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: Start here on 10/8 With q1 and q2 the charges, K a constant, and d the distance between them

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:

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.

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.

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

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).

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

Fusion on MS: p-p chain

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: Starte here on 10/23

Other pp-chains: Eqns (1) & (2) always there 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

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)

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.

CNO Cycle vs p-p Chain

Hydrostatic Equilibrium on MS

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

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.

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.

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

Hydrostatic Equilibrium at Different Times: Pressure & Gravity Adjust

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

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!