Exam #3 Study Guide

• The Hertzsprung-Russell (H-R) Diagram

– Plot of Luminosity vs. Temperature for stars.

• Features:

– Main Sequence (most stars)

– Giant & Supergiant Branches

– White Dwarfs

• Luminosity Classification

H-R Diagram

40,000 20,000 10,000 5,000 2,500

106

104

102

1

10 -2

10 -4

Temperature (K)

Lum

ino

sity

(L

sun)

White Dwarfs

Giants

Supergiants

Main Sequence

• Most nearby stars (85%), including the Sun, lie along a diagonal band called the

• Main Sequence• Ranges of properties:

– L=10-2 to 106 Lsun

– T=3000 to >50,0000 K

– R=0.1 to 10 Rsun

Giants & Supergiants

• Two bands of stars brighter than Main Sequence stars of the same Temperature.

– Means they must be larger in radius.

• Giants

R=10 -100 Rsun L=103 - 105 Lsun T<5000 K

• Supergiants

R>103 Rsun L=105 - 106 Lsun T=3000 - 50,000 K

White Dwarfs

• Stars on the lower left of the H-R Diagram fainter than Main Sequence stars of the sameTemperature.

– Means they must be smaller in radius.

– L-R-T Relation predicts:

R ~ 0.01 Rsun (~ size of Earth!)

• Main Sequence:

– Strong correlation between Luminosity and

Temperature.

– Holds for 85% of nearby stars including the sun

• All other stars differ in size:

– Giants & Supergiants:

Very large radius, but same masses as M-S stars

– White Dwarfs:

Very compact stars: ~Rearth but with ~Msun!

Mass-Luminosity Relationship

• For Main-Sequence stars:

5.3

sunsun M

M

L

L

In words:

“More massive M-S stars are more luminous.”

Not true of Giants, Supergiants, or White Dwarfs.

• Observational Clues to Stellar Structure:

– H-R Diagram

– Mass-Luminosity Relationship

– The Main Sequence is a sequence of Mass

• Equation of State for Stellar Interiors

– Perfect Gas Law

– Pressure = density temperature

• Stars are held together by their self-gravity

• Hydrostatic Equilibrium

– Balance between Gravity & Pressure

• Core-Envelope Structure of Stars

– Hot, dense, compact core

– cooler, low-density, extended envelope

• Stars shine because they are hot.– need an energy source to stay hot.

• Kelvin-Helmholtz Mechanism– Energy from slow Gravitational Contraction

– Cannot work to power the present-day Sun

• Nuclear Fusion Energy– Energy from Fusion of 4 1H into 1 4He

– Dominant process in the present-day Sun

• Energy generation in stars:– Nuclear Fusion in the core.

– Controlled by a Hydrostatic “thermostat”.

• Energy is transported to the surface by:– Radiation & Convection in normal stars

– Conduction in white dwarf stars

• With Hydrostatic Equilibrium, these determine the detailed structure of a star.

• Main Sequence stars burn H into He in their cores.

• The Main Sequence is a Mass Sequence.

– Lower M-S: p-p chain, radiative cores & convective envelopes

– Upper M-S: CNO cycle, convective cores & radiative envelopes

• Larger Mass = Shorter Lifetime

Putting Stars Together

• Physics needed to describe how stars work:

• Law of Gravity

• Equation of State (“gas law”)

• Principle of Hydrostatic Equilibrium

• Source of Energy (e.g., Nuclear Fusion)

• Movement of Energy through star

Proton-Proton Chain:

(twice) eHpp e

2

3-step Fusion Chain

(twice) HepH 32

ppHeHeHe 433

CNO Cycle:

12 C + p N

N C e

C p N

N p O

O N e

N p C He

e

e

13

13 13

13 14

14 15

15 15

15 12 4

Main Sequence Membership

• For a star to be located on the Main Sequence in the H-R diagram:

– must fuse Hydrogen into Helium in its core.

– must be in a state of Hydrostatic Equilibrium.

• Relax either of these and the star can no longer remain on the Main Sequence.

The Main Sequence is a Mass Sequence.

• The location of a star along the M-S is determined by its Mass.

– Low-Mass Stars: Cooler & Fainter

– High-Mass Stars: Hotter & Brighter

• Follows from the Mass-Luminosity Relation:

• Luminosity ~ Mass3.5

Main Sequence Lifetime

• How long a star can burn H to He depends on:

– Amount of H available = MASS

– How Fast it burns H to He = LUMINOSITY

• Lifetime = Mass Luminosity

• Recall:

Mass-Luminosity Relationship:

• Luminosity ~ Mass3.5

Main Sequence Lifetime

• Therefore:

• Lifetime ~ 1 / M2.5

• The higher the mass, the shorter its life.

• Examples:

Sun: ~ 10 Billion Years

30 Msun O-star: ~ 2 Million years

0.1 Msun M-star: ~ 3 Trillion years

Summary of Post-Main Sequence Evolution

•Stage:

•Main Sequence

•Red Giant

•Horizontal Branch

•Asymptotic Giant

•White Dwarf

•Energy Source:

•H Burning Core

•H Burning Shell

•He Core + H Shell

•He Shell + H Shell

•None!

Post-Main Sequence Evolution of a High Mass Star

• End of the Life of a Massive Star:

– Burn H through Si in successive cores

– Finally build a massive Iron core

• Iron core collapse & core bounce

• Supernova explosion:– Explosive envelope ejection

– Main sources of heavy elements

Stellar Remnants

• White Dwarf:– Remnant of a star <8 Msun

– Held up by Electron Degeneracy Pressure

– Maximum Mass ~1.4 Msun

• Neutron Star:– Remnant of a star < 18 Msun

– Held up by Neutron Degeneracy Pressure

– Pulsar = rapidly spinning neutron star

The Milky Way:

• The Milky Way is our Galaxy

– Diffuse band of light crossing the sky

– Galileo: Milky Way consists of many faint stars

• The Nature of the Milky Way

– Philosophical Speculations: Wright & Kant

– Star Counts: Herschels & Kapteyn

– Globular Cluster Distribution: Shapley

The Milky Way and Other Galaxies:

• Disk & Spheroid Structure of the Galaxy

• Pop I Stars:

– Young, metal-rich, disk stars

– Ordered, nearly circular orbits in the disk

• Pop II Stars:

– Old, metal-poor, spheroid stars

– Disordered, elliptical orbits in all directions

• Gives clues to the formation of the Galaxy.