The Distances of Stars

It Sounds Easy! [read the last three lines]

The Importance In order to make the most important astrophysical determinations, including true brightness, true brightness, mass, mass, size, size, structure,… structure,… we have to know the distances.

1. Consider Stellar Brightness First 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 need to know. By contrast, the apparent brightness – what we actually see – is partly an accident of location: nearby stars can look deceptively bright. (Obvious example: the Sun!)

First: Apparent Brightness The ancient Greeks divided the stars into six broad categories - magnitudes. This depended on how soon they appeared in the evening as the sun was setting and the sky darkened. You can watch this behaviour using the Starry Night simulation software. The brightest ones (“first magnitude”) show up first, then the “second magnitude” stars, and so on.

Star Light, Star Bright…

A Confusing Scale (for non-astronomers, that is!) 1. Stars with larger magnitudes are fainter [this perplexes some people!] 2. The scale measures ratios of brightness: if one star is 5 mag brighter than another, it is 100x as bright. if one star is 5 mag brighter than another, it is 100x as bright.

For Example (don’t memorize!)

Real Stars

What About Even Brighter Objects? (Venus, Jupiter, the Moon, the Sun…) Answer: their magnitudes are negative numbers. (And why not? We are not upset when outdoor temperatures are negative! – ‘colder than ice’) e.g. Betelgeuse is a “first magnitude” star. Venus, at its brightest, is 100x (5 mags) brighter. So Venus is magnitude -4

A Huge Range! The (fantastically bright!) sun is at -26 The faintest star seen through the world’s largest telescope is mag 29. This is 55 magnitudes fainter. Every 5 mag ‘step’ corresponds to 100x less 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! 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 Watts 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! A magnitude 7 earthquake is bad; one of magnitude 8 is worse; but magnitude 9 is much, much worse!

So the Sun Appears Very Bright [thanks to its proximity] But how‘average’ is it really? Are there bigger, brighter, more massive stars? Or is the sun a real standout? (Or perhaps it is even rather puny?) We need to work out the distances to many stars to figure out how bright they are intrinsically, and then compare them.

The ‘Obvious’ Approach Let’s go out at night and draw up a list of every star we can see with the unaided eye. Now work out their distances [more on this later] to find out what these stars are like intrinsically. Perhaps this will give you some idea about the ‘average star.’

Night-Time Sky – Lots of Stars

Find Your Nearest Neighbour

More than Meets the Eye!

Beware 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. Meanwhile, myriads of microscopic bacteria and large numbers of tiny bugs swarm unseen all around us. They are the truly average living creatures!

Your Passengers

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!

The Answer: 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 Ten Conspicuous Stars Name True Brightness (solar units) Diameter (solar units) Distance (light years) Sirius2329 Canopus Arcturus Alpha Centauri Vega58327 Capella Rigel60, Procyon Achernar

What Do You Notice? All of these are  bigger and brighter than the sun (some enormously so), and  rather far away (up to hundreds of light years)

To Really Understand the Stars… Find all the stars in the solar neighbourhood, even the little faint ones! This requires telescopes, and many years of work… We also have to determine their distances, to work out how bright they are intrinsically. [Again, more on this later.]

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

Some Very Nearby Stars These are not even visible to the unaided eye! [Remember that we can see down to ~6 th magnitude in a dark sky.] NameDistance (light years)Apparent Magnitude Proxima Centauri4.211 Barnard’s Star4.910 Wolf BD +36 o UV Ceti8.812 / 13 (binary)

One Important Lesson [true in many circumstances] 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: 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!