Consider ‘Average’ Stars

Supremely Important In order to make the most important astrophysical determinations, including True (intrinsic) brightness, mass, size, etc… we have to know the distances.

It Sounds Easy! [read the last three lines] …but it’s actually not that simple! We will defer the actual ‘how’ while we consider a few relevant issues.

1. Stellar Brightness The apparent brightness of a star – that is, what we actually see – is partly an accident of location: nearby stars can look deceptively bright. (The obvious example is the Sun!) But the intrinsic (true) brightness of a star is a good measure of how much energy is being generated, how fast the fuel is being consumed, etc. So it’s something we really need to know. Question: How do astronomers describe the brightness of stars?

First: Apparent Brightness The ancient Greeks divided the stars into six broad categories, called magnitudes. This depended on how soon they appeared in the evening as the sun was setting and the sky darkened. The brightest ones (“first magnitude”) show up first, then the “second magnitude” stars, and so on. The faintest stars visible to the unaided eye are about 6th magnitude.

Star Light, Star Bright… You can watch this behaviour using the Starry Night simulation software. Look to the western horizon, with the sun still up in the sky. Then move your cursor to the time display at the top left, and advance the minutes quickly by holding down the arrow key on your keyboard. This makes the sun set rapidly – and you can watch the stars come out!

A Special Scale Stars with numerically larger magnitudes are fainter [this perplexes some people!] The scale measures ratios of brightness: if one star is 5 mag brighter than another, it is 100x as bright. Note that this illustration suggests that brighter stars are perceptibly bigger, but this is not the case. Except for the sun, essentially all the stars in the sky are completely unresolved (points of light) even through large telescopes.

What About Even Brighter Objects? As noted, the Greeks said the brightest stars were 1st magnitude. Some objects (Venus, Jupiter, the Moon, …) are even brighter – so their magnitudes are negative numbers. (And why not? We are not upset when the temperature outside is negative! The numbers still make sense.) Example: Vega is a “first magnitude” star. But Venus, at its brightest, is 100x (5 magnitudes) brighter. So Venus is magnitude -4.

Real Stars We now do better than the Greeks, measuring star brightnesses very precisely – so there are, for example, stars of magnitude 2.50, or 3.75. They are not merely put into ‘groups.’ Here are some real examples:

A Huge Range! The fantastically bright Sun is at magnitude -26. (The full moon is at -11.) The faintest star seen through the world’s largest telescope is magnitude 29. (It could, of course, actually be a very bright star, but extremely far away!) This is 55 magnitudes fainter than the Sun appears to be. Every 5 mag ‘step’ corresponds to 100x more light. So the Sun gives us 100 x 100 x …. X 100 (11 steps) = 10,000,000,000,000,000,000,000x as much light as that faint star!

Note the Convenience! Magnitudes are small numbers that allow us to depict a huge range of brightness in very concise form. Historically, they arose because of the fact that our human perceptions respond equally to equal ratios of stimuli. (Fechner’s Law). Example: Double the power in your stereo speakers from 10 to 20 Watts. The music now sounds louder. But adding 10 more Watts doesn’t have the same impact! Instead, you have to double it again (from 20 to 40 W).

The Richter Scale is Similar A magnitude 7 earthquake is bad; one of magnitude 8 is worse; but magnitude 9 is much, much worse!

2. Identifying ‘Average’ Stars Let’s go out at night, look up at the sky, and draw up a list of every star we can see. Now work out their distances [more on this later] to find out what these stars are like intrinsically. Does this give you some idea about the‘average star?’ Or are these stars atypical in some way?

Night-Time Sky – Lots of Stars [and, in this picture, two very bright planets!] Note also the Pleiades star cluster to the upper right, and cool (red!) Betelgeuse near the top center.

Challenge: Find the Nearest Living Creature Next to You

Not What You Might Think!

There is a Strong Bias In the lecture hall, or out in the field, we notice the big animals! Meanwhile, myriads of microscopic bacteria and large numbers of tiny bugs swarm unseen all around us. They are the truly average living creatures!

Similarly the Stars Could there be myriads of stars so faint that they are not even visible to the unaided eye? They could be all around us, in their thousands, but simply languish unnoticed! In fact there are such stars! They are the ‘bugs and microbes’ of the astronomical world. So the “obvious approach” of studying the prominent stars is misleading.

Consider Nine Conspicuous Stars Notice their brightnesses, sizes and distances Name True Brightness (solar units) Diameter Distance (light years) Sirius 23 2 9 Canopus 1400 30 110 Arcturus 115 25 36 Alpha Centauri 1.5 1.1 4.5 Vega 58 3 27 Capella 90 13 46 Rigel 60,000 40 810 Procyon 6 2.2 11 Achernar 650 7 120

Distance (light years) Name Distance (light years) Apparent Magnitude Proxima Centauri 4.2 11 Barnard’s Star 4.9 10 Wolf 359 7.5 14 BD +36o2147 8.2 8 UV Ceti 8.8 12 / 13 (binary) Now Some Very Nearby Stars These are not even visible to the unaided eye! [Remember that we can only see down to ~6th magnitude in a dark sky.]

To Really Understand Stars of All Kinds… …we have to find all the stars in the solar neighbourhood, even the little faint ones! This requires telescopes, and many years of survey work. We have to determine their distances, to work out how bright they are intrinsically.

What We Find The truly average star is indeed very small and faint! -- much less imposing than the sun.

One Important Lesson For every big thing in Nature, there are lots of little things. [There are thousands of blue whales, but billions of people, trillions of ants, and uncountable hosts of microbes.]

Similarly in Astronomy On the moon, there are a few big craters, but many more little ones. In the Solar System, there are a few really big asteroids, but trillions of pebbles!