Star Clusters

Jed Rembold

February 11, 2026

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The luminosity of a star is the amount of energy per second it emits at its surface
- Can work backwards if distance and apparent brightness known
- Absolute magnitude is another way to indicate this
A parsec is a distance that corresponds to one arcsecond of parallax angle
Stars are classified according to their spectra, ordered by temperature (OBAFGKM)
Star size increases from lower left to upper right on an HR diagram

The power source for stars is fusion: converting hydrogen to helium in the core
Fusion requires getting atoms so close to one another that the extremely strong but extremely short ranged strong nuclear force can bind them together
The nuclei of atoms are all positively charged though, so they aggressively repel one another
For fusion to have a chance of happening then, you need extraordinary conditions:
- Very high temperatures: implying lots of heat and the atoms really flying around
- Very high densities: implying lots of targets for atoms to run into

Gravity (determined by mass) pulls outer gases inwards
As the gases fall inwards, they gain energy, in the form of heat
The heated gas pressure pushes back on the force of gravity, until things are in equilibrium
The weight the pressure needs to support increases as you go deeper into the star
- Thus temperature and density also increase to keep things in balance

Without an energy source (or with too weak an energy source), a star would slowly cool
- It’s existing temperature would radiate energy out into the universe
With too strong an energy source, a star would swell up and explode!
- No “battery” to store amounts of energy
Stars must also thus be in energy balance
- Energy produced in core = Energy emitted from surface
Whatever mechanism transfers the energy (and there are several), it has to be able to keep up

As a result of both balances, stars are remarkably self-regulating
Is the star slightly too cool?
- Pressure won’t be able to support, so gravity will pull things in tighter
- Things getting tighter means denser, which means more temperature, which pushes back and stops gravity
- Higher temperatures result in more fusion reactions in the core, which correspondingly results in more energy released from the surface
Takeaway:
- As long as a star is in balance, fusing hydrogen, it will remain in the same place on the HR diagram

A small difference in mass can result in a huge difference in the core temperature of the star, and hence its luminosity
- O Star
  - \(60 M_\odot \,\rightarrow\, 100000 L_\odot\)
- M Star
  - \(0.2 M_\odot \,\rightarrow\, 0.01 L_\odot\)
A star’s mass of hydrogen is its fuel source though!

All stars form from collapsing gaseous clouds of hydrogen
Generally then, many are formed around the same time and location
The initial group can slowly “evaporate” over time as stars move away from one another
- If there is still enough mass, stars may remain gravitationally bound nearby
Why are they interesting to us?
- All stars in a cluster around about the same distance away
- All stars in a cluster are around the same age

All stars in a cluster formed around the same time, but some will have shorter lifetimes!
By looking at a cluster, you get a snapshot of stars at various stages of their life
By looking at many clusters, we can start to build up an intuition of how stars evolve throughout their lifetimes

Once we understand the solar lifecycle, we can apply it back when looking at unknown clusters
The key is to look for the main sequence turn-off point
- The further toward the upper-left that this corner or “elbow” appears, the younger the cluster
Can sometimes see stars appearing down in the white dwarf region for really old clusters

Found in the galactic disk
Generally up to several thousand stars
Stars tend to be younger, more newly formed
Most famous the Pleiades structure
- Visible with your naked eye in even moderately dark skies
- A quick scan of the sky will show it easily in your peripheral vision