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Triangulation of Stars D B P = Detecting stellar parallaxes Triangulation of Stars Parallax of the human eye Tycho Brahe (1546-1601) Parallax: the apparent motion of a foreground object relative to the background, as the observer’s location changes The closer the object, the larger the parallax Earth in January Figure 2 • The baseline b, the parallax angle p and the distance d 1 are related by the parallax formula: b A • 2 B Earth in Earth in d Figure 2 January October 1 Earth in 3 July 1 b A d()pc = 2 p arcsec B () Earth in d October Earth in 3 July A simple relationship (often called parallax-distance formula) between distance in parsecs and stellar parallax in arcseconds b The annual (or heliocentric) parallax is half the maximum parallactic shift Proxima Centauri: distance : 4.3 LY = 4.3/3.26 pc = 1.3 pc tan p = parallax : 0.76 arcsec d (two positions of the Earth’s orbit 6 months apart) 1 Proxima Centauri: MORE ABOUT PARALLAX The Closest Star • The nearest stars are more than 1 parsec away, so it's not a surprise that the ancient astronomers could not measure stellar parallaxes. The first measurements of a stellar parallax were made by Friedrich Bessel in 1838, for the star 61 Cygni. Proxima is closer than • With sophisticated instruments and careful observations, astronomers now can Cen A measure parallaxes as small as 0.01" from the ground, reaching distances of up to 100 pc. & Cen B, why is then Proxima • The Hipparcos satellite launched by the European Space Agency in 1997 has measured parallaxes as small as 0.002", reaching as far as 500 pc. fainter than Cen A & Cen B? • The Gaia satellite planned to be launched by the European Space Agency in 2011 will measure parallaxes as small as 0.0002", reaching as far as 5000 pc. Proxima Centauri: The Closest Star Apparent Stellar Brightness Huge variety of stars: – Fainter, brighter – To us all of them seem to be located at the same distance (why?) – Different colors •Blue •White • Yellow distance of about 4.2 light years • Orange intrinsically faint red star •Red ten thousand times fainter than the Sun Small and Cool Red Star it is only visible with a good telescope 2 Stellar Color Stellar Radius Different color means different surface temperature Blue White Yellow Orange Red • Stars are sphere of gas – they have different size, which means different radius R TEMPERATURE – Energy output (Luminosity) ~ R2 Energy output (Luminosity) ~ T4 The blue stars are much brighter than the red stars The large stars are much brighter than the small stars !!! If they have the same size and are located at the same distance !!! If they have the same color and are located at the !!! same distance !!! Apparent brightness (apparent magnitude) The true stellar brightness Real Sky: • Stars of different size and color Stars of different size and color • Different distances – Energy output ~ T4R2 • Energy reaching us depends on distance, T, R • Very different distances – difficult to estimate !!! Same distance to both !!! the true brightness !!! Same distance to both !!! Far away Need to know stellar distances! Nearby 3 Inverse Square Law Apparent brightness, true brightness and the magnitude scale • 6 groups of visible stars: 1st to 6th magnitude – Hipparcos – Apparent brightness and apparent mag m – An increase of 5 mag corresponds to a decrease in brightness of 100 times – An increase of 1 mag corresponds to a decrease in brightness by a factor of ~2.5 times • All stars at 10 pc: – Intrinsic brightness and absolute mag M • Luminosity • m -M = 5 log (d / 10) Studying stellar light : spectroscopy Henry Draper Catalog • In 1872 Henry Draper, an amateur Obtaining spectra astronomer, began recording data on stellar spectra – photographically! A telescope with a • In 1882 – his collection is donated to Harvard University spectrograph measures the • Edward C. Pickering, Antonia spectrum of a star and Maury, Annie Cannon gives the brightness at • Catalog of 225 000 stars (Henry different wavelengths. Draper Catalog) • Stellar spectra have common features - stars can be grouped in spectral classes 4 Annie Jump Cannon • 1920: M. N. Saha – the appearance of of the spectrum depends on temperature of the outer stellar layers • Strength of the • Hydrogen lines got more absorption lines of prominent as the star got Hydrogen hotter, and then less prominent after the star’s surface got so hot that it ionized the hydrogen • Classification at the surface according to the • Cecilia Payne – stars of strength of H lines different spectral classes have – O B A F G K M same composition – Harvard classification • O B A F G K M system: based on is classification according to appearance of stellar temperature spectra Spectral classification Temperature controls strength of the absorption lines because it determines energy levels in which the electrons of atoms are likely to be found 5 The Hertzsprung – Russell Diagram Different stars – different spectra – • Henry Norris Russell different stellar types (US) and Ejnar Hertzsprung (Denmark) • M related to L • Spectral type related to T • Almost all stars fall in fairly well structured bands and zones Classification about surface temperature and size (intrinsic brightness) Emission depends on T Fig. 7.6 1. Higher T shifts the maximum to a higher frequency, or bluer color Wien’s law 0.0029 λ (m) = max T (K) Stellar 2. Higher T, brighter object. Photometry Stefan – Boltzmann law Size, Temperature, and 4 Luminosity of stars E = σ T 6 Color and Studying stellar light : photometry Temperature (Wien’s law) Telescope + set of colored filters. Stars emit radiation over a wide range of colors The intensity of a The dominant color depends on temperature star's image is different at different The higher the temperature, filters, and the bluer the color photometric data can The lower the temperature, thus be used to study the redder the color the distribution of the star's radiation over the wavelength's scale. band c (Å) WHM (Å) The technique of stellar photometry U 3580 550 The technique of stellar photometry uvbyβ photometric system - Strömgren and Crawford (1970) UBV photometric system- Johnson and Morgan - 1953 B 4390 990 V 5450 850 band peak(Å) Width(Å) u 3500 300 v 4110 190 b 4670 180 y 5470 230 H narrow 4859 30 H wide 4890 145 Huge improvement over the UBV photometry. Measure more details Easily to calibrate in terms of temperature, metallicity and intrinsic brightness 7 The technique of stellar photometry uvbyβ photometric system - Strömgren and Crawford (1970) Supergiants High luminosity Giants low density in the star’s ( photosphere Dwarf (width of spectral Low luminosity Same T lines) High density but ↑ L and ↑ R Dwarf Supergiant Spectral type and luminosity class uniquely determine a stars position in the HR diagram HR Diagram The Nearest Stars The Brightest Stars 8 Stellar distances Stellar Physical Parameters ¾ Primary measurements (d < 300 pc) • From spectra or photometry – SpT and LC ¾Parallax measurements • From LC - Absolute Magnitude • SpT – Temperature ¾ Calibrated measurements (300 pc < d < 50 Mpc) • Absolute mag, apparent mag - Distance Find M, then d • Absolute Magnitude – Luminosity • Luminosity, Temperature – Radius ¾Spectroscopic Parallaxes: based on stellar classification: luminosity class and spectral type - stars of same LC L = 4πR2 σT4 and Sp type have same intrinsic brightness (M). • Stellar mass – only for stars in binary systems ¾Photometric Parallaxes: based on the actual energy distribution in stellar spectra Something real Dust tends to absorb and selectively scatter blue light more effectively than red. Interstellar material absorbs light selectively, changes the true stellar radiation and masks the true stellar type and complicate the process of the photometric stellar classification . 9 The technique of stellar photometry • photometry (contaminated by absorption) • stellar classification - find a smart photometric system or use spectra • need to correct the photometry for the reddening - need empirical calibrations for each Sp&LC - need a sample of nearby non-reddened stars • intrinsic brightness - need calibrations for each Sp&LC - need a sample of nearby stars with distance obtained independently of the physical parameters (trigonometric parallaxes) Many nearby A, F, G, K, M stars No nearby O, B stars 10.
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