Astro 10Lecture 9: Properties of Stars

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Astro 10-Lecture 9Properties of Stars

• How do we figure out the properties
• of stars?

• Weve already discussed the tools
• Light
• Gravity (virtually impossible to measure).
• Particles (might not get here).

Now lets apply them to stars!
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Chabot Trip

• Let's pick a Friday (Apr 1? Apr 16?)
• Meet at a BART station
• Need volunteers to drive
• Planetarium show and telescope viewing

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Observation geometry or physics
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Chemical Composition

• Presence of Absorption lines of a particular
  element indicates the presence of that element in
  the star!
• Absence of a spectral line doesn't necessarily
  mean an element is absent.

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Chemical Composition
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Temperature
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Distance (1)
Trigonometric Parallax Youve all used it!
Animation lec9_pix\parallax.mpg
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Distance (1)
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Distance (3)

• Trigonometric Parallax useful to 50pc (ground)
  and 500 pc (space)
• Parsec (pc) Distance of a Star with a Parallax
  of 1 (one) arcsecond (ParSec)
• 1 pc is a little over 3 light years!

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Space Velocity (1)

• Velocity Speed Direction
• Space Velocity has 2 components
• Radial Velocity (Towards/Away)
• Transverse Velocity (sideways)
• Transverse Velocity
• PROPER MOTION DISTANCE
• Animation

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Space Velocity (2)

• Radial Velocity
• DOPPLER EFFECT
• carhorn.wav

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Space Velocity (2)
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Space Velocity (2)
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Space Velocity (2)
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Space Velocity (3)
Radial Velocity Doppler Effect
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ConcepTest

• Two stars lie in the same area of the sky. Star
  Gern has a parallax measurement of 1 arcsecond,
  while Star Zora has a parallax measurement of
  0.5 arcseconds.
• a) Star Gern is closer to us than star Zora
• b) Star Gern has a larger space velocity
  than star Zora
• c) Star Gern and Star Zora are at the same
  distance
• d) Star Gern and Star Zora have the same
  temperature

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Apparent Brightness vs. Luminosity

• Apparent Brightness Energy we intercept per unit
  area per unit time (how bright it appears)
• Luminosity Energy emitted per unit time (how
  bright it really is)
• Inverse Square Law Projector Demo

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The inverse square law

• Brightness proportional to 1/d2
• Demo

LUMINOSITY APPARENT BRIGHTNESS DISTANCE
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Inverse Square Law
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Hertzprung-Russell (H-R) Diagram

• A Plot of Temperature vs. Luminosity

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HR Diagram
Notice that the Temperature axis is
reversed! (So is the magnitude axis, but we
dont use it) NOTE HUGE RANGE OF LUMINOSITIES!
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MASS! (1)

• Period/Size of orbits are related to MASS by
  Newtons version of Keplers Third Law
• Qualitatively, if two masses are orbiting about
  one another very rapidly, then the gravity
  between them must be stronger than if they were
  orbiting more slowly.
• SUM of MASSES Orbital Period Orbital Size
  GRAVITY

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MASS Binary Stars (2)

• We can get stellar masses from observations of
  Binary Stars
• Visual Binary (see the two stars move about one
  another on the sky)
• Spectroscopic Binary (see the motion due to
  Doppler shifts of spectral lines)
• Eclipsing Binary (see the light from one star
  periodically blocked by the other)

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Visual Binaries

• Distance angle measurement gt orbital size
• Period orbital size gravity gt sum of masses
• Center of mass determination gives individual
  masses

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Spectroscopic Binaries

• Orbital velocity determined by Doppler shifts of
  lines in spectrum (OH 69)
• spbin.mov
• Period Maxumum orbital velocity gives size of
  orbit
• INCLINATION PROBLEM
• Some stars in Big Dipper are Binaries!

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Spectroscopic Binaries (2)
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Eclipsing Binaries

• One star passes in front of the other at some
  point during the orbit, reducing the light that
  reaches us
• OH 70
• eclbin.mov

Eclipsing Spectroscopic Binary gt NO
INCLINATION PROBLEMS
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MASS RECAP

• Newtons Laws of Gravity say that if we know 1)
  size of orbit 2) period of orbit then we can find
  the total mass of the system
• Size of orbit need either distance, or eclipsing
  spectroscopic binary
• To find individual masses, must know where the
  Center of Mass of the system is
• Stellar masses are 0.01 to 100 times Suns mass

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Mass-Luminosity Relation
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Radius (size) from Binaries (1)

• In an eclipsing spectroscopic binary system, we
  can find the RADIUS of the stars too!
• Time spent in eclipse orbital velocity of star
  (from Doppler) gt SIZE OF STAR

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Radius from Blackbody Radiation (2)

• Blackbody radiation law says that the energy
  emitted / area / time by the star is determined
  only by its TEMPERATURE
• So if we can determine the LUMINOSITY (energy
  emitted / time) of the Star, we can combine this
  with its TEMPERATURE to determine the RADIUS
• TEMPERATURE LUMINOSITY BLACKBODY RADIATION gt
  RADIUS

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Radius from Blackbody Radiation (2)

• Giants 10 x size of sun (1000 x size of Earth)
• Supergiants 10-1000 x size of sun
  (1000-100,000 x size of Earth)
• White Dwarfs size of Earth

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Radius from Blackbody Radiation (2)

• L4pR2sT4
• Giants 10 x size of sun (1000 x size of Earth)
• Supergiants 10-1000 x size of sun
  (1000-100,000 x size of Earth)
• White Dwarfs size of Earth

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Now What?

• Notice that most of these quantities rely in some
  way upon a determination of DISTANCE
• Remember Trigonometric Parallax is only good to
  500 pc, while the Milky Way Galaxy is 17,000 pc
  across!
• How do we learn anything about more distant stars?

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Spectroscopic Parallax (1)

• Previously Measurement geometry or physics gt
  Quantity
• NOW Lets USE what weve learned to bootstrap
  our way to more distant stars!
• Suppose we KNEW the intrinsic luminosity of a
  star then a measure of its apparent brightness
  would tell us its DISTANCE (remember the INVERSE
  SQUARE LAW?)

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Spectroscopic Parallax (2)

• If all stars were on the Main Sequence in the
  HR diagram, then a measurement of the TEMPERATURE
  of the star would allow you to determine its
  LUMINOSITY from the H-R diagram
• LUMINOSITY APPARENT BRIGHTNESS INVERSE
  SQUARE gt DISTANCE
• Notice that this only works AFTER we have found
  the luminosities of many stars other ways, and
  calibrated the H-R diagram

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• I

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Spectroscopic Parallax (3)

• NOTE Were assuming more distant stars are just
  like nearby ones!
• BUT WAIT! Not all stars lie on the Main Sequence
• Subtle differences in the widths of the stars
  absorption lines can determine its Luminosity
  Class (WD, MS, giant, supergiant)
• Measure spectrum blackbody atomic physics gt
  TEMP and LUMINOSITY CLASS
• CALIBRATED HR DIAGRAM gt LUMINOSITY
• APPARENT BRIGHTNESS INV SQ gt DISTANCE

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• What does the Population of Stars look like?
• What makes a star shine (model)?
• How can we TEST this model with observation?

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Observation geometry or physics
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ConcepTest

• By looking at the spectra of two stars, we learn
  that they are both main sequence stars, and they
  have the same temperature.
• If we can measure the distance to ONE of the
  stars using trigonometric parallax, can we find
  the distance to the other star? (Ayes, Bno)
• If we could not measure the distance to ANY stars
  using trigonometric parallax, can we find the
  luminosity of these stars? (Ayes, Bno)

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Population of Stars

• The Sun isnt special!
• Nearest star is 4 ly away
• Temperatures 2,000-30,000K (sun 5800)
• Luminosities 1/100,000 to gt 1,000,000 x sun
• Fall into classes on the H-R diagram
• Main sequence (sun), white dwarfs, red giants,
  supergiants

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Population of Stars (2)

• Radii
• WD Earth-sized (1/100 of Sun)
• Giants 10-100 x size of sun (Earth orbit in
  our scale model of the solar system)
• Supergiants 100-1000 x size of sun
• Mass
• 0.1 Msun to 55-100 Msun
• Mass Radius gt Density (DEMO)
• MS density sun 1g/cm3 density water
• Giants 0.1 0.01 x density sun
• Supergiants 0.001 0.000001 x density sun
• WD 3 000 000 x density sun (1 tsp 15 tons on
  Earth)

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Mass-Luminosity Relation

• For MAIN-SEQUENCE STARS ONLY
• A relationship between MASS and LUMINOSITY

Most luminous main-sequence stars are also the
most massive (L M3.5)
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POPULATION STATISTICS

• What stars do we see as bright in the night sky?
• LUMINOUS ONES
• What stars are the nearest?
• DIM (RED) ONES
• How many stars of each kind per cubic parsec?
• LUMINOUS RARE, NEAREST DIM

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Comparing HR Diagrams for nearest and brightest
stars
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IN-CLASS EXERCISE