Luminosities and Temperatures of Stars

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Basic Properties of Stars Sizes and Masses
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Outline for Today

• Properties of Stars
• Sizes
• Masses
• Composition
• Lunar Eclipse Antarctic Astronomy
• Star Formation

• Coming Up
• Homework 5 Tomorrow/Weds, 9am
• Telescopes Project AE  Last night Thursday
• Telescopes Project FL Begins next week

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Temperature vs. Luminosity The H-R Diagram

• If the absolute luminosity and temperature of a
  star are both known, they can be plotted against
  each other. This is called the
  Hertzprung-Russell (H-R) diagram.

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Temperature vs. Luminosity The H-R Diagram

• There are patterns in the H-R diagram. About 90
  of the stars are located on a diagonal band,
  which goes from cool/faint to hot/bright. This
  is called the main sequence.

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The Main Sequence

• Blackbody law
• luminosity L ? T4
• Surface area of sphere
• L ? R2
• Stars luminosity
• L ? R2T4
• For normal stars like the Sun
• ? mass ? radius ? temperature

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Red Giants and White Dwarfs

• Some stars are not on the main sequence. Some
  are very cool, but also very bright. Since cool
  objects dont emit much light, these stars must
  be huge. They are red giants.
• Some stars are faint, but very hot. These must
  therefore be very small they are white dwarf
  stars.
• L ? R2T4

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The Sizes of Stars

• Telescopes can measure the sizes of only the
  largest and closets stars.
• All others appear as unresolved points of light,
  and we must measure their temperatures and
  luminosities to estimate sizes
• L ? R2T4

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The Sizes of Stars

• The sizes of stars can be anywhere from 0.01 R?
  to 1000 R? !

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The Masses of Stars

• Stellar masses can only be determined via the
  application of Keplers and Newtons laws, i.e.,

(M1 M2) P2 a3

• where
• M1 and M2 are the stellar masses (in solar
  units)
• P is the orbital period (in years)
• a is the semi-major axis of the orbit (in A.U.)

This requires binary stars!
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Visual Binaries

• When both stars can be seen, its called a Visual
  Binary.

Castor
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Spectrum Binaries
If the stars are too close together to be seen
separately, it is possible to identify the
object as a binary based on its spectrum.
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Spectroscopic Binaries
If the Doppler shift of a stars absorption lines
changes with time (redshift, then blueshift, then
redshift, etc.), its a spectroscopic binary.
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Eclipsing Binaries
If two stars eclipse each other while orbiting,
its an eclipsing binary.
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Eclipsing Binaries
If two stars eclipse each other while orbiting,
its an eclipsing binary.
Eclipsing binaries are somewhat rare, since they
need to be seen edge on. This system is one in
which both stars undergo a total eclipse.
Frequently, the eclipses are partial.
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Determining Masses from Binaries

• The relative speeds of the stars gives you their
  relative masses.

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Determining Masses from Binaries

• The relative speeds of the stars gives you their
  relative masses.

• The absolute velocities of the stars (times the
  period) gives you the circumference of their
  orbits. From that, you can derive the orbits
  semi-major axes. In other words,
• Circumference v t 2 ? a
• (at least for circular orbits)

• From the semi-major axis and the period, you can
  derive the total mass of the system through

(M1 M2) P2 a3

• Since you already know the relative masses, you
  now know everything!

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Results from Binary Stars Measurements

• All stars have masses between 0.1 M? and 100 M?
• Brighter stars on the main sequence have larger
  masses

• The white dwarf stars are all less than 1.4 M?
• There is no pattern to the masses of red giants.

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Summary Basic Properties of Stars

• Temperature vs. Luminosity H-R Diagram
• Most stars form a band from cool T/faint L to
  warm T/bright L Main Sequence
• Red giants and white dwarfs
• Size
• Hard to measure directly for most stars
• Estimate by measuring T and L L ? R2T4
• Mass
• Measure for binary stars w/ Kepler/Newton laws
• Brighter/hotter stars on main sequence have
  higher masses

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The Birth of Stars
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Star Formation

• Stages of star formation
• Stars without fusion Brown dwarfs
• Observations of star forming regions
• Optical
• Infrared
• Hubble Space Telescope

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Formation of the Solar Nebula
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The Beginning of Star Formation

• The interstellar medium is the gas and dust
  floating in space between the stars. This
  material is created by the death of stars, but
  also provides the ingredients for making new
  stars.

Clouds in the interstellar medium can contain
anywhere from 1 to 100,000,000 M? of gas and
dust. So a given cloud could produce 1 newborn
star, or millions of them!
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The Beginning of Star Formation

• Where there is gas, there is also dust, which
  absorbs and scatters light. Dust in space can be
  seen in silhouette, as it blocks out the light
  from more distant stars.

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The Beginning of Star Formation

• Since dust blocks the light, the temperatures
  within these clouds can be just a few degrees
  above absolute zero!

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The Beginning of Star Formation

• Since the temperature is so low inside these
  clouds, gas pressure is almost non-existent.
  There is nothing to stop gravity from condensing
  the cloud. The cloud will get smaller and
  increase in density.

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The Beginning of Star Formation
Rather than collapsing to form just 1 star, most
clouds fragment into many clumps, which then
collapse to form stars. Each fragment is called a
protostar.
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Formation of a Disk

• As a protostar collapses, conservation of angular
  momentum causes the material to spin rapidly.
  The centripetal force fights the collapse in the
  plane of rotation, but not at the poles. As a
  result, the material collapses into a disk.

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Formation of the Solar System
From interstellar cloud to planetary system
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Formation of the Solar System
From interstellar cloud to planetary system
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Star Formation in the HR Diagram

• The protostar collapses and gets smaller and
  smaller (and, due to the increased central
  pressure), hotter and hotter. The stars center
  eventually becomes hot enough to ignite hydrogen
  fusion, which stops its collapse (hydrostatic
  equalibrium), and the star stably fuses hydrogen
  for a long time. At this point, its on the main
  sequence.

protostar
main sequence star
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Brown Dwarfs Stars without Fusion

• In order to fuse hydrogen, the center of a star
  must be hot enough. If a stars mass is too low,
  its central temperature will be too low to
  ignite hydrogen fusion. These objects lack a
  source of energy and cant shine like a normal
  star. They are called brown dwarfs. They grow
  cooler, fainter, and smaller forever, like a
  dying ember.

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Stars 100 to 0.1 M?
Sun
Brown dwarfs below 0.1 M?
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Reddening and Scattering
After stars are born in an interstellar cloud,
their light reflects from the surrounding cloud,
which significantly changes its appearance.
before stars are born
after stars are born
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Reddening and Scattering
Stars behind large piles of dust will be
reddened. Other parts will appear blue, due to
the scattering by dust. This is just like the
daytime sky.
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Emission Lines from Nebulae

• In addition to scattered light from the newborn
  stars, these nebulae produce emission line
  radiation, just like an aurora.

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At IR wavelengths, light can escape from clouds
of dust and gas, allowing us to see young stars
born within them
Optical
Infrared
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Dust young stars are cool, bright in Infrared
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Barnards Taurus
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Star Forming Regions in the Infrared
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Star Forming Regions in the Infrared
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Summary Star Formation

• Stages of star formation
• Gas/dust cloud (produced by deaths of stars)
• Cloud collapses and fragments
• Protostar shrinks until reaching main sequence
• Brown dwarfs no hydrogen fusion
• Observations of star forming regions
• Optical scattering reddening of light
• Infrared dust is transparent, and even glows
• Hubble Space Telescope sharp images of young
  stars and disks