How do we measure distances to other stars?

Hubble Image of a Variable Star
Credit: Wikipedia

Earlier this month, astronomers were excited to discover three supernovas in far-off galaxy, with a huge galaxy cluster sandwiched between us and them. The galaxies’ enormous gravity magnified the light of the exploding stars, an effect called gravitational lensing.

Since these were a particular type of exploding star, they can be used as cosmic yardsticks. That means astronomers were able to check the prescription, as it were, of the gravitational lenses. This is important for measuring the structure of the Universe (including dark matter), and for making sure astronomers’ measuring tools are calibrated correctly.

"We have found Type Ia supernovae that can be used like an eye chart for each [galaxy] cluster," says Hubble astronomer Saurabh Jha of Rutgers University. "Because we can estimate the intrinsic brightness of the Type Ia supernovae, we can independently measure the magnification of the lens."

But what is a cosmic yardstick? How do astronomers measure unimaginably huge distances to other stars and galaxies? They need a whole suite of measurements, depending on how far you want to look. Just as a ruler will help you measure a few inches, while you move up to a measuring tape to gauge several feet, astronomers use different tools for different scales. The whole suite is called the cosmic distance ladder, in which each technique provides information that can be used for the next step up. And they all use the physics of light.

Gravitationally Lensed Supernova

Stars in Our Neighborhood

Astronomers measure nearby stars in the Milky Way with simple trigonometry. As the Earth moves around the Sun, the positions of some stars in the sky appear to change relative to other, more distant stars. This is called parallax.

Our eyes use the same trick to give us depth perception, and you can test it: point at a spot on the wall, and then close one eye at a time. The object appears to move behind your index finger. The closer something is to the observer, the greater the parallax. For astronomy, first you need to know how far the Earth is from the Sun, which gives you the size of its orbit. This measurement forms the bottom of an isosceles triangle. Then you measure a star’s relative position at six-month intervals, noting the difference in its location on the sky. These views give you the two sides of your triangle. The center angle is the parallax. Once you measure that, you can figure out the length of the sides of your triangle — meaning how far away the star is.

This only works for relatively close stars, however — at great distances, the parallax view is vanishingly small. From the ground, the farthest star we can measure is about 326 light years away; from Earth orbit, it’s about 1,600 light years out, according to this helpful explainer. This includes other stars in our immediate neighborhood, but it's not even close to the whole galaxy, let alone the cosmos. To go farther than that, we need to use another trick of light.  

Parallax View

Stars Across the Galaxy

Back in 1908, Henrietta Leavitt was working at the Harvard College Observatory, examining photographic plates to search for variable stars. Variable stars are stars that change in brightness over a period of hours or weeks, as their helium heats and expands, and then cools and contracts. By studying variables in the Small Magellanic Cloud, Leavitt figured out that there was a clear link between the brightness of a star and its period, or how long it took to brighten, dim and brighten again. These stars are called Cepheid variables, and their discovery enabled cosmology as we know it.

Here’s why: stars that are farther away seem fainter, because their light spreads out and gets diffused. This is the inverse square law of photons. So, if you know how bright something is supposed to be, and you can compare that with how bright it actually looks, you’ll be able to tell how far away it is. And Leavitt had found that if you know its period, you know how bright it’s supposed to be. To be sure this method is calibrated properly, you’d need to correlate brightness with the actual distance to one Cepheid — and astronomers did that for Delta Cephei, which is close enough to measure with parallax.

It’s crucial to show that a "standard candle" like Cephid variables is in fact standard everywhere, otherwise all your measurements are off, however. In the 1950s, astronomer Walter Baade figured out that some nearby Cepheid variable stars were different types than faraway Cepheids in other galaxies. This meant astronomers weren’t comparing like with like, and it meant the faraway Cepheids were actually much farther away than anyone thought. His measurements doubled the size of the Universe

Hubble Variable Star V1

Distant Galaxies

Several other standard candles can measure distances within our galaxy, and can be cross-calibrated in different ways. But beyond galactic scales, to objects outside the Milky Way, astronomers frequently rely on exploding stars.

Supernovas come in several shapes and sizes, but one in particular, the Type Ia supernova, is especially important for cosmic yardsticks. These explosions happen in binary systems, where a white dwarf star starts to vacuum up matter from its red dwarf companion. As the white dwarf gains mass, it ignites a runaway nuclear fusion reaction and blows itself to smithereens.

There is a very specific size limit where this happens, so supernovae of this type all have roughly the same mass, which means they have roughly the same brightnesses. If you can compare this to its brightness relative to you, you can tell how far away it is. This means Type Ia supernovae can also be used as standard candles, and at distances far beyond the reach of a Cepheid variable star.

So what does the recent Hubble supernova discovery tell us? Jha, Jakob Nordin and dozens of colleagues explain in two new papers, published in the Astrophysical Journal and the Monthly Notices of the Royal Astronomical Society, that Type Ia standard candles can be used to measure gravitational lensing — and shed some light on dark matter and dark energy. The teams found three new supernovae, nicknamed Tiberius, Didius, and Caracalla, which were each gravitationally magnified by a different massive galaxy cluster. Then, they measured the brightnesses of these supernovae and compared that to their intrinsic, peak brightnesses. These exploding stars looked much brighter than they should have, given their distances from us — an effect of the huge amounts of matter, including dark matter, that warped their light as it traveled toward Earth. How much brighter they got depended on how much matter was in their paths.

Think of it as the prescription of the gravitational lens. The prescriptions give astronomers measurements of the matter inside galaxy clusters. This helps them study how gravity and dark energy interact to form the large-scale structures of the Universe. “The more confirmation we get that our complex cluster models are correct, the more we can rely on them, and use them to probe the early Universe,” says astronomer Jean-Paul Kneib of Ecole Polytechnique Federale de Lausanne in Switzerland.

All thanks to the cosmic distance ladder and its standard candles.

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