# Parallax: Measuring the distance to Stars

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1 Measuring the Stars

2 Parallax: Measuring the distance to Stars Use Earth s orbit as baseline Parallactic angle = 1/2 angular shift Distance from the Sun required for a star to have a parallactic angle of 1 arcsecond 1 parsec (pc) Distance (in pc) = 1/parallax (in arcsec) One parsec = 206,265 AU or 3.3 ly

3 Measuring the distances to the Closest Stars Nearest star Proxima Centauri i( (part of the triple star system Alpha Centauri) has parallax of 0.76 arcsec. Therefore, distance = 1/ = pc (4.29 (429l ly) Next nearest star is Barnard s star, w/ a parallax of 0.55 Therefore, d = 1 / 0.55 = 1.82 pc (5.93 ly)

4 From the ground, we can measure parallactic angles of ~1/30 arcsec, corresponding to distances out to ~30 pc. Th lth d t ithi th t di t f There are several thousand stars within that distance from the Sun.

5 From space, parallax s can be measured down to about 5/1000 arcsec, which corresponds to 200 pc. There are several million stars within that distance.

6 Stellar Proper Motion Parallax is an apparent motion of stars due to Earth orbiting the Sun. But stars s also have real motions o through space Space motion has two components: 1) radial motion along the sightline (measured through Doppler shift) 2) proper motion -- transverse observer proper motion (transverse) component star radial component space motion

7 Stellar Proper Motion: Barnard s Star Two pictures, taken 22 years apart (same time of year no parallax!) Barnard s star has a proper motion of 10.3 arcsec/year Given d = 1.8 pc, this proper motion corresponds to a transverse velocity of ~90 km/s!

8 Luminosity and Apparent Brightness Star B is more luminous, but they have the same brightness as seen from Earth.

9 Apparent Brightness and Inverse Square Law Light appears fainter with increasing distance. If we increase our distance from the light source by 2, the light energy is spread out over four times the area. (area of sphere = 4πd 2 ) Flux = Luminosity 4πd 2 To know a star s luminosity we must measure its apparent To know a star s luminosity we must measure its apparent brightness (flux) and know its distance. Then, Luminosity = Flux *4πd 2

10 The Magnitude Scale 2 nd century BC, Hipparchus ranked all visible stars brightest = magnitude 1 faintest = magnitude 6. Faintest To our eyes, a change of one magnitude = a factor of 2.5 in flux. Hence The magnitudes scale is logarithmic. A change of 5 magnitudes means the flux 100 x greater! Brightest

11 Apparent Magnitude - star s apparent brightness when seen from its actual distance Absolute Magnitude - apparent magnitude of a star as measured from a distance of 10 pc. Sun s apparent magnitude (if seen from a distance of 10 pc) is 4.8. This is then the absolute magnitude of fthe Sun.

12 Enhanced color picture of the sky Notice the color differences among the stars

13 You don t have to get the entire spectrum of a star to determine its temperature. Measure flux at blue (B) and yellow ( visual =V) wavelengths. Get temperature by comparing B -V color to theoretical blackbody curve. Stellar Temperature: Color

14 Stellar Temperature: Spectra 7 stars with same chemical composition Temperature affects strength of absorption lines Example: Hydrogen lines are relatively weak in the hottest star because it is mostly ionized. Conversely, hotter temperatures are needed to excite and ionize Helium so these lines are strongest in the hottest star.

15 Spectral Classification: Before astronomers knew much about stars, they classified them based on the strength of observed absorption lines. Classification by line strength started as A, B, C, D,., but became: Annie Jump Cannon O, B, A, F, G, K, M, (L) A temperature sequence! Cannon s system officially adopted in 1910.

16 Spectral Classification Oh Be A Fine Girl/Guy Kiss Me Oh Brother, Astronomers Frequently Give Killer Midterms

17 Stellar Sizes Almost all stars are so small they appear only as a point of light in the largest telescopes A small number are big and close enough to determine their hi sizes directly through hgeometry

18 Stellar Sizes: Indirect measurement Stefan s Law F = σtt 4 Luminosity is the Flux multiplied by entire spherical surface Giants - more than 10 solar radii 2 Area of sphere A = 4πR less than 1 Dwarfs - solar radii Luminosity = 4πR 2 σt 4 -or- L R 2 T 4

19 Understanding Stefan s Law: Radius L R 2 T 4

20 Understanding Stefan s Law: Temperature L R 2 T 4

21 Hertzsprung-Russell (HR) Diagram HR diagrams plot stars as a function of their Luminosity i & Temperature About 90% of all stars (including the Sun) lie on the Main Sequence. where stars reside during their core Hydrogen-burning phase.

22 From Stefan s law... L = 4πR 2 σtt 4 More luminous stars at the same T must be bigger! Cooler stars at Cooler stars at the same L must be bigger!

23 The HR Diagram: 100 Brightest Stars Most of these luminous stars are somewhat rare they lie beyond 5pc. We see almost no red dwarfs (even though they are very abundant in the universe) because they are too faint. Several non-main Sequence stars are seen in the Red Giant region

24 Using The HR Diagram to Determine Distance: Spectroscopic Parallax Example: 1) Determine Temperature from color Main Sequence 2) Determine Luminosity based on Mi Main Sequence position ii 3) Compare Luminosity with Flux (apparent (pp brightness) 4) Use inverse square law to determine distance Flux = Luminosity 4πd 2

25 The HR Diagram: Luminosity & Spectroscopic Parallax What if the star doesn t happen to lie on the Main Sequence - maybe it is a red giant or white dwarf??? We determine the star s Luminosity Class based on its spectral line widths: These lines get broader when the stellar gas is at higher densities indicating a smaller star. Wavelength A star Supergiant A star Giant A star Dwarf (Main Sequence)

26 The HR Diagram: Luminosity Class Bright Supergiants Supergiants Bright Giants Giants Sub-giants Main-Sequence (Dwarfs)

27 We get distances to nearby yplanets from radar ranging. The Distance Ladder That sets the scale for the whole solar system (1 AU). Given 1 AU plus stellar parallax, we find distances to nearby stars. Use these nearby stars, with known Distances, Fluxes and Luminosities, to calibrate Luminosity classes in HR diagram. Th t l l + Fl i ld L i it + Di t f Then spectral class + Flux yields Luminosity + Distance for farther stars (Spectroscopic Parallax).

28 Stellar Masses: Visual Binary Stars With Newton s modifications to Kepler s laws, the period and size of the orbits yield the sum of the masses, while the relative distance of each star from the center of mass yields the ratio of the masses. The ratio and sum provide each mass individually.

29 Stellar Masses: Spectroscopic Binary Stars Many binaries are too far away to be resolved, but they can be discovered from periodic spectral line shifts. In this example, only the yellow (brighter) star is visible

30 Stellar Masses: Eclipsing Binary Stars How do we identify eclipsing binaries? The system must be observed edge on. Also tells us something about the stellar radii.

31 The HR Diagram: Stellar Masses Why is mass so important? Together with the initial composition, mass defines the entire life cycle and all other properties of the star! Luminosity, Radius, Surface Temperature, Lifetime, Evolutionary phases, end result.

32 Example: On the Main Sequence: Luminosity Mass 3 Why? More mass means more gravity, more pressure on core, higher h core temperatures, t faster nuclear reaction rates, higher Luminosities!

33 How does Mass effect how long a star will live Lifetime Fuel available / How fast fuel is burned So for a star Lifetime Mass / Luminosity Or, since Luminosity Mass 3 For main sequence stars Lifetime Mass / Mass 3 = 1 / Mass 2 How long a star lives is directly related to the mass! Big stars live shorter lives, burn their fuel faster.

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