MAIN SEQUENCE STARS, Red Giants and White Dwarfs

1
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

2
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).

3
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

4
Fusion on MS p-p chain
5
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

6
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

7
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)

8
NEUTRINOS FROM STARS

• 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.

9
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?

10
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).

11
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.

12
CNO Cycle vs p-p Chain
13
Hydrostatic Equilibrium on MS
14
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

15
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.

16
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.

17
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

18
Hydrostatic Equilibrium at Different Times
Pressure Gravity Adjust
19
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

20
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!
21
POST-MAIN SEQUENCE EVOLUTION

• THE END OF THE MAIN SEQUENCE
• A star leaves the MS when it exhausts H at the
  core. During the MS, there is an excellent
  balance between P and gravity HYDROSTATIC
  EQUILIBRIUM
• When H is gone, the core is essentially all He
  and (at between 6 and 40 million K),
  far too cool to start
  nuclear fusion of He.
• The structure must readjust since the H fusion,
  which had provided the energy and pressure, at
  the center.

22
SUBGIANT PHASE

• All H gone in core He "ash" is too cold to
  "burn"
• Pressure provided by energy from fusion in the
  core disappears.
• The He core contracts -- gravity wins over
  pressure again.
• Contraction heats the core.
• Most of this heat is trapped, so core T rises.
• Rising density and T imply core P rises pretty
  fast, so there is a contraction, NOT a collapse.

23
Hydrogen Burning Shell (Subgiant)
24
Thought Question

• What happens when a star can no longer fuse
  hydrogen to helium in its core?
• A. Core cools off
• B. Core shrinks and heats up
• C. Core expands and heats up
• D. Helium fusion immediately begins

25
Thought Question

• What happens when a star can no longer fuse
  hydrogen to helium in its core?
• A. Core cools off
• B. Core shrinks and heats up
• C. Core expands and heats up
• D. Helium fusion immediately begins

26
Subgiant, 2

• Increased core T diffuses into the H BURNING
  SHELL -- the layer of H hot enough to fuse
  outside the inert He core.
• This higher T causes a dramatic increase in L
  from that shell (both pp chains and CNO cycle
  fusion rates are VERY SENSITIVE to T)
• Higher L in shell causes the inert H envelope to
  expand.
• Work is done in producing this expansion, so the
  star's surface T declines (an expanding cloud of
  gas cools just as an opaque contracting one
  heats).
• This corresponds to the star moving to the right
  and up on the H-R diagram and it enters the
  SUBGIANT phase.

27
Life Track after Main Sequence

• Observations of star clusters show that a star
  becomes larger, redder, and more luminous after
  its time on the main sequence is over

28
RED-GIANT PHASE

• As the core continues to contract and heat up, T
  108 K is finally reached
• Then higher electric repulsion of Helium nuclei
  can be overcome
• AND He CAN FUSE INTO CARBON
  3 4He ? 12C ?
  (the TRIPLE-ALPHA REACTION).
  
• Really, 4He 4He ? 8Be but Be-8 is unstable, so
  3 He-4's are needed to come together nearly
  simultaneously.
• This generates more energy, and both L and T in
  core increases.

29
Helium Flash

• For M lt 2 M? this occurs while the He core is
  degenerate (more about this later when we
  discuss White Dwarfs)
• As P doesn't rise with T for degenerate matter,
  the thermostat is broken
• So he core temperature rises fast when He fusion
  begins and the Luminosity from He goes up even
  faster HELIUM FLASH
• until thermal pressure is large again and expands
  core again, again dropping the core temperature
• This causes a very fast expansion of the star's
  envelope, and a further cooling of its surface,
  yielding a RED GIANT (with size 100's of that of
  Sun on MS but lower Ts ).

30
Life Track after Helium Flash

• Models show that a red giant should shrink and
  become less luminous after helium fusion begins
  in the core

31
Pop Quiz

• Print your name (1)
• 1) Complete, and explain the balancing of, the
  following nuclear reaction (5)
• 15N 1H ? 12C ___
• 2) Sketch, on a labeled H-R diagram, the path of
  a 1 M? star from the time of accretion as a
  protostar to the red giant phase. (5)

32
THE HORIZONTAL BRANCH

• He Flash ends quickly, once core pressure has
  grown, causing the core radius to rise, thus,
  yielding a decline in Tc to just about 108 K.
• Now He burns smoothly in the core -- producing
  the He BURNING MAIN SEQUENCE -- which is visible
  on an H-R diagram as the HORIZONTAL BRANCH (lower
  L but higher Ts than during the He flash).
• Stars are again in HYDROSTATIC EQUILIBRIUM
  throughout the thermostat works again
• These are still RGs, and on HB the higher masses
  are to the left part of the HB.
• Most stars spend most of their POST-MS life on
  the HB, but this is typically lt 10 of their MS
  life.

33
Back up to the Red-Giant Branch on the H-R
Diagram (Asymptotic Giant Branch)
34
Thought Question

• What happens when the stars core runs out of
  helium?
• A. The star explodes
• B. Carbon fusion begins
• C. The core cools off
• D. Helium fuses in a shell around the core

35
Thought Question

• What happens when the stars core runs out of
  helium?
• A. The star explodes
• B. Carbon fusion begins
• C. The core cools off
• D. Helium fuses in a shell around the core

36
AGB for Lower Mass Stars

• Increased core T diffuses into the He BURNING
  SHELL -- the layer of He hot enough to fuse
  outside the inert C core.
• This higher T causes a dramatic increase in L
  from that shell.
• Higher L in shell causes the inert He envelope,
  as well as the H burning shell and inert H
  envelope to expand.
• Work is done by the gas in producing this
  expansion, so the star's surface T declines by a
  bit.
• Star is hotter inside and more luminous than
  before

37
Helium Burning Shell
38
Double Shell Burning

• After core helium fusion stops, He fuses into
  carbon in a shell around the carbon core, and H
  fuses to He in a shell around the helium layer
• This double-shell burning stage never reaches
  equilibriumfusion rate periodically spikes
  upward in a series of thermal pulses
• With each spike, convection dredges carbon up
  from core and transports it to surface

39
ON TO WHITE DWARFS

• For stars with MS masses less than about 7 to 8
  M? AGBs or Supergiants lose a good bit of mass,
  and some of these pulsations become so powerful
  that massive shells (of 0.1 to 0.2 M?) are
  ejected.

40
End of Fusion

• Fusion progresses no further in a low-mass star
  because the core temperature never grows hot
  enough for fusion of heavier elements (some He
  fuses to C to make oxygen)
• Degeneracy pressure supports the white dwarf
  against gravity

41
Planetary Nebulae

• Double-shell burning ends with a pulse (or
  pulses) that eject most of the H and He into
  space as a planetary nebula
• The core left behind becomes a white dwarf

42
Ejected Shells Planetary Nebulae
43
CENTRAL STARS OF PN

• The cores of the RGs/SGs are very hot and excite
  the PN gas.
• These Central Stars of PN have C or CO cores,
  and He envelopes (All the H was expelled as winds
  or PN).

44
Dead Core Evolution

• They are not massive enough to compress the C
  core to T gt 7 x 108 K at which it could fuse, so
  these CSPN's just cool off and fade in power,
  slowly shrinking in size
• BUT, when density of the core reaches 106 g/cm3
  (or one ton / teaspoon!) the PAULI EXCLUSION
  PRINCIPLE takes over
• no 2 electrons can be in the same energy state
• this Quantum Mechanical effect provides a HUGE
  DEGENERACY PRESSURE that stops the continued
  contraction at a radius of about 1/100th of R?
  (nearly the same as R? ).

45
White Dwarfs

• Once it is held up by degeneracy pressure
• we call it a WHITE DWARF.
• The MAXIMUM MASS electron degeneracy pressure can
  support is about 1.4 M?-- the CHANDRASEKHAR
  LIMIT.
• So 7-8 M? stars on the MS leave WDs close to the
  Chandrasekhar limit
• But the more common 0.8-2 M? stars leave WDs
  around 0.6-0.7 M? (the typical mass of a WD).

46
Observed White Dwarfs

• Sirius B is a bound companion to the nearby very
  bright star Sirius (A) M1.1 M? R5100 km
• M4 the nearest globular cluster, about 16 pc
  across at 2100 pc distance
• Nearly 100 WDs are seen in a small region

47
Size of a White Dwarf

• White dwarfs with same mass as Sun are about same
  size as Earth
• Higher mass white dwarfs are smaller!

48
Earths Fate
Errors on Scale 100?
10?
1?

• Suns radius will grow to near current radius of
  Earths orbit

49
Earths Fate

• Suns luminosity will rise to 1,000 times its
  current leveltoo hot for life on Earth
• Life and Death of the Sun Applet

50
Summary for Low Mass Stars

• What are the life stages of a low-mass star?
• H fusion in core (main sequence)
• H fusion in shell around contracting core (red
  giant)
• He fusion in core (horizontal branch)
• Double-shell burning (red giant)
• How does a low-mass star die?
• Ejection of H and He in a planetary nebula leaves
  behind an inert white dwarf

51
Asymptotic Giant Branch (for Massive Stars)
?Supergiants

• Once the He in the core is all burned up, we
  reach the end of the He BURNING MAIN SEQUENCE.
• As at the end of the MS Pressure provided by
  energy from fusion in the core disappears.
• The Carbon core contracts -- gravity wins over
  pressure again.
• Contraction heats the core Most of this heat is
  trapped, so core T rises.
• Rising density and T imply core P rises, so again
  there is a contraction, not a collapse.

52
Supergiants for Higher Mass Stars

• For more massive stars the same thing happens,
  but the star starts way up on the H-R diagram,
  and it enters the SUPERGIANT phase.
• The ESCAPE VELOCITY from such big stars gets low
  Vesc (2 G M / R)1/2 as R increases while
  M stays the same.
• They lose a lot of mass via winds.
• Also, RGs and SGs are subject to opacity driven
  instabilities which cause the outer layers to
  expand and cool and contract and heat up.
• This produces VARIABLE STARS if the atmosphere
  lies in the INSTABILITY STRIP.
• Important classes of variable stars are the RR
  LYRAE (horizontal branch) and two types of
  CEPHEID VARIABLES (supergiants), since they are
  wonderful DISTANCE INDICATORS

53
Massive Star Post-MS Evolution

• Stars starting the MS with more than 8M? are
  unlikely to leave behind WDs (though up to about
  10M? may leave behind Carbon-Neon WDs) they
  leave cores w/ M gt 1.4M? the Chandrasekhar
  limit.
• Evolutionary History
• MS
• H is exhausted in core
• H shell burning starts, with modest increase in L
  and fast decrease in TS (fast move to right on
  H-R diagram)
• He fusion starts (non-degenerately, so no flash)
• Modest increase in L and core He burning -- a
  SUPERGIANT
• He is exhausted in core

54
Massive Post-MS Evolution, 2

• So far, pretty similar to lower mass stars
  studied already, but
• Now we feel the big difference higher M means
  gravity can crush the C core until it reaches T gt
  7 x 108 K so
• Carbon CAN ALSO FUSE
• 12C 4He ? 16O ?
• Some 16O 4He ? 20Ne ?
• Also some 12C 12C ? 24Mg ?
• This fuel produces less energy per mass so C is
  burnt quickly.
• Loops in the H-R diagram.

55
Massive Post MS Evolution on H-R Diagram
56
Massive Post-MS Evolution, 3

• The more massive the star the more nuclear
  reactions will occur
• Most such stars will have Oxygen cores that can
  also fuse, typically needs T gt 1 x 109 K!
• 16O 4He ? 20Ne ?
• 20Ne 4He ? 24Mg ?
• Well come back to this type of onion-layer model
  star when we talk about supernova explosions and
  neutron stars.
• The elements cooked here are needed for life

57
Massive Stars Have Powerful Winds
HST picture of AG Carinae 50 solar masses Light
echoes showing shells from V838 Monocerotis
58
Binary Star Evolution

• Most stars are in binary or multiple systems
• If the binary is close enough, evolution is
  affected
• More massive stars still can be on MS while less
  massive has evolved off (like Algol)
• Only possible if there is mass transfer through
  Lagrangian point (L1) between Roche lobes

59
Binary Evolution Depends on Separation

• Detached, evolve separately
• Semi-detached, one fills Roche lobe, dumping on
  other
• Contact or common-envelope, both overflow single
  star w/ two fusion cores

60
Binary Evolution Algol Type

• Start detached
• More massive leaves MS, overflows Roche lobe
• Now 2nd star is more massive but still on MS