1. 22 March 2005AST 2010: Chapter 18 1 Celestial Distances

2. 22 March 2005AST 2010: Chapter 182 Stellar Distances To infer the luminosity, mass, and size of a star from observations (as in a celestial census), we need to know the distance to the star How can we measure the great distances to stars? We use various techniques, useful at different scales, with each scale connecting to the next, like a ladder On the Earth, lengths are specified in precise units such as the meter Distances within the solar system are determined by timing how long it takes radar signals to travel from the Earth to a planet or other body and then return Beyond the solar system, …

3. 22 March 2005AST 2010: Chapter 183 Parallax (1) To observers at points A and B, the tree at C appears in different directions This apparent displacement, or change in direction, of a remote object due to a change in vantage point is called parallax The angle that lines AC and BC makes is also called parallax The distance between A and B (length of line AB) is called the baseline

4. 22 March 2005AST 2010: Chapter 184 Parallax (2) How far away is the tree from each observer? One can use triangulation, a method for finding the distance to an inaccessible object If the baseline (B in this figure) and the parallax angle p are measured, then the observers’ distances to the tree can be calculated using trigonometry

5. 22 March 2005AST 2010: Chapter 185 Parallax for Stars (1) The triangulation method can be applied to relatively nearby stars As the Earth orbits the Sun, a nearby star appears to us to move back and forth against the background of distant stars This parallax can be used to find the distance d to the star if the baseline and the parallax angle are known

6. 22 March 2005AST 2010: Chapter 186 Parallax for Stars (2) Since stellar distances are very large, the for has to be very large as well For a relatively nearby star, a sufficiently large baseline is the Earth-Sun distance, which is 1 AU The farther the star, the smaller the angle p For relatively far stars, extremely sensitive measurements of p are required

7. 22 March 2005AST 2010: Chapter 187 The Parsec Since the parallax shifts of stars are very small, the arcsecond is used as the unit of the parallax angle One arcsec (second of arc) is an angle of 1/3600 of a degree The parallax of the ball on the tip of a ballpoint pen viewed from across the length of a football field is about 1 arc second With a baseline of 1 AU, how far way would a star have to be to have a parallax (p) of 1 arcsec? The answer is 206,265 AU, or 3.26 LY Astronomers take this number as another unit (besides the light year) for astronomical distances, called the parsec (abbreviated pc) In other words, 1 parsec is the distance to a star that has a parallax of 1 second of arc Thus, 1 pc = 206,265 AU = 3.26 LY

8. 22 March 2005AST 2010: Chapter 188 More on the Parsec Which unit to use to specify distances: the light year or the parsec? Both are fine and are used by astronomers For example, Proxima Centauri, the nearest star beyond the Sun, is about 4.3 LY, or 1.3 pc, away from us If the distance (D) of a star is in parsecs and its parallax (p) in arcseconds, then D and p are related by a simple formula: D = 1/p Thus, a star with a parallax of 0.1 arcsec would be found at a distance of 10 pc, and another star with a parallax of 0.05 arcsec would be 20 pc away

9. 22 March 2005AST 2010: Chapter 189 What about More Distant Stars? The triangulation method fails for stars farther than 1000 LY away The baseline of 1 AU would be too small for sufficiently precise measurements of the parallax Thus, completely new techniques are needed for more distant stars The breakthrough in measuring the enormous distances came from the study of variable stars, or variables These are stars that vary in luminosity Thus, their brightness changes with time In contrast, most stars are constant in their luminosity (at least within a percent or two) Many variables change in luminosity on a regular cycle

10. 22 March 2005AST 2010: Chapter 1810 Cepheid Variable Stars One of the two special types of variable stars used for measuring distances are the cepheids They are are large, yellow, pulsating stars named for the first-known one of the group, Delta Cephei Its variability was discovered by English astronomer John Goodricke in 1784 It has a magnitude varying with a period of 5.4 days time Cepheid light curve

11. 22 March 2005AST 2010: Chapter 1811 Cepheid Variables Several hundred cepheids have been found in our Galaxy Most have periods in the range of 3 to 50 days and luminosities in the range of 1,000 to 10,000 times greater than that of the Sun Polaris, the North Star, is a cepheid variable It used to vary by 0.1 magnitude every 4 days More recent measurements indicate that its pulsation is decreasing, which suggests that in the future it will no longer be a pulsating variable Animation

12. 22 March 2005AST 2010: Chapter 1812 Cepheid Variables in NGC 3370 and M100 Galaxies The observations was taken by the Hubble Space Telescope The cepheid in NGC 3370 is in the center of a crowded region of stars and has a period of about 50 days A cepheid in a very distant galaxy called M100

13. 22 March 2005AST 2010: Chapter 1813 RR Lyrae Stars Another special special types of variable stars used for measuring distances are called the RR Lyrae variables They are named for the star RR Lyrae, the best-known member of the group They are more common than the cepheids, but less luminous Their periods are always less than one day, and their changes in brightness are typically less than about a factor of 2 From observations, astronomers have concluded that RR Lyrae variables all have nearly the same intrinsic luminosity, of about 50 times that of the Sun Thus, they are like standard light bulbs The RR Lyrae stars can be detected out to a distance of about 2 million LY

14. 22 March 2005AST 2010: Chapter 1814 Why A Cepheid Variable Varies Its changes in color indicates a change in temperature The Doppler shift of its spectrum indicates a change in its size Its luminosity changes when its temperature and size change  In a normal star, the pressure and gravity balance  In a variable star, the pressure and gravity are out of synch cloud pressure from hot gas weight from gravity

15. 22 March 2005AST 2010: Chapter 1815 Period –Luminosity Relation (1) Studying photographs of the Magellanic Clouds, two small galaxies near ours, Henrietta Levitt in 1908 found 20 cepheids that were expected to be at roughly the same distance and discovered a relation between their luminosities and variation periods The longer the period, the greater the luminosity To define the period-luminosity relation with actual numbers (to calibrate it), astronomers first had to measure the actual distances to a few nearby cepheids (in other clusters of stars) in another way

16. 22 March 2005AST 2010: Chapter 1816 Period –Luminosity Relation (2) Cepheids and their period-luminosity relation can be used to estimate distances out to over 60 million LY under the assumption that all the cepheids obey the same period-luminosity relation

17. 22 March 2005AST 2010: Chapter 1817 Distances from H-R Diagram Variables are rare and, therefore, cannot always be found near the a star of interest If variables are not available, the H-R diagram may come to the rescue A detailed examination of a star’s spectrum can tell us its spectral class/type (O, B, A, etc.) pressure and hence size (bigger stars have lower pressures) Knowing the spectral class and size of a star can help us make an educated guess whether it is a main-sequence, giant, or supergiant star This then allows us to pinpoint where the star is on the H-R diagram and establish its luminosity The luminosity, with the apparent brightness of the star, finally leads to its distance

18. 22 March 2005AST 2010: Chapter 1818 Summary Distances to nearest stars can be measured using the parallax (triangulation) method For farther stars in our own and nearby galaxies, the distances can be determined using the RR Lyrae variables and the H-R diagram The cepheids and their period-luminosity relation are useful for finding larger distances up to 60 million LY