VII. Observation of the Sun and the Stars

We start with our sun as an example:

Energy source of our solar system
Sun is a typical star -> good example for all other stars

The material for the many stars needs to be organized.

1. Luminosity, Distance, Size

A) Magnitudes etc.

First and most obvious parameter: How bright is the star in the sky?

old classification according to sensitivity of the eye
Bright 1 ..... 2 ...... 3 ...... 5 ...... 6 Faint
(higher value of magnitude means fainter)

Brighter can mean -> more luminous and/or
-> closer to us Ergo: We need the Distance!

B) Distances:

Sun: r = 150 Mio km
derived through Kepler's 3rd law and parallax to other planets
Stars: parallax with the orbit of the Earth as baseline
(largest baseline possible)
very skinny triangle (works up to approx. 100 parsec)

C) Size:

Sun: d = 1.39 Mio km derived from angular size (skinny triangle)
Stars appear as points, even in largest telescopes

D) Luminosity

Energy flux (sun): L = 4*1026 Watt

derived from energy flowing through 1 m2 at the distance of the Earth

approx. 1400 Watt/m2 (solar constant)
and multiplied by the surface of the sphere at the distance of the Earth

Total energy radiated on Earth is > 10000 times the energy used by mankind!!

-> may be enough for our energy demands

Our energy usage must remain at tiny fraction of the solar energy flux!

Artificial production of only 1.3% of the solar energy flux
-> 1o C temperature increase on Earth
radiation balance (as discussed for sun below)

Stars: L = total energy emitted by the star
(derived from magnitude and distance: parallax).

Magnitude (or Brightness) scales like Luminosity*1/Distance2

2. Spectroscopic Measurements

A) Temperature:

Sun: T = 5500 K derived from solar radiation
sun is the best "black body" in the solar system
--> photons have many collisions with matter before escaping
--> photons "know" about temperature
Black Bodies: stars, planets, cloud tops, rocks in rings, dust particles
Not Black Bodies: corona, nebulae (not dense)

A "Blackbody" spectrum

a) is peaked with a distinct maximum at a certain wavelength
b) Its total radiation and distribution over wavelength depends only on T

  a) Wien's Law:
temperature* wavelength(max) = constant
sun has maximum at green (our eyes work best for this color) -> T
hot stars: blue, UV.
sun: yellow.
cool stars: red.
very cool stars:
dust heated by stars: IR.

-> We can get the temperature from the color or the wavelength with the maximum

Spectra of Different Temperatures

b) Stefan Boltzmann Law:
energy flux = constant * T4
in words: higher energy flux -> means higher temperature of the star
or a brighter star surface

Application to the observation of stars:

B) Size of stars get:

From distance and magnitude combined ->Luminosity
From Wien's Law -> Temperature
Form Stefan-Boltzmann Law -> Energy Flux/area
Combine Luminosity and Energy Flux/Area -> Surface of Star
-> Diameter

C) Composition:

Sun: 75% H, 23% He, 2% "metals"
Derived from Fraunhofer lines in spectrum
Each atom, ion, molecule absorbs or emits at its own set of frequencies.
Reason: Electrons are confined to specific orbits in atoms
(Bohr's Model of atoms <-> Quantum Mechanics)

Energy output vs. wavelength

Absorption line: material in front of "black body" -> sun's atmosphere
Emission line: thin material radiating -> outer atmosphere
-> identify

Nebulae = gas clouds = emission lines (not black body)

Galaxies = sum of black bodies from many stars (plus the stars' absorption lines)

Uses (for all stars):

a) What's there? (H, He, etc.). determined by specific set of lines
Hydrogen alpha line = red (most abundant element)
(Hydrogen at 10,000K or near a star at 10,000K)
prominences -> red is the color of the universe!

b) Abundances: relative intensity of lines
-> differences in composition

The universe was born with H and He only (almost)  
Population I: 75% H, 23% He, 2% heavy elements ("recycled" material ) Sun is Population I
Population II: 77% H, 23% He, few heavy elements ("more primitive" material)
Where are the true "Þrst" stars (H, He only)?

3. Stellar Mass and Density

A) Solar Mass:

M = 2*1030 kg derived from Kepler's 3rd law (planets)

B) Binary Stars and Mass Determination

Velocities can be measured with Doppler Effect:

Spectral lines key to Doppler: (we know the frequencies when there is no motion)
Velocity Away from us --> frequency decreases = redshift
Velocity Toward us --> frequency increases = blueshift
Velocity Across --> no shift

2 possible ways to get the star mass:

1) Doppler effect -> Velocity of stars
+ orbital period
2) Distance of binary stars -> distance between 2 stars
+ orbital period

use Kepler's 3rd law -> mass of stars

C) Density r:

Sun: r = 1.4 g/cm3 combined from 2B) and 3A)
1.4 times density of water
Red Giants: much less dense
White Dwarfs: much denser

Determination of the Star Parameters

Parameter Observation Deduction

Apparent Magnitude Measure Brightness
Distance Parallax Distance
Luminosity Combine:
Distance and Apparent Magnitude
Surface Temperature Color of Star (Wien's Law)
Spectral Lines
Energy Flux/Area from Temperature
Size Combine: Luminosity
Energy Flux/Area
Composition Spectral Lines Elements
Mass Distance or Velocity and Use Kepler's 3d Law
Orbital Period of Binary Stars

4. Classification

According to their color stars have been organized in classes:

A) H-R diagram.

Essentially luminosity vs. temperature.

Main sequence (distinct line filled with stars through the center diagonal)

H-R Diagram

a) Sizes: White Dwarfs hot (high energy flux density) and dim -> small

b) Spectral Parallax:

c) Variable stars (e.g. Cepheids)

B) Mass Luminosity Relation

Luminosity of stars varies like Mass * Mass * Mass * Mass

The poor are saving and the rich are squandering -> massive stars die faster

Determination of Star Distances

Method Observations How to do?

Geometric Parallax Measure star position Use diameter of Earth's orbit
(6 months apart as baseline!)
(approx. 100 Parsec) -> angle and Earth's orbit lead to distance
(like distance of the moon or planets)

Spectroscopic Parallax Measure temperature Find position of star in HR
of star diagram
-> get luminosity and apparent magnitude
(approx. 20,000 Parsec) -> luminosity and magnitude lead to distance

Cepheid Variables Measure period Period determines of variable luminosity
and apparent magnitude
(approx. 20 million Parsec) -> luminosity and magnitude lead to distance

Go to Chapter VIII