Theory — Stars: Starlight, Distances, and Stellar Evolution
Parts A and B read a star’s light; Parts C and D follow its life cycle.
Starlight carries a star’s vital statistics. Spread into a spectrum, it reveals temperature and composition; measured over time, its position reveals distance.
1. Spectral classification
Stars are sorted by temperature into the sequence O B A F G K M, from the hottest blue O stars (over 30,000 K) to the coolest red M stars (about 3,000 K). Our Sun is a G star at about 5,800 K. The pattern of absorption lines in the spectrum sets the class.
2. Luminosity and the Hertzsprung Russell diagram
A star’s luminosity is its total power output. Plotting luminosity against temperature gives the Hertzsprung Russell diagram. Most stars lie on the diagonal main sequence; cool but very bright stars are giants; hot but faint stars are white dwarfs. Where a star falls tells you what stage of life it is in.
3. Distance from parallax
As the Earth orbits the Sun, a nearby star appears to shift slightly against the distant background. Half of that annual shift is the parallax angle p. Distance follows directly:
d in parsecs, p in arcseconds
A parallax of 1 arcsecond means a distance of 1 parsec (3.26 light-years).
The smaller the parallax, the farther the star. This is the first rung of the cosmic distance ladder.
4. The interstellar medium
Between the stars lies thin gas and dust. Dust dims and reddens starlight passing through it, and glowing clouds of gas form emission nebulae. Accounting for this material is part of reading starlight correctly.
A star’s whole life is a contest between gravity pulling inward and pressure pushing outward. How that contest plays out depends above all on the star’s mass.
5. Star formation
Stars form inside cold, dense molecular clouds. A clump collapses under gravity, heats up, and becomes a protostar; when its core grows hot enough to fuse hydrogen, a star is born onto the main sequence.
6. Life on the main sequence
A star spends most of its life fusing hydrogen to helium in its core. Massive stars are far more luminous and burn their fuel much faster, so they live shorter lives. The main-sequence lifetime scales steeply with mass:
A star twice the Sun’s mass lives only about one-sixth as long.
7. Death by mass
When the core hydrogen runs out, the star swells into a red giant. What follows depends on mass: a low-mass star (below about 8 solar masses) sheds a planetary nebula and leaves a white dwarf; a high-mass star explodes as a supernova, leaving a neutron star or, for the most massive, a black hole.
8. Clusters as clocks
All the stars in a cluster formed at nearly the same time, so a cluster is a snapshot of one age. The most massive stars leave the main sequence first, so the main-sequence turnoff, the brightest point where stars are just leaving, marks the cluster’s age: the mass at the turnoff has a lifetime equal to the cluster’s age.
Apparatus
Reading starlight and tracing stellar lives use instruments that spread, measure, and compare light, and tools for imaging clouds and remnants. In the simulation these are modelled, but the readings match what each instrument would give.
Instructions
Work through all four tabs. Calculate first by hand, then press the button to compare.
Part A — Distance from parallax
- Choose a star and read its parallax angle p in arcseconds.
- Compute the distance d = 1 / p in parsecs by hand.
- Enter your distance and press Check; it compares within 3 percent.
Part B — Spectral class and the Hertzsprung Russell diagram
- Read a star’s temperature and luminosity.
- Predict its spectral class and where it sits on the diagram (main sequence, giant, or white dwarf), then press Check.
Part C — Cluster age from the turnoff
- Read the mass of the stars at the main-sequence turnoff of the cluster.
- Compute the lifetime t = 1010 × M-2.5 years; this equals the cluster’s age.
- Enter your age (in years) and press Check.
Part D — How a star dies
- Choose a star’s mass.
- Predict its end state (white dwarf, neutron star, or black hole), then press Check.
Simulation
Animated view of a nearby yellow star shifting back and forth against a field of fixed background stars as the Earth moves around its orbit; the shift is larger for a larger parallax.
A Hertzsprung Russell diagram with hot stars on the left and cool stars on the right, luminous stars at the top and faint stars at the bottom; the main sequence runs diagonally from upper left to lower right and the chosen star is plotted at its temperature and luminosity.
A cluster Hertzsprung Russell diagram: the main sequence runs diagonally and stops at the turnoff point set by the turnoff mass; stars above the turnoff have left the main sequence.
A star of the chosen mass drawn beside the remnant it leaves behind: a white dwarf for low-mass stars, a neutron star or black hole for high-mass stars.
Team Questions
Example Report
Worked example: the distance to Sirius
Sirius has a measured parallax of p = 0.379 arcsec.
d = 1 / p = 1 / 0.379 ≈ 2.64 parsecs, which is about 2.64 × 3.26 ≈ 8.6 light-years.
Sirius is about 8.6 light-years away, so the calculated and accepted values agree. Measuring the parallax and inverting it to get the distance is the calculate-then-compare core of the lab.
Worked example: the age of a cluster
A cluster’s main-sequence turnoff is at M = 1.5 solar masses.
t = 1010 × M-2.5 = 1010 × 1.5-2.5 = 1010 × 0.363 ≈ 3.6 × 109 years.
The cluster is about 3.6 billion years old, because stars more massive than 1.5 solar masses have already left the main sequence. Reading the turnoff mass and computing the lifetime is the calculate-then-compare core of the lab.