Solar Furnaces

Today’s Lecture:

Interiors of Stars (Chapter 12, pages 276-295)• Pre-main sequence stars• How do stars burn their fuel?• Post main-sequence evolution

Pre-main-sequence stars• Relatively slow gravitational contraction, but still no nuclearreactions.• Gravitational energy still being released as the gascompresses.• When the temperature becomes sufficiently high in thecenter (T > 106 K), get nuclear reactions: A STAR IS BORN!• Star settles onto the main sequence and contractionceases. The star’s L and T don’t change much during themain-sequence lifetime.• Nuclear reactions replenish energy lost from the surface,providing stability.• Star is in mechanical balance: hydrostatic equilibrium.

• Hydrostatic balance does NOT require nuclear reactions.It’s just pressure balancing gravity.• But without another energy source the main sequencewould be much shorter (only 30 millions years for our Sun).

Brown Dwarfs: no long-term fusion

• If M < 0.08 Msun, then T is not high enough forsustained nuclear reactions: get a

“BROWN DWARF” (failed star)(But fusion does occur for a short time.)

• It is held up by “degeneracy pressure” (quantummechanical pressure).• Until the mid-1990s, no confirmed brown dwarfs hadbeen found, but now there are over 1000 known.• They glow faintly at infrared wavelengths.

On the main sequence

• In center of a star, the temperature is very high (inthe Sun, T=1.5 x 107 K). Hydrogen atoms are fullyionized, so they’re basically just protons.• Nuclear fusion produces energy.• Basic reaction is 4 1H1 --> 2He4 + energy2 of the protons turned into neutrons + positrons(antielectrons); positrons annihilated with electrons.• 2He4 is more tightly bound (and therefore lessmassive) than 4 1H1, so energy is emitted.

The proton-proton chain (or pp chain)

On the main sequence (cont.)• 0.7% of the mass of 4 1H1 is converted to energy toproduce 2He4 according to Einstein’s E = mc2.• The protons (1H1) can only overcome the electricrepulsion (because they’re all positively charged) ifthey are moving very fast.• This means nuclear fusion requires hightemperatures.(For all you quantum mechanics aficionados, itactually requires “quantum tunneling” to combine theprotons.)• Energy released replenishes energy lost fromsurface, preventing further contraction.

Sun’s Life on the Main Sequence• In the Sun, nearly 700 million tons of protons (hydrogennuclei) are being converted to helium each second!• But there is plenty of raw material:

Sun’s core has about 15% of Sun’s massSun is mostly hydrogen: 70% H, 28% He, 2% heavier stuff

• Sun’s main-sequence life about 10 billion years!• Note that photons take about 105 years just to leak out.• All main sequence stars are fusing H to He, but in starsmore massive than 1.5 Msun, the pp chain is not fastenough. How do we fuse H in this case?

• The CNO cycleburns hydrogen forstars > 1.5Msun.

• Carbon acts as acatalyst. It isneither created nordestroyed whileturning four protonsinto one heliumatom.

Deaths of stars, 0.08Msun<M<8Msun• For 10 billions years the Sun lives happily on the mainsequence.• During this time the Sun is in hydrostatic balance(gravity pulling in is balanced by pressure pushing out).• Energy is lost from the surface, but nuclear reactionsprovide energy to prevent contraction.• But eventually a helium core builds up to 0.1Msun, andthere isn’t enough hydrogen left in the core for appreciableburning.• Contraction begin in core -> heating the star -> hydrogenburning becomes stronger in surface layers.• Star bloats to a huge size: RED GIANT!

Expanding Henvelope

He CoreH-burning

shell

RED GIANTS!

• Contracting He core heats up --> eventually 108 K is reached3 2He4 --> 6C12 + energy (triple-alpha process)

Also 6C12 + 2He4 --> 8O16 + energy• Carbon and oxygen core forms over 106 years.

He-burning shell

H-burning shell

BIGGER RED GIANTS!• Once again, T is too lowfor C/O core fusion, so thecore contracts.• Off-center burningexpands envelope again,creating an even larger RedGiant.• Depending on the mass ofthe star, this process canrepeat, creating heavierelements.

• For stars like our Sun, it becomes unstable and beginsejecting the outer layers: planetary nebula.

CO

Planetary Nebula• Winds from the star createa planetary nebula.• The star is mostly carbonand oxygen inside, with ahelium layer. Most of thehydrogen is being expelled.• An inner core of carbonand oxygen (0.6-0.9Msun) isleft over, held up by“degeneracy pressure.”• This is left over as aWHITE DWARF star.

CO

Expandingshell of gas

White dwarfs• Roughly the size of the Earth with the mass of the Sun!• If you try to pack electrons into the same place they must beat different energy levels (like the energy levels of an atom).Each electron must be at a higher energy than the one before it.• All these energetic electrons in one place give rise to apressure: ELECTRON DEGENERACY PRESSURE• This is weird stuff: one teaspoon of white dwarf weighs 3 tons!If a white dwarf is more massive, it actually has a smallerradius.• No nuclear reactions are taking place, the white dwarf justradiates its heat and continues to cool over time.• White dwarfs are sometimes used as age indicators inglobular clusters.

Types of White Dwarfs• The Sun will become a carbon/oxygen white dwarf with amass of 0.6Msun.• Stars up to 8Msun become carbon/oxygen white dwarfswith masses up to ~1.1Msun.• Stars below 0.45Msun aren’t massive enough to burnhelium in their core and become helium white dwarfs.• Stars with masses from 8-10Msun have an extra stage ofburning in their core and make oxygen/neon/magnesiumwhite dwarfs with masses of ~1.2Msun.• White dwarfs have a mass limit 1.4Msun (theChandrasekhar limit), above which electron degeneracypressure can’t hold up the star.