Lecture 15 PHYS1005 – 2003/4

Lecture 16: Stellar Structure and Evolution – I

Objectives:• Understand energy transport in stars• Examine their internal structure• Follow their evolutionary paths in H-R diagram

Energy Transport in Stars:

• Sun’s TC = 15 million K, TS = 5800 K• energy (heat) must flow from core surface

• but what physical processes are involved ?

Additional reading: Kaufmann (chap. 21-22), Zeilik (chap. 16)

Lecture 15 PHYS1005 – 2003/4

Energy Transport:• possibilities are:

1) radiation2) convection3) conduction

• but only radiation and convection are important in normal stars• although “radiation” is really more like “conduction”

1) Radiative Diffusion:• Photons follow a random walk from centre to surface of star

– absorbed and re-emitted many times (called “radiative diffusion”) before escaping

• e.g. in Sun’s core, mean distance travelled by photon = 0.1 mm!

• Expect luminosity L to be proportional to:– area = R2

– temperature gradient = TC / R– conductivity = κ

Lecture 15 PHYS1005 – 2003/4

• in very hot gas, electrons impede (scatter) photons

• and since ne α ρ then

• and hence

• recall that TC ~ M / R

– and since fusion is very TC-sensitive then TC ~ constant

R α M and hence – which is the M-L relation for massive (hot) stars!

2) Convection:• Convecting star has blobs rising, giving up heat, then descending again• Large T gradients convection

– which occurs when:

a) L generated in very small region

b) and/or material is very opaque (as at low T)

Lecture 15 PHYS1005 – 2003/4

Stellar Structure

• from basic physics described so far detailed computer models of stars• results stars have 2 basic structures:

High Mass (>2 MO)

Low Mass (<1.5 MO)

• TC > 18 x 106K CNO cycle fusion

• rate α T17 large L in small regioncore is convective

• outer layers hot not very opaque envelope stable, radiative

• TC < 18 x 106K P-P chain fusion

• rate α T4 small L in large region core is radiative

• outer layers cool and opaque envelope is convective

Lecture 15 PHYS1005 – 2003/4

Solar convection:

e.g. outer 1/3 of Sun convects seen as surface granulation (taken by the Swedish Solar Tower on La Palma)

Lecture 15 PHYS1005 – 2003/4

Stellar Evolution:

• 34 Core H-burning– H fuses in core– star on Main Sequence– as H fraction drops, T ↑ to compensate

more energy generated L ↑

• 456 Shell H-burning– at 4, H runs out in core– without fusion, core contracts and

heats up until H re-ignites in shell around core

– higher ρ, g H burns faster increase in L envelope expands as core contracts!

– becomes Red Giant

• 67 He ignition– T in He core reaches 108 K– He ignites (the Helium Flash)– core expands, envelope contracts– star smaller, hotter, on Horizontal

Branch

Evolution of 1MO star in H-R Diagram

Lecture 15 PHYS1005 – 2003/4

• 89 End of the line– fusion dies away– White Dwarf (remnant hot core)

emerges– cools (eventually) to a black dwarf

(as all energy sources now exhausted)

• 78 Loss of envelope– fusion now unstable– huge mass loss in wind (red

giant has R ~ 100 RO, so surface gravity g = G M / R2 is ~ 10,000 times weaker than Sun easy to drive off matter)

– core exposed Planetary Nebula

Evolutionary sequence is:– MS RG HB AGB PN WD

• 78 Shell He-burning– He runs out in core– core contracts until He ignites in shell– envelope expands Asymptotic

Giant Branch star

Lecture 15 PHYS1005 – 2003/4

HST images of planetary nebulae: