Chapter 17. Stellar Parallax

17.1 Introduction

Measuring the parallax of a nearby star

The goals of this module: After completing this exercise, you should be able to:

1. Demonstrate what parallax is and how to measure it.
2. Explain what simplifications astronomers make with the parallax formula and why they are able to do so.
3. Calculate the distance to any star, given its parallax angle.

In this module you will explore:

1. The inverse relationship between the distance to a star and its parallax angle
2. The limitations of ground-based telescopes in measuring parallax angles and why we need space satellites to measure these values
3. The fraction of the Galaxy for which we can measure parallax shifts of stars and the limiting distances using this method

Why you are doing it: One of the most fascinating questions in astronomy is "How far away is everything?" There are a number of distance measurement techniques, each of which relies on the accuracy of other methods to measure smaller distances. Therefore, knowing how astronomers measure distances to high accuracy using stellar parallax is of extreme importance in astronomy and has a deep impact on measurements of the remainder of the universe!

17.2 Background

Observing parallax on Earth

Hold up your index finger on one hand and hold it out at arms length. Now, look at it first through one eye, then the other, blinking back and forth. What do you notice about its apparent position relative to objects further away? You should notice that your finger appears to move relative to background objects. Did you actually move it? No, but it appeared to move anyway. Why? Because you were looking at it from two different perspectives: first through one eye, then the other; and they are not located in the same place. Likewise, in the figure to the right, the position of the tree relative to distant mountains changes when viewed from position B rather than position A.

This phenomenon is known as parallax. Parallax can be defined as an apparent change in position of a nearby object relative to background objects due to a change in perspective of the observer. The concept of parallax has been known for hundreds of years. Ancient astronomers knew about parallax, which influenced their view of the world around them. When they looked at the stars in the sky, they were never able to measure a parallax shift for any star. Viewed with the unaided eye, not a single star in the sky appears to move over time due to parallax. This led astronomers to hypothesize that the Earth was motionless, forming the basis for the geocentric model of the solar system. While other observations eventually demonstrated that the Earth does in fact move as it orbits around the Sun, it wasn't until the invention of the telescope that astronomers were able to measure any parallax shifts for stars.

17.3 Making Parallax Measurements

Your finger appeared to move from side to side because you were looking at it from two different locations. These locations were separated by a given distance (the distance between your two eyes). If you could increase this distance, then the apparent shift of a particular object would be greater. When viewing the parallaxes of stars, astronomers want to take two measurements as far apart as possible so that the parallax is as big as possible.

As the Earth orbits around the Sun, it moves through space, allowing us to see stars from different locations. The farthest apart we can take parallax measurements would be from opposite sides of the Sun. Parallax measurements of nearby stars are taken 6 months apart. Astronomers measure the angular shift of the star's position relative to background stars. Half of this shift is known as the parallax (p) of the star.

Remember the experiment we performed at the beginning of this exercise, where we held up one finger and looked at it with one eye at a time? Now repeat the experiment, but hold up two fingers, one on each hand. Hold one finger close to your eyes, and one at arms length. Now look at them with one eye at a time, blinking back and forth. What do you notice? You can see the same results in the animation below.

Click on PLAY to start.

17.4 An Inverse Relation

The Alpha Centauri system, located at a distance of 1.3 parsecs, contains the closest stars to us (not including the Sun). Credit: Akira Fuji / David Malin Images

The distance (d) to a star is inversely related to its parallax (p); the farther away a star is, the smaller its parallax. We can write this as a formula: d \(\alpha\) 1/p (the distance is proportional to the inverse of the parallax).

At this point, astronomers like to make a simplification which allows us to turn the proportionality into an equality. If the parallax angle is measured in arcseconds (where 60 arcseconds make up 1 arcminute and 60 arcminutes make up 1 degree), then the distance to the star will be measured in parsecs (pc). One parsec is defined as the distance to a star that has a parallax of exactly 1 arcsecond.

17.5 A Survey of Stellar Distances

The Hipparcos satellite measured the parallaxes of millions of stars.

Due to the inverse relationship between distance and parallax angle, the farther away an object is, the smaller its parallax. If you move an object far enough away, its parallax will become so small that you will be unable to measure any shift at all. The object will appear to be a motionless background star.

Because Earth's atmosphere is not stationary, but moves around constantly, there is a limiting parallax which ground-based telescopes can measure. The atmosphere distorts the star light too much and we cannot measure the shifts accurately enough beyond this limiting value. This shortcoming led astronomers to launch Hipparcos (the High Precision Parallax Collecting Satellite) into space in 1989. Its main mission was to measure the parallaxes of stars down to a precision of 0.001 arcseconds. This means that parallaxes as small as 0.005 have an accuracy of 20%. Being located above Earth's atmosphere, it was not limited by atmospheric turbulence. Hipparcos was only limited by its own ability to measure tiny shifts in the positions of stars over time. The parallaxes of over 2 million stars were measured using Hipparcos, before it ultimately ended its mission in 1993.

17.6 Moving Beyond Hipparcos

While Hipparcos determined the distances to millions of stars during its run, it was limited by the accuracy to which it could measure parallax shifts. The figure to the right is an illustration of our Milky Way galaxy, with an arrow pointing to a red dot representing the region around our Sun which contains the majority of stars for which parallaxes where measured by Hipparcos.

Summary

Astronomers planned another mission to build upon the measurements made by Hipparcos. The Gaia satellite was launched in December of 2013. One hundred times better than Hipparcos, it has the capability to measure much smaller parallax shifts, ultimately determining the distances to billions of stars in our Galaxy.

Gaia: the next generation after Hipparcos

17.7 Quick Check Quiz

Indepth Activity: Stellar Parallax