Properties of Stars (continued) Some Properties of Stars Luminosity Temperature of the star s surface Mass Physical size 2 Chemical makeup 3 What is brightness? Apparent brightness is the energy flux (watts/m 2 ) arriving from a star at its actual distance from us. Stars visible to the naked eye are classified into six magnitudes of perceived brightness. These five intervals correspond to a factor of 100 in flux intensity or real brightness. Our eye aperture (pupil) receives photons from the star. The greater the number of photons/second that strikes our retina, the brighter the star appears. Brightest stars have the lowest magnitude. 4 A first magnitude star is about 2.512 times brighter than a second magnitude star, which is about 2.512 times brighter than a third magnitude star, and so on. one interval where 2.512 = 100 1/5 5 Intensity scale Magnitude scale 5 intervals Apparent magnitude (m) measures a star s apparent brightness when it is seen at its actual distance from the Sun. Absolute magnitude (M) is the apparent magnitude when the star is placed exactly 10 parsecs from the Sun. Our eyes see five intervals for a factor of 100 in intensity 7 6 1
Measuring the distance to stars We can also find the luminosity (L) of the star if we know its absolute magnitude (M): This is one of the greatest challenges to Astronomers. (4.83 - M)/5 L (in solar units) = 100 The absolute magnitude of our Sun is +4.83 8 There are several techniques needed to measure the distance to stars, depending on their distance. The first technique, stellar parallax, gives us, directly, the distance to all of the nearby stars. distance (parsecs) = 1 parallax (arc-seconds) 9 We have both the energy flux, at Earth, from the Sun (1370 Watts/m 2 ), and we also have the apparent magnitude of the Sun (-26.7) and the absolute magnitude of the Sun (+4.83). We have the actual distances to a million stars in our neighborhood. Distance of stars measured by parallax in our galaxy ( the circle) We are now able to determine the luminosity of all of these stars. 10 11 Nearby stars appear to move because the Earth travels around the Sun (i.e., parallax) Stars also have real spatial motions through the Milky Way galaxy. A star s movement along our line of sight can be measured by the Doppler effect. This is called radial velocity. A star s movement across the sky can be measured directly. This is called proper motion. 12 Actual velocity of Alpha Centauri in the Milky Way 13 2
Surface Temperature of Stars We notice that some stars appear to have a red color, others yellow, still others, blue-white. The black body radiation from these stars determine the color we see. This radiation also gives us the star s surface temperature. 14 Wien s Law: Surface temperature (K) = 2.9 x 10 6 peak wavelength (nm) 15 Since all black body curves have the same shape, we don t have to find the entire curve to estimate the position of the peak wavelength. Black body curves for stars with different surface temperatures Instead, we sample the intensity at a small number of wavelengths. In practice, sampling the blackbody radiation at just two wavelengths is sufficient to estimate the position and height of the entire blackbody curve. 16 17 Wavelength filters are discussed in your textbook, Section 19.4 Wavelengths passed by various light filters Two of these filters are: A blue filter B = m B @ 440 nm A visible filter V = m V @ 550 nm The color index is CI = B - V 18 19 3
CI is the difference in magnitudes, and CI = B - V There are empirically derived relationships for filters to estimate the surface temperature of stars. (a) CI < 0 (b) CI = 0 very hot hot For stars in the 10 4 K range, use T = 7090 [ (B V) + 0.71 ] (c) CI > 0 cool Recall that higher intensities have lower magnitudes. For stars between 4000 K and 10 4 K T = 8540 [ (B V) + 0.865 ] The color index for our Sun is ~ +0.6 Method of finding the temperatures of stars 20 21 We measure the distance of our one million neighboring stars and measure their brightness. This gives us the luminosities of the stars. We estimate the black body curves and get the surface temperatures of these stars. Sizes of stars Note that we can get the size of the stars if we have L and T. L = 4πR 2 σt 4 22 23 Some Types of Stars What is a star? Type star T (K) R/R sun L/L sun ------------------------------------------------------------------------------------------ Red Dwarf 3,000 0.1 0.0006 White Dwarf 50,000 0.01 0.5 Blue Giant 30,000 10 60,000 Red Giant 3,000 300 6000 24 A star is a celestial object that radiates energy by generating its own energy from fusion of lighter elements into heavier elements. A white dwarf radiates only because it is very hot. No fusion takes place in a white dwarf. Therefore, a white dwarf is not a star. 25 4
We find that there is a great variation in the luminosities and surface temperatures of the million stars we have analyzed. We will organize our results by assigning the stars to a spectral type according to their surface temperatures. We will see shortly that the star s spectra has a great deal to do with spectral types. 26 Spectral Type Spectral Type Surface Temperature Range O 50,000 K B 20,000 K A 10,000 K F 7,000 K G 6,000 K K 4,000 K M 3,000 K 27 In a little more detail, the spectral types, Spectral Images by Harvard Spectral Classification O B A F G K M, become B A.O9 B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 A0 A1 A2. ten subdivisions for each spectral type. The spectral type of our yellow Sun with a surface temperature of 5800 K is G2 28 The white light of the stars are spread out into a spectrum by a prism-like device. 29 The atmospheres of stars show a variety of absorption spectra from atoms that are: 1. excited to higher energy levels 2. partially ionized Hydrogen absorption transitions Photons are absorbed if they have energy matching the energy level differences. Electrons are then excited to higher energy levels. 30 Note: 5000 A = 500 nm 31 5
Ionized atoms are described in the following manner: Roman numerals (I, II, III, IV, etc.) are used to designate the ionization state of an atom. I means that the atom is neutral (not ionized) II means that the atom is singly ionized (one electron missing). Line Strength vs Temperature for several elements whose absorption lines are commonly seen in stellar spectra 32 III means the atom is doubly ionized (two electrons missing). 33 Examples: HI neutral hydrogen HII ionized hydrogen CaIII doubly ionized calcium 34 This is a small section of the Sun s spectra showing absorption lines from many elements in the Sun s lower atmosphere. Note the presence of ionized atoms. The abundance of the ionized atoms allows a determination of the surface temperature of the star. 35 We know the binding energy of each element, and the how tightly bound each electron is in the atoms making up the element. We know what the spectra should look like for excited and singly ionized atoms. The widths of absorption lines are related to the number of excited (or ionized) atoms. We use specialized equations to derive an effective temperature T s. 36 The spectral temperature T s is determined in a different way than the temperature T associated with λ peak of the black body intensity distribution, but it is close. The spectra of a star is closely associated with the temperature near the photosphere of the star. A spectral type now has a temperature and certain spectral characteristics. 37 6