1. 1  Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.  Define brightness (see text), apparent magnitude, absolute magnitude.  Describe the methods used to determine the temperature, luminosity, and radius of a star. Learning goals:

2. 2 Questions: Which stars are the brightest? Which stars are putting out the most watts? (luminosity = energy per second) NEED TO KNOW: Distances The most fundamental and accurate (within a certain range) means of finding distances is measuring the parallaxes of stars.

3. 3 PARSEC: Parallax ARc SECond A star having a parallax of 1 arc second is 1 parsec away 1 parsec (pc) = 3.26 light years 1 kiloparsec (1 kpc) = 1000 pc; 1 megaparsec (1 Mpc) = 1,000,000 pc Baseline is 1 Astronomical Unit Small angle formula for distance in AU’s:

4. 4  Works accurately for stars within about 200 pc (Hipparchos satellite)  Biggest problem: measuring the miniscule shift of a star against more distant stars 6.722 6672170 ly Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.

5. 5 Using SIMBAD to find the parallaxes of the stars of Exercise 2SIMBAD 41 Cygni data (partial) Parallax = 4.24 ± 0.16 mas or 0.00424 ± 0.00016 arc seconds Distance = 1/parallax = 1/0.00424 = 236 pc or ~770 ly

6. 6  Every 5 magnitudes difference means 100 x difference in brightness  One magnitude difference is 2.512 times in brightness. (2.512 5 = 100) Define brightness, apparent magnitude, absolute magnitude

7. 7 Using SIMBAD to find necessary measured (observed) quantitiesSIMBAD 41 Cygni data (partial) V = apparent magnitude through “visual” filter Think of it as m v. UV IR

8. 8 Work on star table -- SIMBAD Search SIMBAD SearchSIMBAD Search F5 Iab 4.024.246,900 G9.5 III 4.2316.224,800 B0 Ib 5.940.3626,000 K4.5 Ib-II 3.723.873,900

9. 9

10. 10 Solar data

11. 11  Absolute magnitude is the apparent magnitude a star would have if its distance = 10 parsecs.  Relates luminosities by “placing” stars on common scale.  Smaller the absolute magnitude number, the more luminous the star. Define apparent magnitude, absolute magnitude 41 Cygni d pc = 236 parsecs m v = 4.016 What does the answer tell you?

12. 12 52 Cygni

13. 13 Relationship between absolute magnitude and luminosity - bring in the Sun! 41 Cygni’s calculations

14. 14 52 Cygni

15. 15 Depends on Size (radius, R) Temperature Describe the methods used to determine temperature, luminosity, radius Luminosity 41 Cygni

16. 16 52 Cygni

17. 17 Work on star table -- SIMBAD Search SIMBAD SearchSIMBAD Search F5 Iab 4.024.246,900 G9.5 III 4.2316.224,800 B0 Ib 5.940.3626,000 K4.5 Ib-II 3.723.873,900