Instructor notes: Cluster Census: Sampling Stars from the Initial Mass Function

The misconceptions this demo is built to surface:

• A cluster contains a typical mix of star types, so the biggest star is about the same everywhere.
• More massive stars live longer because they have more fuel.
• A histogram of a sample and the law it was drawn from should match exactly.

Suggested flow (edit as needed):

1. Students write a prediction before touching controls.
2. Students run the play steps in pairs and record evidence.
3. Whole-class debrief: claim + evidence, then model limitations.

• 1–2 sentence explanation aligned to the “Explain” prompt.
• One claim + one piece of evidence from the demo.

• Masses are drawn from Maschberger (2013) or Kroupa (2001); the high-mass slope $\alpha$ is a control, and $2.3$ is canonical for both.
• Positions come from a Plummer (1911) or truncated EFF (1987) profile, sampled in three dimensions in pc and shown as a projection.
• Zero-age $L$, $R$ and $T_{\rm eff}$ come from Tout et al. (1996); main-sequence lifetimes from Hurley, Pols & Tout (2000) at $Z = 0.02$; remnant kinds from Heger et al. (2003).
• Above $100\,M_\odot$ the Tout fits are extrapolated. Those stars are ringed on the HR diagram and counted separately, because the fit's published domain ends there.
• Below $0.1\,M_\odot$ the fits are not used at all. Those stars appear in the cluster and the histogram but carry no HR point, rather than being clamped onto one.
• There is no post-main-sequence evolution: a star sits at its zero-age point until its lifetime elapses, then becomes a remnant. The turnoff is therefore an edge, not the hook a real cluster shows.
• There are no dynamics and no mass segregation. Dot size scales as the cube root of mass for legibility and is not a stellar radius.
• The same seed and controls always reproduce the same cluster; masses and positions are drawn from independent streams.