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Astrophysics

Astrophysics. E3 Stellar Distances. Stellar Distances Units. Earth in June. Distant stars. Near star. 1 AU. d. θ. Sun. θ. 1 AU. Earth in January. Stellar parallax. d = 1 AU θ. d (parsecs) = 1 p (arc-seconds). Angular Sizes 360 degrees ( 360 o ) in a circle

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Astrophysics

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  1. Astrophysics E3 Stellar Distances

  2. Stellar Distances Units

  3. Earth in June Distant stars Near star 1 AU d θ Sun θ 1 AU Earth in January Stellar parallax d = 1 AU θ d (parsecs) = 1 p (arc-seconds)

  4. Angular Sizes • 360 degrees (360o) in a circle • 60 arcminutes (60’) in a degree • 60 arcseconds (60”) in an arcminute

  5. Stellar Parallax has its limits The farther away the star is, the smaller its parallax angle. Eventually, the movement of the star is too small to see.

  6. Spectroscopic Parallax Text

  7. Luminosity Cephied Variables The luminosity of a Cepheid varies periodically: Changes in the surface and atmosphere cause the star to increase in surface area and thus increase in luminosity periodically.

  8. There is a direct relationship between the peak luminosity of Cepheids and their time periods (‘the luminosity-period relationship’): Peak luminosity / L⊙

  9. b = L 4 π d2 The distance to a Cepheid can be found by... i. Measure the average period of luminosity ii. Use the relationship graph to find peak luminosity from period iii. Measure peak apparent brightness on Earth iv. Find distance using...

  10. Standard Candles Thus the existence of a Cepheid variable star in a distant galaxy enables the luminosity of all the stars in the galaxy to be determined. A standard candleis a star of known luminosity. This means that the luminosity of all other stars in its galaxy can be estimated by comparing their apparent brightness with the standard candle.

  11. The Magnitude Scale • Seen from earth, different stars have different brightness... • Apparent brightness gives us a measurement in standard units. • Apparent magnitude give us a measurement on a logarithmic scale, relative to other stellar bodies.

  12. Asteroid ‘65 Cybele’ and 2 stars with their apparent magnitudes labelled

  13. Greek Magnitude Scale The ancient Greeks first came up with a magnitude scale for stars. They classified the apparent magnitudes by rating the brightest star they could see as magnitude 1 and the faintest as magnitude 6, decreasing by a factor of 0.5 each magnitude. So the 6th magnitude stars were... ½ x ½ x ½ x ½ x ½ = (½)5 = 1/32 as bright as the 1st magnitude

  14. More recently it was thought that the brightest stars visible from earth are about 100 times brighter that the dimmest. So, using the same classification of m = 1 to 6: Fractional change = 5√(1/100) = 1 / 2.512  Each apparent magnitude on the modern scale is 2.512 times dimmer than the previous Modern Apparent Magnitude Scale

  15. Over time, adjustments have had to made to account for dimmer and brighter stars. • e.g. • Vega has apparent magnitude 0, and Sirius (the brightest star) has a negative magnitude (-1.4). • So for the apparent magnitude scale... • the bigger the positive number the dimmer the star • the brightest stars have negative numbers

  16. Calculations involving apparent brightness and apparent magnitude For any star, the relationship between its apparent brightness b1 and apparent magnitude m1 is... b1 b0 b0 = 2.52 x 10-8 Wm-2 i.e. the apparent brightness of a star with apparent magnitude zero. = 2.512-m1

  17. For a second star with magnitude and brightness m2 and b2... So the ratio of the brightness of the two stars is given by... b2 b0 b1 b2 = 2.512-m2 = 2.512m2-m1

  18. Absolute Magnitude Two stars of the same apparent magnitude (i.e. also of the same apparent brightness) may not actually give out energy at the same rate; it could simply be that one is nearer to Earth than the other, brighter star. The absolute magnitudescale gives the magnitude of all stars measured at an equal distance of 10 pc from the observer. Thus it is a measure of luminosity of a star.

  19. It can be shown that for a star at distance d from earth of apparent magnitude m (from earth) and absolute magnitude M (from 10 pc)... ... where d is measured in parsecs. m – M = 5 lg (d/10)

  20. Subtitle Text

  21. Distance measured by parallax: Distance measurement by parallax apparent brightness spectrum Chemical composition of corona Wien’s Law (surface temperature T) Luminosity L = 4πd2 b d = 1 / p L = 4πR2σT4 Stefan-Boltzmann Radius

  22. Distance measured by spectroscopic parallax / Cepheid variables: Apparent brightness spectrum Luminosity class Chemical composition Spectral type Cepheid variable H-R diagram Surface temperature (T) Wien’s Law Period Luminosity (L) Stefan-Boltzmann L = 4πR2σT4 b = L / 4πd2 Distance (d) Radius

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