# Lecture 13: HR Diagrams

## Hurtzprung-Russell Diagrams

We have seen that we are able to measure some critical physical quantities related to stars. That's the first step in science: empirical observation. Now we'd like to understand what it all means. In order to do this we have to examine our raw data in some meaningful way to see if there are any patterns that emerge. Then we'll be able to make hypotheses and test them out with further observation.

Spectral Classes:
The spectra of stars are varied, but there are trends. In the early part of the 20th century a classification scheme was devised for stars based on their spectra. The different classes were then later arranged in order of decreasing surface temperature. From hottest to coolest the order is:

O B A F G K M (L)
The mnemonic most commonly used to remember this sequence is
"Oh Be A Fine Girl/Guy Kiss Me (Lovingly)"
Make up your own and email it to me.
Old Baboons Angrily Fling Green Kiwis, Mangos, and Limes

The surface temperatures that roughly correspond to the different classes are given in the following table.
 Spectral Type Surface Temperature (K) Color O > 25,000 Blue B 11,000 - 25,000 Blue A 7,500 - 11,000 White F 6,000 - 7,500 White G 5,000 - 6,000 White K 3,500 - 5,000 Red M < 3,500 Red

Clearly, O stars being the hottest are also the most blue stars (actually their peak is in the Ultraviolet so they appear to output equal amounts of energy at all visual frequencies, thus making them look white). Likewise the cool M (and L) stars are the most red.

HR-Diagram
In science, the concept of a plot or diagram is a very powerful one. It allows you to visually represent physical characteristics and look for qualitative and quantitative relationships between them.

In 1912 a pair of astronomers (by the names of Hurtzprung and Russell) independently devised a plot of some of the characteristics of a large number of stars. They plotted spectral class vs. luminosity of a large sample of stars and the resulting pattern was most interesting. The stars did not randomly scatter about the plot but rather fell into several well defined zones.

### Main Sequence

Most stars fall on a slightly curvy diagonal path (top left to bottom right). We call this the Main Sequence. The Sun is a Main Sequence, G star. We usually plot the Luminosity of stars in units of the Sun's luminosity (L = 3.83 x 1033 ergs/s). The plot spans a rather large range in luminosity. We see that there are stars with luminosities of only 10-4L and there are stars with huge luminosities of as much as 106L.

In the regions above and below the Main Sequence there are other regions where stars seem to gather on the H-R diagram. On the upper right there are stars that are very luminous and have cool surfaces (hence they are red). In the lower left of the plot there are stars which are "white-hot" but much less luminous than the stars on the Main Sequence.

This leads us to consider what is different about these stars such that they have the same surface temperatures as stars on the main sequence but have different luminosities. The answer comes from the Stefan-Boltzmann Law:

L = 4R2T4
This law tells us that if we approximate the surface of a star as a blackbody then we can see that the luminosity of a star is related to its radius and temperature. So if two stars have the same temperature but different luminosities then they must have different radii. Stars with higher luminosity must therefore be bigger than stars with lower luminosities but the same temperature.

Hence, we call the stars in the upper right Red Giants and the stars in the lower left White Dwarfs.

Further analysis also finds that stars tend to have larger radii on the hotter (blue) end of the main sequence and smaller radii on the cooler (red) end of the main sequence.

### Mass and Luminosity Trends

When we combine the information about mass that we have learned from the careful study of binary stars, we find that there is another important trend in the H-R diagram. The more luminous main sequence stars are also more massive. Thus the O and B main sequence stars are more massive than our Sun (a G star) which is in turn more massive than a K main sequence star. There is a quantifiable relationship between these quantities.
L M4
Luminosity is roughly proportional to the mass raised to the 4th power. The mass of the Sun is M = 2 x 1033 g.

This relationship is only true for Main Sequence stars. There are also trends with the red giants and white dwarfs but they are not as simple. Generally, more luminous Red Giants are more massive.

Why do stars have these differences?

What does the H-R diagram look like for a specific group of stars?