ASTR377:A six week marathon

through the firmament

by

Orsola De Marcoorsola@science.mq.edu.au

Office: E7A 316Phone: 9850 4241

Week 4, May 10-13, 2010

Overview of the course

Core contraction and shell ignition

• What changes first? X/H + Y/He + Z/Z)-1

where H= 1 proton / 2 particles= ½ He=4 protons / 3 particles=4/3

Z=A protons / A/2 particles = 2 will grow when H is running out, why?• Pressure decreases, core shrinks, density and

temperature increase and hydrostatic equilibrium is restored.

• This increases in a shell around the core. (When the Sun joined the main sequence it had 0.7LSun).

… and surface expansion

• The H-depleted core contracts slightly as thermal support dwindles.

• The photosphere keeps radiating and with lesser L supply would like to contract also, but core contraction increases the thermal energy and the layers just above the core heat up enough for H (which is still plentiful just outside the H-depleted core) to ignite. This moves the fusion engine of the star closer to the surface and increases the thermal pressure closer to the surface so that surface expands.

• At first this expansion cools the star, but as ions recombine and molecules form, the opacity rises and convection stars. This carries the increased L to the surface and the star brightens.

• The radius of the Sun will increase in this way to about ~160Ro. Its temperature will drop to ~3000K and its luminosity will rise to ~2200Lo.

An aside

• Any change in stellar evolution, can, at least in principle, have different consequences.

• For instance: The ignition of the shell results in a higher luminosity (because the shell burns at higher temperature), so why does the star not go up on the HRD instead of right?

• Shell generates energy at a rate higher than can be radiated so the luminosity does not increase. Instead, the envelope above the shell heats up and expands.

• Only later, when the energy is transported out by the very efficient method of convection, will the luminosity increase.

On the HRD:

Back to clusters’ HRDs

On the (red) giant branch: the first dredge-up

• The expanding envelope is cool enough for molecules to form so that the opacity goes up and envelope convection sets in.

• As the convective layer grows and extends from H-burning shell to surface, it brings to the surface the by products of H burning (a different N and 13C/12C abundances), which can now be observed. This is called the first dredge up (some stars can have up to three dredge up episodes in the course of their evolution).

• When convection sets in the luminosity of the star grows rapidly as this is the most efficient method of transporting energy outward.

The Hyashi track• As the envelope expands the star gains U (U

becomes less negative). By the Virial theorem the star cools and elements recombine reducing the thermal pressure. The star therefore contracts again to maintain equilibrium.

• There is no hydrostatic equilibrium with a fully recombined star.

• This results in a lower limit for stellar temperature. No star in hydrostatic equilibrium can be cooler.

The tip of the red giant branch

• The He core is contracting till one of two things happen: (1) Tc and c rise to ignition temperatures [more massive stars] or (2) electron degeneracy sets in, so the core pressure does not depend on temperature: as the He core grows and heats up it cannot change size [less massive stars].

• Eventually Tc rises enough for degeneracy to be lifted and pressure to be once again related to temperature. A sudden pressure wave is liberated and the core has a He flash.

Degeneracy• If the core collapse squeezes electrons

beyond a certain threshold before the temperature is higher than the He-fusion temperature of ~108 K, then degeneracy pressure becomes relevant.

• Maxwell v distribution predicts too many electrons at low velocity/energy than allowed by the Pauli uncertainty principle (see plot in hand-outs).

• Those electrons are pushed to higher energy. The pressure provided is independent of temperature:

€

Pdeg ≈ h2 ne5 / 3

me

(Board demo)

On to He fusion

• Bottleneck: there are no stable elements of mass number 5 or 8, so He + p, or He + He, likely to happen in an H and He-rich environment, end up in products that vanish immediately.

• As the Tc rises 8Be, although unstable, can be formed at a rate high enough to result in a non zero abundance of this element which can then react with another 4He.

The triple alpha chain(I had forgotten to give you the reactions last week….)

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612C+ 2

4He→ 816 O + γ

2

(Only a little)

The triple alpha chain(one more thing….)

€

612C+ 2

4He→ 816 O + γ

2

• The energy of one reaction (3xHe=C) is 7.3MeV (compared with ~25MeV for H burning reaction). So the energy per He particle is 10% of what it was for H (7.3/3 MeV).

• This plus the actual supply of He in the core of a star make for a much shorter time burning He in the core.

The horizontal branch

• After He ignition the star returns to a main-sequence like structure, except slightly smaller, hotter and more luminous.

• We call these core-helium burning stars “Horizontal Branch (HB) stars” or even “clump stars”.

• The HB lasts about 100 million years.

Core He exhaustion

• Core helium exhaustion proceeds in a way which is very similar to the hydrogen-exhaustion. The star eventually expands, rejoins the Hayashi track. It is now on the Asymptotic Giant Branch.

Iben 1971

The Asymptotic Giant Branch

• Expansion proceeds as for the RGB. The star ascends once again the Hayashi track.

• At the base of the AGB we have a second dredge-up episode.

• There are two active shell sources, He and H.• Mass-loss is at its peak and mostly dust

driven.• Helium shell flashes in the latter phase of the

AGB.

Mass-loss

• We know stars lose mass looking at giant’s spectra.

• We know that white dwarfs, which descend from 1-10Mo stars, have a mass in the range ~0.5-1.0Mo with most of them having M~0.6Mo. So there is a mass deficit.

Mass-loss

• In 1977 Dieter Reimers expressed the mass-loss from a giant in this way:

€

M.

≈ η 1.4 ×10−13 L /L• R /R•

M /M•

M•yr−1

where η ≈1

• This is an empirical formula, derived from fitting data.

• It embodies no real physics, though of course should be explainable by physics.Does it work for the Sun?

• If the cause of the mass loss is the radiation pressure, i.e., the stellar luminosity. Think of it as the fraction of stellar energy (L) used to counter binding energy (U) of the star: L/U, or L/gR.

€

M.

≈ −η 1.4 ×10−13 L /L•

(g /g• )(R /R• )M•yr−1

where η ≈1

Mass-loss

Mass-loss• Reimers mass-loss is OK for RGB stars,

but fails for AGB stars, which have dusty atmospheres (he did not observe many/any AGB stars because they are dusty).

• During the thermally-pulsating AGB the mass-loss rate surges from 10-7 Mo/yr to about 10-4 or even 10-3 Mo/yr. We call this phase the superwind.

• The mass-loss geometry also seems to change.

• Both the cause of the superwind and the geometry change remain unclear.

Mass-loss causes/helping agent.

• Radiation pressure.

• Radiation pressure on dust.

• Pulsations.

• Binarity.

• Magnetic fields.

Massive stars MMS≥12-15Mo

• The Blue Loop = the HB for massive stars.

• After He exhaustion, the contraction of the C and O core eventually reaches fusion temperatures to make Mg.

• For MMS<2.5-5Mo a degenerate C-O core develops. This may eventually lead to a C-flash (similar to the He-flash).

• This procedes through consecutive stages of fusion till the byproduct is Fe.

Characteristics of massive stars

• The initial mass function dictates that there are very few massive stars.

• The lifetime of a 7Mo star is 30 Myr.

• Sizes of massive stars on the main sequence and as giants.

• Spectra type is O (B) and they have hydrogen rich atmospheres (as usual).

Wolf-Rayet stars• Recognised in 1867 by Charles

Wolf and Georges Rayet as stars having bright lines. Why?

• They are very rare.Georges Rayet French 1839 1906

Wolf-Rayet stars: spectra• Emission lines are caused by large envelopes

where ions scatter photons into the line of sight.• The Doppler effect shifts photons to higher and

lower energies generating broad emission lines.• The region of the

envelope between the core and the observer absorbs radiation creating a blue-shifted component to the emission line (called the Pcygni profile).

Wolf-Rayet stars: mass-loss• WR stars are either dominated by N lines

(called WN stars) or by carbon lines (called WC stars). The latter category has no hydrogen in their atmosphere!

• The loss of the H envelope is due to huge mass-loss (we can measure the mass loss by looking at the spectral lines).

• The origin of the mass-loss is, once again not well identified, but it is certainly due to radiation pressure.

The Eddington limit

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LEdd =4πGmpcM

σ e

LEdd ≈1.3×1038(M /M• ) erg/sec

(Board derivation)

It is the luminosity for which gravity is balanced by radiation pressure.

Luminous Blue Variables

• This is once again something to do with mass-loss. The most massive stars seem to go through unstable phases where not just the huge WR mass loss, but something altogether huger takes place. A real outburst (not a supernova) that loses many solar masses in a short time.

• LBVs might be the most massive stars where radiation pressure is at the limit for stellar stability.

• We observe these LBV nebulae around WR stars.

• Sometime, they have bipolar shapes (e.g., Car) and a binary cause is suspected.

M1-67

Carinae

The end of the line: Fe

• Massive stars keep fusing core elements till the core is made of iron, which does not liberate energy by fusion because it has the highestbinding energy per nucleon (nothing is more tightly bound). What happens then?

Supernovae observations

• Six historical Supernovae in the last 1000 years within an angle of 60 deg near the plane: about 1/28 SN/yr.

Supernovae observations

• Extragalactic supernovae observed in modelrn times: MV ~ -19 mag or L~1010Lo.

• Time integrated output 1049 ergs – similar to a middle sized galaxy!

SN 1999byhttp://www.konkoly.hu/staff/tothi/sn1999by.html

Supernovae observations

• Two types of lightcurves (Type I and type II), though Type II are quite variable. Type I always have the same scaled brightness (more in 2 weeks!)

• Type II happen in spiral galaxies (young populations) while Type I happen also in elliptical galaxies (old populations).

• Type I are 1/300 per year, type II are 1/100 per year.

SN 1999byhttp://www.konkoly.hu/staff/tothi/sn1999by.html

Four types of spectra

• Type I have no H lines, type II do.

• Type Ia,b,c have strong silicon, strong helium and weak silicon, respectively.

• Type II, Ib, Ic derive from massive star collapse – they occur in elliptical galaxies (which host younger populations) in proximity to HII regions. They have intermediate type elements from the many stages of nuclear burning.

• Type Ia are something else…

Supernovae Type II• When the Fe core grows above the Chandrasekhar limit, electron

degeneracy cannot stop the collapse and the core is now in free fall. • Fe atoms are “smashed” by photons in a process called photo-

disintegration. This requires energy.• Also, e- and p recombine to form n and neutrinos. The particle density

decreases and neutrinos take energy out. The Fe core collapse in free fall.• As all the e- and p recombine to n the collapse is suddenly halted by n

pressure (we have made a neutron star).

• When the neutron density rises nutrons are puched closers and closer till the strong nuclear force becomes repulsive. This makes the core suddenly more rigid and sends a pressure wave out. This pressure/shock wave is sent out from the core that ejects the envelope.

• Note that the U to form a neutron star is approximately the one released in the SN explosion: GM2/R~30x1052 erg.

€

Pdeg ≈ h2 nn5 / 3

mn

Nucleosynthesis past the Fe elements

• Nuclei build up by accretion of neutrons. Heavy nuclei have low binding energies and tend to decay. The decay liberates energy.

• Building nuclei heavier than Fe requires energy, but in the supernova environment there is plenty of energy to forge these elements.