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:
	protostars:
	dust heated by stars:	IR.
	planets:
	cloudtops:

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

	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)

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)
	e.g.
		chromosphere
		prominences	-> red is the color of the universe!
		nebulae

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
		or
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
		(Stefan-Boltzmann)
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:

• blue yellow red
• O(hot) B A F G(sun) K M(cool).
• "Oh, Be A Fine Girl (or Guy) Kiss Me"

A) H-R diagram.

Essentially luminosity vs. temperature.

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

• Red supergiants, red giants (upper right).
• White dwarfs (lower left).
• Main sequence: most stars (90%) (stars spend most of their lives on main seq.)
• Main sequence: most stars are less massive than the sun because
• they burn fuel slowly and live a long time (the sun is not an average star).
• Main sequence: few O & B stars: they don't live long
• Few giants, supergiants: don't stay around long ("senility")
• White dwarfs (10%): "dead"

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

• Red Giants cool(low energy flux density) and bright -> huge

b) Spectral Parallax:

• the 2nd way of getting stellar distances
• Each point on the HR diagram has a spectral signature (lines).
• Use spectral lines to locate star on HR diagram.
• HR diagram --> luminosity.
• Luminosity & apparent brightness Þ distance.

c) Variable stars (e.g. Cepheids)

• variation period increases with luminosity
• the 3rd method to determine stellar distances
• Cepheids used as huge standard candles

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?
(Range)

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