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Our Star - the Sun The Sun’s energy is generated by thermonuclear reactions in its core • The energy released in a nuclear reaction corresponds to a slight reduction of mass according to Einstein’s equation E = mc2 • Thermonuclear fusion occurs only at very high temperatures; for example, hydrogen fusion occurs only at temperatures in excess of about 107 K • In the Sun, fusion occurs only in the dense, hot core The Sun’s energy is produced by hydrogen fusion, a sequence of thermonuclear reactions in which four hydrogen nuclei combine to produce a single helium nucleus deuterium A theoretical model of the Sun shows how energy gets from its center to its surface • Hydrogen fusion takes place in a core extending from the Sun’s center to about 0.25 solar radius • The core is surrounded by a radiative zone extending to about 0.71 solar radius – In this zone, energy travels outward through radiative diffusion • The radiative zone is surrounded by a rather opaque convective zone of gas at relatively low temperature and pressure – In this zone, energy travels outward primarily through convection The photosphere is the lowest of three main layers in the Sun’s atmosphere • The Sun’s atmosphere has three main layers: the photosphere, the chromosphere, and the corona • Everything below the solar atmosphere is called the solar interior • The visible surface of the Sun, the photosphere, is the lowest layer in the solar atmosphere The spectrum of the photosphere is similar to that of a blackbody at a temperature of 5800 K Convection in the photosphere produces The chromosphere is characterized by spikes of rising gas • Above the photosphere is a layer of less dense but higher temperature gases called the chromosphere • Spicules extend upward from the photosphere into the chromosphere along the boundaries of supergranules • The outermost layer of the solar atmosphere, the corona, is made of very hightemperature gases at extremely low density • The solar corona blends into the solar wind at great distances from the Sun The corona ejects mass into space to form the solar wind ~106km Activity in the corona includes coronal mass ejections and coronal holes UV Corona (SOHO) Sunspots are low-temperature regions in the photosphere ~1 rotation / 4 weeks Differential rotation Sunspots are produced by a 22-year cycle in the Sun’s magnetic field • • • • The Sun’s surface features vary in an 11-year cycle This is related to a 22-year cycle in which the surface magnetic field increases, decreases, and then increases again with the opposite polarity The average number of sunspots increases and decreases in a regular cycle of approximately 11 years, with reversed magnetic polarities from one 11year cycle to the next Two such cycles make up the 22-year solar cycle Effect of B-fields Hα image 656 nm UV image SOHO 30.4 nm The Sun’s magnetic field also produces other forms of solar activity • A solar flare is a brief eruption of hot, ionized gases from a sunspot group • A coronal mass ejection is a much larger eruption that involves immense amounts of gas from the corona X-ray and UV image FIN The Nature of the Stars The Population of Stars; Luminosity function • Stars of relatively low luminosity are more common than more luminous stars • Our own Sun is a rather average star of intermediate luminosity Astronomers often use the magnitude scale to denote brightness • The apparent magnitude scale is an alternative way to measure a star’s apparent brightness • The absolute magnitude of a star is the apparent magnitude it would have if viewed from a distance of 10 parsecs A star’s color depends on its surface temperature Photometry and Color Ratios • • • Photometry measures the apparent brightness of a star The color ratios of a star are the ratios of brightness values obtained through different standard filters, such as the U, B, and V filters These ratios are a measure of the star’s surface temperature b apparent brightness = observed flux The spectra of stars reveal their chemical compositions as well as surface temperatures • Stars are classified into spectral types (subdivisions of the spectral classes O, B, A, F, G, K, and M), based on the major patterns of spectral lines in their spectra The spectral class and type of a star is directly related to its surface temperature: O stars are the hottest and M stars are the coolest • Most brown dwarfs are in even cooler spectral classes called L and T • Unlike true stars, brown dwarfs are too small to sustain thermonuclear fusion Hertzsprung-Russell (H-R) diagrams reveal the different kinds of stars • The H-R diagram is a graph plotting the absolute magnitudes of stars against their spectral types—or, equivalently, their luminosities against surface temperatures • The positions on the H-R diagram of most stars are along the main sequence, a band that extends from high luminosity and high surface temperature to low luminosity and low surface temperature On the H-R diagram, giant and supergiant stars lie above the main sequence, while white dwarfs are below the main sequence By carefully examining a star’s spectral lines, astronomers can determine whether that star is a main-sequence star, giant, supergiant, or white dwarf Using the H-R diagram and the inverse square law, the star’s luminosity and distance can be found without measuring its stellar parallax Spectroscopic Analysis A Binary Star System Binary star systems provide crucial information about stellar masses • Binary stars are important because they allow astronomers to determine the masses of the two stars in a binary system • The masses can be computed from measurements of the orbital period and orbital dimensions of the system Mass-Luminosity Relation for MainSequence Stars • Main sequence stars are stars like the Sun but with different masses • The mass-luminosity relation expresses a direct correlation between mass and luminosity for main-sequence stars • The greater the mass of a main-sequence star, the greater its luminosity (and also the greater its radius and surface temperature) FIN 47 Spectroscopy makes it possible to study binary systems in which the two stars are close together • • • • Some binaries can be detected and analyzed, even though the system may be so distant or the two stars so close together that the two star images cannot be resolved A spectrum binary appears to be a single star but has a spectrum with the absorption lines for two distinctly different spectral types A spectroscopic binary has spectral lines that shift back and forth in wavelength This is caused by the Doppler effect, as the orbits of the stars carry them first toward then away from the Earth Binary Stars • Binary stars, in which two stars are held in orbit • around each other by their mutual gravitational attraction, are surprisingly common • Those that can be resolved into two distinct star images by an Earth-based telescope are called visual binaries • Each of the two stars in a binary system moves in an elliptical orbit about the center of mass of the system Light curves of eclipsing binaries provide detailed information about the two stars • An eclipsing binary is a system whose orbits are viewed nearly edgeon from the Earth, so that one star periodically eclipses the other • Detailed information about the stars in an eclipsing binary can be obtained from a study of the binary’s radial velocity curve and its light curve Parallax Careful measurements of the parallaxes of stars reveal their distances • • • Distances to the nearer stars can be determined by parallax, the apparent shift of a star against the background stars observed as the Earth moves along its orbit Parallax measurements made from orbit, above the blurring effects of the atmosphere, are much more accurate than those made with Earth-based telescopes Stellar parallaxes can only be measured for stars within a few hundred parsecs The magnetic-dynamo model suggests that many features of the solar cycle are due to changes in the Sun’s magnetic field These changes are caused by convection and the Sun’s differential rotation Rotation of the Solar Interior If a star’s distance is known, its luminosity can be determined from its brightness • A star’s luminosity (total light output), apparent brightness, and distance from the Earth are related by the inversesquare law • If any two of these quantities are known, the third can be calculated Relationship between a star’s luminosity, radius, and surface temperature Stars come in a wide variety of sizes Finding Key Properties of Nearby Stars