How we measure distance to a star
By Quamrul Haider
In our everyday lives we typically deal with distances ranging from millimetres to thousands of kilometres - millions of kilometres at most if we are observing the Sun. But nothing in the human experience prepared us to visualise distances of stars and galaxies that are billions of light years away from us. So how do we measure their distance?
To measure the distance of nearby stars, astronomers use the method of parallax. The principle behind this method is elegant and simple. Parallax is a change in an objects position caused by a change in the observers position. In order to understand what parallax is, hold one of your fingers in front of your nose at arms length. Now view the finger alternately with one eye closed. You will notice that it jumps from right to left. This jump from side to side is called the parallax shift.
Astronomers measure the parallax shift of stars from two different positions on the Earths orbit. The maximum shift occurs when the stars are viewed six months apart, a known distance of about 300 million km. Half the total angular shift is the stars parallax. Because the angular shifts are so small, the angles are measured in seconds of arc (arcsecond) rather than degrees. (1arcsecond = 1/3600 of a degree.)
In astronomy, it is convenient to use parsec (pc) as a unit for distance. A parsec (3.26 light years) is defined as the distance to a star whose parallax angle is exactly one arcsecond. With this definition, the distance to a star is simply the reciprocal of the parallax angle. For example, the parallax angle of our nearest star Alpha Centauri is 0.76 arcsecond. Its distance is therefore 1/0.76 = 1.32 pc, or 4.3 light years. (A light year is about 9.5 trillion km.)
Measuring distances of faraway stars using the parallax method is a daunting challenge. Because of the blurring effects of the atmosphere, Earth-based telescopes have limitations in measuring parallaxes smaller than 0.01 arcsecond, corresponding to a distance of 100 pc. This is less than one percent of the distance to the centre of our galaxy Milky Way. However, space-based telescopes are unhampered by the atmosphere, thereby permitting astronomers to measure distances greater than 100 pc.
In 1989, the European Space Agency launched the satellite Hipparcos containing a special telescope to measure parallax of distant stars with high precision. It can measure parallax as small as 0.001 arcsecond, which is a distance of 1000 pc, about one-thirtieth the size of our galaxy.
To go beyond 1000 pc, astronomers rely on the brightness measurements using Cepheid variable stars. Cepheids are extremely luminous - 500 to 300,000 times greater than the Sun, giant pulsating stars that change their size and temperature, and hence their brightness rhythmically with a regular time period. The term Cepheid originates from observation of periodic light variations in the yellow supergiant, Delta Cephei in the constellation Cepheus, the first star of this type identified by John Goodricke in 1784.
By comparing the actual brightness to apparent brightness of a Cepheid star, astronomers can compute how far it is. The actual brightness is determined from the time it takes the star to complete a cycle of maximum to minimum and then back to maximum brightness.
The Cepheids can reveal distances out to about 25 million pc (Mpc). Indeed, in the late 1920s, American astronomer Edwin Hubble used Cepheids to measure the distance of the Andromeda Galaxy to be 778,000 pc.
To determine the distance of really distant star or galaxy, astronomers use redshift of light from the distant object. Redshift is the stretching of the starlight as it is carried outward by the expansion of space. The effect is somewhat similar to water waves stretched out behind a speedboat. By analysing the redshifted spectrum of light from a star, we can determine its speed of recession which is related to its distance via Hubbles law distance to galaxy is equal to recessional velocity of galaxy divided by the current value of Hubble constant, which is 71 km/second/Mpc.
The farthest distance astronomers measured to date is the distance of a galaxy 13.3 billion light years away. This means light from this galaxy was emitted from a nascent Universe - just 400 million years after the Big Bang.
The entire progression of distance scales, all the way out to the known limits of the Universe, form a pyramid. At every step of the way outward, our ability to measure distances depends on the reliability of those that work at smaller distances. Consequently, if we revise our measurement of local distances, we must accordingly alter all our estimates of the larger scales.
The writer is Professor of Physics at Fordham University, New York.
Photos: Google Image
