Stellar Evolution

What an HR diagram is

• A Hertzsprung–Russell (HR) diagram is a plot that arranges stars by their two most important properties:
  • Luminosity on the vertical axis (more luminous stars near the top, less luminous near the bottom). Often plotted on a log scale, with the Sun's luminosity = 1 as a reference point
  • Surface temperature on the horizontal axis, plotted backwards, with the hottest (blue) stars on the left, the coolest (red) stars on the right
• The diagram is named after the two astronomers who discovered it independently in the early 20th century

The reversed temperature axis

• The horizontal axis runs from high temperature on the left to low temperature on the right, the opposite way round from a normal physics graph. This is a historical convention you just have to remember
• The colour of each region of the diagram matches the temperature scale: blue on the left, white-yellow in the middle, orange-red on the right

The four key regions

A scatter plot of all stars in the night sky reveals four clusters:

1. The main sequence is a long, diagonal band of stars running from the top-left (hot, luminous, blue) to the bottom-right (cool, dim, red). About 90% of all stars lie on the main sequence at any given time. The Sun sits on the main sequence in the middle of the band
2. White dwarfs form a clump of stars in the bottom-left, which are hot (which would normally mean blue) but dim (because they are tiny). They lie below the main sequence
3. Red giants form a cluster in the upper-right, which are cool (red) but bright (because they are huge). They sit above the main sequence
4. Red supergiants sit at the very top-right, even cooler and even more luminous than red giants. They are the brightest stars known by sheer luminosity

What a star's position tells you

Reading the life cycle off an HR diagram

• A star's position on the HR diagram changes over its lifetime as it evolves through the stages described in sections 3 and 4
• For a solar-mass star:
  • Main sequence: sits at the Sun's position for billions of years
  • Red giant: moves up and to the right (cooler surface, much higher luminosity because the star is huge)
  • White dwarf: moves down and to the left (much hotter exposed core, much lower total luminosity because the star is tiny)
• For a massive star:
  • Main sequence: top-left of the diagonal band (hot, blue, very luminous)
  • Red supergiant: moves all the way across to the upper-right (cools as it expands, stays extremely luminous)
  • Supernova → neutron star or black hole: leaves the HR diagram altogether; the remnants are too small and dark to plot

Example — Star X has a surface temperature of 25 000 K and a luminosity of 10 000 times the Sun. Which region of the HR diagram is it in?

• Step 1 — Read off the position. 25 000 K → far left of the temperature axis (very hot, blue). Luminosity 10 000 × Sun → near the top of the luminosity axis (very bright)
• Step 2 — The top-left of the HR diagram is the upper end of the main sequence, the hot, blue, very luminous main-sequence stars
• Star X is a hot, massive, blue main-sequence star (sometimes called a blue giant or O-type star)

Example — Star Y has a surface temperature of 4000 K and a luminosity of 0.0005 times the Sun. Which region of the HR diagram is it in?

• Step 1 — Read off the position. 4000 K → towards the right of the temperature axis (cool, red). Luminosity 0.0005 × Sun → near the bottom of the luminosity axis (dim)
• Step 2 — Cool and dim places the star at the bottom-right of the HR diagram, the lower end of the main sequence
• Star Y is a red dwarf, a small, cool, dim main-sequence star

Example — Star Z has a surface temperature of 12 000 K and a luminosity of 0.002 times the Sun. Which type of star is it?

• Step 1 — Read off the position. 12 000 K → towards the left (hot, blue-white). Luminosity 0.002 × Sun → near the bottom (very dim)
• Step 2 — Hot but very dim: that combination only fits the white dwarf region in the bottom-left of the HR diagram
• Star Z is a white dwarf