Determining Stellar Distances Distance Determinations in Real Life We use various ways. (Think of some!) Heres an important one: binocular vision depth perception Parallax Two different points of view. The Trick Each eye sees a slightly different image. The brain merges these and interprets the three-dimensional nature of the situation. As Here [compare the lampstand to the building] Simulated - and Exaggerated! Accomplishing the Trick - two images, one per eye Need a Background Frame of Reference Fundamental Limitation More remote objects display less parallax! (Our depth perception fails us beyond a few tens of metres, and we have to use other methods.) To Improve Binocular Vision: Spread the eyes apart! Our Objective Remember that some stars are nearby, others much farther away (in the background). If we can spread our eyes far enough apart, we will see the nearby stars slightly displaced against the background pattern. Geocentric Parallax Imagine two eyes separated by hundreds of kilometers, looking at something relatively close. Limitations of Geocentric Parallax If the target is too far away, the parallax effect becomes immeasurably noticeable, even from widely-separated locations on Earth. How About the Stars? Even the very nearest stars are so far away that we dont notice any geocentric parallax. These two people are looking in essentially parallel directions, because the star is so remote! The Solution Remember that the Earth moves around the sun once a year! We can take one picture now, then a second one six months later from a much different location (300,000,000 km away). This spreads our eyesto yield the effect known as heliocentric parallax. That Sounds Easy Note: Its Not Exactly Equivalent to HumanDepth Perception Our binocular vision works because we compare two different views (one with each eye) at the same time. In heliocentric parallax, we are comparing two images taken at different times. But the principle is fundamentally the same. The Expected Result We should see any nearby star shift back-and-forth once a year relative to more remote stars in the background. Indeed, This MUST Happen! If the sun is truly at the centre of the Solar System, nearby stars should show this kind of parallax (because the Earth moves!) If they dont, we have problems! It Seems Trivially Easy! If the red star is nearby, then: in Jan, we see this in July, we see this - a conspicuous change in its position! Note: You Dont Have to Wait The change is of course the largest after 6 months (since we are then on opposite sides of the Sun in our orbit), but you can observe at intermediate times and watch the star appear to move back and forth across the background. Try the Animations/Other Animations on this site:This shows the parallax effects we would see if we orbited the Sun in a really huge orbit (1.5 light years across!). So Whats the Problem? Why did it take ~240 years, following Galileos first use of the telescope, to detect this behaviour? First, Lets Choose Convenient Units Stellar distances are vast: many tens of trillions of kilometers at least. So, we can use light years. One light year = the distance that light travels in a year ( ~ 10 trillion km). The nearest star is about 4 l.y. away. Sobering Reality As we will learn, the nearest star is ~ 300,000x as far away as the Sun. Try drawing our geocentric parallax sketch again, correctly scaled. The parallax angle is very small. The position of the nearby star changes almost imperceptibly against the background even after 6 months! In the Original Drawing: The red star is shown to be less than 1.5 times as far away from the Sun as we are -- thats closer than Mars!! Lets Define Some Angles Degrees, Minutes, Seconds of arc Successive Subdivisions Look horizontally, then straight up. That shift of viewpoint is through 90 degrees (a right angle) Take just one of those degrees and split it into 60 smaller angles: minutes of arc Take one of those minutes and split it into 60 yet smaller angles: seconds of arc So a second of arc is a truly tiny angle. How Big Does a Dime Look? [obviously it depends on the distance!] (A dime is 18 mm in diameter) (A dime is 18 mm in diameter) Its Angular Size is One degree if its about 1 metre away One minute of arc if its 62 metres away One second of arc if its 3.7 km away In Other Words: Stand on the grounds of St Lawrence College Have a friend hold up a dime in downtown Kingston Now shift your gaze from the top edge of the dime to the bottom. Thats 1 arcsec -- a truly tiny angle! A New Unit of Distance If the parallax angle, p, is one second of arc then the star is, by definition, exactly one parsec away. (if there are any stars even closer than that, they will show greater parallax. Remote stars show less.) 1 parsec = 3.26 light years Relating These Units Astronomers quote distances in parsecs (for the nearby stars) parsecs (for the nearby stars) kiloparsecs (for distances within the Milky Way) kiloparsecs (for distances within the Milky Way) megaparsecs (for distances to other galaxies) megaparsecs (for distances to other galaxies) gigaparsecs (for the most remote observable parts of the universe) gigaparsecs (for the most remote observable parts of the universe) Remember the look-back times. One megaparsec is about 3 million light years. Is She Fast? Now a Sobering Dose of Reality Other than the Sun, no star is as close as one parsec. In other words, as we orbit the Sun, no star will seem to shift back and forth against the background by even as much as as one second of arc. Meet Proxima Centauri (lower right) --the very closest star Ask yourself how this picture will look six months from now. Proxima will seem to have moved, but by less than the size of the little dot of light! -- and this is the closest star of all. And We Have it Comparatively Easy! We can take pictures of the sky, months apart, and intercompare them later, at leisure. In the early 1800s, no such technology existed. Astronomers had to measure the angles between stars to map out the detailed pattern. Repeat the exercise six months later to see if things had changed perceptibly. Repeat, year after year! An Additional Complication Individual stars move through space! Consequently, the annual parallactic shift (a tiny back-and-forth motion) is superimposed on a general accumulating change in position of any individual star. Example: Barnards Star It travels across the sky (because of its own motion), and also appears to shift back and forth (thanks to our changing vantage point as the Earth orbits the Sun). Thats Why, Historically parallax was devilishly hard to discover! Astronomers simply couldnt look at ALL stars, to try and detect this tiny effect among a few of them that happen to be nearby. Thats impractical! Narrow the Field They needed to focus their efforts on stars that are probably nearby. But there are literally millions of stars visible through telescopes. Which ones do you suspect are the closest ones to us? On what grounds? To Make Progress: Find some independent indication that a particular star may be nearby. Then study its position over years and years, with the hope of detecting its parallax. 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: pick the stars that look brightest to the eye! (Betelgeuse, Antares, Sirius, Rigel, Vega) Perhaps they are on our doorstep This Doesnt Work Most of the apparently bright stars actually lie at very large distances and display very little parallax. So why do they look so bright? Its because they are so ultra-luminous that they show up conspicuously despite their large distances! (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 its so close to us! Stymied! (late 1700s) The brightest stars are not the optimal targets. Studying stars chosen at random seems to be likewise hopeless! Studying stars chosen at random seems to be likewise hopeless! How will we make progress? One Clever Idea (from Herschel) Two Stars Apparently Side-by-Side Maybe one is close to us, the other one a lot farther away As Time Passes, We Expect Because the Earth goes back and forth in its orbit, the nearer star seems to shift back and forth relative to the more remote one. Analogy Hold up two fingers as shown, and blink your eyes alternately. Note how one finger seems to move relative to the other. ` What Herschel Discovered Instead - the stars are in mutual orbit! That is, Binary Stars Exist!! [A critical discovery. They are very important] Binary stars allow us to determine stellar masses! Binary stars allow us to determine stellar masses! They are the homes of exotic physics (such as when one member is a neutron star or black hole). They are the homes of exotic physics (such as when one member is a neutron star or black hole). They explain some interesting variability (such as eclipsing binaries) 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) 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 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) 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) 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: (pumping in and out like a heart beating): Cepheids, RR Lyrae stars, (pumping in and out like a heart beating): Cepheids, RR Lyrae stars, 2. Extrinsic Variables One example: eclipsing binaries Eclipses Simulated Visit this siteand try out the simulations shown there. Notice how the precise behaviour of the eclipse depends on the nature of the stars involved, and the angle from which we see it. Anyway, Herschels Clever Idea Failed Lets forget about binary stars for now. How will we select stars that we think are probably close, and then hunt for parallax effects? Whats another indicator of close proximity? Hint: Compare These Motions The Solution Assume that all stars move through space with comparable speeds (not unreasonable) 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 Visitand 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 Important Implications 1. The Earth really does orbit the Sun! 2. The stars really are far away! 3. We are now able to work out the physics of the stars their intrinsic luminosities, their masses (using binaries), and so on. The Critical Point If we can 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). 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 Until Recent Decades Reliable parallaxes had been measured for only a few thousand stars (There are an estimated hundred billion in our own galaxy!) Recent Improvements Telescopes in satellites! This does not increase the baseline (spread our eyes apart), but it allows sharper, crisper images since we avoid the blurring caused by the Earths atmosphere. Result: better precision, many more stars. HIPPARCOS ( ) What it Did 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. Visit But Even With HIPPARCOS parallax measurements, though critical and fundamental, have a definitely limited range. (Fewer than 0.01% of the stars in the Milky Way galaxy are within reach of our direct parallax measurements.) To derive distances to more remote stars, and to other galaxies, different techniques are used. Where We Stand Now Now that we know the true distances to many of the stars, we can work out lots of things: Their true brightnesses Their true brightnesses Their masses (thanks to binaries) Their masses (thanks to binaries) Their sizes Their sizes etc.. etc.. Given this information, we can do astrophysics!
