STELLAR PROPERTIES

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STELLAR PROPERTIES

• How do we know what we know about stars?
  (and the rest of the universe!)

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What do YOU want to know about a random star?

• What are the most IMPORTANT stellar properties?
• Mass (always quoted in terms of
  M? 2 x 1033 g 2 x 1030
  kg) is MOST IMPORTANT
• Age is VERY IMPORTANT
• Composition (relative amounts of different
  elements) is also VERY IMPORTANT
• Rotation velocity
• Magnetic field
• Together the above DETERMINE the ALL other
  properties of all stars, but NONE of them is EASY
  to determine.

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Pop Quiz 2

• Take out a piece of paper and PRINT your name
  neatly in the upper right corner (1)
• Draw a cut-away diagram of the sun, labelling
  at least 3 interior and 3 atmospheric zones. (8)
• What are the mass and luminosity of the sun? (2)

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What are the (relatively) EASY TO DETERMINE
stellar properties?

• Location on the sky, (RA, dec) (first thing you
  do!)
• Brightness or Intensity, I (via apparent
  magnitude, m)
• Surface temperature, T (via Wein's Law
  spectroscopy)
• Distance, d (via parallax other methods
  discussed later)
• Luminosity, L, or Power (via absolute magnitude,
  M)
• Size or radius (from T and L via Stefan-Boltzmann
  Law)
• Velocity, V (radial via Doppler shift motion
  across sky)
• Multiplicity (single, binarydouble, triple
  etc.)
• Do they have planets? very hard, but now
  sometimes possible to tell

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Distances (d) via Parallax

• This is a direct measurement of the apparent
  location of the star with respect to more distant
  stars. The closer a star
  is the more its apparent position shifts as the
  earth moves around the Sun.
  Our slightly differing vantage
  point at different times of the year causes this
  apparent motion
• The parallax angle, p, is defined as the angle
  subtended by the Sun-Earth distance (1 AU) at the
  location of the star. It is geometrically equal
  to 1/2 of the shift in location over a six-month
  period.

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The brightness of a star depends on both distance
and luminosity
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Parallax Hipparcos
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Parallax Applets

• Introduction to Parallax Applet
• Measuring Parallax Angle
• Parallax Angle vs Distance
• Parallax of Nearby Star

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Parallax math

• Parallax angle p ? tan p 1 AU / d
• Biggest observed p 0.75 arcsec -- very small!
• If d is in PARSECS, p'' 1/d
• 1 parsec 1 pc 3.26 light-years
  3.085678 x 1018cm 3.1 x 1016 m 3.1 x 1013
  km
• Recall, 1 AU 1.496 x 1013 cm 1.5 x 1011 m
  1.5x108 km
• Example 1 closest star has p 0.75'' so
• The distance, d (pc) 1/0.75'' 1.3 pc 4.1
  lt-yr
• Example 2 A star has d 50 pc. What is p?
• Parallax, p 1/d 1/50 0.02 arcsec 0.02''

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The Nearest Stars
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What are some good examples of parallax?

• A) Hold your thumb out and blink your eyes. Your
  thumb moves more than the background
• B) Driving down a road a nearby fence appears to
  shift more than distance scenery
• C) Planets shift their position in the sky partly
  because the earth moves, shifting our position
• D) Stars shift their position at different times
  of the year, as Earth orbits the Sun
• E) All of the above

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What are some good examples of parallax?

• A) Hold your thumb out and blink your eyes. Your
  thumb moves more than the background
• B) Driving down a road a nearby fence appears to
  shift more than distance scenery
• C) Planets shift their position in the sky partly
  because the earth moves, shifting our position
• D) Stars shift their position at different times
  of the year, as Earth orbits the Sun
• E) All of the above

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Luminosity Amount of power a star radiates
(energy per second Watts 107 erg s-1)
Apparent brightness Amount of starlight
that reaches Earth (energy per second per
square meterW m-2)
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Luminosity passing through each sphere is the
same Area of sphere 4p
(radius)2 Divide luminosity by area to get
brightness
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The relationship between apparent brightness
and luminosity depends on distance
Luminosity Brightness
4p (distance)2
We can determine a stars luminosity if we can
measure its distance and apparent brightness
Luminosity 4p (distance)2 x
(Brightness)
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BRIGHTNESS, LUMINOSITY AND MAGNITUDES

• Apparent magnitude is an historical way of
  describing the brightness or intensity of a star
  or planet. The brightest objects visible to
  the naked eye were called 1st magnitude and the
  faintest, 6th magnitude.
• Quantified to say a factor of 100 in brightness
  (or intensity -- erg/s/cm2) corresponds to
  exactly 5 mag.
• ?m 5 ?100 times brighter (e.g., m 1 vs m 6)
  
• ?m 1 ? (100)1/5 2.512 times brighter
• ?m 2 ? (100)2/5 2.5122 6.31 times brighter
• ?m 3 ? (100)3/5 2.5123 15.85 times brighter
  
• ?m 10 ? 100 x 100 104 times brighter
• ?m 15 ? 100 x 100 x 100 106 times brighter

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Absolute Magnitudes and The Inverse Square Law

• The absolute magnitude is a measure of the POWER
  or LUMINOSITY of a star.

We can measure apparent magnitude or INTENSITIES
easily and DISTANCES pretty easily, and so
determine absolute magnitudes or LUMINOSITIES
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If a star was moved four times as far away, what
would happen to it?

• A) It would get four times fainter
• B) It would get sixteen times fainter
• C) It would get fainter and redder
• D) It would get fainter and bluer
• E) If moved only four times farther, you wouldnt
  notice much change

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If a star was moved four times as far away, what
would happen to it?

• A) It would get four times as faint
• B) It would get sixteen times fainter
• C) It would get fainter and redder
• D) It would get fainter and bluer
• E) If moved only four times farther, you wouldnt
  notice much change

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To measure a stars true brightness, or
luminosity, you need to know

• A) Its temperature and distance
• B) Its temperature and color
• C) Its apparent brightness and distance
• D) Its apparent brightness and color
• E) Its distance, apparent brightness, and color
  or temperature

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To measure a stars true brightness, or
luminosity, you need to know

• A) Its temperature and distance
• B) Its temperature and color
• C) Its apparent brightness and distance
• D) Its apparent brightness and color
• E) Its distance, apparent brightness, and color
  or temperature

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MAGNITUDES AND DISTANCES

• Measuring the brightness, or apparent magnitude
  of a star is easy.
  If we also know the
  distance we can get the ACTUAL luminosity, or
  absolute magnitude. Alternatively, if we know
  both the APPARENT and ABSOLUTE magnitudes we can
  find the DISTANCE to a star.
• The absolute magnitude can often be accurately
  estimated from the star's spectrum, so this
  method of distance determination (spectroscopic
  parallax) is often used beyond 100 pc where
  regular (trigonometric) parallax cant be
  accurately found.
• A more distant but very luminous star can appear
  as bright as a nearer, fainter, star.

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Different distances, same brightnesses
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Review of Logs (common, base 10)

• log10 10 1.0 log 1
  0.0 log 100 2.0
  log 1000 3.0 log 100,000
  5.0
• log 0.1 -1.0 log 0.0001
  -4.0
• log 2 0.30 log 3
  0.48 log 5 0.70
  
• log 30 1.48 log 500
  2.70
• log 0.5 -0.30 log 0.2
  -0.70
• Simple rule log10(10x) x
• Very useful since log(xy) log x log y

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Mathematics of Magnitudes

• EXAMPLES Given m 7 and d 100 pc, find M
  M m - 5 log (d/10pc)
• M 7 - 5 log(100pc/10pc) 7 - 5 log
  10
• so M 7 - 5(1) 2
• What if m 18 and d 105 pc?
• M m - 5 log (d/10pc)
• M 18 - 5 log(105 pc / 101 pc) 18 - 5 log
  (104)
• or M 18 - 5(4) -2

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Apparent Magnitudes
Note that mags are backwards More negative is
Brighter and More positive is Fainter!
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Getting Distances from Magnitudes

• Now, given M -3 and m 7, find d.
• m - M 5 log (d/10 pc)
  7 -(-3) 10 5 log
  (d/10 pc)
• So 2 log (d/10pc)
• Therefore 102 d/10 pc and finally,
• d 102(10 pc) 103 pc 1000 pc

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COLORS and TEMPERATURES of STARS

• Bluer stars are hotter and redder ones are
  cooler.
• The simplest and quickest way to estimate the
  temperature is to measure the magnitudes of stars
  in different COLORS, using FILTERS on a telescope
  that only let particular wavelengths through --
  the technique of FILTER PHOTOMETRY.
• Standard filters are U, B, V, R, I
  with U UV
  (really very blue), B blue, V visible (really
  yellow), R red, and I IR (very long red).
• Filters actually in the IR are H, K, L and can be
  used with telescopes in space or at very high
  altitudes.
• Color index, C B - V
• Since lower magnitudes are brighter, C -0.4 is
  hot (i.e., more blue light than yellow) and C
  1.2 is cold (vice versa) for a star.

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Stellar Colors
Cool, red, Betelgeuse Hot, blue, Rigel Dense
star field
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Blackbody Curves Filter Photometry

1. B-V lt 0, hot and blue
2. B-V 0, medium and yellow
3. B-V gt 0, cool and red

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Stellar Temperatures

• Better TEMPERATURE measurements can be obtained
  with more work from a SPECTROMETER, where
  brightnesses at many, many wavelengths are
  determined.
  But you must look at the
  star for a longer period, since all the light is
  spread out into many wavelength bins.
• This allows finding ?max, therefore T via Wien's
  Law T(K) 0.29 cm?K/ ?max (cm)
• Even more precise measurements of T come from a
  detailed analysis of the strengths of many
  spectral absorption lines.
• Wien's Law Applet

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STELLAR SIZES

• A very small number of nearby and large stars
  have had their radii directly determined by
  INTERFEROMETRY. The CHARA Array is substantially
  adding to this number.
• Usually we must use the STEFAN-BOLTZMAN LAW.
• L 4 ? ? R2 T4
• L is found from M via m and d
• T is found from color index, Wiens Law, or
  spectroscopy
• So we solve for R,

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Stars Come in a WIDE Range of Sizes
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SPECTRAL LINES TELL US

• Composition (mere presence of absorption lines
  say which elements are present in the star's
  photosphere -- fingerprints)
• Abundances (relative strengths of lines)
• Temperature (relative strengths of lines)
  (equations are solved simultaneously for T and
  abundances)
• Pressure (higher P makes for broader lines)
• Rotation (faster spin makes for broader lines)
  (rotationally broadened line shapes are slightly
  different from those produced by pressure
  broadening)
• Velocity (radial velocity from Doppler shift)
• Magnetic field strength (causes splitting of
  energy levels within atoms, therefore splitting
  of spectral lines -- but only visible if B is
  higher than is typical for most stars).

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STELLAR MOTION and VELOCITY

• The radial, or line-of-sight, velocity can be
  determined from the Doppler shift, as already
  discussed.
• Long-term measurements of nearby stars (when
  determining parallaxes for distance measurements)
  also showed many exhibited enough PROPER MOTION
  to be detected.
  This is motion in the plane of the sky (i.e.
  in Right Ascension and Declination)
• PM is measured in "/year BUT actual TRANSVERSE
  VELOCITY PM x d
• The SPACE VELOCITY is the full 3-D velocity of a
  star
  the VECTOR SUM of
  the Radial and Transverse Velocities.

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Proper and Space Motions
Barnards Star ?
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IDEA QUIZ

• Star A has M-3 and d100 pc
• Star B has m6 and d1000 pc
• Star C has m3 and M3
• Which star is
• 1) Most luminous (most powerful)
• 2) Brightest (most intense)
• 3) Closest
• Remember m-M 5 log(d/10pc)

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Answers

• B Mm-5log(1000/10)6-5log(100)
• 6-5(2)6-10-4 most luminous
• A mM5log(d/10pc)
• -35log(100/10)-35(1)2 brightest
• C 5log(d/10pc)m-M0,
• So log(d/10pc)0 and d10pc closest