Investigating an aspect of astronomy with real data

What AS 91415 asks of you

• AS 91415 is a 4-credit internal. You research one aspect of astronomy, gather information and data from a wide range of reliable sources, process it, and report.
• Achieved: select and process good-quality information about the aspect and the science behind it, and explain the aspect.
• Merit: explain the key science in depth, such as the gravity, light or nuclear physics that makes the aspect work.
• Excellence: explain the key links between the aspect and that science, showing how each piece of science accounts for what is observed.
• The aspect can be an event (a supernova, an eclipse, a comet), a discovery (exoplanets, gravitational waves), a principle (Kepler's laws, stellar evolution) or knowledge gained from a space probe or telescope.

Choosing a question

• Pick an aspect narrow enough to explain fully and rich enough to have real data you can process yourself.
• Turn it into a question: not 'exoplanets', but 'How do astronomers find the size and orbit of a planet from a star's light curve?'
• A New Zealand link can make a strong report: the MOA project at Mt John Observatory near Tekapo has found planets by gravitational microlensing, and the stars of Matariki are a young cluster whose distance Gaia has measured.

Where to find real data

• Exoplanets: the NASA Exoplanet Archive lists every confirmed planet with its period, radius, mass and the star's properties, each with uncertainties and a reference to the paper.
• Light curves: the Kepler and TESS space telescopes measured the brightness of hundreds of thousands of stars; their data are public through NASA's MAST archive.
• Star catalogues: ESA's Gaia mission has measured positions, parallaxes, brightness and colours for well over a billion stars.
• Orbits: NASA's planetary fact sheets and JPL's Small-Body Database give orbital data for planets, moons, asteroids and comets.
• Primary data from space agencies and peer-reviewed papers are the most reliable; news stories and websites are useful for ideas but must be checked against them.

Reading a transit light curve

• A light curve is a graph of a star's brightness against time. If a planet's orbit is lined up with our view, the planet blocks a little of the star each time it passes in front: a transit.
• The fraction of light blocked equals the fraction of the star's disc covered: depth = (Rp ÷ Rs)², where Rp is the planet's radius and Rs the star's.
• The time between dips is the orbital period, and repeated dips of the same depth rule out a one-off event such as a starspot or an instrument glitch.
• From the period and the star's mass, Kepler's third law gives the orbit's size, so a light curve and a star catalogue together give a planet's size and orbit.

Try it: find a planet by its transit

Orbital data and Kepler's third law

• Kepler's third law: the square of a planet's orbital period is proportional to the cube of its average distance from its star, T² ∝ a³. For anything orbiting the Sun, with T in years and a in astronomical units, T² = a³.
• It follows from gravity: Newton showed T² = 4π²a³ ÷ GM, so the constant depends only on the mass M of the central star, which is how astronomers weigh stars from their planets.
• Plotting log T against log a turns the curve into a straight line with gradient 1.5, a good way to test the law with real data.

Star catalogues and parallax

• As Earth orbits the Sun, a nearby star seems to shift against distant ones. Half that shift, measured from opposite sides of the orbit, is the parallax angle p.
• Distance in parsecs is d = 1 ÷ p, with p in arcseconds; 1 parsec = 3.26 light years. The smaller the parallax, the further away the star.
• With distance and apparent brightness you can find a star's true luminosity; with its colour you know its surface temperature, and the two together place it on the Hertzsprung-Russell diagram, which shows its stage of life.
• Gaia's parallaxes are precise for stars out to thousands of light years, but every value comes with an uncertainty, and for distant stars that uncertainty can be large.

Try it: the HR diagram

Evaluating sources and conclusions

• For each source, record who produced it, whether it was peer reviewed, how recent it is, and whether it gives the uncertainty in its numbers; quote the uncertainty when you use a value.
• Check your processed results against the archive: if your planet radius from a light curve matches the catalogue value within its uncertainty, your method is supported.
• State the assumptions behind each calculation: a circular orbit, a star's radius that is itself measured with error, a transit that crosses the middle of the star.
• Separate what the data show from what is inferred: a transit shows a dark object of a certain size; that it is a gas giant is an inference from its size and, if known, its mass.

What Achieved, Merit and Excellence look like

• The same idea, written up at each grade for a report on the transit method.