1. The structure and evolution of stars
Lecture 10: The evolution of 1M mass stars

2. Learning Outcomes
The student will learn the standard ideas of the evolution of solar type stars, including theories and ideas of the
Main-sequence
The Subgiant phase
The red giant branch
The horizontal branch and red clump
The AGB (asymptotic giant branch)
Planetary nebula and WD

3. Example set of models - “the Geneva Group”
See handout of paper of Schaller et al. (1992): the “standard” set of stellar evolutionary models form the Geneva group.
1st line in table
NB = model number (51)
AGE = age in yrs
MASS = current mass
LOGL = log L/L
LOGTE = log Teff
X,Y,C12…NE22 = surface abundance of H,He, 12C … 22Ne (these are mass fractions)
2nd line
QCC =
MDOT = mass loss rate:
RHOC=central density
LOGTC = log Tc
X,Y,C12…NE22 = central abundances 

4. Schemactic picture of convective regions
“Cloudy” areas indicate convective regions
Solid lines show mass values for which radius is 0.25 and 0.5 of total radius
Dashed lines show masses within which 0.5 and 0.9 of the luminosity is produced

5. The main-sequence phase
See handouts for the distribution of mass, temperature, pressure and density for the young Sun at the age of 5.4 x 107 yrs (Böhm-Vitense p156, Table 13.1), and compare with the observed estimates now.
For zero-age Sun Tc=13.62x106 ; current estimate Tc=15.6x107 K. Why ?
During H-burning, 4H4He. After 50% of H has been transformed, number of particles has decreased by factor 0.73, if He was originally 10% (by number).
What are the implications of this ?
As core becomes hotter, slightly more energy is generated and the star’s luminosity increases. Tables show that since the Sun’s arrival on the main-sequence, it has become ~30% more luminous. Hence stars of a given mass but different ages populate the main-sequence with a width of ~0.5 dex.

6. The main-sequence phase
The Sun on the main-sequence: Figures from Böhm-Vitense Ch. 13.
2% of mass is in heavy elements
CNO cycle operates very slowly in central regions
After ~4.5x109yr there is enough time to reach equilibrium abundances. N enriched by factor 7, C depleted by factor 200
Pressure increases steeply in centre
50% of mass is within radius 0.25R
Only 1% of total mass is in the convection zone and above

7. H-exhaustion early evolution
The cores of 1M stars become He rich. There is no convective processes required, hence the star does not become fully mixed. Fusion is most efficient in the centre, where T is highest.
As He content increases, core shrinks and heats up  He rich core grows
The T is not high enough for the triple- process
H-burning continues in a shell around the core, and as T increases, the CNO process can occur in the shell
As CNO T16 energy generation is concentrated in the regions of highest T and highest H content (in shell T ~ 20 x106 K)
This high T causes high P outside the core and the H envelope expands.
This expansion becomes more pronounced when >10% of the stellar mass in the He core.
This early expansion terminates the main-sequence lifetime
Luminosity remains approximately constant, hence Teff must decrease, star moves right along the red subgiant branch.
Subgiant branch

8. The red-giant phase
The shell source slowly burns, moving through the star, as the He core grows. But the star cannot expand and cool indefinitely.
When the temperature of the outer layers reach <5000 K the envelopes become fully convective. This enables greater luminosity to be carried by the outer layers and hence quickly forces the star almost vertically in the HR diagram
The star approaches the Hayashi line, and a small increase in the He core mass causes a relatively large expansion of the envelope.
There is no physically simple, step by step explanation of how a star becomes a red giant. All numerical computations obtain red giant configurations. as solutions to the structure equations.

9. The He-flash and core He-burning
The helium core does not reach threshold T for further burning as it ascends the RGB, and as it is not producing energy it continues to contract until it becomes degenerate.
At tip of the RGB the e– in core are completely degenerate. P is due to degenerate e– pressure, which is independent of T.
T is defined mainly by the energy distribution of the heavy particles (He nuclei). Remember gravitational collapse is resisted by e– degeneracy pressure.
For T~108K, triple- reactions start in the very dense core. They generate energy, heating core, and KE of He nuclei increases, increasing the energy production. Energy generation and heating under degenerate conditions leads to runway - the He Flash

10. The He-flash and core He-burning
During the He-flash, the core temperature changes within seconds. The rapid increase in T leads the e– again following Maxwell velocity distribution and degeneracy is removed. The pressure increases and core expands.
The star finds a new equilibrium configuration with an expanded non-degenerate core which is hot enough to burn He. The H-burning shell source has also expanded, and has lower T and density and generates less energy than before. The star sits in the Red Clump (metal rich stars) or the Horizontal Branch (metal poor stars).

11. Globular clusters and the horizontal branch and
47 Tuc – Globular cluster
Globular clusters are old and metal poor - we don’t see a red clump. We see a horizontal branch:
H-burning shells, He burning cores
Mass-loss drives bluewards evolution
Lowest mass H-envelope stars are bluest
More metal rich stars appear towards red
Clump stars  extreme red end of HB
Why do low metallicity stars end up on HB ?
Why and how do they loose mass after He-flash, and metal rich stars do not ?
Structure equations give equilibrium configurations on HB

12. The AGB and thermal pulses
The triple- reaction is even more T-dependent ( T30), hence energy generation is even more centrally condensed. Note the H-burning shell is generating energy.
The core will soon consist only of C+O, and in a similar way to before, the CO-core grows while a He-burning shell source develops.
These two shell sources force expansion of the envelop and the star evolves up the red giant branch a second time - these is called the asymptotic giant branch.
For high metallicity stars, the AGB coincides closely with the first RGB.
For globulars (typical heavy element composition 100 times lower than solar) they appear separated.

13. The stellar wind and planetary nebula phase
Large radiation pressure at tip of AGB probably drives mass-loss. Particles may absorb photons from radiation field and be accelerated out of the gravitational potential well. Observations of red giants and supergiants (more massive evolved stars) are in the range 10-9 to 10-4 M yr-1
Mass-loss is generally classified into two types of wind.
Stellar wind: described by empirical formula (Dieter Reimers), linking mass, radius, luminosity with simple relation and a constant from observations. Typical wind rates are of order 10-6 M yr-1
A superwind: a stronger wind, leading to stellar ejecta observable in shell surrounding central star

14. The existence of a superwind is suggested by two independent variables
The existence of a superwind is suggested by two independent variables. The high density observed within the observed shells in stellar ejecta, and relative paucity of very bright stars on the AGB.
The latter (Prialnik P. 161) comes from the number of AGB stars expected compared to observed is >10. Hence a process prevents them completing their movement up the AGB, while losing mass at the Reimer’s rate.
This is a superwind which removes the envelope mass before the core has grown to it’s maximal possible size. Direct observations of some stars indicate mass-loss rates of order 10-6 M yr-1 . Probably this is due to pulsational instability and thermal pulses in envelope e.g. Mira type variables.
Superwind causes envelope ejection. The cores evolve into C-O white dwarfs (see Lecture 12). Core mass at tip of AGB ~0.6 M and most white dwarfs have masses close to this.

16. Summary of 1 M evolution
Approximate typical timescales
Phase  (yrs)
Main-sequence x109
Subgiant x109
Redgiant Branch 1 x109
Red clump x 108
AGB evolution ~5x106
PNe ~1x105
WD cooling >8x109
Full AGB models :
Vassiliadis & Wood 1993, ApJ, 413, 641

17. Summary of 1 M evolution