Roger A Freedman William J Kaufmann III Universe

Roger A. Freedman • William J. Kaufmann III Universe Eighth Edition CHAPTER 17 The Nature of Stars

M 39 is an Open or Galactic Cluster

Review of Concepts Covered in Previous Class Determining a star’s “L” and “R” from a knowledge of its “d” and “T” Determining a star’s “Luminosity Class” from an analysis of its spectrum

Determining a Star’s “L” & “R” from a knowledge of “d” & “T”

LUMINOSITY CLASS Based on the width of spectral lines, it is possible to tell whether the star is a supergiant, a main sequence star or a white dwarf. These define the luminosity classes shown on the left occupying distinct regions on the HR diagram. The complete spectral type of the Sun is G 2 V. The “G 2” part tells us Teff, the “V” part tells us to which sequence or luminosity class the star belongs. Example: M 5 III is a red giant with Teff ~ 3500 K, M=0 (or L=100 Lsun).

HR Diagram This template will be used in the upcoming test. Please become familiar with it. We will do a few examples in class of how to read off the temperature, luminosity and size of a star given a full spectral type.

HR Diagram I expect you to know which of the gray sequences is which luminosity class. From top to bottom: Ia, luminous supergiants Ib, supergiants III, giants V, main sequence Examples: G 2 V The Sun M 5 III B 4 Ib M 5 Ia

Today we will learn 17 -8 How we can estimate a star’s distance from its spectrum (spectroscopic parallax) 17 -9 How we can use binary stars to measure the masses of stars 17 -10 How we can learn about binary stars in very close orbits 17 -11 What eclipsing binaries are and what they tell us about the sizes of stars

Binary star systems provide crucial information about stellar masses. l Double star – a pair of stars located at nearly the same position in the night sky. l l l Optical double stars – stars that lie along the same line of sight, but are not close to one another. Binary stars, or binaries – stars that are gravitationally bound and orbit one another. Visual binary – binaries that can be resolved Spectroscopic binary – binaries that can only be detected by seeing two sets of lines in their spectra Eclipsing binary – binaries that cross one in front of the other.

Binary star systems provide crucial information about stellar masses. l Double star – a pair of stars located at nearly the same position in the night sky. l l l Optical double stars – stars that lie along the same line of sight, but are not close to one another. Binary stars, or binaries – stars that are gravitationally bound and orbit one another. Visual binary – binaries that can be resolved Spectroscopic binary – binaries that can only be detected by seeing two sets of lines in their spectra Eclipsing binary – binaries that cross one in front of the other.

Binary Star Krüger 60 (upper left hand corner) About half of the stars visible in the night sky are part of multiple-star systems.

Mizar A, z 1 UMa or Zeta-one Ursae Majoris, a~0. 01”, P = 20. 5 d Courtesy: Navy Prototype Optical Interferometer http: //leo. astronomy. cz/mizar/article. htm

Ch. 17, problem #66

Ch. 17, problem #66 l What’s measured observationally? l l Orbital period (P = 87. 7 yr) Parallax (p = 0. 2 arcsec) Apparent length of semimajor axis as seen on the sky (a = 4. 5 arcsec) What can we determine from this information? l l l Distance (d) in parsecs Actual length of semimajor axis (a) in AU Total mass of this binary system (M 1 + M 2) in solar masses

Measured Masses of Main Sequence Stars in Binary Systems

Hertzsprung-Russell (H-R) Diagram

Binary star systems provide crucial information about stellar masses. l Double star – a pair of stars located at nearly the same position in the night sky. l l l Optical double stars – stars that lie along the same line of sight, but are not close to one another. Binary stars, or binaries – stars that are gravitationally bound and orbit one another. Visual binary – binaries that can be resolved Spectroscopic binary – binaries that can only be detected by seeing two sets of lines in their spectra Eclipsing binary – binaries that cross one in front of the other.

Spectroscopy makes it possible to study binary systems in which the two stars are close together. k Ari

Binary star systems provide crucial information about stellar masses. l Double star – a pair of stars located at nearly the same position in the night sky. l l l Optical double stars – stars that lie along the same line of sight, but are not close to one another. Binary stars, or binaries – stars that are gravitationally bound and orbit one another. Visual binary – binaries that can be resolved Spectroscopic binary – binaries that can only be detected by seeing two sets of lines in their spectra Eclipsing binary – binaries that cross one in front of the other.

Light curves of eclipsing binaries provide detailed information about the two stars: Sizes, effective temperatures, shapes, etc

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Light curves of eclipsing binaries provide detailed information about the two stars.

Light curves of eclipsing binaries provide detailed information about the two stars.

Light curves of eclipsing binaries provide detailed information about the two stars.

Key Ideas l l Measuring Distances to Nearby Stars: 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 Inverse-Square Law: A star’s luminosity (total light output), apparent brightness, and distance from the Earth are related by the inverse-square law. If any two of these quantities are known, the third can be calculated.

Key Ideas l l l The Population of Stars: Stars of relatively low luminosity are more common than more luminous stars. Our own Sun is a rather average star of intermediate luminosity. The Magnitude Scale: 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 version of the inverse-square law relates a star’s absolute magnitude, apparent magnitude, and distance.

Key Ideas l l l 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. Spectral Types: 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.

Key Ideas l l Hertzsprung-Russell Diagram: The Hertzsprung. Russell (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.

Key Ideas l l 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 mainsequence 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.

Key Ideas l l l 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. 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.

Key Ideas l l Mass-Luminosity Relation for Main-Sequence 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 mainsequence stars. The greater the mass of a mainsequence star, the greater its luminosity (and also the greater its radius and surface temperature).

Key Ideas l l Spectroscopic Observations of Binary Stars: Some binaries can be detected 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.

Key Ideas l l 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. An eclipsing binary is a system whose orbits are viewed nearly edge-on 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.