UniverseUniverseEighth EditionEighth Edition

Roger A. Freedman • William J. Kaufmann III

CHAPTER 17CHAPTER 17The Nature of StarsThe Nature of Stars

M 39 is an Open or Galactic Cluster

Determining a star’s “L” and “R” from a Determining a star’s “L” and “R” from a knowledge of its “d” and “T”knowledge of its “d” and “T”

Determining a star’s “Determining a star’s “Luminosity ClassLuminosity Class” from ” from an analysis of its spectruman analysis of its spectrum

Review of Concepts Covered in Previous Class

Determining a Star’s “L” & “R”Determining a Star’s “L” & “R”from a knowledge of “d” & “T”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 giant, 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 G2 V. The “G2” part tells us Teff, the “V” part tells us to which sequence or luminosity class the star belongs.

Example: M5 III is a red giant with Teff ~ 3500K, 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, supergiantsIII, giantsV, main sequence

Examples:

G2V The Sun

M5III

B4Ib

M5Ia

17-8 How we can estimate a star’s distance from its 17-8 How we can estimate a star’s distance from its spectrum (spectroscopic parallax)spectrum (spectroscopic parallax)

17-9 How we can use binary stars to measure the 17-9 How we can use binary stars to measure the masses of starsmasses of stars

17-10 How we can learn about binary stars in very close 17-10 How we can learn about binary stars in very close orbitsorbits

17-11 What eclipsing binaries are and what they tell us 17-11 What eclipsing binaries are and what they tell us about the sizes of starsabout the sizes of stars

Today we will learn

Double star – a pair of stars located at nearly the Double star – a pair of stars located at nearly the same position in the night sky.same position in the night sky. Optical double stars – stars that lie along the same line Optical double stars – stars that lie along the same line

of sight, but are not close to one another.of sight, but are not close to one another. Binary stars, or binaries – stars that are gravitationally Binary stars, or binaries – stars that are gravitationally

bound and orbit one another.bound and orbit one another. Visual binary – binaries that can be resolved Visual binary – binaries that can be resolved Spectroscopic binary – binaries that can only be Spectroscopic binary – binaries that can only be

detected by seeing two sets of lines in their spectradetected by seeing two sets of lines in their spectra Eclipsing binary – binaries that cross one in front of Eclipsing binary – binaries that cross one in front of

the other.the other.

Binary star systems provide crucial Binary star systems provide crucial information about stellar masses.information about stellar masses.

Double star – a pair of stars located at nearly the Double star – a pair of stars located at nearly the same position in the night sky.same position in the night sky. Optical double stars – stars that lie along the same line Optical double stars – stars that lie along the same line

of sight, but are not close to one another.of sight, but are not close to one another. Binary stars, or binaries – stars that are gravitationally Binary stars, or binaries – stars that are gravitationally

bound and orbit one another.bound and orbit one another. Visual binary – binaries that can be resolved Visual binary – binaries that can be resolved Spectroscopic binary – binaries that can only be Spectroscopic binary – binaries that can only be

detected by seeing two sets of lines in their spectradetected by seeing two sets of lines in their spectra Eclipsing binary – binaries that cross one in front of Eclipsing binary – binaries that cross one in front of

the other.the other.

Binary star systems provide crucial Binary star systems provide crucial information about stellar masses.information about stellar masses.

Binary Star Krüger 60 (upper left hand corner)

About half of the stars visible in the night sky are part of multiple-star systems.

izar UMa or Zeta-one Ursae Majoris, a~0.01”, P = 20.5 dCourtesy: Navy Prototype Optical Interferometer

http://leo.astronomy.cz/mizar/article.htm

Ch. 17, problem #66Ch. 17, problem #66

Ch. 17, problem #66Ch. 17, problem #66 What’s measured observationally?What’s measured observationally?

Orbital period (P = 87.7 yr)Orbital period (P = 87.7 yr) Parallax (p = 0.2 arcsec)Parallax (p = 0.2 arcsec) Apparent length of semimajor axis as seen on the sky Apparent length of semimajor axis as seen on the sky

(a = 4.5 arcsec)(a = 4.5 arcsec) What can we determine from this information?What can we determine from this information?

Distance (d) in parsecsDistance (d) in parsecs Actual length of semimajor axis (a) in AUActual length of semimajor axis (a) in AU Total mass of this binary system (MTotal mass of this binary system (M11 + M + M22) in solar ) in solar

massesmasses

Measured Masses of Main Measured Masses of Main Sequence Stars in Binary SystemsSequence Stars in Binary Systems

Hertzsprung-Russell (H-R) DiagramHertzsprung-Russell (H-R) Diagram

Double star – a pair of stars located at nearly the Double star – a pair of stars located at nearly the same position in the night sky.same position in the night sky. Optical double stars – stars that lie along the same line Optical double stars – stars that lie along the same line

of sight, but are not close to one another.of sight, but are not close to one another. Binary stars, or binaries – stars that are gravitationally Binary stars, or binaries – stars that are gravitationally

bound and orbit one another.bound and orbit one another. Visual binary – binaries that can be resolved Visual binary – binaries that can be resolved Spectroscopic binary – binaries that can only be Spectroscopic binary – binaries that can only be

detected by seeing two sets of lines in their spectradetected by seeing two sets of lines in their spectra Eclipsing binary – binaries that cross one in front of Eclipsing binary – binaries that cross one in front of

the other.the other.

Binary star systems provide crucial Binary star systems provide crucial information about stellar masses.information about stellar masses.

Spectroscopy makes it possible to Spectroscopy makes it possible to study binary systems in which the two study binary systems in which the two

stars are close together.stars are close together.

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Double star – a pair of stars located at nearly the Double star – a pair of stars located at nearly the same position in the night sky.same position in the night sky. Optical double stars – stars that lie along the same line Optical double stars – stars that lie along the same line

of sight, but are not close to one another.of sight, but are not close to one another. Binary stars, or binaries – stars that are gravitationally Binary stars, or binaries – stars that are gravitationally

bound and orbit one another.bound and orbit one another. Visual binary – binaries that can be resolved Visual binary – binaries that can be resolved Spectroscopic binary – binaries that can only be Spectroscopic binary – binaries that can only be

detected by seeing two sets of lines in their spectradetected by seeing two sets of lines in their spectra Eclipsing binary – binaries that cross one in front of Eclipsing binary – binaries that cross one in front of

the other.the other.

Binary star systems provide crucial Binary star systems provide crucial information about stellar masses.information about stellar masses.

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 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 The Population of Stars:The Population of Stars: Stars of relatively low luminosity Stars of relatively low luminosity

are more common than more luminous stars. Our own Sun are more common than more luminous stars. Our own Sun is a rather average star of intermediate luminosity.is a rather average star of intermediate luminosity.

The Magnitude Scale:The Magnitude Scale: The apparent magnitude scale is The apparent magnitude scale is an alternative way to measure a star’s apparent an alternative way to measure a star’s apparent brightness.brightness.

The absolute magnitude of a star is the apparent The absolute magnitude of a star is the apparent magnitude it would have if viewed from a distance of 10 magnitude it would have if viewed from a distance of 10 parsecs. A version of the inverse-square law relates a parsecs. A version of the inverse-square law relates a star’s absolute magnitude, apparent magnitude, and star’s absolute magnitude, apparent magnitude, and distance.distance.

Key Ideas Photometry and Color Ratios:Photometry and Color Ratios: Photometry measures the Photometry measures the

apparent brightness of a star. The color ratios of a star are the apparent brightness of a star. The color ratios of a star are the ratios of brightness values obtained through different standard ratios of brightness values obtained through different standard filters, such as the U, B, and V filters. These ratios are a measure filters, such as the U, B, and V filters. These ratios are a measure of the star’s surface temperature.of the star’s surface temperature.

Spectral Types:Spectral Types: Stars are classified into spectral types Stars are classified into spectral types (subdivisions of the spectral classes O, B, A, F, G, K, and M), (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 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 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.temperature: O stars are the hottest and M stars are the coolest.

Most brown dwarfs are in even cooler spectral classes called L Most brown dwarfs are in even cooler spectral classes called L and T. Unlike true stars, brown dwarfs are too small to sustain and T. Unlike true stars, brown dwarfs are too small to sustain thermonuclear fusion.thermonuclear fusion.

Key Ideas Hertzsprung-Russell Diagram:Hertzsprung-Russell Diagram: The Hertzsprung- The Hertzsprung-

Russell (H-R) diagram is a graph plotting the absolute Russell (H-R) diagram is a graph plotting the absolute magnitudes of stars against their spectral types—or, magnitudes of stars against their spectral types—or, equivalently, their luminosities against surface equivalently, their luminosities against surface temperatures.temperatures.

The positions on the H-R diagram of most stars are The positions on the H-R diagram of most stars are along the main sequence, a band that extends from high along the main sequence, a band that extends from high luminosity and high surface temperature to low luminosity and high surface temperature to low luminosity and low surface temperature.luminosity and low surface temperature.

Key Ideas On the H-R diagram, giant and supergiant stars lie On the H-R diagram, giant and supergiant stars lie

above the main sequence, while white dwarfs are below above the main sequence, while white dwarfs are below the main sequence.the main sequence.

By carefully examining a star’s spectral lines, By carefully examining a star’s spectral lines, astronomers can determine whether that star is a main-astronomers can determine whether that star is a main-sequence star, giant, supergiant, or white dwarf. Using sequence star, giant, supergiant, or white dwarf. Using the H-R diagram and the inverse square law, the star’s the H-R diagram and the inverse square law, the star’s luminosity and distance can be found without measuring luminosity and distance can be found without measuring its stellar parallax.its stellar parallax.

Key Ideas Binary Stars:Binary Stars: Binary stars, in which two stars are held in Binary stars, in which two stars are held in

orbit around each other by their mutual gravitational orbit around each other by their mutual gravitational attraction, are surprisingly common. Those that can be attraction, are surprisingly common. Those that can be resolved into two distinct star images by an Earth-based resolved into two distinct star images by an Earth-based telescope are called visual binaries.telescope are called visual binaries.

Each of the two stars in a binary system moves in an Each of the two stars in a binary system moves in an elliptical orbit about the center of mass of the system.elliptical orbit about the center of mass of the system.

Binary stars are important because they allow astronomers Binary stars are important because they allow astronomers to determine the masses of the two stars in a binary to determine the masses of the two stars in a binary system. The masses can be computed from system. The masses can be computed from measurements of the orbital period and orbital dimensions measurements of the orbital period and orbital dimensions of the system.of the system.

Key Ideas 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 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).

Key Ideas Spectroscopic Observations of Binary Stars:Spectroscopic Observations of Binary Stars: Some Some

binaries can be detected and analyzed, even though the binaries can be detected and analyzed, even though the system may be so distant or the two stars so close system may be so distant or the two stars so close together that the two star images cannot be resolved.together that the two star images cannot be resolved.

A spectrum binary appears to be a single star but has a A spectrum binary appears to be a single star but has a spectrum with the absorption lines for two distinctly spectrum with the absorption lines for two distinctly different spectral types.different spectral types.

Key Ideas A spectroscopic binary has spectral lines that shift back A spectroscopic binary has spectral lines that shift back

and forth in wavelength. This is caused by the Doppler and forth in wavelength. This is caused by the Doppler effect, as the orbits of the stars carry them first toward effect, as the orbits of the stars carry them first toward then away from the Earth.then away from the Earth.

An eclipsing binary is a system whose orbits are viewed An eclipsing binary is a system whose orbits are viewed nearly edge-on from the Earth, so that one star nearly edge-on from the Earth, so that one star periodically eclipses the other. Detailed information periodically eclipses the other. Detailed information about the stars in an eclipsing binary can be obtained about the stars in an eclipsing binary can be obtained from a study of the binary’s radial velocity curve and its from a study of the binary’s radial velocity curve and its light curve.light curve.