ASTR-1020: Astronomy II - Stellar Evolution and Death - Prof. Donald G. Luttermoser, Study notes of Astronomy

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ASTR-1020: Astronomy II

Course Lecture Notes

Section VII

Dr. Donald G. Luttermoser East Tennessee State University

Edition 4.

Abstract

These class notes are designed for use of the instructor and students of the course ASTR-1020: Astronomy II at East Tennessee State University.

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4. 1. 08 M < M < 0. 4 M : These stars are totally convective, and as such, helium ash gets uniformly mixed throughout the star. No inert He core develops, hence no H-shell burning and no expansion into a red giant. After hydrogen is exhausted, the entire star contracts until the helium becomes degenerate (see the white dwarf section [§VIII.A]) and the star becomes a helium-rich white dwarf.
5. 1. 4 M < M < 4 M : These stars ignite He in a degenerate core (He-flash, see §VI.C.3). During the core He-fusion stage, the star sits in the red giant clump (Population I stars — see §IX.B) or the horizontal branch (Population II stars) on the H-R diagram. He-fusion creates 12 C and 16 O ash and once the He-fusion stops, the carbon-oxygen core continues to collapse. a) This causes energy to be dumped into the He-rich layer just above the core which ignites =⇒ star now has a He-burning shell and H-burning shell. This extra energy source expands the outer layers of the star further — the star becomes a bit more red and a lot more luminous.

b) Burning in the He-burning shell is quite unstable. i) The He-burning shell is subject to a series of ex- plosive helium-shell flashes (also called thermal pulses), caused by the enormous pressure in the He-burning shell and the extreme sensitivity of the triple-alpha burning rate to small changes in tem- perature..

ii) During a thermal pulse, the luminosity of the star increases for a short time (approximately 100 years). Also, the surface pulsations (see §VII.C) can change their periods during this time as well.

Donald G. Luttermoser, ETSU VII–

R Hya is a long-period variable that has just gone through such a thermal pulse.

iii) While this is going on, the interior of the star also experiences dredge-ups. A “dredge-up” sim- ply means that nuclear processed material is being brought from the interior of the star up into the stellar atmosphere where it can be detected in the emergent spectrum of the star.

c) During this time, the star moves up the asymptotic giant branch (AGB) on the H-R diagram.

d) For stars 2M and above while on the AGB, carbon pro- duced in the He-burning shell finds its way to the surface through deep convection cells =⇒ the star becomes ei- ther an S star (with C/O ∼ 1.0) or a carbon (R or N) star (with C/O > 1.0). TX Psc is an example of a carbon star that has already gone through a series of thermal pulses.

e) The outer layers of the star can become unstable during this phase (see §VII.C) and it can begin to pulsate =⇒ Mira-type variables.

f) Strong stellar winds begin at this phase which produce planetary nebula. The mass loss continues until only the core of the star remains.

g) The contracting carbon-oxygen core becomes degenerate before carbon fusion can begin — the star is now dead as a carbon-oxygen rich white dwarf.

Donald G. Luttermoser, ETSU VII–

(^14) O + 4 He −→ 20 Ne + γ (^20) Ne + 4 He −→ 24 Mg + γ (^24) Mg + 4 He −→ 28 Si + γ (^28) Si + 4 He −→ 32 S + γ (^32) S + 4 He −→ 36 Ar + γ (^12) C + 12 C −→ 24 Mg + γ (^16) O + 16 O −→ 32 S + γ

note that Ne = neon, Mg = magnesium, Si = silicon, S = sulfer, and Ar = argon in the table above.

d) Various silicon burning reactions can occur at tempera- tures exceeding 3 × 109 K in the core. Silicon burning produces the iron (Fe) group elements.

e) Once Fe is formed, reactions that produce heavier ele- ments are all endothemic (i.e., requiring an energy in- put) and have a tough time forming via standard ther- monuclear burning. Such elements, and the elements not built upon α-particles, are created via the r- (for rapid neutron capture) and s- (for slow neutron capture) pro- cesses. These processes will be discussed in the super- novae subsection below.

f) As a result of this characteristic of Fe, the collapse of the core cannot be halted by the onset of further thermonu- clear reactions. The core can do one of 2 things during its final collapse: i) Achieve nuclear densities (e−^ + p −→ n + ν) and bounce when neutron degeneracy sets in =⇒ a neutron star forms during a Type II super- nova explosion (see below).

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ii) The core collapses past the neutron degeneracy state (if Mcore > 3 M ) down to a black hole (see §VIII.D).

B. Stellar Evolution in Binary Star Systems.

1. Stars in binary or multiple star systems will evolve like isolated stars (described in the previous subsection) if the component stars are well separated from each other.
2. Here we will concentrate on stellar evolution in close binary star systems where mass transfer has a large impact of the evolution of these systems. a) By “close,” we mean that the separation ‘a’ of the two stars are at most the diameter of the larger star (i.e., a ≤ 2 R 1 , where ‘1’ is the larger of the two stars).

b) Such stars will be tidally (i.e., rotationally) “locked” to each other due to the conservation angular momentum.

c) For such systems, 5 points exist where the gravitational force on a small mass near the two larger masses equals zero. These points are called Lagrangian points: i) L 1 : The zero-force point that lies between the two masses =⇒ the inner Lagrangian point.

ii) L 2 : The zero-force point that lies on the far side of M 2 (the smaller mass).

iii) L 3 : The zero-force point that lies on the far side of M 1 (the larger mass).

iv) L 4 : The zero-force point that lies in the orbit

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nary star independent of what its mass might be with respect to the primary star.

iii) If both stars fill their Roche lobe, the system is called a contact binary.

3. The semidetached and contact system have mass that transfers from one star to the other star. An important quantity in the evolution of such systems depends upon the mass transfer rate.

a) As material flows through L 1 , M 1 loses mass and M 2 gains mass through the process of accretion.

b) This mass transfer can slow the speed of the evolutionary “steps” of the M 1 star (if it is fast enough) and increase the speed of the evolutionary “steps” of the M 2 star.

c) Nuclear processed material can then be transferred to the companion (this is how dwarf S stars and dwarf carbon stars are made).

d) Sooner or later, one of the stars will reach the final stage of its thermonuclear lifetime.

e) If such a star is massive enough, it will supernovae as described in this section of the notes. Depending upon the distance of the two stars, three possible outcomes will take place of the “secondary” star: i) It will be ejected from the system.

ii) It will be completely disrupted by the shock wave of the supernova.

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iii) It will experience mass loss (perhaps a substan- tial amount) by the shock and radiation pressure of the blast.

f) If the star in it final thermonuclear stages has too small a mass to supernova, it will lose its envelope through the creation of a planetary nebula (which will have little impact on the secondary) forming a white dwarf star in orbit about the secondary star of the system. i) As this secondary star starts to fill its Roche lobe through stellar evolution, it will begin to dump material onto the white dwarf.

ii) Since the two stars are in orbit about each other, the material misses the white dwarf on first pass and goes into orbit about the white dwarf forming an accretion disk.

iii) Viscosity (i.e., internal fluid friction) causes the material in the disk to slowly spiral in towards the white dwarf. As the gas falls into the potential well, its orbital speed increases, which increases the viscosity, which increases the thermal energy of the gas in the disk =⇒ the inner portion of the disk is much hotter than the outer portion.

iv) The bulk of the light that is emitted in such a system comes from the inner region of the accre- tion disk and not from the “normal” star nor the white dwarf.

g) Instabilities can arise in the disk which can result in a rapid increase of the mass flow down through the disk,

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f) Such an outburst is called a classical nova or just nova. They all reach the approximate same maximum bright- ness of MV ≈ − 4 .5. i) A fast nova takes a few weeks to dim by 2 mag- nitudes after reaching maximum brightness.

ii) A slow nova may take nearly 100 days to decline by the same amount from maximum.

iii) The fast and the slow speed classes of novae are probably due to variations in the mass of the white dwarf and in the degree of CNO enrichment of the hydrogen surface layer.

iv) It takes about 10^4 to 10^5 years to accumulate enough material for another runaway to occur. Since this is short in comparison to stellar evolu- tionary time scales, such systems can go through numerous nova episodes.

5. If the mass-transfer rate can get as high as 10−^6 M /yr or greater, the white dwarfs mass may build fast enough for its mass to ex- ceed the Chandrasekhar limit of 1.4 M (see §VIII.A of these notes). a) The white dwarf collapses since the degenerate electron pressure is insufficient to support that weight of this burnt-out core.

b) This sets up a runaway thermonuclear event in the core of the white dwarf which completely destroys the white dwarf as was the case in the carbon detonation of the 4- M main sequence stars (see page VII-4 of these course

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notes).

c) Such supernova (see §VII.A.6) are called Type Ia Su- pernovae.

6. Besides white dwarfs in a close binary system, the primary also can be a neutron star or black hole (see next section). Indeed, X-ray binary systems are suspected to contain one of these two objects =⇒ the X-rays are emitted from the extremely hot (perhaps a high as a billion Kelvins!) inner portion of the ac- cretion disk as shown below.

X-Ray Binary

Black Hole Candidate X-Ray Photons

Normal Star

Accretion Disk Black Hole

X-Ray Emitting Region

C. Stellar Pulsations and Mass Loss.

1. The first variable star discovered was o Cet in 1596. Astronomers were so surprised by this finding that they renamed the star Mira (the wonderful). a) This was the discovery of the first long period variable (LPV) star. i) Most LPV stars change in brightness on a some- what periodic time frame anywhere from 150 to

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of these stars (see Figure 23.7 in the text) =⇒ by mea- suring a Cepheid’s period, we can deduce its absolute magnitude MV , then by comparing MV to its apparent magnitude V , we can deduce its distance via the distance modulus formula (i.e., Eq. III-7).

e) Population I star Cepheids (called Type I or classical Cepheids) have a slightly different period-luminosity re- lationship than the Population II star cepheids (called Type II Cepheids or W Virginis stars).

3. Lower mass versions of Cepheids exist called RR Lyrae type variables, which change in brightness with period shorter than 1 day. These stars are horizontal branch stars, and as such, all have the approximate same luminosity (e.g., 100L ), hence can also be used as distance indicators.
4. All of these different types of variables pulsate due to their in- ternal structure — they all lie on an instability strip on the H-R diagram. a) The pulsations are due to the kappa effect, kappa (κ) for opacity, which results from an ionization zone that lies just beneath the photospheres of these stars.

b) Miras pulsate from a hydrogen ionization zone just be- neath the surface of the star.

c) Cepheids and RR Lyr’s pulsate from a helium ionization zone just beneath the surface.

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D. The Explosive Death of Stars.

1. Supernovae are classified based primarily upon their spectra and their light curves (i.e., how brightness changes with time). We have already discussed a few different types. We now present the complete supernova classification scheme. The primary classifi- cation is based upon the appearance of hydrogen Balmer lines. a) Type I supernovae do not show hydrogen Balmer lines and reach a maximum brightness of MV ≈ −19. They are classified into 3 subclasses: i) Type Ia supernovae display a strong Si II line at 6150 ˚A. These are white dwarfs in close binary star systems that exceed the Chandrasekhar limit and explode from a runaway thermonuclear reac- tion in the carbon-oxygen core of the white dwarf. These types of supernovae are seen in both ellip- tical galaxies and throughout spiral galaxies.

ii) Type Ib supernovae display strong helium lines. These tyeps of supernovae are only seen in the arms of spiral galaxies near star forming regions. Hence, this implied that short-lived massive stars in binary systems are probably involved. These explosions are similar to that of a Type II super- nova, only in a binary star system where the outer H envelope has been transferred to the secondary star in the system before the Fe-core bounce.

iii) Type Ic supernovae display weak helium lines and no Si II is seen. Other than this, they are ob- served in the same location in galaxies as Type Ib. These types of supernovae are likely the same as Type Ib, except the helium-shell has been trans-

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3. Supernovae send the envelope of the star, with its nuclear- processed material, out into the ISM at supersonic speed. As this material collides with the ISM material, shocks form which ionizes the gas which induces the gas to “light up” as the elec- trons recombine with the ions =⇒ a supernova remnant is seen.