Lecture 16: Red Giants and White DwarfsRGB to AGB to White Dwarf (~1 Solar Mass Star)

The advanced evolution of low mass stars leads first to the red giant phase, where an “inert” core of Helium has accumulated inside a H-burning shell. The densities are sufficient in the core for electron degeneracy pressure to be important. The core is nearly isothermal due to efficient conductive energy transport. As the Helium mass increases the core is forced to higher and higher densities and the H-burning shell produces more and more energy. The star ascends the red giant branch. Helium burning is delayed by the fact that the Be-8 atom is unstable, so essentially one requires a 3-body interaction (the triple-alpha) reaction to gain energy. This requires temperatures exceeding 100 million degrees.

The reactions of the triple-alpha process are as follows:

The second reaction generates an excited state of the carbon atom that is 7.65 Mev above its ground level. This is a “resonant” reaction, meaning that its cross-section is much higher than would otherwise be expected. The decay of the excited state, in the third line, completes the conversion of Helium to Carbon. atom.

4He + 4He ↔8Be

4He + 8Be →12C∗ + γ

12C∗→

12C + γ

Because the temperature and density required for the triple alpha process is so high, the following reaction also occurs, even though its Coulomb barrier is steep:

Note that the temperature sensitivity of the triple-alpha process is extremely high, with the reaction rate (which depends on the Gamow energy) going like temperature to the 30th power!

The consequence of this for the star is quite substantial. Helium burning does not turn on quiescently, like Hydrogen burning does. The star does not “settle” into Helium burning .. it gets into it via a series of eruptive “fits” and “starts” known as the Helium “flash”. This effectively truncates the red giant branch (RGB). Basically, once Helium burning can begin in the degenerate core of a red giant at the “tip” of the RGB, it spreads rapidly and the luminosity and temperature in the core rise extremely rapidly (note that this luminosity burst never makes it to the surface, as such, since the photons must random walk their way through the star and the Helium core flashes are on much shorter time scales. The radiative transfer smooths out the bursts as seen at the surface, but can drive substantial mass loss. The energy is put in so rapidly that the star cannot transport it all and loses matter, perhaps as much as 30% of its initial mass!

12C + 4He →16O + γ

The effect of the increased temperature in the core during a Helium flash is to heat the atoms to the point where they transfer heat to the electrons and eventually lift the degeneracy. Then the core can expand and cool. This, in turn, shuts down the triple-alpha process and the star settles back into an inert core and shell-H-burning phase, until contractive heating starts the cycle again. These rapid phases of the helium flash are impossible to follow precisely via stellar modeling, so the process is discontinuous at this point.

We know, however, that eventually the star settles into a stable “He main sequence” burning structure, where it has a non-degenerate Helium-burning core, a H-burning shell and a relatively stable structure. At this point, the star is on the “Horizontal Branch” (HB) and referred to as a Horizontal Branch star. Many HB stars are within the Instability Strip on the HR diagram and appear as RR Lyrae variables.

Subsequent evolution is somewhat analogous to evolution off the Hydrogen burning main sequence. The star exhausts its core fuel (Helium) and is left with the products of that reaction (Carbon and Oxygen). Those atoms cannot fuse at the temperatures and densities of the stars because of the extreme Coulomb barrier. As the star adjusts its structure to having an increasingly inert core, it ascends the “Asymptotic Giant Branch” (AGB) in the HR diagram.

Helium rich material is brought to higher and higher densities. Finally, Helium-burning switches over to shell burning (and there is still Hydrogen shell burning, as well). Because of the high temperature dependence, Helium shell burning is rather unstable and generates trememdous energy fluctuations which drive substantial mass loss. This finally terminates the AGB and produces a “planetary neubula” composed of the ejecta from the star. The core remains as a degenerate and inert mass of (primarily) Carbon and Oxygen in roughly equal amounts. At first, its temperature is 100 million plus, but it rapidly cools, contracts a bit and stabilizes as a white dwarf.

Five Solar Mass Star Evolution: Stars that begin life with a bit more mass have similar evolution, although different in details. For example, their central densities are not as high at the tip of the RGB so they can begin Helium burning quiescently, without the flash stage. Their evolution on the HB and AGB is also a bit different. However, they also lose sufficient mass to get under the Chandrasekhar mass limit for an electron degenerate supported star and end up as white dwarfs.

As is common in science, our theories do not do justice to the complexities of the observations and it is clear fromlooking at planetary nebulae thatother factors are involved, such as rotation, magnetic fields, possible binarity and complex interactions between episodes of mass loss.

The r, s and p processes: The nuclear reactions mentioned to this point are all built on a sequential

transition from H to He to C and beyond. If He nuclei were the only building blocks, then there would be no odd-atomic number nuclei. Clearly, other reactions occur at some astrophysical location which produce the odd-numbered elements (albeit with only about 10% of the abundance of their even numbered neighbors). Also, the distribution of isotopic abundances among the heavy elements requires free neutrons (r, s process) and free protons (p process). It is thought that the AGB stars may be an important astrophysical site for the production of many elements (and their distribution into the ISM via the strong mass loss of these stars). They may also be the site of some s process isotopes.

s is for “slow” neutron capture in which the nucleus has time to Beta-decay before it captures another neutron.

r is for “rapid” neutron capture in which the nucleus captures more neutrons before it can Beta-decay.

p is for “proton” capture, which is just a nuclear reaction with a proton involved. (Note that the problem is having free protons -- i.e. H-atom) at a temperature and pressure where H-burning would have long since turned any free protons into He nuclei. Clearly these free protons must have been recently created as the products of other nuclear reactions.

The chart on the next page shows how the s, r and p process isotopes are identified. Z (number of protons) increases upward and N (number of neutrons) increases to the right. Stable isotopes are indicated by letters in their boxes, showing how they could have arisen (by the s, r or p process). Unstable isotopes undergo Beta decays on short timescales (hours to days). A beta decay transforms a neutron into a proton, with the ejection of a “Beta particle”, which is an energetic electron.

The addition of neutrons to atoms moves them to the right on this chart. A rapid addition will produce a nucleus with way too many neutrons which will beta decay along a diagonal line (arrows) until it reaches a stable isotope. Isotopes that can only come from this process are indicated as “r process” isotopes.

The slow addition of neutrons will allow time for the beta decay of any unstable isotopes and this defines the “s process path” (shown as the solid line) through the chart. All isotopes along this path could come from the s process. If the diagonal route up from smaller Z is blocked by a stable isotope, then that particular isotope could ONLY come from the s process. It could not have an r process component. Such isotopes are labeled as “s process ONLY”.

Finally, there are proton-rich stable isotopes that are not on the s process path. These could only have come from reactions involving protons and are referred to as “p process” isotopes.

p s,r

p s only s,r s

only r

s,r

s,r s only s,r r r

s,r r

Z

N (number of neutrons)

Reactions important in 4-8 solar mass stars in AGB phase Carbon Burning Reactions:

Oxygen Burning Reactions:

12C + 12C →20Ne + 4He

12C + 12C →23Na + 1H

12C + 12C →24Mg + γ

16O + 16O →32S + γ

16O + 16O →31S + n

16O + 16O →31P + 1H

16O + 16O →28Si + 4He

White Dwarfs: The C/O cores of the low mass stars (or O/Ne of somewhat higher mass stars) can be supported by electron degeneracy pressure as long as their masses are less than 1.44 solar masses (the Chandrasekhar limit). The structure of white dwarfs is fairly simple, since they roughly obey a polytropic equation of state. Low mass ones are polytropes of index 1.5 and high mass ones are polytropes of index 3. Their composition is also simple, since they are primarily composed of a C/O mix. Their evolution is also simple. Since pressure is independent of temperature and since they have no internal energy source (neither nuclear nor gravitational) they can only cool off at constant radius. Their luminosity at first is such that they typically have effective temperatures near 10,000 K, hence the term “white” dwarfs. As they cool, at constant radius their luminosity drops and, hence, so does their effective temperature, so that they appear redder.

They define a cooling sequence in the HR diagram. Every white dwarf ever created is still luminous at some level and the lower limit to the luminosities that can be detected provide an interesting age estimate for any stellar population (e.g. the galactic disk) and for the Universe. Since cooling slows down as the white dwarfs age, the cooling sequence develops into a cooling “clump” for the oldest white dwarfs. Studying these stellar “corpses” in the “graveyard” can tell us a lot about the luminosity function of the cluster when it was younger and its age.

Observed Properties of White Dwarfs:

As usual, the observations reveal many more complexities than the basic theory would suggest. In particular, there are many classes of white dwarf spectra, DA and DB, representing stars with Hydrogen-rich atmospheres (YES!, Hydrogen!) analogous to the A stars (DA), and Helium I atmospheres analogous to the B stars (DB) being the most common. In all cases, the spectral features are EXTREMELY broad, the broadening being due to the high pressure at the photospheres. The radius of a typical White Dwarf is about the radius of the Earth, but the mass is about the mass of the Sun, so surface gravity is several hundred thousand times greater than it is on the surface of the Earth!History:Bessell discovered variability in the proper motions of Sirius and Procyon indicating the presence of dark companions in 1844. Sirius B was seen visually in 1861. Its spectrum was obtained in 1915 and recognized to be of type A -- a major surprise. By the mid-twenties the mass and radius of the star were determined, proving that its density was ~50,000 gm/cc and that it must be supported by electron degeneracy pressure, not gas pressure. By the early thirties, Chandrasekhar produced a theory of white dwarf structure and predicted the upper mass limit of 1.44 Msun. He also predicted the mass -radius relationship.

Increasing numbers of WD’s were discovered through the years and a modern classification scheme is based on the work of Sion (1983)

D is for “degenerate”Second Letter-primary spectroscopic signature in optical

DA-Hydrogen lines (5000K<Teff<80,000K)DB-He I lines (10,000<Teff<30,000K)DO - He II lines (T > 45,000K)DC-Continuous spectrum (Teff<11,000K)DZ-Metal lines (Mg, Ca, Fe)DQ-Atomic/Molecular carbon featuresAdditional letters indicate increasingly weaker or secondary features, e.g. DAZ, DQABP-polarized magnetic, H-non-polarized magnetic, V-variable

Teff is sometimes indicated by digit at end; 50,400/Teff, e.g. DA4.5

DA Spectra

Rapid settling of elements heavier than H in high log g

DB Spectra

From Web presentation by Tala Monroe of Indiana U.

DO Spectra

DC Stars & Spectra• Featureless, no line

deeper than 5% of continuum

• Higher resolution reveals weak features

• Many reclassified as DB or DA

• True DCs remain, among coolest WDs, Teff < 11,000 K

DQ Stars & Spectra

• Helium-rich stars, generally characterized by C2-Swan bands

• Hotter DQs have C I

DZ Stars & Spectra

• He-rich stars too cool to show He I, below (DB5-9000K) still show metal features

• Ca I, Ca II H and K, Mg I, Fe I, Na I

PG 1159 Spectra• Features due to

CNO ions, Teff>100,000K

• Absence of H or He I features; He II, C IV, O VI

ZZ Ceti

Magnetic WDs

• About 5% of field white dwarfs display strong magnetism

• 3 classes of H-atmosphere MWDs based on field strength

• He-atmosphere MWDs have unique features

Basic Picture

• 75% DA, 25% non-DA• Spectral classification provides info about

principal constituent, with some T info• Progenitors: Post-AGB stars, central stars of

planetary nebulae (CSPN), hot subdwarfs• Expected structure-stratified object with

<M>~0.6Msun– C-O core, He-rich envelope, H-rich shell

• O-Ne cores-most massive

– Atmosphere contains <10-14 M• Many WDs have pure H or He atmospheres• Thicknesses of H and He

Mechanisms in Atmosphere

• Gravitational diffusion

• Convection

• Radiative levitation

• Magnetism

• Accretion

• Wind-loss

• T-sensitive