Properties of Stars

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Properties of Stars

• Chapter 8
• Mr. Saks
• Astronomy

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Measuring Distance to Star

• Surveyors Method
• If a distance between to places (S) is known and
  two angles (A and B) then you can find the
  distance to any object (D).
• This is kind of they way we are able to measure
  distance to stars

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Astronomers Method

• To find stars we must have large baseline
• Use diameter of Earths orbit
• Take a picture of a star
• Wait six months
• Take another picture of star
• Baseline is 2 AU
• The star will shift in the sky
• This shift is known as a parallax
• Apparent change in position of an object due to
  change in location of observer

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Astronomers Method

• Stellar Parallax (p) is half the total shift of
  the star.
• Nearest star to us has a shift of .76 second of
  arc
• Parsec (pc) is a distance to an imaginary star
  that has a parallax of 1 second of arc
• 206,265 AU
• Roughly 3.26 ly
• Because of seeing, ground based parallax are
  limited to the closest stars
• 10,000 stars

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Further Stars

• 1989 Hipparcos launched
• European Space Agency
• Above atmosphere
• Worked for 4 years
• 1997 made two catalogs
• One had 120,000 stars with parallaxes 20 times
  more accurate
• Second catalog had over a million stars with
  parallaxes as accurate as ground

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Intrinsic Brightness

• Intrinsic means belonging to the thing
• Intrinsic brightness is the measure of the total
  amount of light a star emits
• A bright star far away might appear dim
• To find true brightness of a star we must correct
  for influence of its distance

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Brightness and Distance

• Flux is the amount of energy in joules (J) per
  second falling on 1 square meter
• Flux we receive from a light source is inversely
  proportional to the square distance to the source
• Inverse square relation

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Absolute Visual Magnitude

• If all stars were same distance we could easily
  measure and compare brightness
• Absolute visual magnitude (Mv) places all stars
  at 10 pc away to measure true brightness
• Apparent magnitude tells us how bright a star
  looks
• We can use apparent magnitude and the distance to
  the star (found with parallax) to figure absolute
  magnitude

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Luminosity

• Luminosity (L) is how much energy per second each
  star is emitting
• Note this is all energy not just light
• We can use absolute magnitude to compare a star
  with the Sun
• We can use absolute magnitude, but we must make a
  small adjustment to account for the energy that
  is not visible

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Diameters of Star

• Two factors that affect L is surface area and
  temperature
• Example
• You can eat dinner by candlelight
• Even though the fire is hot, it has a small
  surface area and therefore low L
• Compare this to a 14 foot flame
• Same flame temperature but bigger surface area

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Luminosity, Radius, and Temperature

• L is proportional to surface area
• Hot star, small surface area, low luminosity
• Cool star, large surface area, high luminosity
• Hertzsprung-Russell diagram (H-R diagram
• Ejnar Hertzsprung and Henry Norris Russell
• Graph that seperates temperature and surface area
  on stellar L
• Sorts stars according to their diameters

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H-R Diagram

• Points near the top of the diagram are very
  luminous
• Points near the bottom are not luminous
• Points at the right of the chart are cool stars
• Closer to red
• Points to the left are hot stars
• Closer to blue
• Diagram has nothing to do with stars place in
  space
• Star may change position on diagram as it ages

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H-R Diagram

• Main Sequence is region that runs from upper left
  to lower right
• Contains 90 of all stars
• Hot main-sequence star more L than cool
  main-sequence star

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Family of Stars

• Giant Stars lies at right above the main sequence
• Cool but very large
• Supergiants near top of diagram
• 10-1000 times size of Sun high L
• White Dwarf among the hottest of stars but among
  the smallest low L

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Luminosity Classification

• Classified on the stars spectrum
• Larger stars have less dense atmosphere
• Widths of spectral lines are partially determined
  by density
• Usually more dense gas the broader the spectral
  lines
• Giant stars have narrow spectra lines
• Supergiant stars have really narrow spectra lines

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Stellar Luminosity Classes

• Stars spectrum will tell how roughly big it is
• Rigel is a bright supergiant (Ia)
• Polaris is a regular supergiant (Ib)

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• Adhara is a bright giant (II)
• Capella is a giant (III)
• Altair is a subgiant (IV)
• The Sun is a main sequence star (V)

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Spectroscopic Parallax

• Spectroscopic Parallax is the estimation of the
  distance to a star from its spectral type,
  luminosity class, and apparent magnitude
• Used for stars too far away to get a parallax
• Not an actual parallax measurement
• We can use its spectrum to determine spectral
  class, gives horizontal location on H-R diagram
• Luminosity can be found by spectral lines width
  to get vertical position on H-R diagram
• Once plotted on HR diagram we can get absolute
  magnitude
• Distance can be found by comparing apparent and
  absolute magnitudes

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Masses of Stars

• A third goal is to find mass of stars
• Light tells us nothing about the mass of a star
• Gravity is the key
• Matter produces gravity
• Can find amount of matter in star by watching an
  object move through the stars gravitational
  field
• To find masses of stars we look at binary stars
• These are pairs of stars that orbit each other

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Binary Stars in General

• Two stars
• Mutual gravitational pulls them away from their
  straight line path
• Makes them follow closed orbits around a point
• Center of mass is the center or balance point of
  the system

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Binary Stars

• If both stars are equal size the center of mass
  is directly between the stars
• If one star is more massive the center of mass is
  then moved toward the bigger, more massive star

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Binary Star Mass

• There is an inverse relationship
• If one star has an orbit twice as large as the
  other stars orbit then it must be half as
  massive
• That means we know the ratio of mass between the
  stars, but not the true mass of each star
• Knowing the size of the orbit and the orbital
  period
• Length of time the stars take to complete one
  orbit

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Finding Mass

• Looking at orbital period
• Shorter the orbital period
• Stronger the stars gravitational pull must be to
  hold the orbit
• Knowing the overall size of orbit AND orbital
  period we can then determine mass

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Affecting Mass Calculations

• Elliptical Orbits
• Orbital planes tipped at an angle from our line
  of sight
• There are three types of binary stars that are
  especially important in determining stellar mass
• Visual Binary System
• Spectroscopic Binary System
• Eclipsing Binary System

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Visual Binary Stars

• Visual Binary System are stars that are
  separately visible in the telescope
• This requires large orbits
• Therefore have long orbital periods
• Some take hundreds even thousands of years to
  complete orbit
• Sirius A a bright star, and Sirius B a white
  dwarf, have a 50 year orbital period
• More than half of all stars are members of binary
  stars

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Spectroscopic Binary Systems

• Looking at spectrum, formed by light from both
  stars and spectral lines of both
• Using Doppler shift
• We could not officially see the two stars, but
  their spectrum and shift would alert us
• We measure orbital period from start of shift
  until it returns to starting position

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Spectroscopic Binaries

• Use Doppler effect to find orbital velocity
• Using velocity times orbital period we can then
  find the circumference of the orbit
• We can then find the radius of orbit
• Use orbital period and size of orbit we can
  calculate the mass
• This binary system will not allow us to find true
  mass because we cannot tell if the orbit is at an
  incline.
• We may only find lower mass levels from this type
  of system
• More than half of all stars are in a binary
  system
• Most of those are spectroscopic binaries
• Many of the stars in our sky are actually pairs
  of stars

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Eclipsing Binary System

• Binary star system seen on edge as viewed from
  Earth
• One star will cross in front of the other causing
  an eclipse
• It may block some of the light depending on size
• This is a eclipsing binary system

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Eclipsing Binary Stars

• The system looks like a single point of light
• Light Curve resulting variation in the brightness
  of the system as one star eclipses the other

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Family of Stars

• Now we know luminosity, diameters, and masses of
  stars
• Now we can focus on star families
• We can try to understand how stars are born and
  die
• What is the average star?

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Mass, Luminosity, and Density

• Using the H-R diagram we can see patterns of mass
  and luminosity
• Main sequence obey the mass-luminosity relation
• The more massive the more luminous
• Giant and supergiant stars do not follow this
  relationship
• White Dwarfs do not follow this

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Density of Stars

• Main sequence stars have average densities
  similar to Sun
• Giant stars are lower density of about 0.1 - 0.01
  g/cm3.
• Supergiants are lower density yet about 0.001 -
  0.000001 g/cm3. (thinner than air)
• However center is 3,000,000 g/cm3
• A teaspoon of this on earth would be 15 tons
• Densities divide stars into three groups
• Main sequence, giants and supergiants, white
  dwarfs

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Surveying the Stars

• First it is difficult
• Need an honest sample (large amount)
• Second, most stars are really faint and most
  luminous are rare
• Most common are lower main-sequence red dwarfs
  and white dwarfs