Lecture 9: Synthesis: The Hertzsprung-Russell Diagram

Key Ideas:

• 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

Summary of Stellar Properties

Large range of Stellar Luminosities:

• 10^-4 to 10⁶ L_sun

Large range of Stellar Radii:

• 10^-2 to 10³ R_sun

Modest range of Stellar Temperatures:

• 3000 to >50,000 K

Wide Range of Stellar Masses:

• 0.1 to ~50 M_sun

Luminosity-Radius-Temperature Relation

Stefan-Boltzmann Law:

Energy/sec/area = sigma*T⁴

The area of a spherical star:

area = 4*pi*R²

Predicted Stellar Luminosity (energy/sec):

In words: "The Luminosity of a star depends on its Temperature to the 4-th power, and its Radius squared."

Example 1:

Example 2:

Hertzsprung-Russell Diagram

Plot of Luminosity versus Temperature:

• estimate T from Spectral Type
• estimate L from apparent brightness & distance

Done independently by:

• Eljnar Hertzsprung (1911) for star clusters
• Henry Norris Russell (1913) for nearby stars

Main Sequence

Ranges of properties:

• L=10^-2 to 10⁶ L_sun
• T=3000 to >50,0000 K
• R=0.1 to 10 R_sun

Giants & Supergiants

This means they must be larger in Radius than Main Sequence stars.

Giants

• R=10 to 100 R_sun
• L=10³ to 10⁵ L_sun
• T<5000 K

Supergiants

• R>10³ R_sun
• L=10⁵ to 10⁶ L_sun
• T=3000 to 50,000 K

White Dwarfs

This means they must be smaller in radius than Main Sequence stars.

How Small? The L-R-T Relation predicts:

• R ~ 0.01 R_sun (~ size of Earth!)

An Aside:
The Hipparcos H-R Diagram of the Solar Neighborhood

The Hipparcos satellite has provided enough data to compile an H-R diagram for 4907 stars with distances measured to better than 5% accuracy. Click Here to view a full-size GIF image of this plot (Size: 32Kb). Because many stars will overlap, they use color to show how many stars sit under a single point. Red means more than 10 stars at the place on the plot.

Note the following features:

• Most nearby stars (~85%) lie along the Main Sequence, as advertised. Why this is true is an important clue to the nature of stellar evolution.
• There are few if any Supergiants in the Solar Neighborhood. In later lectures we'll learn why Supergiant stars are so rare.
• There are also few White Dwarfs on this diagram. This time, however, it is an artifact. White dwarf stars are very faint, and so Hipparcos can generally only get poor quality parallaxes for them. Since this particular H-R diagram only used the 4907 best parallaxes measured by Hipparcos, it excludes the white dwarf stars with poorer-quality parallaxes. This is an illustration of what we call "selection effects". We'll be meeting selection effects at various times later on in the class.

Luminosity Classification

• Lines get broader as the pressure increases.
• Big stars are puffier, which means lower pressure, so that

Larger stars have narrower absorption lines.

Hence:

• Giant stars have narrower absorption lines than Main Sequence stars.
• Supergiant stars have absorption lines that are narrower still.

Luminosity Classes:

Ia = Bright Supergiants

Ib = Supergiants

II = Bright Giants

III = Giants

IV = Subgiants

V = Dwarfs = Main-Sequence Stars

Spectral + Luminosity Classification of Stars:

The Sun:

G2v (G2 Main-Sequence star)

In Winter Sky:

Betelgeuse: M2Ib (M2 Supergiant star)

Rigel: B8Ia (B8 Bright Supergiant star)

Sirius: A1v (A1 Main-Sequence star)

Aldebaran: K5III (K5 Giant star)

Questions:

Why is there a distinct Main Sequence of stars?

Answer: