • They called it a pulsar, but what was it? Jocelyn Bell

Light Curve of Jocelyn Bell’s Pulsar Angular Momentum conservation The mystery was solved when a pulsar was discovered in the heart of the Crab Nebula.

The Crab pulsar also pulses in visual light. Pulsars and Neutron Stars • All pulsars are neutron stars, but all neutron stars are not pulsars!! • Synchotron emission --- non-thermal process where light is emitted by charged particles moving close to the speed of light around magnetic fields. • Emission (mostly radio) is concentrated at the magnetic poles and focused into a beam. • Whether we see a pulsar depends on the geometry. – if polar beam sweeps by Earth’s direction once each rotation, the neutron star appears to be a pulsar – if polar beam is always pointing toward or always pointing away from Earth, we do not see a pulsar Pulsars and Neutron Stars

Pulsars are the lighthouses of Galaxy! Rotation Periods of Neutron Stars

• As a neutron star ages, it spins down. • Youngest pulsars have shortest periods. • Sometimes pulsar will suddenly speed up. – This is called a glitch! • There are some pulsars that have periods of several milliseconds. – they tend to be in binaries. Black Holes • After a massive star goes supernova, if the core has a mass > 3 M, the force of gravity will be too strong for even neutron degeneracy to stop. • Star will collapse into oblivion. – GRAVITY FINALLY WINS!! • Makes a black hole. • Star becomes infinitely small – creates a “hole” in spacetime

• >3 M compressed into tiny space => gravity HUGE! • Newton’s Law of Gravity breaks down Schwarzschild Radius of Black Hole • Radius at which escape speed = speed of light

• c = Vesc = Sqrt[2 GM/RBH]

2 • RBH = 2 GM/c = 3 km (M/Msun)

• Nothing (even light)can escape from inside RBH !! Black Holes

• According to Einstein’s Theory of Relativity, gravity is really the warping of spacetime about an object with mass. • This means that even light is affected by gravity. Warping of Space by Gravity

• Gravity curves space. – bends light (even though it has no rest mass) – within “event horizon”, it can not escape

• As matter approaches event horizon… – tidal forces become tremendous – any objects would be streched like spaghetti Warping of Time by Gravity

• In vicinity of black hole, even time slows down. • If we launched a probe to it, as it approached the event horizon: – e.g., it takes 50 min of time on mother ship for 15 min to elapse on probe – from mother ship’s view, probe takes forever to reach event horizon – light from the probe is red-shifted – probe would eventually disappear as light from it is red-shifted beyond radio

• From the probe’s view: – it heads straight into black hole – light from the mother ship is blue-shifted What are the life stages of a high-mass star? How do high-mass stars make the elements necessary for life? Big Bang made 75% H, 25% He; stars make everything else. Insert image, PeriodicTable2.jpg.

Helium fusion can make carbon in low-mass stars. CNO cycle can change carbon into nitrogen and oxygen. Helium Capture

• High core temperatures allow helium to fuse with heavier elements. Helium capture builds carbon into oxygen, neon, magnesium, and other elements. Advanced Nuclear Burning

Insert TCP 6e Figure 17.11b

• Core temperatures in stars with >8MSun allow fusion of elements as heavy as iron. Insert image, PeriodicTable5.jpg

Advanced reactions in stars make elements like Si, S, Ca, Fe. Multiple Shell Burning

• Advanced nuclear burning proceeds in a series of nested shells. Iron is a dead end for fusion because nuclear reactions involving iron do not release energy.

(This is because iron has lowest mass per nuclear particle.) Evidence for helium capture:

Higher abundances of elements with even numbers of protons How does a high-mass star die? Iron builds up in core until degeneracy pressure can no longer resist gravity.

The core then suddenly collapses, creating a supernova explosion. Insert figure, PeriodicTable6.jpg

Energy and neutrons released in supernova explosion enable elements heavier than iron to form, including gold and uranium. Supernova Remnant

• Energy released by the collapse of the core drives the star’s outer layers into space.

• The Crab Nebula is the remnant of the supernova seen in A.D. 1054. Supernova 1987A

Insert TCP 6e Figure 17.18

• The closest supernova in the last four centuries was seen in 1987. Supernovae

Veil Nebula Tycho’s Supernova (X-rays) exploded in 1572 Summary on Stellar remnants

• Minit < 8 Msun => Planetary nebula + – white dwarf with

• MWD < 1. 4Msun

• RWD ~ Rearth

• Minit > 8 Msun => massive-star Supernova – leaving behind either neutron star with:

• 1. 4 Msun < MNS < 3 Msun

• RNS ~ 15 km – or a black hole with:

• MBH > 3 Msun • RBH = 3 km (M/Msun)