Stellar Spectra

1. Stellar Spectra • Flux and Luminosity • Brightness of stars • Temperature vs heat • Temperature vs color • Colors/spectra of stars • Classifying stars: H-R diagram • Stefan-Boltzman law, stellar radii • Measuring star masses • Mass-luminosity relation

2. Flux and luminosity • Luminosity - A star produces light – the total amount of energy that a star puts out as light each second is called its Luminosity. • Flux - If we have a light detector (eye, camera, telescope) we can measure the light produced by the star – the total amount of energy intercepted by the detector divided by the area of the detector is called the Flux.

4. Flux and luminosity • To find the luminosity, we take a shell which completely encloses the star and measure all the light passing through the shell • To find the flux, we take our detector at some particular distance from the star and measure the light passing only through the detector. How bright a star looks to us is determined by its flux, not its luminosity. Brightness = Flux.

5. Flux and luminosity • Flux decreases as we get farther from the star – like 1/distance2

6. Brightness of stars • The brightness of a star is a measure of its flux. • Ptolemy (150 A.D.) grouped stars into 6 `magnitude’ groups according to how bright they looked to his eye. • Herschel (1800s) first measured the brightness of stars quantitatively and matched his measurements onto Ptolemy’s magnitude groups and assigned a number for the magnitude of each star.

7. Brightness of stars • In Herschel’s system, if a star is 1/100 as bright as another then the dimmer star has a magnitude 5 higher than the brighter one. • Note that dimmer objects have higher magnitudes

9. Apparent Magnitude Consider two stars, 1 and 2, with apparent magnitudes m1 and m2 and fluxes F1 and F2. The relation between apparent magnitude and flux is: For m2 - m1 = 5, F1/F2 = 100.

10. Flux, luminosity, and magnitude

11. Distance-Luminosity relation:Which star appears brighter to the observer? Star 1 10L L Star 2 d 10d

12. Flux and luminosity Star 2 is dimmer and has a higher magnitude.

13. Flux and luminosity Star 2 is dimmer and has a higher magnitude.

14. Absolute magnitude • The magnitude of a star gives it brightness or flux when observed from Earth. • To talk about the properties of star, independent of how far they happen to be from Earth, we use “absolute magnitude”. • Absolute magnitude is the magnitude that a star would have viewed from a distance of 10 parsecs. • Absolute magnitude is directly related to the luminosity of the star.

15. Absolute Magnitude Absolute magnitude, M, is defined as where D is the distance to the star measured in parsecs. For a star at D = 10 parsecs, 5log10 = 5, so M = m.

16. Absolute Magnitude and Luminosity The absolute magnitude of the Sun is M = 4.83. The luminosity of the Sun is L Note the M includes only light in the visible band, so this is accurate only for stars with the same spectrum as the Sun.

17. Absolute Bolometric Magnitude and Luminosity The bolometric magnitude includes radiation at all wavelengths. The absolute bolometric magnitude of the Sun is Mbol = +4.74.

18. Is Sirius brighter or fainter than Spica: • as observed from Earth [apparent magnitude] • Intrinsically [luminosity]?

19. Sun

20. Little Dipper (Ursa Minor) Guide to naked-eye magnitudes

21. Which star would have the highest magnitude? • Star A - 10 pc away, 1 solar luminosity • Star B - 30 pc away, 3 solar luminosities • Star C - 5 pc away, 0.5 solar luminosities • Charlize Theron

22. Temperature lower T higher T • Temperature is proportional to the average kinetic energy per molecule k = Boltzmann constant = 1.3810-23 J/K = 8.6210-5 eV/K

23. Temperature vs. Heat lower T higher T • Temperature is proportional to the average kinetic energy per molecule • Heat (thermal energy) is proportional to the total kinetic energy in box less heat more heat same T

24. Wien’s law • Cooler objects produce radiation which peaks at lower energies = longer wavelengths = redder colors. • Hotter objects produce radiation which peaks at higher energies = shorter wavelengths = bluer colors. • Wavelength of peak radiation: Wien Law max = 2.9 x 106 / T(K) [nm]

25. A object’s color depends on its surface temperature • Wavelength of peak radiation: Wien Law max = 2.9 x 106 / T(K) [nm]

26. What can we learn from a star’s color? The color indicates the temperature of the surface of the star.

27. Observationally, we measure colors by comparing the brightness of the star in two (or more) wavelength bands. U B V This is the same way your eye determines color, but the bands are different.

28. Use UVRI filters to determine apparent magnitude at each color

30. Stars are assigned a `spectral type’ based on their spectra • The spectral classification essentially sorts stars according to their surface temperature. • The spectral classification can also use spectral lines.

31. Spectral type • Sequence is: O B A F G K M • O type is hottest (~25,000K), M type is coolest (~2500K) • Star Colors: O blue to Mred • Sequence subdivided by attaching one numerical digit, for example: F0, F1, F2, F3 … F9 where F1 is hotter than F3 . Sequence is O … O9, B0, B1, …, B9, A0, A1, … A9, F0, … • Useful mnemonics to remember OBAFGKM: • Our Best Astronomers FeelGood Knowing More • Oh Boy, An F Grade Kills Me • (Traditional) Oh, Be a Fine Girl (or Guy), Kiss Me

32. Very faint

34. The spectrum of a star is primarily determined by • The temperature of the star’s surface • The star’s distance from Earth • The density of the star’s core • The luminosity of the star

35. Classifying stars • We now have two properties of stars that we can measure: • Luminosity • Color/surface temperature • Using these two characteristics has proved extraordinarily effective in understanding the properties of stars – the Hertzsprung-Russell (HR) diagram

36. HR diagram

37. HR diagram • Originally, the HR diagram was made by plotting absolute magnitude versus spectral type • But, it’s better to think of the HR diagram in terms of physical quantities: luminosity and surface temperature

38. If we plot lots of stars on the HR diagram, they fall into groups

39. These groups indicate types of stars, or stages in the evolution of stars

40. Luminosity of a ‘Black Body’ Radiator Stephan-Boltzmann Law: an opaque object at a given temperature will radiate, per unit surface area, at a rate proportional to the surface temperature to the fourth power : P/m2 = T4  = Stephan-Boltzman constant = 5.6710-8 W/m2·K4 T = surface temperature P/m2 = power radiated per square meter

41. Luminosity of a ‘Black Body’ Radiator For the spherical object, the total power radiated = the total luminosity is: L = 4R2T4 T = temperature  = Stephan-Boltzman constant = 5.6710-8 W/m2·K4 R = radius

42. Luminosity of a ‘Black Body’ Radiator Suppose the radius of the Sun increased by a factor of 4 but the rate of power generated by fusion remained the same, how would the surface temperature of the Sun change?

43. If we know luminosity and temperature, then we can find the radius: L = 4pR2sT4 Small stars will have low luminosities unless they are very hot. Stars with low surface temperatures must be very large in order to have large luminosities. Stars come in a variety of sizes

44. Sizes of Stars on an HR Diagram • We can calculate R from L and T. • Main sequence stars are found in a band from the upper left to the lower right. • Giant and supergiant stars are found in the upper right corner. • Tiny white dwarf stars are found in the lower left corner of the HR diagram.

45. Hertzsprung-Russell (H-R) diagram • Main sequence stars • Stable stars found on a line from the upper left to the lower right. • Hotter is brighter • Cooler is dimmer • Red giant stars • Upper right hand corner (big, bright, and cool) • White dwarf stars • Lower left hand corner (small, dim, and hot)

46. Luminosity classes • Class Ia,b : Supergiant • Class II: Bright giant • Class III: Giant • Class IV: Sub-giant • Class V: Dwarf The Sun is a G2 V star

47. ‘Spectroscopic Parallax’Measuring a star’s distance by inferring its absolute magnitude (M) from the HR diagram • If a star is on the main-sequence, there is a definite relationship between spectral type and absolute magnitude. Therefore, one can determine absolute magnitude by observing the spectral type M. • Observe the apparent magnitude m. • With m and M, calculate distance Take spectrum of star, find it is F2V, absolute magnitude is then M = +4.0. Observe star brightness, find apparent magnitude m = 9.5. Calculate distance:

48. Masses of stars • Spectral lines also allow us to measure the velocities of stars via the Doppler shift that we discussed in searching for extra-solar planets. Doppler shift measurements are usually done on spectral lines. • Essentially all of the mass measurements that we have for stars are for stars in binary systems – two stars orbiting each other. • The mass of the stars can be measured from their velocities and the distance between the stars.

49. Double star – a pair of stars located at nearly the same position in the night sky. Optical double stars – stars that appear close together, but are not physically conected. Binary stars, or binaries – stars that are gravitationally bound and orbit one another. Visual binaries – true binaries that can be observed as 2 distinct stars Spectroscopic binaries binaries that can only be detected by seeing two sets of lines in their spectra They appear as one star in telescopes (so close together) Eclipsing binaries – binaries that cross one in front of the other. Binary star systems Classifications

50. Visual Binary Star Krüger 60 (upper left hand corner) About half of the stars visible in the night sky are part of multiple-star systems.