The Hertzsprung-Russell Diagram (HSC SSCE Physics): Revision Notes

The Hertzsprung-Russell diagram

What is the Hertzsprung-Russell diagram?

The Hertzsprung-Russell diagram (often called the H-R diagram) is one of the most important tools in astronomy for understanding stars and their evolution. It reveals fundamental relationships between a star's brightness, temperature, and stage of life.

The diagram is named after two astronomers who independently made the same discovery. In 1911, Danish astronomer Ejnar Hertzsprung plotted the actual brightness of stars against their colour. Two years later in 1913, American astronomer Henry Russell created a similar plot showing absolute magnitude against spectral class. Both scientists discovered something remarkable: stars don't scatter randomly across the diagram, but instead cluster in distinct regions. This pattern tells us that certain combinations of brightness and temperature are common, whilst others are rare or don't exist at all.

Understanding the axes of the H-R diagram

The H-R diagram has two axes that contain crucial information about stars.

Vertical axis: absolute magnitude

The vertical axis shows absolute magnitude, which measures a star's true brightness. This scale might seem backwards at first: lower numbers (including negative values) represent brighter stars, whilst higher positive numbers represent dimmer stars. This historical scale originated when ancient astronomers called the brightest stars "magnitude 1" and fainter stars "magnitude 2, 3" and so on. When more precise measurements became possible, brighter stars were assigned negative magnitudes.

On the H-R diagram, absolute magnitude ranges from about $-10$ (extremely bright) at the top to $+15$ (very dim) at the bottom.

Horizontal axis: spectral type and temperature

The horizontal axis shows spectral type, which classifies stars by their surface temperature and colour. The spectral types are designated by letters: O B A F G K M, running from hottest to coolest (left to right on the diagram). A useful mnemonic to remember this sequence is: "Oh Be A Fine Guy/Girl Kiss Me".

The diagram also shows temperature along the top, ranging from approximately $25,000°C$ on the left to $3,000°C$ on the right. Each spectral type is further divided into ten subtypes (for example, A0, A1, A2... A9) for more precise classification.

Star groups on the H-R diagram

When thousands of stars are plotted on an H-R diagram, they form distinct regions that correspond to different types of stars at different stages of their lives.

Main sequence

The main sequence is the most prominent feature of the H-R diagram - a diagonal band stretching from the upper left (hot and luminous) to the lower right (cool and dim). Most stars, including our Sun, belong to this group. What defines a main sequence star is what's happening in its core: these stars are actively fusing hydrogen into helium through nuclear reactions.

The main sequence exists because there's a direct relationship between a star's mass and its temperature. More massive stars have stronger gravity, which compresses their cores to higher densities and temperatures. This causes fusion reactions to proceed more rapidly, making the star both hotter at its surface and more luminous overall. Conversely, less massive stars have cooler surfaces and lower luminosity.

Red giants and red supergiants

Red giants occupy the upper right region of the H-R diagram. These stars present an interesting puzzle: they have relatively cool surface temperatures (hence their red colour and M or K spectral types), yet they're extremely luminous. The only way a cool star can be very bright is if it has an enormous surface area - these stars are truly gigantic in size.

This large size is confirmed by examining the width of absorption lines in their spectra, which indicates lower atmospheric pressure. Despite having greater mass than smaller stars, the surface of a red giant is so far from the centre that gravity is weaker there, resulting in lower atmospheric density and pressure.

White dwarfs

White dwarfs are found in the lower left region of the H-R diagram. These stars are hot (giving them white or blue-white colours), yet they're very dim. This combination tells us they must be extremely small - typically about the same size as Earth.

White dwarfs are not actively fusing elements in their cores. Instead, they're the collapsed remnants of stars like our Sun that have exhausted their nuclear fuel. They shine only from residual heat, gradually cooling over billions of years. Their high surface gravity creates dense atmospheres, which can be detected through narrow spectral lines.

Blue giants

Blue giants are rare, short-lived stars found in the upper left region of the H-R diagram. They're both very hot and very luminous. Importantly, blue giants are not main sequence stars despite being massive. The key difference is that they're fusing heavier elements (not just hydrogen) in their cores, indicating they're in a more advanced stage of stellar evolution.

Subgiants

Subgiants (luminosity class IV) occupy a region between the main sequence and the red giant region. These stars are transitioning from main sequence stars to giants, having exhausted the hydrogen in their cores but not yet fully expanded into red giants.

Stellar evolution and the H-R diagram

The H-R diagram isn't just a snapshot of different types of stars - it's also a map of stellar evolution. As stars age, they move through different regions of the diagram.

The life cycle of a star

Stars begin their lives and evolve through distinct stages, with the path they follow depending primarily on their mass.

Protostar stage

Before a star is born, it exists as a protostar - a hot ball of gas collapsing under its own gravity. During this stage, no nuclear reactions are occurring yet. The energy that makes the protostar glow comes from gravitational potential energy: as material falls inward, gravitational energy converts to heat.

This process continues until the core becomes dense and hot enough for nuclear fusion to begin. A star is truly "born" when hydrogen fusion ignites in its core.

Main sequence stage

Once hydrogen fusion begins, the star enters the main sequence stage, where it will spend most of its life. During this stage, the star remains stable because there's a balance between two opposing forces:

• The outward pressure from radiation and hot gas
• The inward pull of gravity

Stars of different masses spend vastly different amounts of time on the main sequence:

• Stars with the Sun's mass remain on the main sequence for about $10$ billion years
• Massive stars (about $10$ solar masses) consume their fuel rapidly and may last only tens of millions of years
• Low-mass stars ($0.1$ solar masses) burn their fuel so slowly they could theoretically last as long as the current age of the Universe

Post-main sequence evolution

When the hydrogen fuel in a star's core becomes depleted, gravity takes over and the core collapses. This collapse increases the core's density and temperature dramatically. The layer of helium that has accumulated around the core gets compressed so much that helium fusion can begin - an event called the "helium flash".

What happens next depends critically on the star's mass:

Using the H-R diagram to classify stars

The H-R diagram is a powerful tool for analysing different populations of stars. An interesting comparison can be made between the brightest stars we see in the night sky versus the closest stars to Earth.

When we plot the $20$ brightest stars visible from Earth on an H-R diagram, we get a very different pattern compared to plotting the $20$ closest stars. The brightest stars include many red giants, supergiants, and blue giants - all extremely luminous objects that can be seen from great distances. In contrast, the closest stars are predominantly small, dim main sequence stars and white dwarfs.

Investigation 13.2: Plotting stars on an H-R diagram

Aim: To compare the results of plotting the $20$ brightest and the $20$ closest stars on an H-R diagram

Materials:

• Data tables provided below
• Pen, paper, ruler (or graphing software)

Data:

The $20$ brightest stars in the night sky:

Star	Apparent magnitude, $m$	Absolute magnitude, $M$	Spectral type
Sirius	1.45	+1.41	A1
Canopus	0.73	+0.16	F0
Rigil Kentaurus (Alpha Centauri A)	0.10	+4.3	G2
Arcturus	0.06	−0.2	K2
Vega	0.04	+0.5	A0
Capella	0.08	−0.6	G8
Rigel	0.11	−7.0	B8
Procyon	0.35	+2.65	F5
Achernar	0.48	−2.2	B5
Hadar	0.60	−5.0	B1
Altair	0.77	+2.3	A7
Betelgeuse	0.80	−6.0	M2
Aldebaran	0.85	−0.7	K5
Acrux	0.9	−3.50	B2
Spica	0.96	−3.4	B1
Antares	1.0	−4.7	M1
Pollux	1.15	+0.95	K0
Fomalhaut	1.16	+0.08	A3
Deneb	1.25	−7.3	A2
Mimosa	1.26	−4.7	B0

The $20$ closest stars to Earth:

Star	Distance (ly)	Apparent magnitude	Absolute magnitude	Spectral type
Proxima Centauri	4.2	11.1	15.5	M5
Rigil Kentaurus	4.3	−0.01	4.4	G2
Alpha Centauri B	4.3	1.33	5.7	K1
Barnard's Star	6.0	9.54	13.2	M4
Wolf 359	7.7	13.5	16.7	M6
BD +362147	8.2	7.5	10.5	M2
Luyten 726-8A	8.4	12.5	15.5	M6
Luyten 726-8B	8.4	13.0	16.0	M6
Sirius A	8.6	−1.46	1.4	A1
Sirius B	8.6	8.3	11.2	A
Ross 154	9.4	10.45	13.1	M4
Ross 248	10.4	12.29	14.8	M5
Epsilon Eridani	10.8	3.73	6.1	K2
Ross 128	10.9	11.1	13.5	M4
61 Cygnus A	11.1	5.2	7.6	K4
61 Cygnus B	11.1	6.0	8.4	K5
Epsilon Indi	11.2	4.7	7.0	K3
BD +4344A	11.2	8.1	10.4	M1
BD +4344B	11.2	11.1	13.4	M4
Procyon A	11.4	0.4	2.6	F5

Method:

1. Draw axes for your H-R diagram using about half an A4 page. The vertical axis should show absolute magnitude ($M$) ranging from $-10$ at the top to $+15$ at the bottom. The horizontal axis should show spectral type from O on the left through B, A, F, G, K to M on the right.
2. Using the brightest stars data table, plot each star's position using its absolute magnitude and spectral type. Note that each spectral type is divided into ten subtypes (for example, A0, A1, A2... A9).
3. On the same axes but using a different colour, plot the closest stars data.

Results:

1. Keep your completed diagram for your notes.
2. Identify and draw lines around the main sequence, red giant, and white dwarf regions on your diagram.

Discussion questions:

1. Compare and contrast the plots from the two data sets. The brightest stars show a much wider spread across the H-R diagram, including many giants and supergiants in the upper right, and some blue giants in the upper left. The closest stars cluster predominantly on the lower main sequence, with mostly M-type red dwarfs, plus a few white dwarfs.
2. Which data set provides a more valid random sample of stars in our night sky? The closest stars represent a better random sample because they include all types of stars within a certain distance, regardless of how bright they appear. The brightest stars data is biased toward intrinsically luminous stars (giants and supergiants) because these can be seen from great distances, even if they're actually quite rare.
3. Why does the brightest stars data contain many very luminous stars but few small main sequence stars? Luminous stars (giants, supergiants, blue giants) can be seen from enormous distances across the galaxy, so even though they're rare, many appear in our night sky. Small main sequence stars are actually very common, but they're so dim that we can only see them if they're very close to Earth. Therefore they're under-represented in the "brightest stars" list but dominate the "closest stars" list.

Conclusion:

When comparing the H-R diagrams of the brightest versus closest stars, clear differences emerge. The brightest stars include a disproportionate number of giants and supergiants because these extremely luminous objects can be seen from great distances. The closest stars predominantly consist of dim main sequence stars (especially red dwarfs) and white dwarfs, which reflects the true distribution of stellar types in our galaxy. This demonstrates that what we observe in the night sky is biased toward intrinsically bright objects, not representative of the actual stellar population.