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Most physicists in the 1990s expected the expansion of the universe to be slowing down, the way a ball thrown upwards slows as gravity pulls it back. Two teams set out to measure the slowing. They found the opposite. Saul Perlmutter led one of those teams. This post tells how they did it, works through the magnitude arithmetic behind "fainter than expected", and ends with what his approach can teach you.
Who is Saul Perlmutter?
His Nobel facts page says he was born in 1959 in Champaign-Urbana, Illinois, grew up near Philadelphia, studied at Harvard and earned his PhD at the University of California, Berkeley, in 1986. He is a co-founder of the Supernova Cosmology Project and a professor of physics at Berkeley.
The 2011 press release records that half of the prize went to Perlmutter and the other half jointly to Brian Schmidt and Adam Riess of the High-z Supernova Search Team, "for the discovery of the accelerating expansion of the Universe through observations of distant supernovae". Perlmutter's project began in 1988; Schmidt's team started at the end of 1994.
Why use exploding stars as a ruler?
To measure how expansion changes, you need distances to very far galaxies. The Nobel Committee's popular science background explains that type Ia supernovae work as "standard candles". Each is the explosion of a white dwarf, an old star as heavy as the Sun but as small as the Earth, which pulls gas from a companion until it reaches about 1.4 solar masses and blows apart. For a few weeks one such supernova can shine as brightly as a whole galaxy, so it can be seen across billions of light years.
If every such explosion has nearly the same peak brightness, then how bright it looks tells you how far away it is: the fainter, the farther.
How do you find a supernova on schedule?
Supernovae are rare and unpredictable, and telescope time must be booked months ahead. In his Nobel lecture, Perlmutter describes the "batch" strategy he developed. Take wide images of many galaxies just after new moon, take them again about two and a half weeks later just before the next new moon, and subtract one set from the other. With enough galaxies, this reliably turned up more than half a dozen new supernovae, all still brightening, on a known date. That made it possible to book the large telescopes in advance for follow-up. When he warned the International Astronomical Union's telegram service that a batch of discoveries was coming, he recalls, they laughed, because nobody had predicted supernova discoveries before.
He also used the shape of each supernova's light curve: brighter explosions fade more slowly, so a "stretch factor" corrects each peak brightness.
What did the team find?
The Supernova Cosmology Project's main paper, Perlmutter et al. 1999 in The Astrophysical Journal, analysed 42 type Ia supernovae at redshifts from 0.18 to 0.83. The data were strongly inconsistent with a universe without a cosmological constant and indicated, with 99% confidence, that it is positive. The Nobel Committee summarises the two teams' result: some 50 distant supernovae looked weaker than expected, which meant the expansion is accelerating. The cause is called dark energy, thought to make up about three quarters of the universe.
Worked example: what does "fainter than expected" mean?
Astronomers measure brightness in magnitudes, where a bigger number means fainter. Two objects that differ by Δm magnitudes have a flux ratio
F₂ / F₁ = 10^(−0.4 Δm).
Suppose (as a sample number for practice) a supernova appears 0.25 magnitudes fainter than a slowing universe would predict.
Step 1: flux ratio. 10^(−0.4 × 0.25) = 10^(−0.1) ≈ 0.794. It delivers about 79% of the expected light.
Step 2: distance. For a standard candle, flux falls as 1/d². So d₂/d₁ = √(F₁/F₂) = √(1/0.794) ≈ 1.12.
The supernova is about 12% farther away than predicted. Light from it has travelled farther than a slowing universe would allow, so the expansion must have sped up while the light was on its way.
Common mistakes:
Reading magnitudes backwards. +0.25 means fainter, not brighter.
Forgetting the square root. Flux scales with 1/d², so a 21% drop in flux is only a 12% increase in distance.
Dropping the minus sign in 10^(−0.4 Δm).
For the history behind this, read about Edwin Hubble and the expanding universe and Henrietta Leavitt's Cepheid yardstick.
What can a student take from Perlmutter?
Design around your hardest constraint. His batch method came from asking what stopped the project, then planning to remove it.
Correct your measuring stick. The stretch factor made imperfect candles usable.
Trust the data, even when it surprises you. The Nobel Committee notes the result surprised the laureates themselves; independent agreement between two teams made it convincing.
If logarithms and inverse-square laws still feel shaky, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can revise each one before applying it.
Try it now: rework the example for a supernova 0.5 magnitudes fainter than expected and find how much farther away it is.
