Star clusters are not only spectacularly beautiful, they are also spectacularly useful for helping us understand how stars form and evolve — and even for helping us understand what physical processes take place deep in their cores that cause them to shine, and the factors that affect their luminosities at different stages of evolution. The reason for this is quite simple: star clusters are groups of stars that all formed from the same gas cloud, at about the same place (within a few parsecs) and about the same time (within a few million years). All the stars within a cluster therefore have the same chemical composition, essentially the same age, their light has all travelled to us from the same distance, and it has been partially obscured by the same clouds of interstellar gas and dust.
And because of all these things, those variations you noticed in images of star clusters — in apparent brightness and colour — have to be true, intrinsic differences in the stars’ brightnesses and colours.
From this observation, we can already draw an important empirical inference: individual stars do vary — rather dramatically, as you’ve seen — in both intrinsic brightness and colour.
And yet, despite these differences, young stars are all fundamentally the same in one crucial respect: they’re giant balls of matter that generate energy by fusing hydrogen atoms into helium atoms within their cores. That energy is absorbed by particles in the core, heating it, and through subsequent re-emission and absorption the energy generated in the core slowly makes its way to the surface through a random walk, where it is finally emitted by the star as thermal radiation.
Beyond the general description of young stars—as balls of mainly hydrogen and helium, which generate energy through hydrogen fusion in their cores and emit thermal radiation from their surfaces—the apparent differences in brightness and colour that we see from one star to the next can be easily understood through three observations:
- A star must emit as much energy from its surface as it generates inside its core—otherwise, it would expand due to the outward pressure this energy generates. The rate at which the star emits energy in the form of electromagnetic radiation is called its luminosity.
- A star emits thermal energy, which depends on its surface temperature. Equilibrium at the star’s surface is maintained when the energy that is emitted into space is replenished by energy generated in core fusion reactions; therefore, the surface temperature does not fluctuate. A star emits a constant blackbody spectrum (with absorption features that depend on the state of its atmosphere), and its apparent colour depends on how much light is emitted at different wavelengths across the visible spectrum.
- The two intrinsic physical characteristics of a young star that determine both its luminosity and its surface temperature are mass and the abundance of elements heavier than hydrogen in its core. Essentially:
- Greater mass means both luminosity and surface temperature will be greater; and,
- Higher concentrations of heavy elements increase luminosity but decrease surface temperature.
The physical reasons underlying these last two bullet points are straightforward to explain.
The reason greater mass increases both luminosity and temperature in young stars is essentially due to the fact that more mass creates greater internal pressure, increasing core temperature and hydrogen fusion reaction rates. This already explains the increased luminosity by point 1 above. But the increased gravitational pressure in a more massive star also more than compensates for the increased outward radiative pressure that comes with higher luminosity. Therefore, the star ends up more compact, and its surface temperature is also greater.
In contrast, the reason higher concentrations of heavy elements increase luminosity but decrease surface temperature is that all elements heavier than hydrogen (which do not participate in these reactions) effectively screen those reactions — so the core temperatures and pressures needed for fusion to occur in a star of the same mass must increase with increasing concentrations of heavy elements. This extra screening forces the core to work harder, increasing energy production and therefore luminosity. But this extra luminosity increases the outward radiative pressure without any corresponding increase in gravitational pull — so the outer layers are pushed further out, the star’s radius grows, and its surface temperature ends up lower despite the higher luminosity.
Both effects — increasing mass and increasing heavy-element abundance — lead to greater luminosity. What separates them is gravity: more massive stars have stronger gravitational fields that keep their surfaces hot and compact despite the higher energy output, while stars with more heavy elements do not.
Astronomers refer to the total abundance of elements heavier than hydrogen and helium as a star’s metallicity. This effect of metallicity on surface temperature is not just relevant for comparing stars of different compositions — it also operates within a single aging star. As a young star fuses hydrogen into helium over its lifetime, the helium accumulating in its core acts as a screening contaminant, gradually increasing the star’s luminosity, increasing its radius due to the corresponding outward pressure increase, and ultimately cools its surface. The Sun today is more luminous and cooler than it was when it formed 4.5 billion years ago. And when stars eventually exhaust their core hydrogen entirely and evolve into red giants, this same mechanism operates in a far more dramatic way — luminosities surge, causing stars to swell to enormous sizes, while surface temperatures drop.
Now, how does all this connect back to the observational features of star clusters?
Well, as you determined at the outset, the stars in a cluster vary most prominently in colour and brightness. And — since all the stars in a cluster have the same chemical composition (metallicity), they’re all at the same distance, and their light passes through the same amount of interstellar dust en route to Earth — the three observations above effectively mean that (as long as the stars in a cluster have not run out of hydrogen to fuse in their cores):
- the variations we see in color and brightness must only be due to differences in mass of the individual stars in the cluster; and
- if we graph each star’s brightness against its color we should find that the stars in a young cluster range from bright blue (i.e. luminous and hot) to dim red (i.e. dim and cool).
This graph of brightness vs color is commonly called a Hertzsprung-Russell (HR) Diagram, after the two astronomers who first studied these graphs of luminosity vs temperature in stellar populations. As you will learn through the course of this activity, the HR Diagram is an incredibly powerful tool for examining the properties of a star cluster — and for understanding the physical processes involved in stellar evolution.
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