Lecture 12: The Classification of Stars

Chapter 17: pages 442-456

The Secrets Unlocked by the Spectrum of a Star

In 1735, the philosopher August Comte wrote the following statement about the stars:

"We see how we may determine their forms, their distances, their bulk, their motions, but we can never know anything of their chemical structure or their mineralogical structure."

The Sun's Spectrum

In 1816, Joseph Fraunhofer passed sunlight through a prism, revealing its spectrum.

He saw a continuous band of colors just as in a rainbow.

However, certain colors are missing and one just sees a black line instead.

Fraunhofer determined that the two missing yellow lines had the exact same wavelength as the two yellow lines emitted by sodium when heated by a bunsen burner.
We now call the dark lines in the Sun's spectrum the Fraunhofer lines.

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The Spectra of Other Stars

Other stars also have absorption spectra.
The darkness of an absorption line is called its strength.
Different types of stars show different absorption line strengths.


	This star has very strong Hydrogen absorption lines.


	This star has very weak Hydrogen absorption lines. This star has very strong Sodium absorption lines.

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Classification based on (mostly) Hydrogen Absorption Lines

In the late 1800's and early 1900's observatories took the spectra of thousands of stars.
A group of astronomers at Harvard began to try to classify the spectra in order to make some sense of the information.
Williamina Fleming led a group that classified the stars based on the strength of their Hydrogen absorption lines.
The classification was alphabetical:
- Class A = Stars with darkest H absorbtion lines
- Class B = Stars with not as dark lines as Class A
- Classes later in the alphabet correspond to weaker lines.
- Latter classes has lots of lines
- O,P,Q were special classes
Today we only use the letters: ABFGKMO

Each spectral type showed a different characteristic set of dark lines.


	Type A
	Type B
	Type F
	Type G
	Type K
	Type M
	Type O

At first, astronomers thought that this meant that each spectral type had a different chemical composition. This was wrong !
This classification is example of the mess you get as the first step, when you have no idea what is responsible for what you see. Recall, even structure of atoms was unknown then !

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Temperature and the Spectral Sequence

With the knowledge of the structure of atoms, we know that absorption spectral lines are very sensitive to the temperature. They are quite "fragile" when temperature changes.

Hydrogen Balmer lines example:
- Balmer absorption lines are jumps from/to n=2 level. Balmer absorption is larger more atoms are in n=2 excited state.
- Increase temperature - atom is ionized and cannot absorb, spectral lines disappear.
- Decrease temperature - all atoms are in ground state, there is no Balmer absorption and for Lyman absorption you need very energetic UV photons.

Same with other lines in more complex atoms: You need to be hot enough to have properly excited atoms, and not too hot to pull out all electrons from the levels that are responsible for those lines.

Strength of a spectral lines is non-monotonic with temperature !
Rather it has a bell-like shape

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Idea: Spectral types are surface temperature classification, but shuffled in a wrong order !

Proof is in the pudding: The idea works if one can sort the spectral types in the order such that intensities of all observed line sequences, (not just for hydrogen, but for all other elements as well) follow the temperature "bell-like" curves.

Indeed, such order can be found and the Spectral classes, in order of hottest to coolest are: OBAFGKM

One mnemonic for remembering the sequence is:

"Oh Be A Fine Girl/Guy, Kiss Me".
Further fine-tuning: Subdivide each letter class into 10 divisions: K is split into
K0, K1, K2, ... K9 with K0 hotter than K9.

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The Spectral Sequence from Coolest to Hottest:

Type	Temperature		Examples
M0	3900 K	Red Stars	Betelgeuse
K0	5200 K	Hotter than M, so more H absorption than M	Aldebaran, Pollux
G0	5900 K	Hotter than K, so more H absorption than K	The Sun, Capella
F0	7500 K	Hotter than G, so more H absorption than G	Procyon, Polaris
A0	11,000 K	Darkest H Absorption lines	Sirius, Castor, Mizar
B0	30,000 K	Hotter than A, more H ionization so less absorption than A	Rigel, Regulus
O5	50,000 K	Hotter than B, most H is ionized so even less absorption	Mintaka (Right-most belt star in Orion)

Our Sun is a G2 star.

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The Hertzsprung-Russell Diagram

Ejnar Hertzsprung and Henry Norris Russell (1913) investigated the relation between spectral class and luminosity of stars.
They considered a number of stars with known distance d, brightness b and spectral class.
From d and b find the luminosity L which gives information about the actual power output by the star.
From spectral type (or colour) find the surface temperature T of the star.
Plot of L versus T called a Hertzsprung-Russell Diagram (H-R diagram)
This program can be performed only for nearby stars (Why ?). Modern data relies on parallaxes for thousands of nearby stars from Hipparcos satellite

H-R diagram is an example of what scientists call scatter plot. If one observes objects with two parameters - just mark these objects on the plot by points.

The aim is to see of there are any dependencies between the two parameters.

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The H-R Diagram

Temperature decreases to the right since blue colour is on the left and red colour is on the right.

The luminosity (or power) of the stars increases upwards.

Most stars (90%) lie on the diagonal band running from top left to bottom right.

This band is called the Main Sequence

Main Sequence stars have the following property: The hotter their surface temperature, the more powerful they are.

Stars which are more luminous than the main sequence stars are called Giants and Supergiants.

Stars which are less luminous than the main sequence stars are called White Dwarfs.

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Sizes of Stars: Giants and Dwarfs

A star's luminosity obeys the Stefan-Boltzmann equation
L = 4 &pi R² &sigma T⁴

Knowing the luminosity L and temperature T of a star, one can determine its radius R

R = (L / (4 &pi &sigma T⁴) )^1/2

On H-R diagram the stars

of same temperature, lie on a vertical line
of the same luminosity, lie on a horizontal line
of the same radius, lie on an inclided line

Therefore

From two stars of the same temperature the larger star is more luminous.
From two stars of the luminosity the larger star is cooler.
Stars above the Main Sequence (MS) are larger than MS stars so we call them giants.
Stars above the giants are larger than the giants so we call them supergiants.
Stars below the MS are smaller than MS stars, so we call them white dwarfs.
(One piece of confusing terminology: Some people call MS stars dwarfs! Red dwarfs are just type K and M MS stars.)

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Luminosity Classes

Further classification:
Roman Numerals denote how relatively powerful the star is.

The full classification includes both Temperature and Luminosity classification.
For example:
- The Sun is a Type G2 Main Sequence Star: G2V
- Aldebaran is a Red Giant: K5III

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Next lecture: Binary Stars
Read Chapter 18, pages 456-463