22 March 2005 AST 2010: Chapter 171 The Stars: A Celestial Census

22 March 2005 AST 2010: Chapter 17 2 The Lives of Stars Stars live for a very long time, up to 100 million years or more No humans can possibly observe a star this long! How can we learn about the stages in a star’s life? We can perform a celestial census, getting a snapshot of many stars at different stages of their life We can then try to infer the stages that a star goes through from the data we assemble in the census But we can be misled if the star sample in the census is biased (like political surveys)

22 March 2005 AST 2010: Chapter 17 3 A Stellar Census (1) We measure distances in light years (LY) Astronomical distances are difficult to measure, to be discussed in Ch. 18 Small stars are less luminous and, therefore, harder to see If not corrected for these hard-to-see stars, our sample of stars will be biased Careful observation reveals that small stars (brown dwarfs) are more common than large stars While less numerous, large stars are easier to see at large distances Most of the stars visible to the naked eye are large

22 March 2005 AST 2010: Chapter 17 4 A Stellar Census (2) Stars that appear very bright are not necessarily very close to us, and those appearing faint are not necessarily very distant from us In fact, the brightest stars are bright mainly because they are intrinsically very luminous Most of them are very far away Moreover, most of the nearest stars are intrinsically very faint The luminosity (L) of stars ranges from more than 10 6 L Sun for the most luminous stars to L Sun for brown dwarfs

22 March 2005 AST 2010: Chapter 17 5 Measuring Stellar Masses Mass is one the most important characteristics of a star Knowing the mass can help us estimate the behavior and life cycle of the star Yet, a star’s mass is very difficult to measure directly Indirect measurements of stellar masses can be done for binary-star systems Each system consists of two stars that orbit each other, bound together by gravity Strictly speaking, each of the binary stars orbits a common point called the center of mass

22 March 2005 AST 2010: Chapter 17 6 Orbits and Masses of Binary Stars The masses of the 2 stars can be estimated using Kepler's third law The orbital period P (in years) and semimajor axis D (in AU) of the ellipse are related to the masses M 1 and M 2 (in units of the Sun’s mass) by D 3 = (M 1 +M 2 ) P 2 Thus, if D and P are measured, the sum of the masses can be found If the relative orbital speeds of the 2 stars are also measured, the mass of each star separately can be calculated as well D

22 March 2005 AST 2010: Chapter 17 7 Visual Binaries Binary-star systems in which both of the stars can be seen with a telescope are called visual binaries Binary stars: Sirius A and B

22 March 2005 AST 2010: Chapter 17 8 Visual Binaries: Wobbling Motion Animation

22 March 2005 AST 2010: Chapter 17 9 Sirius A and B Sirius A is normal star Sirius B is a white dwarf companion The orbits are drawn to scale, but the sizes of the stars are exaggerated Sirius A is considerably larger than the Sun, while Sirius B is about the size of the Earth

22 March 2005 AST 2010: Chapter Spectroscopic Binaries In some binary-star systems, only one of the stars can be seen with a telescope, but the presence of the companion star is revealed by spectroscopy Such stars are called spectroscopic binaries The binary nature is indicated in the periodic Doppler-shift of their spectral lines as they orbit around each other Doppler-shift

22 March 2005 AST 2010: Chapter Doppler Effect in Binary Stars If the line spectra of the spectroscopic binaries can be observed, their motion is reflected in the Doppler shifts of the spectral lines Radial velocities of spectroscopic binaries

22 March 2005 AST 2010: Chapter Range of Stellar Masses How large and small can stars be? Stars with masses up to about 100 times that of the Sun have been discovered Some stars may have masses up to about 200 solar masses Theoretical calculations suggest that the mass of a true star must be at least 1/12 that of the Sun A “true” star is one that becomes hot enough to fuse protons to form helium (see Ch. 15) Objects with masses between 1/100 and 1/12 that of the Sun are called brown dwarfs They may produce energy for a brief time by nuclear reactions, but do not become hot enough to fuse protons They are intermediate in mass between stars and planets Objects with masses less than about 1/100 that of the Sun are considered planets

22 March 2005 AST 2010: Chapter Mass-Luminosity Relation There is a correlation between the mass and luminosity of a star The more massive stars are generally also the more luminous (they give off more energy) For about 10% of the stars, this relationship is violated They include the white dwarfs

22 March 2005 AST 2010: Chapter Diameters of Stars The diameter of a star can be determined by measuring the time it takes an object (the Moon, a planet, or a companion star) to pass in front of it and blocks its light The blocking of the star’s light is an eclipse The brightness of the star decreases gradually during the eclipse The time for the brightness decrease depends on size of star Accurate sizes for a large number of stars come from measurements of eclipsing binaries

22 March 2005 AST 2010: Chapter Eclipsing Binary System Some binary stars are lined up in such a way that, when viewed from the Earth, each star passes in front of the other during every revolution Thus, we can observe periodic eclipses in these binary-star systems, which are therefore called eclipsing binaries

22 March 2005 AST 2010: Chapter Summary

22 March 2005 AST 2010: Chapter H-R Diagram There is a relationship between the temperature (color) and luminosity of 90% of stars They lie along a band called the main sequence The plot of stars’ luminosities versus their temperatures is called the Hertzsprung-Russell diagram (H-R diagram)

22 March 2005 AST 2010: Chapter H-R Diagram for Many Stars H-R Diagram for Many Stars

22 March 2005 AST 2010: Chapter Features of H-R Diagram The main-sequence band contains almost 90% of the stars Large blue stars Medium yellow stars Small red stars About 10% of the stars lie below the main sequence They are the hot, but dim, white dwarfs No more than 1% of the stars lie above the main sequence They are cool and very luminous They must be giants and supergiants

22 March 2005 AST 2010: Chapter Characteristics of Main-Sequence Stars The main sequence turns out to be a sequence of stellar masses (for almost 90% of the stars) The more massive stars have the more weight and can thus compress their centers to the greater degree, which implies that they are the hotter inside and the better at generating energy from nuclear reactions deep within

22 March 2005 AST 2010: Chapter The other 10% stars About 10% of the stars do not follow the mass-luminosity relationship do not lie on the main sequence Giant and supergiant stars lie on the upper-right section of the H-R diagram are very luminous because they are large in diameter, although they are cool make up less than 1% of the stars White dwarfs lie on the lower-left section of the H-R diagram are small in diameter (similar to Earth’s) are hot, but dim make up about 10% of the stars Betelgeuse

22 March 2005 AST 2010: Chapter Main Sequence: Typical Stars The Sun lies on the middle of the main sequence Is the Sun an "average'' or "typical''? The meaning of "average'' depends on how one chooses the sample! Compared to the nearby stars, the Sun is luminous, hot, and big Compared to the apparently bright stars, the Sun is dim, cool, and small Compared to the stars in globular clusters, the Sun is very young Compared to the stars in open (galactic) clusters, the Sun is very old

22 March 2005 AST 2010: Chapter 17 23Comparisons The Sun is compared to 100 apparently brightest stars in our sky and 100 nearest stars (both from Hipparchus’ survey) Most stars that appear bright in our sky turn out to be also intrinsically luminous Near stars are all within about 25 LY from the Sun Near stars are mostly cool and faint

22 March 2005 AST 2010: Chapter More Comparisons (1) Population percentages of the spectral types for bright and near stars Most of the apparently bright stars are the hot and luminous A- and B- type stars The bright-star sample includes a few of the very hot O-type stars All but one of the K-type stars in the bright-star sample are giants or supergiant stars All of the M-type stars are giants or supergiants

22 March 2005 AST 2010: Chapter More Comparisons (2) The distribution of the near stars is very different from that of the bright stars The majority of the near stars are cool and faint K- and M- type stars Only one star in the entire near-star sample is a giant The rest of the near- star sample are main-sequence stars

22 March 2005 AST 2010: Chapter Representative Sample Which of these samples is more representative of the entire population of stars in our galaxy? A representative sample includes all parts of the population of the objects your are investigating in their proper proportions The relative proportion of common things will be greater than the relative proportions of rare things In fact, the uncommon things may not be found in a small representative sample because they are so rare! With better instruments, more data on stars, even new types of stars or other objects, will be collected, making the celestial census more complete