Stellar Evolution

• Hertzsprung-Russell (HR) Diagram: A graph plot

indicating individual stars as points, with stellar luminosity

on the vertical axis & surface temperature (spectral type)

on the horizontal axis

• We can use spectroscopy to determine the spectral type

& luminosity of a star

• Main Sequence (MS): Prominent line of points running

from the upper left to lower right on an HR Diagram;

these stars shine by fusing hydrogen in their core

• For the Main Sequence

! Mass increases from right to left along the MS

! Most stars have low mass

! High-mass stars have short MS lives; low mass

stars have long MS lives

Hertzsprung-Russell Diagram or Color-

Magnitude Diagram

Stars stay on the main sequence most of

Their lives, burning H to Hei.e., Temperature

Increasing mass

Spectral Types

Blue Red

Emission/Absorption Features

Associated with Different S.T.s

Surface gravity, g, sets the Pressure

Gradient of Atmosphere

g = G M / R2

Spectral Sequence

Stellar radii

on HR

Diagram

Luminosity Class

• I = Supergiants

• II = Bright Giants

• III = Giants

• IV = subgiants

• V = dwarfs (Main Sequence)

Initial Mass Function -

• IMF, ! (M) = distribution in mass of freshly formed stars

• Form 1: Salpeter IMF

! (M) " M-2.35

• Form 2: Scalo IMF For M # 0.2 Msun.

• I.e., there are lots of low-mass stars & very few high-mass

stars

! (M) " M-2.45 for M > 10 Msun.

! (M) " M-3.27 for 1 Msun > M > 10 Msun.

! (M) " M-1.83 for M < 0.2Msun.

Different Mass Stars Follow Different

Tracks Along this Diagram

MS masses & lifetimes

Estimating Lifetimes on the Main

Sequence• Recall that, for the Sun, the H-burning lifetime is

• The more generic expression is

10 MSolar Star – 107 years

2 MSolar Star – 109 years

1 MSolar Star – 1010 years

Stars spend most of their lives on the MS

• For the horizontal branch, the luminosity of a star is LHB

= 50 Lsun

• During a star’s life on the HB, it converts M(He core) =

0.45 Msun into O & C

• About 0.5 of the He " O & the other 0.5 He " C

• Thus,

Pressure

• There are three sources of pressure in a star:

• Normal gas pressure -

• Radiation Pressure

• Electron Degeneracy Pressure

Electron Degeneracy

1) Pauli Exclusion Principle: No two electrons can

have exactly the same set of quantum numbers

2) It is impossible to define the position & momentum of

a particle to an accuracy better than Planck’sconstant, h. I.e., if !x & !px are the uncertainties in

the position & momentum of a particle, respectively,

then

• Pressure arises from the random motions of particles.

Thus, for electrons, even if the temperature is 0 K,

they still have motion resulting from quantummechanical effects (& !px different by at least h/!x

such as not to violate the exclusion principle),especially if #x is small

Electron Degeneracy

• To get an idea of where the pressure expression

comes from, rewrite the idea gas law as

• where vx and px are the mean x velocity & momentum

of electrons, respectively. Thus,

Electron Degeneracy

• Given the condition of charge neutrality, n+ ion perunit volume with atomic number Z & weight µ and ne

electrons per unit volume

• The density is

• And thus,

Evolutionary Tracks

Life of a Low-Mass Star1) Fusion of hydrogen into helium

2) Core hydrogen ends, star collapses, hydrogen fusion begins in

outer shell

3) Core continues to collapse, outer shell expands because of

hydrogen fusion, star becomes luminous

4) Core becomes degenerate (sustained by electron pressure), outer

shell dumps helium ash onto core

5) Helium flash! Helium fusion (into carbon) begins in core

6) Core helium fusion ends, eventually leading to both hydrogen &

helium fusion shells & a degenerate carbon core

7) End results ! outer layers drift away (planetary nebula), leaving a

naked core (white dwarf)

Life Track of 1 Solar Mass Star

Example of a Planetary Nebula

Life Cycle of a Massive Star

1) Successive episodes of shell fusion occur, leading up

to a degenerate iron core

2) Iron is unlike other elements in that no energy is

released through fusion or fission

3) Thus, core continues to accrete iron ash until

degeneracy is finally broken

4) Supernova may result in part from:

! core bounce associated with collapse into a

neutron star! release of neutrinos ($) which deposit energy

into the dense outer envelopes of the star (i.e, p+ + e- ! no + $)

The importance of Iron (Fe)

Nucleus sufficiently small for strong force to

overcome coulomb repulsion

Massive star core near end of life

Time for massive star to go supernova

• 1.4 Msun of H " Fe before exploding

• So, the mass of a Fe56 ~ 55.5 & H = 1, so, the efficiency is,

• And thus,

• If L3 x 103 Lsun, then,

Elements heavier than Fe56

• Are built through the s- & r-processes.

• The slow-process occurs as neutrons bombard &

combine with heavy nuclei at a rate < the time for

beta decay if the isotope formed is unstable

• The rapid-process occurs as neutron bombard &

combine with heavy nuclei at a rate much faster than

the beta decay timescale. Free neutrons exist in large

quantity during a supernova event

Supernova Remnant

More comments on abundances

• H, He, Li, Be, B - primordial ratios

• C, N, O, Fe - stellar nucleosynthesis

• Th, U - stellar nucleosynthesis, but must have formed

very recently

Remnants: condensed matter

• For Mstar < 8 Msolar " white dwarf

• For 8 Msolar $ Mstar $ 60 Msolar " neutron star

• For Mstar > 60 Msolar " Black Hole

Leftover after much mass loss

MWD " 0.55 – 0.6 Msolar

Typical Radius = 107 m (about Earth size)

Optically invisible, but visible as radio pulsars

MNS " 1.4 Msolar

Typical Radius = 104 m (a little taller than Mt Everest)

Optically invisible

MBH > 1.4 Msolar

Radius = 2GM /c2

Remnants: radius - mass relation

• Recall that, for a degenerate (non-relativistic) core,

• And the central pressure of a star is,

• Equating the two gives

• I.e., the volume of degenerate objects like a whitedwarf is inversely proportional to the mass

Remnants: Some numbers - Density

• Density of a white dwarf ~ 106 g cm-3. One

sugarcube-size piece of WD matter would weigh

more than a car

• Density of a neutron star ~ 2x1014 g cm-3. One

sugarcube-size piece of neutron matter would weigh

as much as the total human population of the Earth.

Note that, for a neutron,

I.e., in a neutron star, the neutrons are almost

touching.

Remants: some numbers - escape

velocity• Escape velocity of a white dwarf -

• Escape velocity of a neutron star -

• Escape velocity of a black holes = c

Remnants: Final observation

• Stars ending their lives as white dwarfs & neutron

stars have their fate determined by quantum

mechanics (degeneracy)

• Stars ending as black holes have their fate

determined by gravity