The Cosmological Distance Ladder

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The Cosmological Distance Ladder
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• Overlapping rungs
• Earth
• Earth-Mars
• Earths orbit
• Parallax
• Spectral Parallax
• RR Lyrae variables
• Cepheid variables
• Type I Supernovae
• Type II Supernovae
• Galaxy brightness

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Measuring Earth - Geometry
? s/r Two wells E-W Measure s Time sun ?/2?
t/24 hr
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Measuring Earth-Mars
In 1672
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Calculating Earths Orbit
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Parsecs - Parallax Seconds
You know that Tan(Ø ) d/D Today we have
accurate parallaxes for about 10,000 stars.
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Spectroscopic parallax
Since astronomers can tell by the spectrum of a
star if and where it falls on the main
sequence, they can get the absolute
magnitude. If you then measure the apparent
magnitude,
it is a relatively simple process to calculate
the distance to the star M m - 5
log10(d/10) And you know M, and m
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Variable Stars

• RR Lyrae (cluster variables)
• Cepheids (Very Bright)
• Eclipsing Binary
• Mira (long period)
• Eta Carinae

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Variable Stars
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RR Lyrae Variables
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RR Lyrae Variables

• How to measure the distance to a galaxy using RR
  Lyrae variable stars
• Find the RR Lyrae by magnitude curve
• Measure its apparent magnitude.
• They all have about the same absolute magnitude
  (0 lt M lt 1)
• Use M m - 5 log10(d/10) to find d

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Cepheid Variables

1. Star contracts, heats up
2. Singly ionized He gets double ionized
3. Double ionized is opaque.
4. Absorbs energy, expands cools
5. Doubly ionized becomes singly
6. Goto 1
7. Polaris 466 Ly Cepheid

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Cepheid Variables

• In 1912, Henrietta Leavitt observes Cepheids in
  the Large and small Magellenic clouds.
• These Stars are all the same distance from Earth
  more or less.
• She discovers a period-brightness relationship
• Star is like a gong

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Cepheid Variables

• How to measure the distance to a galaxy using
  Cepheid variable stars
• Find the Cepheid, measure its spectrum
• Measure a couple periods, and its apparent
  magnitude m
• Look up its absolute magnitude
• Use M m - 5 log10(d/10) to find d

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Type I Supernovae
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Type I Supernovae

• Binary system
• A sub-Chandrasekhar white dwarf
• A less dense companion star
• Gravity strips material off companion star
• Dwarf gets more and more massive
• Mass exceeds Chandrasekhar limit (1.4 Msun)
• Kablooey
• Kablooey has a certain absolute magnitude
• Kablooey is very very bright.
• Use apparent/absolute magnitude to calculate
  distance
• Finding SupernovaePeople vs. robots

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Type II Supernovae

1. A Huge star
2. Runs out of fuel.
3. Kablooey
4. Kablooey has a different magnitude each time
5. Kablooey gives off most of its energy as
   Neutrinos.
6. Neutrinos are observable for a long long way
7. Were still working on this one

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Galaxy Brightness

• Spiral galaxies
• 21 cm line width
• Doppler shift
• The wider the line, the faster the rotation
• The faster the rotation, the more mass
• The more mass, the brighter
• Working on this one too