Determining Stellar Distances: Parallax Detected!

The Problem Faced by Astronomers [cast your mind back to the 1700s and 1800s] There are hundreds of thousands of stars visible through small telescopes Only a tiny fraction of them will display measureable heliocentric parallax -- and you don’t know which they are! It will take many years of careful work to detect and measure the effect, so you certainly can’t study all the observable stars You have to identify some ‘likely candidates’ – stars that are probably nearby. But how do you do that?

Any Suggestions? Which of these stars is likely to be closest to us?

The Obvious Thought If all stars were similar, the nearest ones would be the brightest ones. So: to start with, let’s study the stars that look brightest to the eye! (Betelgeuse, Antares, Sirius, Rigel, Vega…) Perhaps they are ‘on our doorstep’and will display measurable parallax…

This Doesn’t Work! Most of the apparently bright stars actually lie at very large distances and display very little parallax. Betelgeuse, for example, is more than 600 light years away. Why do these stars look so bright? It’s because they are so ultra-luminous intrinsically that they show up conspicuously despite their large distances! . (Tright star Sirius is an exception: it actually is moderately close, only 9 light years away.)

Look Again at Proxima Centauri It is quite undistinguished – very faint. Who would have guessed that it’s so close to us!

Stymied! (in the late 1700s) The brightest stars are not the optimal targets. Studying stars chosen at random seems to be likewise hopeless! How will we make progress? Some clever astronomer needs to come up with a bright idea…

Herschel’s Clever Idea: Study Stars that are Side-by-side [“optical doubles”] What we see What Hershel assumed

If One Star is Close, and the Other Far Away… …because the Earth goes back and forth in its orbit, the nearer star will seems to shift back and forth relative to the more remote one. This is a parallax effect.

Analogy ` Hold up two fingers as shown, and blink your eyes alternately. Note how one finger seems to move relative to the other.

But No! Here’s what Herschel discovered instead - the stars are in mutual orbit, moving around each other!

Herschel Had Discovered Binary Stars This is a really critical discovery: they are very important! Binary stars allow us to determine stellar masses! They are the homes of exotic physics (as when one member is a neutron star or black hole). They explain some interesting variability (such as eclipsing binaries) There is general astrophysical interest: about 50% of all stars are in binary or multiple systems (but not the Sun)

Determining Stellar Masses Remember the see-saw (see ASTR 101)

Newton Tells Us How [see ASTR 101]

A Brief Digression: Variable Stars There are two kinds: intrinsic variables (in which the star itself changes in some way) extrinsic variables (where a star appears to change because of some independent effect, like being eclipsed by another object)

1. Intrinsic Variables Exploding stars: novae, supernovae, cataclysmic variables, flare stars, etc. Some of these happen because the star is in a close binary system. Pulsating variables: Cepheids, RR Lyrae stars,… (pumping in and out like a heart beating)

2. Extrinsic Variables One example: eclipsing binaries

Back to the Parallax Problem Herschel’s clever idea, although ultimately important, did not produce measured parallaxes. Let’s forget about binary stars for now. We need a different clever idea! How will we select stars that we think are probably close, and then hunt for parallax effects? What’s another indicator of close proximity?

Hint: Compare These Motions

The Solution Assume (not unreasonably) that all stars move through space with comparable speeds Then those that are closest to us will seem to shift position across the sky more quickly than the more remote ones. So identify the stars that have high proper motions and try to measure their parallaxes!

For Example Visit http://www.astronexus.com/node/28 and look at the 3D animations (based on real astronomical data!). Notice the stars with high ‘proper motions’ – in particular, 61 Cygni.

Success!! In 1837, parallaxes were measured for three different stars (by three different astronomers!): 61 Cygni Vega Proxima Centauri (the closest of all)

The Important Implications The Earth really does orbit the Sun! (if not, we would not see parallax effects) The stars really are far away! (the parallaxes are so tiny) We are now able to work out the physics of the stars – their intrinsic luminosities, their masses (using binaries), and so on.

A Reminder of Why it Works If we can simply measure the parallax, we can determine the distance of the star. It is just like surveying! We only need to know the ‘baseline’ (the separation between the two observing points) plus the measured angle (the parallax). Then it’s simple geometry…

But Remember the Fundamental Limitations The method of parallaxes only works for relatively nearby stars (just as our depth perception has a limited range) The reason is the same: a limited ‘baseline’

And We Need a Background Frame of Reference The more remote stars provide the backdrop against which we measure the apparent shifts of the nearby stars.

Where Do We Stand Now? Until recent decades, reliable parallaxes had been measured for only a few thousand stars (out of the estimated hundred billion in our own Milky Way galaxy!) But then came telescopes in satellites! This does not increase the baseline (‘spread our eyes apart’), since the satellites are only hundreds of km overhead. But it allows sharper, crisper images since we avoid the ‘blurring’ caused by the Earth’s atmosphere. Result: better precision, many more stars

A Great Example HIPPARCOS = High Precision Parallax and Coordinates for Stars. (A great acronym! The name is in homage to Hipparchus, the great astronomer of antiquity.) This led to very precisely determined parallaxes for 100,000 stars; and less precise results for 1-2 million more.

Beyond HIPPARCOS… The Gaia probe, now in orbit, will eventually provide positions and parallaxes for up to a billion stars! But this is still only 1% of the stars in the Milky Way. Parallax measurements, though critical and fundamental, have a definitely limited range. To derive distances to more remote stars, and to other galaxies, different techniques must be used.

What Can We Do Now? Now that we know the true distances to many of the stars, we can work out lots of things: Their true brightnesses Their masses (thanks to binaries) Their sizes etc.. Given this information, we can do astrophysics!