Variable stars and the distance ladder

Most stars look the same night after night. Some do not. They grow brighter, fade, and brighten again, over and over. These are called variable stars.

One kind is especially useful. A Cepheid is a giant star that swells and shrinks on a steady beat, getting brighter and dimmer as it does. Some take a few days over each beat and some take weeks. The slower the beat, the brighter the star really is.

That is a great help, because a light in the dark does not tell you how far away it is. A dim light could be a torch nearby or a lighthouse far off. But if you know how bright it really is, you can work out its distance from how faint it looks. Time a Cepheid’s beat and you know how bright it really is.

In 1923 the astronomer Edwin Hubble found a Cepheid in a hazy patch of sky called Andromeda. Its beat took a month, so it had to be a very bright star, and yet it looked very faint. It was far too distant to be part of our own galaxy. Andromeda was a galaxy of its own, and the universe was much bigger than most people had thought.

Stars that change. A variable star is one whose brightness changes. There are several reasons it can happen. Some stars are really two, and one passes in front of the other. Others truly change, because the star itself swells and shrinks. Mira, a red giant, takes 331 days over each cycle and at its faintest is more than a hundred times dimmer to the eye than at its brightest.

Cepheids. The most useful pulsing stars are the Cepheids, named after Delta Cephei, a star you can see without a telescope. In 1784 John Goodricke noticed that it brightens and fades every 5.366 days. At its brightest it gives about twice the light it does at its faintest. A Cepheid is a supergiant, far more luminous than the Sun. Its core burns steadily. The pulse comes from its outer layers, which swell past the point of balance, fall back under gravity, and bounce out again. Cepheids have periods from about 1 day to 70 days. The nearest one is Polaris, the Pole Star, 430 light years away.

Leavitt’s law. In the early 1900s Henrietta Leavitt, working at Harvard College Observatory, searched photographs of the two Magellanic Clouds and listed 1,777 variable stars in them. In 1908 she remarked that the brighter ones had the longer periods. By 1912 she had the periods of 25 in the Small Magellanic Cloud and the pattern held. What made this so valuable is that all the stars in the Cloud are at much the same distance from us. If one looks brighter than another, it really is brighter. So the period of a Cepheid tells you its true brightness.

From brightness to distance. Light thins out as it spreads. A lamp moved twice as far away looks a quarter as bright, and one ten times as far looks a hundred times fainter. So if two Cepheids keep the same beat, and one looks a hundred times fainter than the other, it is ten times further away. An object whose true brightness is known, so that its distance can be read from how faint it looks, is called a standard candle.

Leavitt’s law gave the distances of Cepheids compared with each other. To turn those into light years, somebody has to measure the distance to a few Cepheids in another way.

The star that moved Andromeda. In the early 1920s astronomers argued over the faint spiral patches seen in telescopes. Some thought they were clouds inside the Milky Way. Others thought they were whole galaxies far beyond it. In October 1923 Edwin Hubble photographed the largest, Andromeda, and found a star in it that turned out to be a Cepheid with a period of 31.4 days. A Cepheid that slow is very luminous, yet this one was extremely faint. Hubble worked out that it was about a million light years away, more than three times Harlow Shapley’s estimate of the width of the whole Milky Way, which was itself too generous. Andromeda was a galaxy. Hubble’s figure was too small, and the distance used today is about 2.5 million light years, but the conclusion has stood ever since.

The ladder. No one method reaches all the way out, so astronomers use several, each one set by the one below. This is the distance ladder.

Rung	What is measured	How far it reaches
Parallax	The tiny shift of a star as the Earth goes round the Sun	Stars in our own galaxy
Cepheids	The period of a pulsing star	Galaxies out to about 130 million light years with the Hubble telescope
Type Ia supernovae	The peak brightness of an exploding white dwarf	Far beyond the Cepheids
Redshift	How fast a galaxy is moving away	Everything further still

The Gaia spacecraft measured the parallax of Cepheids in the Milky Way, which fixes how bright a Cepheid of a given period really is. Cepheids then give the distances of nearby galaxies. Some of those galaxies have also held a Type Ia supernova. These explosions all reach nearly the same peak brightness, so they are standard candles too, and far brighter ones. With their true brightness set by the Cepheids, they give distances to galaxies much too far away for a single star to be picked out. Those distances, set beside the galaxies’ speeds, give the Hubble constant, and after that a galaxy’s speed alone gives its distance.

A mistake on a low rung is carried up to every rung above, which is why so much work goes into the bottom of the ladder.

Other pulsing stars. RR Lyrae stars are fainter cousins of the Cepheids, with periods of a day or less. They all have about the same true brightness, and they are common in globular clusters. Early in the 20th century Shapley used them to estimate the size of our galaxy.

Still being worked out. The ladder now gives a Hubble constant of 73 km/s for every megaparsec, with an uncertainty of about 1. A quite different method, which starts from the oldest light in the universe and works forward, predicts 67.4. The two do not agree, and nobody yet knows why. Neither figure is used on this site, which takes a round 70.

What the 3D view shows. The view opens outside our galaxy with Andromeda marked. It is drawn 2.55 million light years away, the modern measured distance, and the star Hubble found is far too faint to be shown. Close beside the Milky Way are the two Magellanic Clouds where Leavitt found her law, the Large Cloud at 166,000 light years and the Small Cloud at 209,000. Further out, every galaxy on the map of the cosmic web is placed by the top rung of the ladder: its measured speed divided by a Hubble constant of 70. Among the stars of the night sky, Polaris is drawn in its place, but the stars here are drawn at a steady brightness, so it does not pulse.