This is a piece about my favourite diagram in all of science, the Hertzsprung-Russell (HR) diagram. It’s such a cool thing, I need to stop writing and just put it here, at the top. Here it is (please do scroll down and read the post though!).
This diagram describes and charts the properties of the stars in the galaxy. I have been meaning to write this post for a while and have been spurred into action by XKCD’s brilliant take on the subject – surely the only HR diagram ever to include a blue whale. So here goes…
Firstly, what do all the words and symbols mean?
Since unfamiliar vocabulary and structure can be confusing, let’s get some of that sorted before we begin the good stuff… This diagram is a graph of stars’ properties – it is NOT a map of where the stars are in the sky. It has surface temperature of stars on the horizontal axis, measured in kelvin. The kelvin is the SI unit of temperature. It is closely related to the degree Celsius – just subtract 273.15 from the kelvin temperature to reach °C. And when we are dealing in the thousands of degrees, as in this diagram, you could be forgiven for just taking the numbers on the axis to be approximate temperatures in Celsius.
The vertical axis shows the ‘luminosity’ of stars. This can be loosely translated as ‘star brightness’. There is actually more than one version of luminosity, depending on whether an astronomer is interested in a star’s total energy output, or output in the visible (or some other) part of the spectrum. For our purposes, if you visualise a star’s luminosity as how powerful a light source it is, you won’t go far wrong.
Notice that the scale on the luminosity axis is a logarithmic scale. That means that it doesn’t step up in equal intervals, but instead in equal ratios. So every mark on the axis is 10 times the luminosity of the previous mark. Logarithmic scales are useful when trying to display values with wide variation. Indeed, the top of the graph represents a luminosity a hundred billion times that at the bottom.
Each of the circles drawn on the graph represents a star in our galaxy, with some indication of size. The galaxy contains several hundred billion stars; we have chosen to represent that myriad with a sample of 76. The symbol ‘circle with a dot inside’ represents the Sun, so a star at ‘8 M-subscript-circle-with-a-dot-inside’ has a mass eight times that of the Sun.
So now we have decoded the graph, let’s delve into some of the patterns it contains.
Stars have colour
Perhaps the most obvious feature of the graph is that stars have colour. This is not that obvious to the naked eye, because stars are only visible at night (except the Sun!) and our eyes are not good at colour vision in low light levels (we have written about that before in a post asking why stars and planets look similar, and we have also written about colour in general). Perhaps the most obvious comparison of star colours to see yourself comes from looking at Betelgeuse (red) and Rigel (blue) at opposite corners of the constellation Orion.
Stars do have colour, and it is clear from the HR diagram that the colours of stars form vertical bands on the diagram. If we ‘collapse’ the diagram downwards, so that we lose all the luminosity information, and all the stars sit on the horizontal axis, then we can see the colours even more clearly…
As you can see, the colour of a star is basically a function purely of its surface temperature. The hotter the star, the ‘bluer’; the cooler the star, the ‘redder’, so Betelgeuse is comparatively cool, and Rigel is comparatively hot. It is worth taking time to explain this. Stars are often referred to as ‘balls of burning gas’. Now, apart from the fact that they are plasma rather than gas (we have written about that before too), it’s important to realise that they are not ‘burning’ in the conventional Earth-bound sense. The word ‘burning’ usually means ‘combusting’, which involves chemical reactions with oxygen. When we talk of a star ‘burning’, we are referring to a very different process:
- Firstly, there’s not much oxygen in space, so it can’t be combustion
- Secondly, it’s not a chemical reaction at all. Chemical reactions involve interactions between the electrons of atoms. There aren’t really any atoms as such in a star, as the star is a plasma. There are electrons in stars, but they mostly swim freely, unbound to particular atoms.
A star generates energy by nuclear reactions, not chemical reactions (it doesn’t help that we talk about ‘nuclear fuels’ which reinforces the (non)-connection with combustion). Nuclear reactions involve stronger forces and higher energies than chemical reactions, which is why stars emit so much energy. The nuclear reactions that power a star only happen in the core. In fact, that’s slightly backward reasoning – I should say, the part of a star that is hot enough for nuclear reactions to take place is called the core. And it is only hot enough (with high enough pressure) to do that in the centre (core!). For example the core of the sun is at a temperature of approximately 15 million kelvin / °C.
You will notice that 15 million degrees does not figure on the horizontal axis of the HR diagram. That is because that figure is the temperature of the core, whereas the HR diagram plots the temperature of the surface. Surrounding the core (where the energy generation is taking place), is an ‘envelope’ of potential, rather than actual fuel. The envelope is opaque to the radiation from the core. The envelope constantly absorbs and re-emits the photons (packets of energy) from the core, so that it takes thousands of years for a photon to reach the surface, before breaking free into interstellar space and, perhaps, making its way to your eyes.
It is the temperature of the surface, then, that dictates the colour of the star. A red star is ‘glowing red hot’; a white star is glowing ‘white hot’. On Earth, we don’t tend to get things hot enough to glow ‘blue-hot’; in space they do! The Sun’s surface temperature is approximately 5800 K – a yellowish-white (or whitish-yellow…).
Regions of the HR diagram
Another thing that is easily visible from the HR diagram is that stars do not just have any old combination of luminosity and temperature – those quantities are correlated. In addition, there are distinct regions on the diagram, in which the stars congregate (remember, this means sharing properties, not congregating physically in space). The Main Sequence is healthy stars in the prime of life, happily burning their fuel. At the bottom of it, labelled ZAMS, is the Zero Age Main Sequence. Baby stars are born onto the ZAMS and then burn their fuel through their lifetimes, with slowly increasing luminosity, so that the Main Sequence is broadened into a band, rather than the line of the ZAMS. (Apologies for anthropomorphising these stars – we have warned about this before, but it does make thing more poetic. And no, stars are not living things).
All the regions of the diagram apart from the Main Sequence – the giants, supergiants and white dwarfs – are stages in the retirement and deaths of stars, once the store of fuel has begun to run out. As we will see in a follow up post, not all stars retire gracefully!
There is a link between colour and brightness in the stars of the Main Sequence. The hotter the star, the brighter. That probably makes intuitive sense, and is the reason that the Main Sequence band goes from top left to bottom right. But if that’s true, why is Sirius right in the middle of the diagram? After all, isn’t Sirius the brightest star in the sky? Well, yes and no. It is true that Sirius appears brighter than all other stars from Earth (where we tend to be watching from). But that is because the apparent brightness of a star is a function of two things: how bright is really is, and how far away it is. Sirius happens to be quite luminous (though not amazingly so), and quite close to us, relatively speaking; no star apart from the Sun has a more favourable combination of luminosity and distance.
What we perceive from Earth is apparent brightness. It has been a truly immense achievement to work out the actual luminosity of the stars. That requires knowing how far away they are, which is not straightforward to say the least! The story of measuring distances in the universe is brilliantly recounted in Kitty Ferguson’s book ‘Measuring the Universe’.
Relative abundances
The HR diagram seems to show that the smaller, redder stars are more common that the larger, hotter, bluer stars. That is true, and to an extent that isn’t fully conveyed by the diagram. Up to 90 % of all stars are red dwarfs (the small dim red stars in the bottom right hand corner). 50 of the 60 closest stars to Earth are red dwarfs. But red dwarfs are so faint that not a single one is visible with the naked eye. Next time you look at the night sky, try to imagine all those close red dwarfs that you can’t see (of course, close is a relative term!).
The brighter stars are rarer, but because they are brighter they ‘shout louder’ and dominate the naked eye night sky. Sirius, Vega, Polaris, Rigel, Betelgeuse – the ones you may have heard of, all appear bright and demand attention. Unless you are a specialist in the field, it’s very unlikely you have heard about the less romantically-named red dwarfs HD 79930 or HIP 12961, and they are two of the larger ones!
Masses and lifetimes
There is a link between position on the Main Sequence and mass. The more massive stars are more luminous. So the ‘top-left’ of the Main Sequence are the more massive Main Sequence stars. In fact, position on the Main Sequence is almost entirely a function of mass, with a bit to do with age. As we have seen, the Main Sequence is broadened out from the ZAMS line because of changes that stars undergo during their lifetime. Baby stars all fall on the ZAMS, with their positions entirely determined by their masses.
The HR diagram does not extend indefinitely, which suggests that there might be upper and lower limits for the possible masses of stars. And indeed there are. The upper limit is not well defined but is several tens of solar masses. If you somehow made a star more massive than this, its radiation would be so intense that it would cause the star to disintegrate. The lower limit is more well-established. An object less than 0.08 solar masses cannot become a star, because its gravity is insufficient to provide enough heating for nuclear reactions to be initiated.
The masses of stars are shown in green in the diagram below of the ‘straightened out’ Main Sequence below.
The purple figures are the lifetimes of the stars; they display a counter-intuitive trend. The more massive the star, the shorter its lifetime. More massive stars have more ‘fuel’ available so you might expect them to last longer. But they ‘burn’ that ‘fuel’ at a disproportionately furious rate, so that in fact they use it up in a shorter time. Blue Main Sequence stars live fast and die young, at an age of perhaps only ten million years. In contrast, red dwarfs use their ‘fuel’ so slowly that there lifetime is longer than the age of the universe, which means that every red dwarf that has ever existed is still there.
Star sizes
So far, we have been careful to use the words ‘more massive’, rather than ‘larger’ because we are reserving the term ‘larger’ for discussions of size. You might think that the more massive the star, the larger it will be. For the Main Sequence that is true – the more massive, more luminous stars at top-left are also larger in size than less massive, dimmer stars at bottom right. But this connection does not apply to the giants and supergiants – these were once those self-same Main Sequence stars, but they have become bloated in old age, their mass spread out over vast volumes, giving them enormous diameters. When our own Sun becomes a red giant, it will swallow Mercury and Venus in its tenuous outer envelope. If we replaced the Sun with Betelgeuse, Mars and Jupiter would also be at risk.
Although we have drawn the circles on the HR diagram to give a sense of relative size, it is impossible to show the range of sizes in this way. The diameters of the stars are more accurately shown, compared to the Sun, by the green lines. For clarity, we will strip away the extraneous information and reproduce the HR diagram, with size information only, below.
Like the luminosity scale before, the scale of diameters is logarithmic: each dashed green line represents a diameter ten times that of the one below. So Beta Centauri, for example, is approximately ten times the diameter of the Sun, whereas Betelgeuse is approximately 1000 times the diameter of the Sun.
There are many good videos out there showing the scale of celestial objects. Here is one from morn1415. But remember, although the Sun is the second smallest star shown on the video, the vast majority of stars are red dwarfs. In fact, the Sun is bigger than 95 % of all stars.
Surveys and lifecycles
The HR diagram hasn’t finished there; we are about to discover its greatest miracle. The HR diagram is not just a static chart of the properties of all the stars; encoded within it is the lifecycle and fate of any one of these stars. It is billions of years’ worth of video distilled into a single frame.
How so? Consider this analogy. A Martian lands on Earth and has a year to learn as much as possible about human beings. It could sample a large number of humans and gather data about them. It would see births and deaths, and it would see babies change significantly, but the adults it encountered would seem relatively unchanging. And yet from the snapshot in time of a great many humans, it would be possible to make inferences about the human lifespan. A Martian would see a child growing, and infer that humans tend to get bigger rather than smaller. It might be able to realise that humans reach maturity and stop growing. It might even sense that at some point humans’ physical faculties start to wane. It would discern the ‘seven ages of humans’, without ever having seen a human go through the seven ages.
The Martian might want to take quantitative information back to Mars. It could measure certain quantities for each human it sampled, and look for correlations. It might, for example, measure the height and the speed (look, just go with this – we’re talking about Martians after all) of the humans it samples. Then a plot of these quantities might look like this…
Now admittedly, it might not too! Do not go thinking this is actual data – I’m making this bit up as I go along! Anyway, what can we tell from the ‘plot’. Well, on its own, maybe not much. But there might be accompanying information that gives clues. Such as the humans in the bottom left corner with no speed all seem to spend a lot of their time in tiny rooms with bars instead of walls. Humans call them babies – they don’t go anywhere and so have no speed. Looking at babies, it might seem perverse to think anything other than that they are young versions of humans. But that wouldn’t necessarily follow for the Martian – that’s an inference based on knowing about Earth-bound life forms. If a Martian saw a birth, however, it might link babies to youth.
And so on. The more supplementary information the Martian gathers, the more inferences it can make about the human lifecycle. At the top of the large rectangle of people on the right are young adults in the prime of life who have stopped growing. Further down that rectangle might be people who stopped growing many years ago and have lost some of their physical capability.
But here is the really important point. The green arrow might represent migration through a snapshot of a sample of humans from younger ones to the elderly. But the arrow might also represent the ‘path’ through time of a single human.
That’s really amazing – and the HR diagram does the same thing for stars. Yes, it is a survey of all stars. But it also gives information about the fate of any one star.
Astronomy is unusual in the physical sciences, in that it is not possible to set up experiments that involve meticulously changing an independent variable to see what happens. Astronomers have to deal with what they are given. And what they are given is the light (and other electromagnetic radiation) arriving at Earth from space. The length of time we have been studying the stars is insignificant in comparison to the lifetime of a star. And yet we can make inferences about the lifecycles of stars, just like Martians with humans.
That ‘life cycle’ for stars is what the second part of this post will cover. For now, just marvel at the properties of stars in our galaxy…
Acknowledgements and notes:
I have been interested in space all my life. It’s probably why I chose physics as my degree. But any rigour in this post is due to James Kaler’s wonderful book ‘Stars’. Any errors are not.
No Martians need crediting.
If you enjoyed learning about the HR diagram, I suggest your next port of call should be to learn about the spectra of stars, and the information that can be gained just from the ‘amount’ of the different wavelengths of the light they send us.
@A_Weatherall has pointed out the following video to me. Watch this – it is brilliant.