Distances to the stars Friedrich Bessel Cygni 10 light years. Just beat Struve and Henderson who measured Vega and α Centauri respectively.

Transcription

1 Distances to the stars Friedrich Bessel Cygni 10 light years. Just beat Struve and Henderson who measured Vega and α Centauri respectively.

2 Distances to the stars the technique p < 1arcsecond d = 1/p parsecs 1 parsec = 3.26 lyrs

3 The Power of the Stars Once we know the distances to the stars we can work out their true luminosities, L, from their apparent luminosities, l, using the equation: l = L 4πd hence 2 L = 4πd 2 l d L Area = 4πd 2 Find 10-5 L sun <L<10 5 L sun A vast range!

4 The Magnitudes of Stars a number representing the brightness of a star (given the symbol m). First developed by Hipparchus in 134BCE Brightest stars = 1 st magnitude Faintest (naked eye) stars = 6 th magnitude the magnitude scale i.e. fainter objects have a larger number as the magnitude! The scale looks linear to the naked eye in actual fact it is found that each difference of one magnitude corresponds to a multiplicative factor of 2.5 in true brightness brightness ratio A difference of 5 magnitudes corresponds to a factor of 100 in brightness i.e magnitude difference

5 Very bright objects can therefore have negative magnitudes. e.g. Sirius, m = -1.4 Venus = -4.4 Full Moon = -12 Sun = -27 Faintest stars with naked eye, m = +6.5 With binoculars = +10 With the Hubble Space Telescope and the largest ground based telescopes = +30 Remember each difference of one magnitude corresponds to a factor of 2.5 in real terms so the difference in brightness between the full moon and the sun corresponds to 15 magnitudes which amounts to = 1 million!

6 The human eye works on what is known as a logarithmic scale the previous graph plotted on a logarithmic scale becomes linear. the magnitude scale log(brightness ratio) magnitude difference Mathematically for stars of brightness b1 and b2 and corresponding magnitudes m1 and m2: b b / 5( m -m )

7 Absolute magnitudes, M The absolute magnitude of a star is defined as the apparent magnitude a star would have at a standard distance of 10 parsecs. Absolute magnitudes are therefore related to the true luminosities of stars (in the same rather complex logarithmic way) e.g. M for the Sun = +5 i.e. at 10 parsecs distance the sun would look like a rather average star which we now know it is. From the equation on the previous slide and the inverse square law discussed previously it can be shown that: m M = 5 log d 5 This is in fact the inverse square law expressed in magnitude terms. If we know m and M we can find d from this formula or knowing d and m we can find M (d will be in parsecs).

8 Light from the sun and stars Newton s prism experiment (1670 s) White Light Rainbow spectrum We now know that the prism splits the light into its component colours because the amount of bending, or refraction, depends on the wavelength of the light red is refracted least because of its longer wavelength.

9 Wollaston (1802) and Fraunhofer (1814) observed dark lines in more detailed spectra of the Sun. Fraunhofer, measured wavelengths of the lines in detail.

10 Huggins the spectroscope in astronomy

11 Huggins the spectroscope in astronomy

12 Types of Spectra Spectra of hot solids Spectrum of a low density gas Spectrum of gas seen in front of continuous source Each gas/element has a unique bar code - discovered by Kirchoff and Bunsen in the 1860s.

13 The spectra of low density gases showed a series of bright emission lines. If the gas was placed in front of a source of continuous (rainbow) light the lines were reversed to a series of dark absorption lines.

14 1913

15 Energy levels in the Hydrogen atom.

16 The spectra of stars therefore tells us their composition. Temperature Spectral types O B A F G K M The classification system developed over many years at the Harvard observatory directed by Henry Draper.

17 Early classification in terms of strengths of H lines by Pickering and Fleming in the 1880s (alphabetical) 1901 re-ordered by Annie Jump Cannon understood in the 1920s by Cecilia Payne as sequence of increasing temperature.

18 The surface temperature of stars Intensity Theory shows that the temperature of the gas/star is related to where the black-body curve peaks. Hot stars will look bluish, cooler stars will look red. It is found that: 3000<T<100000K

19 A modern day spectrum of the Sun

20 The Hertzsprung-Russell diagram first drawn in 1910

21 Radii of stars given by L = 4πr 2 σt 4 the diagonal lines are

22 Relative sizes of some other stars Most stars are red dwarfs larger than Jupiter but smaller than the Sun some are much larger and more luminous than the Sun. All stars are so far away that they only appear as specks of light even through the worlds largest telescopes.

23 Velocities of stars Doppler 1842 Fizeau 1848

24 Fizeau carried out the first terrestrial measurement of the speed of light in teeth Focault used a similar method in 1862 to obtain a more accurate figure.

25 1851 Focault at the Paris Obsrvatory demonstrated the Earth s rotation with a long heavy pendulum. At the latitude of Paris the pendulum traced out a full turn in 32.7hrs (only 24hrs at the poles). W (deg/day)=360sin(l) because of Coriolis forces.

26 Doppler shifts of spectral lines can be used to measure velocities - and detect the motions of objects that cannot otherwise be seen. Note Star A has fixed blue lines for clarity These observations can also tell us the masses of the stars. We find: 0.1M sun <M<100M sun

27 Even if only one set of lines are visible they may appear to wobble. This type of observation is currently used to detect the presence of otherwise invisible extra-solar planets and black holes. Extra-solar planets can also be detected by studying variations in the light output of stars as planets transit in front of them.

28 William Herschel discovered visual binary stars in Sirius A and B Astrometric binary only one component seen originally Bessel discovered the wobbles of Sirius and Procyon in 1844.

29 Alpha Centauri If the stars orbital plane is in the line of sight then the star will appear to vary in brightness (even if the two components can t be directly seen). An eclipsing binary or eclipsing variable star.

30 John Goodricke of York Algol 1782 (variability first noticed by Montanari 1672)

31 Some other eclipsing binary light curves

32 Mira type variables were the first discovered by Fabricius The important Cepheids by Edward Pigott of York who worked with Goodricke.

33

34 Gas clouds between 0.01 and 0.1 times the mass of the sun become a brown dwarf almost a star less mass than this will become a gas giant planet sun s mass