FOUR FORCES OF NATURE (S4)

1. FOUR FORCES OF NATURE (S4) • In declining order of strength, on nuclear scales we have the fundamental things that hold everything together (or apart): • STRONG (NUCLEAR) FORCE: a range of 10-15m it controls reactions like 3He + 3He 4He + p + p. The STRONG force holds together the nuclei of atoms, even though the protons in them repel each other, via: • ELECTROMAGNETIC FORCE, with infinite range: With q1 and q2the charges, K a constant, and d the distance between them

2. Forces of Nature, 2 3. the WEAK FORCE, also with a range of 10-15 m: it controls reactions like p + p  d + e+ + neutrino. the weak force only acts in reactions that include LEPTONS: These light particles are: electrons (e), positrons (e+ ), neutrinos (), and anti-neutrinos; (There are also muon and tau families of LEPTONS, but we will not worry about them more in this course.) 4. the GRAVITATIONAL FORCE, also with an infinite range:

3. Comparing the Four Forces • If you put two protons (or electrons) 1 cm apart: the STRONG and WEAK forces have no role to play (their ranges are too short), but the ELECTROMAGNETIC and GRAVITATIONAL forces act in opposite directions: • the EM force pushes them apart (like charges repel) while the gravitational force pulls them together (all particles attract all others via gravity). • The EM force is about 1043 times as strong as gravity, so the protons (or electrons) are repelled from each other, not attracted. • Since both forces have infinite ranges and 1/d2 fall-offs, this ratio is true everywhere d >10-15 m. • Inside a nucleus the strong force is about 100 times more powerful than the EM force, which is about 1000 times stronger than the weak force.

4. Gravity vs. Electromagnetism • The EM force does hold together molecules, cells, people and mountains -- it rules the human scale. • BUT gravity dominates to hold together planets, stars, binary systems, galaxies and the universe! How can weaker gravity win out over stronger electricity? • Most objects are electrically neutral -- they have nearly equal numbers of protons (+) and electrons (-) so the net charge is essentially zero. But all particles have "positive" mass, so gravity is always attractive and can't be cancelled. • Small moons like Mars' Phobos and Deimos are irregularly shaped objects the size of cities on earth -- EM still wins over gravity. But big moons like ours are pretty much spherical -- above a few hundred km in radius, gravity wins over EM forces.

5. MAIN SEQUENCE STARS, Red Giants and White Dwarfs Stars are powered by fusion reactions. When a fuel is exhausted the star’s structure changes dramatically, producing Post-Main Sequence Evolution

6. ENERGY GENERATION • Key to all MS stars’ power: • conversion of 4 protons (1H nuclei) into 1 alpha particle (4He nucleus) • with the emission of energy in the form of • gamma-ray photons, • neutrinos, • positrons (or electrons) • and fast moving baryons (protons).

7. Stellar Mass and Fusion • The mass of a main sequence star determines its core pressure and temperature • Stars of higher mass have higher core temperature and more rapid fusion, making those stars both more luminous and shorter-lived • Stars of lower mass have cooler cores and slower fusion rates, giving them smaller luminosities and longer lifetimes

8. Fusion on MS: p-p chain

9. The Proton Proton Chains • The ppI chain is dominant in lower mass stars (like the Sun) • Eq 1) p + p  d + e+ +  • Eq 2) d + p 3He +  • Eq 3) 3He + 3He 4He + p + p • We saw all of these when talking about the Sun --so this is a review. • But at higher temperatures or at later times, particularly for stars which have less metals (mainly CNO) than the sun, and when there is: • more 4He around and • less 1H (or p) left, other reactions are important:

10. ppII chain instead of Eq (3): (4) 3He + 4He 7Be +  (5) 7Be + e-7Li +  (6) 7Li + p 4He + 4He Net effect: 4 p4He This dominates if T>1.6x107K ppIII chain Eqs (1) (2) and (4), but then, in lieu of (5): (7) 7Be + p 8B +  (8) 8B 8Be + e+ +  (this was the first solar neutrino detected) (9) 8Be 4He + 4He Net effect: 4 p 4He This dominates if T>2.5x107K Other pp-chains: Eqns (1) & (2) always there

11. Balancing Nuclear Reactions • Balance baryons (protons+neutrons) • Balance charge (protons and positrons vs electrons) • Balance lepton number (electrons and neutrinos vs positrons and anti-neutrinos) • Balance energy and momentum (with photons if only one particle on the right hand side)

12. Alternative Nuclear Reactions:The CNO Bi-Cycle • This is a complicated network of reactions involving isotopes of Carbon, Nitrogen and Oxygen (and Fluorine) that eventually adds 4 protons to a C or O nucleus which finally also gives off an alpha particle. • BUT IT STILL YIELDS THE SAME NET REACTION: • 4 protons  1 4He nucleus, plus energy • Here 12C or 16O acts like a catalyst in chemical reactions • The CNO bi-cycle dominates energy production in: -Pop I stars (i.e., those with compositions similar to the Sun's -- roughly 2% "metals") -which are also more massive than about 1.5 M -i.e., O, B, A, F0-F5 spectral classes.

13. CNO Cycle vs p-p Chain

14. Hydrostatic Equilibrium on MS

15. Sources of Pressure • Hydrostatic equilibrium holds on the MS: • that is to say, pressure balances gravity, essentially perfectly, at every point inside the star. • Most stars, those up to 10 M, are mainly supported by THERMAL or GAS PRESSURE: • Pgas T, with  the density and T the temperature. • RADIATION PRESSURE is very important in the most massive, hottest stars • (above about 10 M): • Prad T4

16. Energy Transport • The internal structures of stars depend upon their masses and the temperatures go up for higher mass stars. • This means different energy transport mechanisms dominate in different parts of different stars. • For stars < 0.5 M(M stars) the entire star is convective. • For stars like the sun (between 0.5 and 2 M) the interior is radiative and the outer layer is convective. • For stars between 2 and 5 Mthere is a complex structure: convective core, radiative middle zone, convective envelope. • Stars more massive than 5 Mare convective at the centers and radiative in their envelopes.

17. X-rays and Mass Loss on MS • Stellar chromospheres and coronae are produced in low mass stars by the convective outer layers; these can yield X-rays. • Hot stars can also produce X-rays from powerful winds, driven by very strong radiation pressure in their outer layers. • Stars of above 20 M lose appreciable fractions of their masses during their short life times. • The winds of these massive stars are driven by radiation pressure; • winds of lower mass stars are driven by energy from their convective outer layers.

18. On the MS Things Change SLOWLY • Fusion depletes H and increases He, mainly in the core • Only slight adjustments in temperature, density and pressure are required to retain hydrostatic equilibrium for millions, billions or trillions of years

19. Hydrostatic Equilibrium at Different Times: Pressure & Gravity Adjust

20. STELLAR LIFETIMES • The amount of fuel is proportional to the star's mass, so you might think more massive stars live longer. • BUT the rate at which it is burned is proportional to the star's luminosity. • AND more massive stars are hotter in the core, meaning their nuclear reactions go much faster and they are more luminous. • This explains the MASS-LUMINOSITY relation for MS stars. Specifically we have, as you will • RECALL: L  M3.5 --- on the MS (only). • So the lifetime, t  (amount of fuel / burn rate) • Main Sequence Lifetime Applet

21. Lifetimes in Math That’s  the proportionality. As an equation  Example: you know the Sun lives 1.0x1010yr, so how long does a 5 M star live? So a 5M star lives less than 200 million years!