Stars !

1. Stars !

4. Measurement of Distances to Nearby Stars Parallax Revisited Parallax Angle R Θ d R Tan Θ = d

5. Measurement of Distances to Nearby Stars Parallax Revisited Parallax Angle R Θ d R Tan Θ = d For small angles (valid for stellar measurements): Tan Θ≈Θ where Θ is measured in radians

6. Measurement of Distances to Nearby Stars Parallax Revisited Parallax Angle R Θ d R Θ (radians) = d For astronomical measurements R and d are measured in A.U.

7. Measurement of Distances to Nearby Stars Parallax Revisited R (in A.U.) d (in A.U.) = Θ (radians) A convenient variation: 1 radian = 206265 arc seconds R (in A.U.) R (in A.U.) 206265 R (in A.U.) d (in A.U.) = = = Θ (radians) Θ (arc seconds) Θ(arc seconds) 206265

8. Measurement of Distances to Nearby Stars Parallax Revisited One parsec is defined to be 206265 A.U. AND, if you use the radius of the earth orbit for R (earth based measurements, R = 1 a.u., then d (a.u.) 1 = 206265 au/pc Θ (arc seconds) 1 d (in parsecs) = Θ (arc seconds)

9. Measurement of Speeds of Nearby Stars Radial Speed – Doppler Shift Revisited Blue Shift toward Earth Red Shift away from Earth

10. Measurement of Speeds of Nearby Stars Radial Speed – Doppler Shift Revisited Doppler shifts are caused by line of sight velocities (called radial velocity) of the source. Sources moving away from the earth are red shifter. Sources moving toward the earth are blue shifted.

11. Measurement of Speeds of Nearby Stars Radial Speed – Doppler Shift Revisited Astrophysics and Cosmology Longer , lower f Shorter , higher f In general Apparent Wavelength True Frequency Velocity of Source = = 1 + True Wavelength Apparent Frequency Wave Speed Note: If the source and detector are moving apart, the Velocity of the Source is POSITIVE. If the source and detector are toward one another, the Velocity of the Source is NEGATIVE.

12. Measurement of Speeds of Nearby Stars Transverse (sideways) Speeds Proper motionis defined to be the transverse motion of the star across the sky Motion of Barnards Star captured: left 1997 (Jack Schmidling), right 1950 (POSS)

13. Measurement of Speeds of Nearby Stars Transverse (sideways) Speeds Measurement made same time during the year Θ w d w Θ (radians) = d w = d xΘ (radians) If the time interval between measurements is measured, then v = w/ t

14. Measurement of Speeds of Nearby Stars v vt vR Pythagorian Theorem: v2 = vR2 + vt2

15. Luminosity (brightness) of a Star Luminosity is the amount of energy per second (Watts) emitted by the star Recall: The luminosity of the sun is about 4 x 1026 W Absolute Brightness: The luminosity per square meter emitted by the star at it’s surface. This is an intrinsic property of the star. Apparent Brightness: The power per square meter as measured at the location of the earth.

16. Luminosity (brightness) of a Star Note: Power (or Luminosity) Absolute Brightness = Surface Area of star Also Note: Because of conservation of energy, the energy per second radiated through the area of a sphere of any radius must be a constant. Therefore Power (or Luminosity) Apparent Brightness = Surface Area of sphere of radius equal to the distance between the star and the earth

17. Luminosity (brightness) of a Star Power (or Luminosity) Apparent Brightness is proportional to d2 Apparent brightness can be measured at the earth with instruments. d is measured using parallax. These pieces of information can be used to measure the luminosity of the star.

18. Photometry Revisited Photometer – An instrument which measure the brightness of an object Will measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the object

19. Photometry Photometer – An instrument which measure the brightness of an object Will measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the object Intensity X X X Wavelength

20. Photometry Photometer – An instrument which measure the brightness of an object Will measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the object Intensity X X X Wavelength

21. Photometry Photometer – An instrument which measure the brightness of an object Will measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the object Temperature of object is 7000 K Intensity X X X Wavelength

22. Temperature of a Star Photometry Revisited Different typical filters used: B (blue) Filter: 380 – 480 nm V (visual) filter: 490 – 590 nm (range of highest sensitivity of the eye) U (ultraviolet) filter: near ultraviolet

23. Stellar Magnitude (brightness) Magnitude is the degree of brightness of a star. In 1856, British astronomer Norman Pogson proposed a quantitative scale of stellar magnitudes, which was adopted by the astronomical community. Each increment in magnitude corresponds to an increase in the amount of energy by 2.512, approximately. A fifth magnitude star is 2.512 times as bright as a sixth, and a fourth magnitude star is 6.310 times as bright as a sixth, and so on. Originally, Hipparchus defined the magnitude scale of stars by ranking stars on a scale of 1 through 6, with 1 being the brightest and six the dimmest. Using modern tools, it was determined that the range of brightness spanned a range of 100, that is, the magnitude 1 stars were 100 times brighter than magnitude 6. Therefore, each change in magnitude corresponds to a factor of 2.512 change in brightness, since (2.512)5 = 100 (to within roundoff)

24. Stellar Magnitude (brightness) The naked eye, upon optimum conditions, can see down to around the sixth magnitude, that is +6. Under Pogson's system, a few of the brighter stars now have negative magnitudes. For example, Sirius is –1.5. The lower the magnitude number, the brighter the object. The full moon has a magnitude of about –12.5, and the sun is a bright –26.51!

25. Stellar Magnitude (brightness)

26. Stellar Magnitude (brightness) Star Magnitude Table Showing How Much DimmerOther Magnitudes are as Compared to a -1 Magnitude Star

27. Stellar Radii Stefan’s Law Power Emitted per unit Area = σ T4 • σ = 5.67 x 10-8 W / m2 – K4 (Stefan-Boltzmann constant) Note: The power in this expression is the star’s luminosity

28. Stellar Radii Stefan’s Law Power Emitted per unit Area = σ T4 Once the absolute luminosity and temperature is measured, the star’s radius can be calculated.

29. Stellar Classifications Spectral Classes

30. Stellar Classifications Stellar Spectral Types Stars can be classified by their surface temperatures as determined from Wien's Displacement Law, but this poses practical difficulties for distant stars. Spectral characteristics offer a way to classify stars which gives information about temperature in a different way - particular absorption lines can be observed only for a certain range of temperatures because only in that range are the involved atomic energy levels populated. The standard classes are: Type Temperature O 30,000 - 60,000 K Blue stars B 10,000 - 30,000 K Blue-white stars A 7,500 - 10,000 K White stars F 6,000 - 7,500 K Yellow-white stars G 5,000 - 6,000 K Yellow stars (like the Sun) K 3,500 - 5,000K Yellow-orange stars M < 3,500 K Red stars The commonly used mnemonic for the sequence of these classifications is "Oh Be AFine Girl, Kiss Me".

31. Stellar Classifications Stellar Spectral Types Type Temperature O 30,000 - 60,000 K Blue stars B 10,000 - 30,000 K Blue-white stars A 7,500 - 10,000 K White stars F 6,000 - 7,500 K Yellow-white stars G 5,000 - 6,000 K Yellow stars (like the Sun) K 3,500 - 5,000K Yellow-orange stars M < 3,500 K Red stars The commonly used mnemonic for the sequence of these classifications is "Oh Be AFine Girl, Kiss Me".

32. O-Type Stars The spectra of O-Type stars shows the presence of hydrogen and helium. At these temperatures most of the hydrogen is ionized, so the hydrogen lines are weak. Both HeI and HeII (singly ionized helium) are seen in the higher temperature examples. The radiation from O5 stars is so intense that it can ionize hydrogen over a volume of space 1000 light years across. One example is the luminous H II region surrounding star cluster M16. O-Type stars are very massive and evolve more rapidly than low-mass stars because they develop the necessary central pressures and temperatures for hydrogen fusion sooner. Because of their early development, the O-Type stars are already luminous in the huge hydrogen and helium clouds in which lower mass stars are forming. They light the stellar nurseries with ultraviolet light and cause the clouds to glow in some of the dramatic nebulae associated with the H II region

40. Each Spectral class is divided into 10 subclasses, ranging from 0 (hottest) to 9 (coolest). Stars are also divided into six categories according to luminosity: 1a (most luminous supergiants), 1b (less luminous supergiants), II (luminous giants), III (normal giants, IV (subgiants), and V (main sequence and dwarfs). For instance, Sol is classified as a G2V, which means that it is a relatively hot G-classed main sequence star.