STELLAR PROPERTIES

1. STELLAR PROPERTIES How do we know what we know about stars? (and the rest of the universe!)

2. What do YOU want to know about a random star? • What are the most IMPORTANT stellar properties? • Mass (always quoted in terms of M = 2 x 1033 g = 2 x 1030 kg) is MOST IMPORTANT • Age is VERY IMPORTANT • Composition (relative amounts of different elements) is also VERY IMPORTANT • Rotation velocity • Magnetic field • Together the above DETERMINE the ALL other properties of all stars, but NONE of them is EASY to determine.

3. What are the (relatively) EASY TO DETERMINE stellar properties? • Location on the sky, (RA, dec) (first thing you do!) • Brightness or Intensity, I (via apparent magnitude, m) • Surface temperature, T (via Wein's Law + spectroscopy) • Distance, d (via parallax + other methods discussed later) • Luminosity, L, or Power (via absolute magnitude, M) • Size or radius (from T and L via Stefan-Boltzmann Law) • Velocity, V (radial via Doppler shift + motion across sky) • “Multiplicity” (single, binary=double, triple etc.) • Do they have planets? [very hard, but now sometimes possible to tell]

4. Distances (d) via Parallax • This is a direct measurement of the apparent location of the star with respect to more distant stars. The closer a star is the more its apparent position shifts as the earth moves around the Sun. Our slightly differing vantage point at different times of the year causes this apparent motion • The parallax angle, p, is defined as the angle subtended by the Sun-Earth distance (1 AU) at the location of the star. It is geometrically equal to 1/2 of the shift in location over a six-month period.

5. The brightness of a star depends on both distance and luminosity

6. Parallax & Hipparcos

7. Parallax Applets • Introduction to Parallax Applet • Measuring Parallax Angle • Parallax Angle vs Distance • Parallax of Nearby Star

8. Parallax math • Parallax angle = p tan p = 1 AU / d • Biggest observed p = 0.75 arcsec -- very small! • If d is in PARSECS, p'' =1/d • 1 parsec = 1 pc = 3.26 light-years = 3.085678 x 1018cm = 3.1 x 1016 m = 3.1 x 1013 km • Recall, 1 AU = 1.496 x 1013 cm = 1.5 x 1011 m = 1.5x108 km • Example 1: closest star has p = 0.75'' so • The distance, d (pc) = 1/0.75'' = 1.3 pc = 4.1 lt-yr • Example 2: A star has d = 50 pc. What is p? • Parallax, p = 1/d = 1/50 = 0.02 arcsec = 0.02''

9. The Nearest Stars

10. What are some good examples of parallax? • A) Hold your thumb out and blink your eyes. Your thumb moves more than the background • B) Driving down a road a nearby fence appears to shift more than distance scenery • C) Planets shift their position in the sky partly because the earth moves, shifting our position • D) Stars shift their position at different times of the year, as Earth orbits the Sun • E) All of the above

11. What are some good examples of parallax? • A) Hold your thumb out and blink your eyes. Your thumb moves more than the background • B) Driving down a road a nearby fence appears to shift more than distance scenery • C) Planets shift their position in the sky partly because the earth moves, shifting our position • D) Stars shift their position at different times of the year, as Earth orbits the Sun • E) All of the above

12. Luminosity: Amount of power a star radiates (energy per second = Watts = 107 erg s-1) Apparent brightness: Amount of starlight that reaches Earth (energy per second per square meter=W m-2)

13. Luminosity passing through each sphere is the same Area of sphere: 4π (radius)2 Divide luminosity by area to get brightness

14. The relationship between apparent brightness and luminosity depends on distance: Luminosity Brightness = 4π (distance)2 We can determine a star’s luminosity if we can measure its distance and apparent brightness: Luminosity = 4π (distance)2 x (Brightness)

15. BRIGHTNESS, LUMINOSITY AND MAGNITUDES • Apparent magnitude is an historical way of describing the brightness or intensity of a star or planet. The brightest objects visible to the naked eye were called 1st magnitude and the faintest, 6th magnitude. • Quantified to say a factor of 100in brightness (or intensity -- erg/s/cm2) corresponds to exactly 5 mag. • m = 5 100 times brighter (e.g., m = 1 vs m = 6) • m = 1  (100)1/5 = 2.512 times brighter • m = 2  (100)2/5 = 2.5122 = 6.31 times brighter • m = 3  (100)3/5 = 2.5123 = 15.85 times brighter • m = 10  100 x 100 = 104 times brighter • m = 15  100 x 100 x 100 = 106 times brighter

16. Absolute Magnitudes and The Inverse Square Law • The absolute magnitude is a measure of the POWER or LUMINOSITY of a star. We can measure apparent magnitude or INTENSITIES easily and DISTANCES pretty easily, and so determine absolute magnitudes or LUMINOSITIES

17. If a star was moved four times as far away, what would happen to it? • A) It would get four times fainter • B) It would get sixteen times fainter • C) It would get fainter and redder • D) It would get fainter and bluer • E) If moved only four times farther, you wouldn’t notice much change

18. If a star was moved four times as far away, what would happen to it? • A) It would get four times as faint • B) It would get sixteen times fainter • C) It would get fainter and redder • D) It would get fainter and bluer • E) If moved only four times farther, you wouldn’t notice much change

19. To measure a star’s true brightness, or luminosity, you need to know: • A) Its temperature and distance • B) Its temperature and color • C) Its apparent brightness and distance • D) Its apparent brightness and color • E) Its distance, apparent brightness, and color or temperature

20. To measure a star’s true brightness, or luminosity, you need to know: • A) Its temperature and distance • B) Its temperature and color • C) Its apparent brightness and distance • D) Its apparent brightness and color • E) Its distance, apparent brightness, and color or temperature

21. MAGNITUDES AND DISTANCES • Measuring the brightness, or apparent magnitude of a star is easy. If we also know the distance we can get the ACTUAL luminosity, or absolute magnitude. Alternatively, if we know both the APPARENT and ABSOLUTE magnitudes we can find the DISTANCE to a star. • The absolute magnitude can often be accurately estimated from the star's spectrum, so this method of distance determination (“spectroscopic parallax”) is often used beyond 100 pc where regular (“trigonometric”) parallax can’t be accurately found. • A more distant but very luminous star can appear as bright as a nearer, fainter, star.

22. Different distances, same brightnesses

23. Review of Logs (common, base 10) • log10 10 = 1.0 log 1 = 0.0 log 100 = 2.0 log 1000 = 3.0 log 100,000 = 5.0 • log 0.1 = -1.0 log 0.0001 = -4.0 • log 2 = 0.30 log 3 = 0.48 log 5 = 0.70 • log 30 = 1.48 log 500 = 2.70 • log 0.5 = -0.30 log 0.2 = -0.70 • Simple rule: log10(10x) = x • Very useful since log(xy) = log x + log y

24. Mathematics of Magnitudes • EXAMPLES: Given m = 7 and d = 100 pc, find M: M = m - 5 log (d/10pc) • M = 7 - 5 log(100pc/10pc) = 7 - 5 log 10 • so M = 7 - 5(1) = 2 • What if m = 18 and d = 105 pc? • M = m - 5 log (d/10pc) • M = 18 - 5 log(105 pc / 101 pc) = 18 - 5 log (104) • or M = 18 - 5(4) = -2

25. Apparent Magnitudes Note that mags are backwards: More negative is Brighter and More positive is Fainter!

26. Getting Distances from Magnitudes • Now, given M = -3 and m = 7, find d. • m - M = 5 log (d/10 pc) 7 -(-3) = 10 = 5 log (d/10 pc) • So 2 = log (d/10pc) • Therefore 102 = d/10 pc and finally, • d = 102(10 pc) = 103 pc = 1000 pc

27. COLORS and TEMPERATURES of STARS • Bluer stars are hotter and redder ones are cooler. • The simplest and quickest way to estimate the temperature is to measure the magnitudes of stars in different COLORS, using FILTERS on a telescope that only let particular wavelengths through -- the technique of FILTER PHOTOMETRY. • Standard filters are U, B, V, R, I with U = UV (really very blue), B = blue, V = visible (really yellow), R = red, and I = IR (very long red). • Filters actually in the IR are H, K, L and can be used with telescopes in space or at very high altitudes. • Color index, C = B - V • Since lower magnitudes are brighter, C = -0.4 is hot (i.e., more blue light than yellow) and C = 1.2 is cold (vice versa) for a star.

28. Stellar Colors Cool, red, Betelgeuse & Hot, blue, Rigel + Dense star field

29. Blackbody Curves & Filter Photometry B-V < 0, hot and blue B-V = 0, medium and yellow B-V > 0, cool and red

30. Stellar Temperatures • Better TEMPERATURE measurements can be obtained with more work from a SPECTROMETER, where brightnesses at many, many wavelengths are determined. But you must look at the star for a longer period, since all the light is spread out into many wavelength bins. • This allows finding max, therefore T via Wien's Law: T(K)= 0.29 cmK/ max (cm) • Even more precise measurements of T come from a detailed analysis of the strengths of many spectral absorption lines. • Wien's Law Applet

31. STELLAR SIZES • A very small number of nearby and large stars have had their radii directly determined by INTERFEROMETRY. The CHARA Array is substantially adding to this number. • Usually we must use the STEFAN-BOLTZMAN LAW. • L = 4  R2T4 • L is found from M via m and d • T is found from color index, Wien’s Law, or spectroscopy • So we solve for R,

32. Stars Come in a WIDE Range of Sizes

33. SPECTRAL LINES TELL US • Composition (mere presence of absorption lines say which elements are present in the star's photosphere -- fingerprints) • Abundances (relative strengths of lines) • Temperature (relative strengths of lines) (equations are solved simultaneously for T and abundances) • Pressure (higher P makes for broader lines) • Rotation (faster spin makes for broader lines) (rotationally broadened line shapes are slightly different from those produced by pressure broadening) • Velocity (radial velocity from Doppler shift) • Magnetic field strength (causes splitting of energy levels within atoms, therefore splitting of spectral lines -- but only visible if B is higher than is typical for most stars).

34. STELLAR MOTION and VELOCITY • The radial, or line-of-sight, velocity can be determined from the Doppler shift, as already discussed. • Long-term measurements of nearby stars (when determining parallaxes for distance measurements) also showed many exhibited enough PROPER MOTION to be detected. This is motion in the plane of the sky (i.e. in Right Ascension and Declination) • PM is measured in "/year BUT actual TRANSVERSE VELOCITY ~ PM x d • The SPACE VELOCITY is the full 3-D velocity of a star: the VECTOR SUM of the Radial and Transverse Velocities.

35. Proper and Space Motions Barnard’s Star 

36. IDEA QUIZ • Star A has M=-3 and d=100 pc • Star B has m=+6 and d=1000 pc • Star C has m=+3 and M=+3 • Which star is • 1) Most luminous (most powerful) • 2) Brightest (most intense) • 3) Closest • Remember: m-M = 5 log(d/10pc)

37. Answers • B: M=m-5log(1000/10)=6-5log(100) • =6-5(2)=6-10=-4: most luminous • A: m=M+5log(d/10pc)= • -3+5log(100/10)=-3+5(1)=+2: brightest • C: 5log(d/10pc)=m-M=0, • So log(d/10pc)=0 and d=10pc: closest