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Galaxy NGC4414 from HST Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Lecture 11: The Internal Structure of Stars

Readings: none(!)

Key Ideas

From Stellar Properties to Stellar Structure

Any successful theory of stellar structure must explain the observed properties of stars.

Seek clues in correlations among the observed properties, in particular:

The Hertzsprung-Russell Diagram

Recall the Hertzsprung-Russell (H-R) Diagram introduced back in Unit 1. This is a plot of Luminosity vs. Temperature for stars:

H-R Diagram

The most prominent feature of the H-R diagram is the Main Sequence (M-S):

All other stars differ in size:

Giants & Supergiants:

White Dwarfs:

Mass-Luminosity Relationship

If we make a plot of Luminosity vs. Mass for the Sun and all Main Sequence stars in binary systems that have good mass measurements, we that a Main Sequence star's Luminosity is very strongly correlated with its Mass:

Mass-Luminosity Relationship

This strong correlation is called the Mass-Luminosity Relationship. It is expressed mathematically as:

M-L Relation
In words:
"More massive M-S stars are more luminous."
This relation is only true for Main Sequence stars: Giants, Supergiants, and White Dwarfs do not follow the Mass-Luminosity relation.

The graph above shows data for the Sun and 121 binary stars for which there are reliable mass estimates (mostly eclipsing binaries with some nearby visual binaries, particularly at the low-mass end). Clicking on the plot will show a full-size version. The line drawn is the best-fit M-L relation.[11.1]

Mean Stellar Density

The mean density[11.2] of a star is:
Mean Density = Mass / Volume
Main Sequence: small range of mean densities

Giants: Low-density stars: ~10-7 g/cc (e.g., K5III)

Supergiants: Very low-density: ~10-9 g/cc (e.g., M2I)

White Dwarfs: High-density stars: ~105 g/cc

For reference, at sea level on Earth, water has a density of 1 g/cc, and air has a density of ~0.001 g/cc.

Interpreting the Observations:

For Main-Sequence Stars:

Implies that they have similar structures & governing laws.

Giants, Supergiants, and White Dwarfs must have very different internal structures from M-S stars of similar mass.

Laws of Stellar Structure I: The Ideal Gas Law

Most stars obey the Ideal Gas Law:[11.3]
Pressure = Density x Temperature

In words:

Tells us how changes in the internal Temperature of a star affects its internal Pressure.

Laws of Stellar Structure II: The Law of Gravity

Stars are very massive & bound together by their Self-Gravity

Gravitational Binding Energy increases as 1/R

In words:

Hydrostatic Equilibrium

Two opposing forces are at work within a star:

Pressure & Gravity work on each other:

Hydrostatic Equilibrium

When there is exact balance between the two, we have a condition of Hydrostatic Equilibrium.

In this condition, the star neither expands nor contracts.

Core-Envelope Structure

Outer layers press down on the inner layers.
The deeper you go into a star, the greater the pressure.
The Gas Law says:
Great pressure = hotter, denser gas
The consequence is that the star develops a Core-Envelope structure:
Core-Envelope Structure Schematic

Example: The Sun

Core: Envelope:

The Essential Tension

The life of a star is a constant tug-of-war between Gravity & Pressure.

Tip the internal balance either way, and it will change the star's outward appearance. This establishes an important principle for how stars work:

Internal Changes have External Consequences

Thus, changes in the interior conditions of stars will be reflected in their outward appearances, and hence affect where they will be located in the H-R Diagram.

Return to [ Unit 2 Index | Astronomy 162 Main Page ]
Updated: 2006 January 15
Copyright Richard W. Pogge, All Rights Reserved.