Stellar distances OBJECTIVES describe the method of heliocentric
Stellar distances OBJECTIVES: - describe the method of heliocentric parallax to determine distances to nearby stars - recall the definition of one parsec (pc) - describe the use of H-R Diagrams to determine stellar distances
How can we measure how far away stars are? Parallax colour spectrum convergent point method Hold a pencil up in front of your face. Look at it with one eye with the other closed. Now look at it with the other eye. Notice that the pencil appears to move relative to the background. Why? Because you are looking at it from a different angle This phenomena is known as parallax and can be used to view relatively nearby stars.
Heliocentric Parallax The distance to nearly 2000 nearby stars can be measured accurately with this method. Most distant stars do not appear to move. There is a very small angular shift (closer star appears in different position relative to distant ones). Parallax angle p can be measured. p p The radius of the Earth's orbit around the Sun is about 1. 5 x 10¹¹ m (or 1 AU). The star Alpha Centauri appears to change direction by 4. 2 x 10⁻⁴ degrees when observed in June and December. How far away is Alpha Centauri?
The Parsec is defined using the method of parallax Parallax angles measured are very small - Sensitive instruments used Using degrees for the angles is too big! The arcsec is used instead 1° is divided into 60 mins 1 min is divided into 60 secs - the arcsec 1 arcsec is 3600 th of a degree! The Parsec is the distance at which a star would have a parallax angle of one arcsec How far is a parsec in metres? (1 AU = 1. 5 x 1011 m)
The Parsec in metres Convert this to light years (one year is 31556926 s)
Some numbers. . . Earth to Sun distance Pluto to Sun distance Distance to nearest star (not the Sun) Diameter of the Milky Way Separation between galaxy clusters The most distant galaxies observed 1 AU 40 AU 4. 2 light years or 1. 29 parsecs 100, 000 light years or 30 kpc 10 Mpc Thousands of Mpc
Spectroscopic Parallax You can use the correlation between luminosity and temperature (spectral type) for main sequence stars to get their distances. This method is called spectroscopic parallax because a distance is found from knowledge of a star's spectral type. Distances for stars too far away to show a detectable trigonometric parallax are found this way. Here are the steps you use to find a star's distance using the spectroscopic parallax method: • Determine the star's spectral type from spectroscopy and measure the star's apparent brightness (flux). • Use a calibrated main sequence to get the star's luminosity. The Hyades cluster in the Taurus constellation is the standard calibrator. • Use the Inverse Square Law for Brightness to get the distance: unknown distance = calibrator distance × Sqrt[calibrator flux/unknown star's flux. ]
How do you do that? dun = d. Cal x SQRT(FLUXcal/FLUXun) • A G 2 star appears 25 times dimmer than it would if it was at the standard distance of 10 parsecs used for the absolute magnitude. • The G 2 star is at a distance of = 10 × Sqrt[1/(1/25)] = 10 × Sqrt[25/1] = 50 parsecs from us.
Spectroscopy Answers
Distances Answers
Standard candles Parallax is used to find out how far away nearby stars are. What about stars further away where the parallax angle is too small to be measured accurately or even detect? Number of very useful objects in the Universe called Standard Candles. Objects of known luminosity, i. e. we know their absolute magnitude. Comparing with apparent magnitude - can calculate how far away. This gives a good indication how far away their neighbours are and galaxies they are in.
Cepheid variables (again) One type of standard candle is a Cepheid Variable. First example was discovered in constellation of Cephius Absolute magnitude (luminosity) of this type of star varies with time Graph shows how apparent magnitude changes, getting brighter and dimmer again with fixed, measurable period Changing Balance between nuclear and gravitational forces within star Clear relationship between period of Cepheid variable and its absolute magnitude The greater the period then the greater the maximum luminosity of the star. Cephieds typically vary in brightness over a period of about 7 days. Delta Cephius, the first discovered, has a period of 5. 3 days
Cepheid variables (again) So to find out how far away it is: 1. Measure how long it takes to get brighter and dimmer 2. Use the graph on the right to find its absolute magnitude M 3. Measure how bright it appears (maximum) 4. Calculate how far away it is.
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