🔭 Overview
What this project is, and why it's built this way
This is an individual, guided research task (roughly one week of lessons + independent work) for IB Physics students. It doesn't introduce new isolated facts — it takes understandings students already have in pieces (a thermal law here, a wave phenomenon there, a diagram they memorised for a test) and forces them to be combined to answer one real scientific question, in the way an actual astrophysicist has to.
The throughline is photons in, physical story out: every stage of the journey adds one more thing you can legitimately claim to know about a star, using only the light arriving from it. By the end, students aren't just able to state Wien's law or the Doppler effect — they can explain how those separate tools, used together, are literally how humanity knows the Universe is expanding, how stars live and die, and what that implies for where everything is heading.
Two models run through the whole thing side by side:
🔥 The Thermal Model
Treats a star as a black-body radiator. From its spectrum (colour) and brightness, we infer temperature, luminosity, radius.
🌊 The Wave Model
Treats starlight as waves whose spectral lines shift with relative motion, revealing velocity — and, scaled up, the expansion of space itself.
Where every syllabus understanding lands in the journey:
| Code | Understanding | Stage |
|---|---|---|
| B1 | Stefan–Boltzmann law, L = σAT⁴ | Stage 1 — Thermal |
| B1 | Apparent brightness, b | Stage 1 — Thermal |
| B1 | Luminosity, L | Stage 1 — Thermal |
| B1 | Wien's displacement law, λmaxT = 2.9×10⁻³ mK | Stage 1 — Thermal |
| C5 | Spectral line shifts reveal motion | Stage 2 — Wave |
| C2 | Intensity (wave model — inverse-square spreading of energy) | Stage 2 — Wave |
| E5 | Stellar equilibrium: radiation pressure vs. gravity | Stage 3 — Structure |
| E5 | Fusion as the energy source in stars | Stage 3 — Structure |
| E5 | Density/temperature conditions for fusion | Stage 3 — Structure |
| E5 | Effect of stellar mass on evolution | Stage 4 — Evolution |
| E5 | HR diagram: regions and stellar properties | Stage 4 — Evolution |
| E5 | Stellar parallax, d(pc) = 1/p(arcsec) | Stage 5 — Scale |
| E5 | Determining stellar radii | Stage 5 — Scale |
⭐ Your Star & Finding Real Data
Choose one star from the shortlist below, then pull its real measurements yourself from SIMBAD and the Gaia Archive
Every value in this project — temperature, brightness, distance, velocity — is going to come from a real, professionally-measured catalogue, not a worksheet. Pick one star below to be your star for the whole project. Stars are grouped by where they'll eventually sit on the HR diagram, so a spread of choices across the class will give a great class-wide comparison at Stage 4.
| Region | Star | Why it's worth choosing | |
|---|---|---|---|
| Cool dwarfs (main sequence) | Tau Ceti | Nearest single Sun-like star; has its own planetary system | Great starter |
| 61 Cygni A | The very first star to ever have its parallax measured (Bessel, 1838) | Great starter | |
| Epsilon Eridani ("Ran") | Young Sun-like star with a debris disk and confirmed planets | Great starter | |
| Barnard's Star | Closest single star to the Sun after the Alpha Centauri system | Great starter | |
| Proxima Centauri | The single closest star to the Sun; hosts the planet Proxima b | Great starter | |
| Hot dwarfs (main sequence) | Sirius A | The brightest star in the night sky | Great starter |
| Vega | The historic reference star the whole magnitude scale was once calibrated against | Great starter | |
| Procyon A | Bright, and already visibly evolving off the main sequence | Great starter | |
| Giants | Arcturus | Brightest star in the northern sky; a red giant seen with the naked eye | Rich comparison |
| Pollux | The nearest giant star to the Sun; has a confirmed planet | Rich comparison | |
| Supergiants | Betelgeuse | Red supergiant nearing the end of its life — will one day go supernova | Rich comparison |
| Rigel | Blue supergiant; one of the most luminous stars visible to the naked eye | Rich comparison | |
| Spica | Hot, massive, close binary system | Rich comparison | |
| Stellar corpses (evolved endpoints) | Sirius B | The white dwarf companion of Sirius A — same distance, wildly different physics | Advanced |
| Procyon B | The white dwarf companion of Procyon A | Advanced | |
| Van Maanen's Star | An isolated white dwarf, with no bright companion to compare it to | Advanced |
Strongest extension: choose Sirius A + Sirius B, or Procyon A + B, as a pair — same distance, same age, but one is still fusing and one is a stellar corpse. Excellent material for the Stage 3–4 equilibrium/evolution argument. (Drawn from and extending your existing Star Cards 3.0 set — the rest of that set, including the ultra-cool dwarfs and brown dwarfs, works well as a further extension for students who want a harder challenge.)
How to find your star's real data
- SIMBAD (simbad.cds.unistra.fr/simbad) — search your star's name. Under Basic data, note its spectral type. Under Measurements → Fluxes, note its apparent magnitude (V if available, otherwise G). Under Measurements, note its parallax (in mas — divide by 1000 for arcsec) and, if listed, its radial velocity.
- Gaia Archive (gea.esac.esa.int/archive) — search the same star by name to find its Gaia DR3 parallax and photometry independently. Comparing the two sources is genuine evaluation material for your write-up: do they agree, and if not, why might that be?
From magnitude to apparent brightness, b
Archives report brightness as an apparent magnitude, not directly as b in W m⁻². Bridge the two using the Sun as your calibration star, since you already know its brightness (the solar constant) and its magnitude:
bstar = b☉ × 10^(0.4 × (m☉ − mstar))using b☉ = 1361 W m⁻² and m☉ = −26.74. This comes directly from how the magnitude scale is defined (a ratio scale in steps of 100.4 ≈ 2.512 per magnitude) — it isn't a new law, just a translation between a more common way of recording the information and apparent brightness — both are ways of describing the same brightness.
🧭 The Journey
Five stages, each adding one more layer of knowledge about the same target star
The Thermal Model — What colour tells you about temperature
Every student is issued (or chooses, see Design Notes) a real star with a published spectrum and apparent brightness. The guiding question: if all I have is a graph of intensity against wavelength, and a brightness measurement, what can I already say about this star?
Tools
λmaxT = 2.9 × 10⁻³ m K L = σAT⁴ b = L / (4πd²)Guiding questions
- From the peak of your star's black-body curve, what is its surface temperature?
- Why does a black-body spectrum let us treat a star — which is not literally black — as a black-body radiator?
- If you know luminosity and apparent brightness, what have you actually determined, and why is that useful before you even know the distance?
The Wave Model — What a shifted line tells you about motion
Now students look at their star's real radial-velocity data and at a second, larger-scale dataset, to see the same physics operating at two completely different scales.
Tools
Δλ / λ ≈ v / cPart A — your star
Look up your star's radial velocity on SIMBAD (see Your Star & Data). Using the Hα line (rest wavelength 656.3 nm) as your reference, calculate the wavelength shift Δλ that radial velocity would produce, and state whether the line is redshifted or blueshifted.
Part B — how far, how fast: a galaxy cluster dataset
The table below is a simplified teaching dataset (Ca II K line, rest wavelength 393.4 nm) modelled on the classic multi-cluster redshift–distance exercise. For each cluster: calculate the wavelength shift, then the recession velocity, then plot velocity (y) against distance (x).
| Cluster | Distance (Mpc) | Observed λ of Ca II K (nm) |
|---|---|---|
| Virgo | 17 | 395.0 |
| Ursa Major | 210 | 413.1 |
| Corona Borealis | 320 | 422.3 |
| Boötes | 480 | 438.0 |
| Hydra | 650 | 452.4 |
(Rest wavelength of Ca II K: 393.4 nm. This dataset is simplified/idealised for teaching, not raw archive data — built so the gradient of your graph comes out close to the accepted value of the Hubble constant.)
Guiding questions
- Is your star's spectrum redshifted or blueshifted relative to lab values? What does that mean physically?
- What does the gradient of your velocity–distance graph represent, and what are its units?
- What would it mean if, when astronomers looked at galaxy after galaxy, almost all of them showed redshift, and the further away a galaxy was, the larger its redshift?
- The formula Δλ/λ ≈ v/c is only a non-relativistic approximation, so it becomes less accurate as v gets closer to c. Roughly what fraction of c is "too fast" for it to be trusted, and why doesn't that limit matter much for the velocities in this dataset?
Structure — Why the star hasn't collapsed, or exploded, yet
Now the question shifts from "what is this star doing" to "why does this star exist in a steady state at all." Students build the equilibrium argument and connect it to the nuclear process that actually powers the radiation measured in Stage 1.
Guiding questions
- What two forces/pressures are in balance inside a stable star, and what happens if one temporarily "wins"?
- Where does the outward pressure actually come from, physically?
- Why does fusion require both extreme density and extreme temperature — what is each one doing to make fusion possible?
- What would happen to your Stage-1 star's equilibrium if fusion in its core stopped tomorrow?
Evolution — Where mass takes you
Students place their star on a Hertzsprung–Russell diagram using the T (Stage 1) and L (Stage 1) they already calculated, then use its position and estimated mass to argue about its past and predict its future.
Guiding questions
- Where does your star sit on the HR diagram, and what does that position alone tell you about its current life stage?
- How does a star's mass set both how brightly it burns and how long it lasts?
- Trace your star's likely future track across the HR diagram. What will it become?
- Why do only the most massive stars end their lives explosively, while low-mass stars fade quietly?
Scale — Putting real numbers on distance and size
The final piece: how far away is this star, actually, and how big is it? This stage closes the loop — once distance is known independently (parallax), apparent brightness from Stage 1 becomes a true measurement of luminosity, and radius can be derived without ever needing to "see" the star's disc.
Tools
d (pc) = 1 / p (arcsec) L = σAT⁴Finding & cross-checking your parallax
Pull your star's parallax from both SIMBAD and the Gaia Archive (see Your Star & Data). If the two disagree, that's not a mistake — it's real measurement uncertainty, and worth commenting on directly in your write-up.
Guiding questions
- Why does parallax only work for relatively nearby stars — what breaks down at large distances?
- Now that you have a genuine distance, combine it with your Stage-1 brightness to check or refine your luminosity value.
- Using L and T, calculate your star's radius. How does it compare to the Sun's?
🌌 Synthesis — So, what is the future of the Universe?
Where the two models meet
By Stage 5, you'll have a complete physical biography of one star, built entirely from light. Now zoom out from that single star to the Universe as a whole, using exactly the same two tools:
The local future
Every star's story ends. Your Stage 3–4 work already predicts your star's death. Multiply that across every star in every galaxy, and stellar evolution alone tells you the Universe's light sources are finite — stars form, burn, and go dark on characteristic timescales set by their mass.
The large-scale future
Your Stage 2 Doppler measurement, repeated across thousands of galaxies, is the actual historical evidence (Hubble, 1929, and everyone since) that the Universe is expanding — and that the expansion is accelerating. That single measurable quantity, redshift, is the observational basis for every serious model of the Universe's ultimate fate.
By the end of this project, you should be able to give a physics-grounded (not just popular-science) answer to the driving question — naming exactly which measurement (spectral shift, black-body spectrum, HR position) supports which claim about the future: of your star, and of everything.
📝 Choose Your Assessment
Data-Based Investigation Report
Students choose a real star from the shortlist (see Your Star & Data) and pull genuine data from SIMBAD and the Gaia Archive. They reconstruct T, L, R, distance and velocity as in the journey, then write a structured report culminating in a discussion linking their star's fate to the Universe's future.
Assessed against: the current DP Sciences IA criteria — Research Design, Data Analysis, Conclusion, Evaluation (6 marks each, 24 total) — applied here to this project rather than to the IA itself.
Comparative Poster + Oral Defence
Students choose 3–4 stars spanning different HR-diagram stages, produce a poster or infographic comparing them, then face a short oral defence probing whether they actually understand the physics behind their claims, not just the numbers on the page.
Assessed against: Content & Accuracy, Comparative Insight, Design & Communication, Oral Defence (6 marks each, 24 total) — a poster/oral-adapted version of the same four skills.
Structured Exam-Style Paper
A standalone structured-question workbook, in the same numbered-question / command-term / mark-allocation style as your existing exam reviews, using given spectra/parallax/brightness data and finishing with a longer "discuss" question on implications for the Universe's future.
Why it works: fastest and most consistent to mark at scale; doubles as direct, realistic exam preparation under timed conditions.