FOUR FORCES OF NATURE (S4)

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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 q2 the charges, K a constant, and d
the distance between them
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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

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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
  gt10-15 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.

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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.

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MAIN SEQUENCE STARS, Red Giants and White Dwarfs

• Stars are powered by fusion reactions.
• When a fuel is exhausted the stars structure
  changes dramatically, producing
• Post-Main Sequence Evolution

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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).

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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

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Fusion on MS p-p chain
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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

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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 Tgt1.6x107K

• 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 Tgt2.5x107K

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Balancing Nuclear Reactions

• Balance baryons (protonsneutrons)
• 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)

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NEUTRINOS FROM STARSExtra Material Review from
Ch. 14

• NEUTRINOS (or ghost particles) are of very low
  mass (long thought to be zero)
• and are electrically neutral (neutrinolittle
  neutral one)
• They barely interact with matter trillions pass
  through your body every minute, but maybe only
  one reacts with you in your whole lifetime!
• The first experiment to detect neutrinos from the
  Sun was led by Raymond Davis (co-winner of 2002
  Nobel Prize in Physics) using a large tank of
  cleaning fluid deep in the Homestake Silver Mine
  in South Dakota.
• The neutrinos would occasionally react with a
  Chlorine nucleus to make an Argon nucleus that
  could be pumped out of the tank and whose
  radioactive decay could be measured.

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The Solar Neutrino Problem

• That first experiment was sensitive only to the
  high energy Boron-8 neutrino (Eq 8)
• They found only about 1/3 of the predicted rate.
• All tests of the experiment showed it was good
  and so models for a different type of Sun with a
  cooler core (and thus fewer neutrinos) were
  proposed.
• Later experiments (Kamiokande, GALEX, SAGE, SNO)
  were sensitive to the other, more numerous,
  neutrinos including (Eq 1).
• All experiments agreed that the detected
  neutrinos were fewer than predicted
• Were solar models very wrong? Too hot? Fast core
  rotation? Strong magnetic pressure?

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Solution Neutrinos have Mass

• It is very small, but not zero
• Then some of the ELECTRON NEUTRINOS (produced in
  all the reactions above) are converted to other
  "flavors" of neutrinos muon neutrinos or tau
  neutrinos.
• Direct measurements in the late 1990's showed
  neutrinos do indeed have tiny masses --
• but despite their huge number, they contribute
  not too much matter to the total in the universe
• since their masses are less than 0.00001 of that
  of an electron (the lightest regular particle).
• END OF EXTRA MATERIAL

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Alternative Nuclear ReactionsThe 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.

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CNO Cycle vs p-p Chain
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Hydrostatic Equilibrium on MS
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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

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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 lt 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.

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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.

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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

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Hydrostatic Equilibrium at Different Times
Pressure Gravity Adjust
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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

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Lifetimes in Math

• Thats ? 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!