Properties of Stars

“All men have the stars,” he answered, “but they are not the same things for different people. For some, who are travelers, the stars are guides. For others they are no more than little lights in the sky. For others, who are scholars, they are problems. For my businessman they were wealth. But all these stars are silent. You – you alone – will have the stars as no one else has them.” Antoine de Saint-Exupery (1900 – 1944) from The Little Prince

WHAT DO YOU THINK? How near to us is the closest star other than the Sun? What colors are stars, and why do they have these colors? How luminous is the Sun compared with other stars? Are brighter stars hotter than dimmer stars? Compared to the Sun, what sizes are other stars? Are most stars similar to the Sun, one star with planets, or in multiple-star groups?

A Snapshot of the Heavens How can we learn about the lives of stars, which last tens of millions to hundreds of billions of years? we will never observe a particular star evolve from birth to death so how can we study stellar evolution?

How can we Study the Life Cycles of Stars? Key: All stars were NOT born at the same time. stars we see today are at different stages in their lives we observe only a brief moment in any one star’s life by studying large numbers of stars, we get a “snapshot” of one moment in the history of the stellar community we can draw conclusions just like we would with human census data…we do stellar demographics!

A Snapshot of the Heavens What two basic physical properties do astronomers use to classify stars? What does that classification tell us?

Classification of Stars Stars were originally classified based on: their brightness their location in the sky This classification is still reflected in names of the brightest stars…those we can see with our eyes:

Classification of Stars Order of brightness within a constellation Latin Genitive of the constellation  Orionis  Geminorum

Classification of Stars The old classification scheme told us little about a star’s true (physical) nature. a star could be very bright because is was very close to us; not because it was truly bright two stars in the same constellation might not be close to each other; one could be much farther away

Classification of Stars In 20th Century, astronomers developed a more appropriate classification system based on: a star’s luminosity a star’s surface temperature These properties turn out to depend on: a star’s mass and its stage in life measuring these=> reconstruct stellar life cycles

WHAT DO YOU THINK? How near to us is the closest star other than the Sun? What colors are stars, and why do they have these colors? How luminous is the Sun compared with other stars? Are brighter stars hotter than dimmer stars? Compared to the Sun, what sizes are other stars? Are most stars similar to the Sun, one star with planets, or in multiple-star groups?

WHAT DO YOU THINK? How near are stars? DISTANCE What colors are stars? TEMPERATURE How luminous are stars? LUMINOSITY Are brighter stars hotter? TEMP vs. LUMIN. What sizes are stars? SIZE Single or Multiple? ORBITS  MASS

Step 1: Distance! How near are stars? DISTANCE What colors are stars? TEMPERATURE How luminous are stars? LUMINOSITY Are brighter stars hotter? TEMP vs. LUMIN. What sizes are stars? SIZE Single or Multiple? ORBITS  MASS

PARALLAX Determines distance based on Earth’s Orbit around Sun. SMALL angular shift! Even closest stars (4.3 light years) show shift less than 1/4000th of a degree! FIGURE 11-1 Using Parallax to Determine Distance (a, b) Our eyes change the angle between their lines of sight as we look at things that are different distances away. Our eyes are adjusting for the parallax of the things we see. This change helps our brains determine the distances to objects and is analogous to how astronomers determine the distance to objects in space. (c) As Earth orbits the Sun, a nearby star appears to shift its position against the background of distant stars. The star’s parallax angle (p) is equal to the angle between the Sun and Earth, as seen from the star. The stars on the scale of this drawing are shown much closer than they are in reality. If drawn to the correct scale, the closest star, other than the Sun, would be about 5 km (3.2 mi) away. (d) The closer the star is to us, the greater the parallax angle p. The distance to the star (in parsecs) is found by taking the inverse of the parallax angle p (in arcseconds), d 1/p. (a, b: Mark Andersen/ JupiterImages)

PARALLAX Example http://www.solstation.com/stars/61cygni2.htm Animation http://ircamera.as.arizona.edu/NatSci102/NatSci102/lectures/otherstars.htm Current telescopes can measure angles as small as 1/400,000th of a degree (400+ light years) FIGURE 11-1 Using Parallax to Determine Distance (a, b) Our eyes change the angle between their lines of sight as we look at things that are different distances away. Our eyes are adjusting for the parallax of the things we see. This change helps our brains determine the distances to objects and is analogous to how astronomers determine the distance to objects in space. (c) As Earth orbits the Sun, a nearby star appears to shift its position against the background of distant stars. The star’s parallax angle (p) is equal to the angle between the Sun and Earth, as seen from the star. The stars on the scale of this drawing are shown much closer than they are in reality. If drawn to the correct scale, the closest star, other than the Sun, would be about 5 km (3.2 mi) away. (d) The closer the star is to us, the greater the parallax angle p. The distance to the star (in parsecs) is found by taking the inverse of the parallax angle p (in arcseconds), d 1/p. (a, b: Mark Andersen/ JupiterImages)

Step 2: TEMPERATURES! How near are stars? DISTANCE What colors are stars? TEMPERATURE How luminous are stars? LUMINOSITY Are brighter stars hotter? TEMP vs. LUMIN. What sizes are stars? SIZE Single or Multiple? ORBITS  MASS

lead to Surface Temperatures! COLORS of stars lead to Surface Temperatures! FIGURE 11-4 Temperature and Color (a) This beautiful Hubble Space Telescope image shows the variety of colors of stars. (b) These diagrams show the relationship between the color of a star and its surface temperature. The intensity of light emitted by three stars is plotted against wavelength (compare with Figure 4-2). The range of visible wavelengths is indicated. The location of the peak of a each star’s intensity curve, relative to the visible light band, determines the apparent color of its visible light. The insets show stars of about these surface temperatures. Ultraviolet (uv) extends to 10 nm. See Figure 3-6 for more on wavelengths of the spectrum. (a: Hubble Heritage Team/AURA/STScI/NASA; left inset: Andrea Dupree/Harvard-Smithsonian CFA, Ronald Gilliland/STScI, NASA and ESA; center inset: NSO/AURA/NSF; right inset: Till Credner, Allthesky.com)

FIGURE 11-6 Classifying the Spectra of Stars The modern classification scheme for stars, based on their spectra, was developed at the Harvard College Observatory in the late nineteenth century. Female astronomers, initially led by Edward C. Pickering (not shown) and (a) Williamina Fleming, standing, and then by (b) Annie Jump Cannon, analyzed hundreds of thousands of spectra. Social conventions of the time prevented most female astronomers from using research telescopes or receiving salaries comparable to those of men. (a: Harvard College Observatory; b: © Bettmann/CORBIS)

FIGURE 11-5 The spectra of stars with different surface temperatures. The corresponding spectral types are indicated on the right side of each spectrum. (Note that stars of each spectral type have a range of temperature.) The hydrogen Balmer lines are strongest in stars with surface temperatures of about 10,000 K (called A-type stars). Cooler stars (G- and K-type stars) exhibit numerous atomic lines caused by various elements, indicating temperatures from 4000 to 6000 K. Several of the broad, dark bands in the spectrum of the coolest stars (M-type stars) are caused by titanium oxide (TiO) molecules, which can exist only if the temperature is below about 3500 K. Recall from Section 4-5 that the Roman numeral I after a chemical symbol means that the absorption line is caused by a neutral atom; a numeral II means that the absorption is caused by atoms that have each lost one electron. (R. Bell, University of Maryland, and M. Briley, University of Wisconsin at Oshkosh)

Spectral Type Classification System O B A F G K M (L) Oh Be A Fine Girl/Guy, Kiss Me! 50,000 K 3,000 K Temperature

FIGURE 11-4 Temperature and Color (a) This beautiful Hubble Space Telescope image shows the variety of colors of stars. (b) These diagrams show the relationship between the color of a star and its surface temperature. The intensity of light emitted by three stars is plotted against wavelength (compare with Figure 4-2). The range of visible wavelengths is indicated. The location of the peak of a each star’s intensity curve, relative to the visible light band, determines the apparent color of its visible light. The insets show stars of about these surface temperatures. Ultraviolet (uv) extends to 10 nm. See Figure 3-6 for more on wavelengths of the spectrum. (a: Hubble Heritage Team/AURA/STScI/NASA; left inset: Andrea Dupree/Harvard-Smithsonian CFA, Ronald Gilliland/STScI, NASA and ESA; center inset: NSO/AURA/NSF; right inset: Till Credner, Allthesky.com)

Step 3: BRIGHTNESS! How near are stars? DISTANCE What colors are stars? TEMPERATURE How luminous are stars? LUMINOSITY Are brighter stars hotter? TEMP vs. LUMIN. What sizes are stars? SIZE Single or Multiple? ORBITS  MASS

How BRIGHT are stars? Bright because they are nearby… or… Bright because they are really, truly bright?

FIGURE 11-2 Apparent Magnitude Scale (a) Several stars in and around the constellation Orion, labeled with their names and apparent magnitudes. For a discussion of star names, see Guided Discovery: Star Names. (b) Astronomers denote the brightnesses of objects in the sky by their apparent magnitudes. Stars visible to the naked eye have magnitudes between m 1.44 (Sirius) and about m 6.0. However, CCD (charge-coupled device) photography through the Hubble Space Telescope or a large Earth-based telescope can reveal stars and other objects nearly as faint as magnitude m 30. (a: Okiro Fujii, L’Astronomie)

Apparent Magnitudes Magnitude Scale Ancient method for measuring stellar brightness from Greek astronomer Hipparchus (c. 190 – 120 B.C.) Magnitude Scale This scale runs backwards: The bigger the number, the fainter the star Brightest stars are #1, next brightest are #2, etc.

Inverse Square Law for Light – how distance relates to brightness… FIGURE 11-3 The Inverse-Square Law (a) The same amount of radiation from a light source must illuminate an ever-increasing area as the distance from the light source increases. The decrease in brightness follows the inverse-square law, which means, for example, that tripling the distance decreases the brightness by a factor of 9. (b) The car is seen at distances of 10 m, 20 m, and 30 m, showing the effect described in part (a). (b: Royalty Free/CORBIS)

FIGURE 11-3 The Inverse-Square Law (a) The same amount of radiation from a light source must illuminate an ever-increasing area as the distance from the light source increases. The decrease in brightness follows the inverse-square law, which means, for example, that tripling the distance decreases the brightness by a factor of 9. (b) The car is seen at distances of 10 m, 20 m, and 30 m, showing the effect described in part (a). (b: Royalty Free/CORBIS)

Relating Measurable Quantities Measure distances of nearby stars Deduce how bright they really are Determine surface temperatures from spectra HOW do temperatures and brightness relate to one another?

Sun is much, much dimmer than most “bright” stars FIGURE 11-7 A Hertzsprung-Russell Diagram On an H-R diagram, the luminosities of stars are plotted against their spectral types. Each dot on this graph represents a star whose luminosity and spectral type have been determined. Some well-known stars are identified. The data points are grouped in just a few regions of the diagram, revealing that luminosity and spectral type are correlated: Main-sequence stars fall along the red curve, giants are to the right, supergiants are on the top, and white dwarfs are below the main sequence. The absolute magnitudes and surface temperatures are listed at the right and top of the graph, respectively. These are sometimes used on H-R diagrams instead of luminosities and spectral types. (Answer to text question: An M0 star is the next coolest after a K9.) Sun is brighter than most “nearby” stars

BRIGHT HOT COOL FAINT

90% of all stars lie on the main sequence! WHY??

Hypotheses to Explore Stars are born like children, cool and small, and then heat up and grow brighter over time. Stars are like candles, hot and bright, and then cool off and get dimmer over time. Stars are born with different temps and brightnesses, and change little over 90% of their lives.

Hypotheses to Explore IF…. Stars are born like children, cool and small, and then heat up and grow brighter over time. THEN… new clusters of stars should all be hot O stars, and old clusters only M stars.

Hypotheses to Explore IF…Stars are like candles, hot and bright, and then cool off and get dimmer over time. THEN… new clusters should show only M stars, and older ones should show O stars.

Hypotheses to Explore IF…. Stars are born like children, cool and small, and then heat up and grow brighter over time. IF…Stars are like candles, hot and bright, and then cool off and get dimmer over time. But “new” clusters like the Pleiades show all kinds of stars!

The Pleiades

Step 4: HR Diagram! How near are stars? DISTANCE What colors are stars? TEMPERATURE How luminous are stars? LUMINOSITY Are brighter stars hotter? TEMP vs. LUMIN. What sizes are stars? SIZE Single or Multiple? ORBITS  MASS

Diameter (Size) of Stars Calculated from known values: Luminosity Temperature Laws of Physics Stefan-Boltzmann Law: Luminosity ~ Surface Area x T4 PingPong balls, volleyballs, and Stars…

Bigger HUGE TINY Smaller

Determining Size Larger stars can be less dense at edges Less dense gas will change absorption lines

Luminosity Classes of Stars Based on Spectral Line Shapes& Density Tied to physical SIZE We’ll discover they are unstable… FIGURE 11-10 Luminosity Classes Dividing the H-R diagram into regions, called luminosity classes, permits finer distinctions between giants and supergiants. Luminosity classes Ia and Ib encompass the supergiants. Luminosity classes II, III, and IV indicate giants of different brightness. Luminosity class V indicates main-sequence stars. White dwarfs do not have their own luminosity class.

Step 5: Size! How near are stars? DISTANCE What colors are stars? TEMPERATURE How luminous are stars? LUMINOSITY Are brighter stars hotter? TEMP vs. LUMIN. What sizes are stars? SIZE Single or Multiple? ORBITS  MASS

Masses from BINARY STARS FIGURE 11-11 A Binary Star System About one-third of the visible “stars” are actually double stars. Mizar in Ursa Major is a binary system with stars separated by only about 0.01 arcsec. The images that surround this diagram show the relative positions of the two stars over nearly half of their orbital period. The orbital motion of the two binary stars around each other is evident. Either star can be considered fixed in making such plots. (Navy Prototype Optical Interferometer, Flagstaff, AZ. Courtesy of Dr. Christian A. Hummel)

Masses from BINARY STARS FIGURE 11-15 Spectral Line Motion in Binary Star Systems (a) The diagrams at the top indicate the positions and motions of the stars, labeled A and B, relative to Earth (below the diagram), and their spectra at the four selected moments (Stages 1, 2, 3, and 4) during an orbital period. The changes in colors (wavelengths) of the spectral lines are due to changes in the stars’ Doppler shifts, as seen from Earth. (b) This graph displays the radial velocity curves of the binary HD 171978. (The HD means that this is a star from the Henry Draper Catalogue of stars.) The entire binary is moving away from us at 12 km/s, which is why the pattern of radial velocity curves is displaced upward from the zero-velocity line. Doppler Shift of Spectra Lines tells us orbital velocities Velocities get us Orbital Sizes Orbits get us Mass

FIGURE 11-16 A Double-Line Spectroscopic Binary The spectrum of the double-line spectroscopic binary (kappa) Arietis has spectral lines that shift back and forth as the two stars revolve around each other. (a) The stars are moving parallel to the line of sight, with one star approaching Earth, the other star receding, as in Stage 1 or 3 of Figure 11-15a. These motions produce two sets of shifted spectral lines. (b) Both stars are moving perpendicular to our line of sight, as in Stage 2 or 4 of Figure 11-15a. As a result, the spectral lines of the two stars have merged. (Lick Observatory)

FIGURE 11-15 Spectral Line Motion in Binary Star Systems (a) The diagrams at the top indicate the positions and motions of the stars, labeled A and B, relative to Earth (below the diagram), and their spectra at the four selected moments (Stages 1, 2, 3, and 4) during an orbital period. The changes in colors (wavelengths) of the spectral lines are due to changes in the stars’ Doppler shifts, as seen from Earth. (b) This graph displays the radial velocity curves of the binary HD 171978. (The HD means that this is a star from the Henry Draper Catalogue of stars.) The entire binary is moving away from us at 12 km/s, which is why the pattern of radial velocity curves is displaced upward from the zero-velocity line.

Eclipsing BINARY STARS FIGURE 11-13 Representative Light Curves of Eclipsing Binaries The shape of the light curve (blue) reveals that the pairs of stars have orbits in planes nearly perpendicular to our line of sight. They also provide details about the two stars that make up an eclipsing binary. Illustrated here are (a) a partial eclipse and (b) a total eclipse. (c) The binary star NN Serpens, indicated by the arrow, undergoes a total eclipse. The telescope was moved during the exposure so that the sky drifted slowly from left to right. During the 10.5-min eclipse, the dimmer, but larger, star in the binary system (an M6 V star) passed in front of the more luminous but smaller star (a white dwarf). The binary became so dim that it almost disappeared. (European Southern Observatory)

Mass from Light Curve Know periods from the light curve…  Get orbit distances from Kepler’s Laws  Get relative masses from Newton’s Law of Gravity! Match mass to stellar main sequence star type O-stars are more massive than M stars…

Mass-Luminosity Relationship for Main Sequence stars FIGURE 11-14 The Mass-Luminosity Relation (a) For main-sequence stars, mass and luminosity are directly correlated—the more massive a star, the more luminous it is. A main-sequence star of mass 10 M has roughly 3000 times the Sun’s luminosity (3000 L); one with 0.1 M has a luminosity of only about 0.001 L. To fit them on the page, the luminosities and masses are plotted using logarithmic scales. (b) On this H-R diagram, each dot represents a main-sequence star. The number next to each dot is the mass of that star in solar masses (M). As you move up the main sequence from the lower right to the upper left, the mass, luminosity, and surface temperature of main-sequence stars all increase.

Mass-Luminosity Relationship for Main Sequence stars FIGURE 11-14 The Mass-Luminosity Relation (a) For main-sequence stars, mass and luminosity are directly correlated—the more massive a star, the more luminous it is. A main-sequence star of mass 10 M has roughly 3000 times the Sun’s luminosity (3000 L); one with 0.1 M has a luminosity of only about 0.001 L. To fit them on the page, the luminosities and masses are plotted using logarithmic scales. (b) On this H-R diagram, each dot represents a main-sequence star. The number next to each dot is the mass of that star in solar masses (M). As you move up the main sequence from the lower right to the upper left, the mass, luminosity, and surface temperature of main-sequence stars all increase.

So… what is going on? Why are only SOME stars in the supergiant regions? Why are 10% in the “giant” region What are the tiny ones in the “white dwarf” region?

Clusters of Stars as Key Tests Look at large populations of stars Open clusters in Milky Way’s “disk” Globular Clusters around galaxy Assume all stars *about* same age Assume all stars *about* same distance

gas or nebulosity is sometimes seen Open Clusters 100’s of stars 106 - 109 years old irregular shapes gas or nebulosity is sometimes seen Pleiades (8 x 107 yrs)

8 to 15 billion years old (1010 yrs) spherical shape Globular Clusters 105 stars 8 to 15 billion years old (1010 yrs) spherical shape NO gas or nebulosity M 80 (1.2 x 1010 yrs)

Globular Cluster H-R Diagram Pleiades H-R Diagram Palomar 3

Summary of Key Ideas

Magnitude Scales Determining stellar distances from Earth is the first step to understanding the nature of the stars. Distances to the nearer stars can be determined by stellar parallax, which is the apparent shift of a star’s location against the background stars while Earth moves along its orbit around the Sun. The distances to more remote stars are determined using spectroscopic parallax. The apparent magnitude of a star, denoted m, is a measure of how bright the star appears to Earth-based observers. The absolute magnitude of a star, denoted M, is a measure of the star’s true brightness and is directly related to the star’s energy output, or luminosity.

Magnitude Scales The absolute magnitude of a star is the apparent magnitude it would have if viewed from a distance of 10 pc. Absolute magnitudes can be calculated from the star’s apparent magnitude and distance. The luminosity of a star is the amount of energy emitted by it each second.

The Temperatures of Stars Stellar temperatures can be determined from stars’ colors or stellar spectra. Stars are classified into spectral types (O, B, A, F, G, K, and M) based on their spectra or, equivalently, their surface temperatures.

Types of Stars The Hertzsprung-Russell (H-R) diagram is a graph on which luminosities of stars are plotted against their spectral types (or, equivalently, their absolute magnitudes are plotted against surface temperatures). The H-R diagram reveals the existence of four major groupings of stars: main-sequence stars, giants, supergiants, and white dwarfs. The mass-luminosity relation expresses a direct correlation between a main-sequence star’s mass and the total energy it emits. Distances to stars can be determined using their spectral types and luminosity classes.

Stellar Masses Binary stars are surprisingly common. Those that can be resolved into two distinct star images (even if it takes a telescope to do this) are called visual binaries. The masses of the two stars in a binary system can be computed from measurements of the orbital period and orbital dimensions of the system. 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 with a telescope.

Stellar Masses A spectroscopic binary is a system detected from the periodic shift of its spectral lines. This shift is caused by the Doppler effect as the orbits of the stars carry them alternately toward and away from Earth. An eclipsing binary is a system whose orbits are viewed nearly edge-on from Earth, so that one star periodically eclipses the other. Detailed information about the stars in an eclipsing binary can be obtained by studying its light curve. Mass transfer occurs between binary stars that are close together.

Key Terms absolute magnitude apparent magnitude binary star center of mass close binary eclipsing binary giant star Hertzsprung-Russell (H-R) diagram initial mass function inverse-square law light curve luminosity luminosity class main sequence main-sequence star mass-luminosity relation OBAFGKM sequence optical double photometry radial-velocity curve red giant spectral types spectroscopic binary spectroscopic parallax stellar evolution stellar parallax stellar spectroscopy supergiant visual binary white dwarf

WHAT DID YOU THINK? How near to us is the closest star other than the Sun? Proxima Centauri is about 25 trillion mi (40 trillion km) away. Light from there will take about 4 years to reach Earth.

WHAT DID YOU THINK? How luminous is the Sun compared with other stars? The most luminous stars are about a million times brighter, and the least luminous stars are about a hundred thousand times dimmer than the Sun.

WHAT DID YOU THINK? What colors are stars, and why do they have these colors? Stars are found in a wide range of colors, from red through violet as well as white. They have these colors because they have different temperatures.

WHAT DID YOU THINK? Are brighter stars hotter than dimmer stars? Not necessarily. Many brighter stars, such as red giants, are cooler but larger, than hotter, dimmer stars, such as white dwarfs.

WHAT DID YOU THINK? Compared to the Sun, what sizes are other stars? Stars range from more than 1000 times the Sun’s diameter to less than 1/100 the Sun’s diameter.

WHAT DID YOU THINK? Are most stars isolated from other stars, as the Sun is? No. In the vicinity of the Sun, one-third of the stars are found in pairs or larger groups.