28 July 2005 AST 2010: Chapter 17 1

The Stars:The Stars:A Celestial A Celestial

CensusCensus

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Stellar QuestionsStellar Questions

What’s a census?

What’s it for?

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The Lives of StarsThe Lives of StarsStars live for a very long time, up to 100 million years or moreNo 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 lifeWe can then try to infer the stages that a star goes through from the data we assemble in the censusBut we can be misled if the star sample in the census is biased (as in political surveys)

28 July 2005 AST 2010: Chapter 17 4

A Stellar Census (1)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 biasedCareful 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

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A Stellar Census (2)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 usIn 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 faintThe luminosity (L) of stars ranges from more than 106 LSun for the most luminous stars to 10-

6 LSun for brown dwarfs

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Measuring Stellar MassesMeasuring Stellar MassesMass 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 directlyIndirect measurements of stellar masses can be done for binary-star systems

Each system consists of two stars that orbit each other, bound together by gravityStrictly speaking, each of the binary stars orbits a common point called the center of mass

Animation

About half of stars are binary stars

28 July 2005 AST 2010: Chapter 17 7

Orbits and Masses of Binary StarsOrbits and Masses of Binary StarsThe 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

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Visual BinariesVisual BinariesBinary-star systems in which both of the stars can be seen with a telescope are called visual binaries

Binary stars: Sirius A and BBinary stars: Sirius A and B

AnimationAnimation

28 July 2005 AST 2010: Chapter 17 9

Sirius A and BSirius A and B

Sirius A is normal star Sirius B is a white dwarf companionThe 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

10AST 2010: Chapter 1728 July 2005

Spectroscopic BinariesSpectroscopic BinariesIn 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 spectroscopySuch 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

28 July 2005 AST 2010: Chapter 17 11

Doppler Effect in Binary Doppler Effect in Binary StarsStars

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 binariesRadial velocities of spectroscopic binaries

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Range of Stellar MassesRange of Stellar MassesHow 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 massesTheoretical 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 protonsThey 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 13

Mass-Luminosity RelationMass-Luminosity RelationThere is a correlation between the mass and luminosity of a starThe 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

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Diameters of StarsDiameters of StarsThe 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 eclipseThe star’s brightness decreases gradually during the eclipseThe 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

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Eclipsing Binary SystemEclipsing Binary SystemSome 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 revolutionThus, we can observe periodic eclipses in these binary-star systems, which are therefore called eclipsing binaries

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Techniques for Measuring Characteristics Techniques for Measuring Characteristics of Starsof Stars

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H-R DiagramH-R DiagramThere is a relationship between the temperature (color) and luminosity of 90% of starsThey lie along a band called the main sequenceThe plot of stars’ luminosities versus their temperatures is called the Hertzsprung- Russell diagram (H-R diagram)

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H-R Diagram for Many StarsH-R Diagram for Many Stars

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Features of H-R DiagramFeatures of H-R DiagramThe main-sequence band contains almost 90% of the stars

Large blue starsMedium yellow starsSmall 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 luminousHence they must be the giants and supergiants

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Stellar QuestionStellar QuestionWhere would you put a brown dwarf on this diagram?

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Characteristics of Main-Sequence Characteristics of Main-Sequence StarsStars

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

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The Other 10% of StarsThe Other 10% of StarsRoughly 10% of the stars

do not follow the mass-luminosity relationshipdo not lie on the main sequence

Giant and supergiant starslie on the upper-right section of the H-R diagram are very luminous because they are large in diameter, although they are coolmake up less than 1% of the stars

White dwarfs lie on the lower-left section of the H-R diagramare small in diameter (similar to Earth’s) are hot, but dim make up about 10% of the stars

BetelgeuseBetelgeuse