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Properties of the Stars The stars in the sky vary greatly in brightness, color, and distance. These are the basic properties of the stars, and measuring them is fundamental to understanding their lives and evolution.

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Brightness and Magnitude

The most obvious thing about the stars is that they differ in brightness. The brightness of the stars was first estimated by the Greek astronomer Hipparchus in the second century B.C.. Hipparchus’ system divided the stars into five magnitude classes. The brightest stars in the sky were assigned first magnitude and the faintest stars were classified as fifth magnitude, with all others falling somewhere in between. In general, the brighter an object is, the smaller its magnitude is. The brightest objects, like the Sun or the Moon, actually have negative magnitudes. The Magnitude Scale This scale has been formalized in modern times so that two stars which differ by 5 magnitudes have a ratio of brightness of exactly 100. A first magnitude star is exactly 100 times brighter than a sixth magnitude star. A difference of one magnitude corresponds to a brightness ratio of 2.512 (the fifth root of 100), and the ratio for a difference of two magnitudes is 6.31 (2.512 times 2.512). The magnitude scale is not linear! Using this system, the brightest star in the night sky is Sirius, and has a magnitude of -1.46. The planet Venus is even brighter at magnitude -4.6, and the daytime Sun has magnitude -27. The faintest stars visible on a clear night are about 6th magnitude. A small telescope allows one to easily see stars to 10th magnitude and fainter. The world’s largest telescopes are capable of detecting objects of magnitude 25, and the Hubble Space Telescope reaches magnitude 28 and fainter.

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Star Color and Temperature

It is apparent to any observer that the stars vary in color as well as brightness. Stars differ in color because they have different temperatures. By accurately measuring the colors of the stars, astronomers can calculate the temperature on the surface of the star. When a piece of metal is heated, it changes colors as the temperature changes. As it starts to glow, it first changes to red. As the metal gets hotter, it turns orange. Next it turns yellow-white, then blue-white. This color pattern also applies to the stars. The reddish stars Betelgeuse and Antares are cool stars, though still about 2,500 degrees Kelvin. Stars like Arcturus are orange at about 5,000 degrees Kelvin. Sun-like stars are yellow at 6,000 degrees Kelvin. White stars like Vega are hotter still at 10,000 degrees Kelvin. The Blue giants like Rigel and Deneb have surface temperatures of about 20,000 degrees Kelvin. Measuring the apparent color of a star requires observing its magnitude at different wavelengths. This involves several factors: the wavelengths considered (some objects are brighter at infrared or ultraviolet wavelengths than in visible light), and the sensitivity of the detector (the eye is less sensitive to blue light than standard photographic film). A star’s visual or “V” magnitude represents its brightness at the wavelength to which the human eye is most sensitive. A star’s blue or “B” magnitude is its brightness at the wavelength to which photographic film is most sensitive. The difference in these magnitudes, or “B-V”, is called the star’s Color Index, and it represents an accurate measurement of the star’s color. Star surface temperature vs. B-V color index. The coolest, reddest stars, such as Betelgeuse and Antares, have a B-V color index of about +2.0. The hottest, bluest stars, like Rigel in Orion, have a color index of about -0.25. Stars with a color index of 0.0, such as Vega, appear white. The Sun has a color index of about +0.62.

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Parallax and Distance

The first measurement of the distance to a star was published in 1838 by the German astronomer Friedrich Bessel. The star was 61 Cygni, an inconspicuous 5th magnitude star in the constellation Cygnus. To find the distance to 61 Cygni, Bessel measured the star’s parallax. Parallax is the apparent shift in the position of an object caused by a shift in the observer’s position. To see how this works, hold your thumb in front of your face, and view it with your left eye. It will be seen against the background objects in the room. If you now close the left eye and use your right eye, your thumb will appear to move in comparison with the other eye. Your thumb seems to shift back and forth as you alternate viewing with your right and left eye. This is parallax. In a similar way, we can observe the position of a star at a particular time of year against the more distant background stars. Then, six months later, when the Earth is on the opposite side of its orbit, a second observation will show a small shift in the star’s position in relation to the distant stars. This angular shift is the parallax of the star, measured by observing from opposite sides of the Earth’s orbit. Since the radius of the Earth’s orbit is exactly 1 AU, or about 150 million kilometers (93 million miles), the distance to the star can be calculated. @ Diagrams/Parallax @ | The Parallax of a star (p) lets us calculate its distance (d). | A nearby stars will have a large parallax, and a more distant star will have a small parallax. Unfortunately, even the nearest stars have a parallax angle smaller than 1 arc second or 1/3600 of a degree. This is about the size of a postage stamp when seen from a distance of 5 miles. 61 Cygni is in fact one of the nearest stars known, with a parallax of 0.287 arc seconds. The nearest star, Proxima Centauri, has a parallax of 3/4 arc second, and it is over 4.2 light-years from our solar system. The parallax technique is still the most reliable method of finding stellar distances. The European Space Agency’s Hipparcos satellite, launched in 1991, measured the parallaxes of over 120,000 stars with unprecedented accuracy. The Hipparcos Catalog, resulting from that mission, remains the most accurate compendium of stellar distances today.

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Light-Years and Parsecs

To express the very large distances to the stars, astronomers need a special unit of distance. Miles or kilometer are much too small to be practical. The method of parallax leads to an astronomical yardstick called the “parsec”. One parsec is simply the distance at which a star would have a parallax of 1 arc second. One parsec is an immense distance - over 30 trillion kilometers, or 19 trillion miles. Astronomers also use a unit of distance called the light-year. One light-year is the distance that light travels in one year. Since the velocity of light is 300,000 kilometers per second or 186,000 miles per second, light travels very far in one year - about 10 trillion kilometers (6 trillion miles). One parsec is about 3.26 light-years. Light-years and parsecs are analogous to feet and meters. When discussing distant clusters and nebulae, distances are often measured in “kiloparsecs”. A kiloparsecs is 1000 parsecs, just as a kilometer is 1000 meters. When discussing the distances to galaxies, the term “Megaparsec” is commonly used. A Megaparsec is 1 million parsecs or one thousand kiloparsecs.

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Absolute Magnitude and Luminosity

A star can be bright because it is relatively close to our solar system, or because it is far away, but very luminous. Two stars of the same apparent magnitude will differ in their true brightness, or luminosity, if one star is at a greater distance. To determine the true brightness of a star, its magnitude must be adjusted to indicate how bright the star would appear if it were seen at some standard distance. The standard distance used to compare the brightness of stars is 10 parsecs. The magnitude that a star would have if it were at a distance of 10 parsecs is called its absolute magnitude. The absolute magnitude measures the intrinsic brightness or luminosity of the star; its apparent magnitude measures how bright the star appears. The Sun has an apparent magnitude of -26.7, but its absolute magnitude is a modest +4.85. From 10 parsecs, the Sun would be a faint 5th magnitude star. The brightest star in the sky is Sirius has an apparent magnitude of -1.46, and is about 2.64 parsecs (or 8.6 light-years) away. With an absolute magnitude of +1.45, Sirius is 23 times more luminous than our Sun. But its energy output is modest when compared with some other giant stars. We see Sirius as a bright star because it is very close to our Sun. The second brightest star in our night sky is Canopus (magnitude -0.62), which is almost as bright as Sirius. But Canopus is nearly 96 parsecs away - 36 times farther away than Sirius. Canopus must be a very luminous star to appear so bright from such a great distance. It has an absolute magnitude of -5.53. The bluish-white star Deneb in Cygnus is among the brightest stars in the summer sky (magnitude +1.33), and yet it is nearly 1000 parsecs (3200 light-years) away. Deneb is bright because it is a very luminous star. It emits over 250,000 times as much light energy as the Sun. At a distance of only 10 parsecs, Deneb would shine at magnitude -8.65. It would rival the first quarter moon in brightness, and it could be easily seen in the daytime sky.

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Star Spectral Types

When directed through a prism, the light of a star divides into a rainbow or spectrum of colors that can be observed and recorded on photographic film. Under careful observation, the spectrum of a star usually has a sequence of dark lines, marking wavelengths of light that are absorbed by the chemical elements in the star’s atmosphere. The temperatures and chemical compositions of the stars vary greatly, which affects the strengths of their spectral lines. Early 20th-century astronomers divided stellar spectra in a sequence of classes designated by letters. This system has evolved into the present-day set of spectral classes: O, B, A, F, G, K, and M. A few stars do not fit into this scheme, and they have been given their own special classes: R, N, S, W. Modern instruments are able to resolve a star’s spectra into tenths of a class. For example, you will see stars of spectral type B9, G4, and K3. Dark lines in the spectrum of star reveal the chemical elements in its atmosphere. The O and B stars are hot and blue. The bright star Sirius is of spectral type A. The Sun is a yellow G type star. The K and M stars are red in color and comparatively cool. The brightest of these are the red giants such as the stars Antares and Betelgeuse. The main stellar spectral types: O, B, A, F, G, K, M. Within a given spectral class, stars are divided into luminosity classes. These classes permit differentiating, for example, between a red giant and red dwarf. The luminosity classes are: I - Supergiant II - Bright Giant III - Giant IV - Subgiant V - Main Sequence VI - Subdwarf VII - Dwarf Doppler Shift and Radial Velocity A star’s spectrum tells us something else about the star: how fast it is moving toward or away from us. We can determine this because of the Doppler Effect, named after Johann Christian Doppler (1803-1853) who first proposed the effect in 1842. You are already familiar with the Doppler effect - you hear it every time a train or an ambulance comes towards you, then goes past you. The pitch of the sound made by the train rises as it approaches you, then drops as it goes by - this is the Doppler effect for sound waves. As the train moves towards you, its sound waves are compressed, so their wavelength is shortened. We hear the decrease in wavelength as a rise in pitch. As the train moves away from you, the sound waves stretch out. We hear the increase in wavelength as a drop in pitch. For light waves, the same thing happens when the light comes from a source that is moving toward or away from us. But we see the change in wavelength as a change in color, not pitch. So if a star is moving towards us, the light waves it emits will have their wavelength shortened, and we will see a shift toward the short-wavelength end of the spectrum - a blue shift. If the star is moving away from us, its light will have its wavelength increased, and we will see a shift toward the long-wavelength end of the spectrum - a red shift. We can precisely measure the blue or red shift by observing the positions of the star’s spectral lines, compared to the corresponding spectral lines from a stationary light source. This is how the Doppler effect is used by astronomers to work out the velocity of a star toward or away from the Earth. The Doppler Effect for sound (top left), for light (top right) and its effect on a star’s spectral lines. Radial velocity is the term which astronomers use to mean the velocity that an object is moving toward or away from us. As a convention, radial velocity is positive if the source is moving away from us, and negative if the source is moving towards us. For example, the spectral lines emitted by hydrogen gas in distant galaxies is often observed to be considerably redshifted. The spectral line emission, normally found at a wavelength of 21 centimeters on Earth, might be observed at 21.1 centimeters instead. This 0.1 centimeter redshift would indicate that the galaxy is moving away from Earth at over 1,400 kilometers per second (over 880 miles per second). Modern astronomical spectrographs are capable of extremely precise measurements of radial velocity. They can detect doppler shifts which correspond to radial velocity changes of only a few meters per second. With this level of precision, astronomers can detect the very slight changes in a star’s radial velocity caused by a nearby planet’s gravitational pull tugging the star back and forth as the planet orbits the star. In fact, this is exactly how the first confirmed planet orbiting another star, 51 Pegasi B, was discovered in 1995.