Introduction
Cosmic Rulers
Period-Luminosity Relationship
RR Lyrae: Tapping Out a Beat
Cosmic Distance Scale
Planetary Planarity
Tools of the Trade

Cosmic Rulers

Astronomers are using Hubble Space Telescope to more accurately measure the distances to stars that form an important ‘ruler’ for measuring the size of the universe

Have a friend hold up a quarter coin next to the Space Needle in Seattle, and keep your eye on it as you back away. Keep backing up until you reach, oh, let’s say the Opera House in Sydney, Australia. Ignoring the fact that you can’t actually see over the horizon, how big would the quarter appear? In the units that astronomers use to measure angles in the sky, just two-tenths of a milliarcsecond. In other words, if you split a circle into 6,480,000,000 equal segments, the quarter would be the width of one segment.

Such a tiny angle is almost impossible for the mind to grasp. And yet University of Texas astronomer Fritz Benedict and his colleagues are using Hubble Space Telescope to measure just such tiny slivers of sky by tracking tiny back-and-forth motions in the positions of stars. The size of this “wiggle” reveals a star’s distance from Earth, which can help reveal distances to similar stars in other galaxies.

The astronomers are looking at two types of “variable” stars — stars that periodically get brighter and fainter. One class is known as Cepheids, while the other is known as RR Lyraes.

These stars pulse in and out like beating hearts. Each pulse can last anywhere from a few days to a few weeks.

More than a century ago, astronomers discovered that there is a relationship between the length of each pulse and the star’s true brightness, known as the period-luminosity relationship. That makes these variable stars good “standard candles” for measuring astronomical distances.

Cepheid variable

ABOVE: Artist's concept of the Cepheid variable star Polaris, the North Star, and one of its small, faint companions. [NASA/ESA/G. Bacon (STScI)]

The idea is that if you know such a star’s true brightness, then by measuring the length of its pulses you can determine its distance.

Cepheids are especially important because they are quite bright, so they can be detected in other galaxies. In fact, Edwin Hubble, for whom Hubble Space Telescope is named, used Cepheid stars in M31 to determine that it is a separate galaxy far outside the Milky Way. His discovery greatly expanded the known universe by confirming that it contains a myriad of galaxies like our own.

Measuring the distances to Cepheids in other galaxies is one important marker in the cosmic distance scale, which uses different techniques to determine the distances to objects that are farther and farther away. This scale is critical for measuring the rate at which the universe is expanding, and the rate at which the expansion is changing as a result of the mysterious acceleration of dark energy.

For this concept to work, though, you must have accurate distances to some of the variable stars. The distances allow astronomers to measure the true brightnesses of the stars, which then allows them to calibrate the relationship between brightness and the length of the stars’ pulses. And for that you need another technique, known as parallax.

parallax

This illustration shows how Hubble Space Telescope uses parallax to measure the distances to relatively nearby stars.

To demonstrate the concept, hold a finger in front of your face. Look at it first with just your left eye, then with just your right. As you blink back and forth, the finger appears to shift a little bit against the background of more-distant objects. By measuring the distance between your eyes and the angle of the back-and-forth shift, you can determine the distance to your finger.

Astronomers do the same thing for nearby stars, using the width of Earth’s orbit around the Sun as the two “eyes.” They measure the position of a star relative to the other stars around it in January, for example, then again in July, when Earth is on the opposite of the Sun — 186 million miles (300 million km) away. Nearby stars shift back and forth against the background of more distant objects. Once they know the size of this shift, astronomers can easily calculate the star’s distance. Even for the closest stars, though, the shift is tiny, so it takes patient observations to measure it.

Astronomers have used the parallax technique to measure the distances to more than a million stars out to distances of several thousand light-years, including many variable stars. Even so, astronomers continue to improve the measurements, increasing the accuracy and level of precision.

Cepheid variables

Although they pulsate like Cepheids, RR Lyrae variables, which are named for the prototype (above), are older, fainter, and less massive. Their pulsations are shorter, too. [ESO Digitized Sky Survey]

Benedict and his colleagues are using HST’s Fine Guidance Sensors to do just that.

The sensors are essentially telescopes within a telescope. They were designed to help keep the telescope stable and to maintain a precise lock on its targets. They do so by locking onto reference stars with precisely known positions. The telescope has three Fine Guidance Sensors, but only two of them are needed to keep the telescope pointed in the right direction. That leaves the third free for other purposes.

Benedict and his colleagues are using the third sensor to precisely measure the positions of several variable stars that are inside the Milky Way galaxy, within a few thousand light-years of Earth.

As HST orbits Earth, the sensors periodically measure the positions of the target stars compared to the reference stars around them. So far, the team of astronomers has measured back-and-forth motions as small as one-fifth of a milliarcsecond for several target Cepheids. That provides parallax measurements that are more accurate than any yet obtained from either ground- or space-based telescopes. From those measurements, the astronomers have produced a more accurate period-luminosity relationship, which other astronomers are applying to measure Cepheids in other galaxies.

standard candles

If you know the true brightness of a distant light bulb, you can calculate its distance by measuring how bright it appears. The reduction in brightness follows a well-defined rule: The brightness diminishes by the square of the distance. If you move a bulb twice as far away, it will appear just one-fourth as bright; move it three times farther, and it's just one-ninth as bright (left). The same thing happens with stars, including Cepheid variables. If astronomers know a star's true brightness, then measuring its apparent brightness reveals its distance, and therefore the distance to its parent galaxy (right). [Tim Jones]

The astronomers have expanded their work by examining the distances to another class of Cepheids, which are older and therefore have lower percentages of heavy elements than the types of Cepheids studied earlier, and to RR Lyrae stars, which also pulse in and out but operate a little differently from Cepheids.

The project has provided the most accurate measurements of the distances to variable stars in the Milky Way and some nearby galaxies. And that is giving astronomers the most accurate “ruler” to date for measuring the scale of the universe.