The Stars: A Celestial Census 28 July 2005 AST 2010: Chapter 17

What’s a census? What’s it for? Stellar Questions What’s a census? What’s it for? 28 July 2005 AST 2010: Chapter 17

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 take 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 (as in political surveys) 28 July 2005 AST 2010: Chapter 17

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 28 July 2005 AST 2010: Chapter 17

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 106 LSun for the most luminous stars to 10-6 LSun for brown dwarfs 28 July 2005 AST 2010: Chapter 17

Measuring Stellar Masses Mass is one of a star’s most important characteristics Knowing the mass can help us estimate how long it will shine and what its ultimate fate will be 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 Animation About half of stars are binary stars

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 M1 and M2 (in units of the Sun’s mass) by D3 = (M1+M2) P2  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 http://www.jimloy.com/astro/binaryx.gif 28 July 2005 AST 2010: Chapter 17

Visual Binaries Binary-star systems in which both of the stars can be seen with a telescope are called visual binaries Animation Binary stars: Sirius A and B 28 July 2005 AST 2010: Chapter 17

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 28 July 2005 AST 2010: Chapter 17

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 Animation http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/

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 http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/spanim.gif 28 July 2005 AST 2010: Chapter 17

Range of Stellar Masses How large and small can stars’ masses be? Stars with masses up to about 100 times that of the Sun have been discovered Some 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 28 July 2005 AST 2010: Chapter 17

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 28 July 2005 AST 2010: Chapter 17

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 star’s brightness decreases gradually during the eclipse The time for the brightness decrease depends on the size of the star Accurate sizes for a large number of stars come from measurements of eclipsing binaries 28 July 2005 AST 2010: Chapter 17

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 28 July 2005 AST 2010: Chapter 17

Techniques for Measuring Characteristics of Stars 28 July 2005 AST 2010: Chapter 17

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) 28 July 2005 AST 2010: Chapter 17

H-R Diagram for Many Stars 28 July 2005 AST 2010: Chapter 17

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 Hence they must be the giants and supergiants 28 July 2005 AST 2010: Chapter 17

Where would you put a brown dwarf on this diagram? Stellar Question Where would you put a brown dwarf on this diagram? 28 July 2005 AST 2010: Chapter 17

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 28 July 2005 AST 2010: Chapter 17

The Other 10% of Stars Roughly 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 28 July 2005 AST 2010: Chapter 17