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The Cosmological Distance Ladder

The Cosmological Distance Ladder. Overlapping rungs: Earth-Mars Earth’s orbit Parallax Spectral “Parallax” RR Lyrae variables Cepheid variables Type I Supernovae Type II Supernovae Galaxy brightness. Paris. Ø. Cayenne (in French Guiana). This angle was measured simultaneously.

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The Cosmological Distance Ladder

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  1. The Cosmological Distance Ladder

  2. Overlapping rungs: • Earth-Mars • Earth’s orbit • Parallax • Spectral “Parallax” • RR Lyrae variables • Cepheid variables • Type I Supernovae • Type II Supernovae • Galaxy brightness

  3. Paris Ø Cayenne (in French Guiana) This angle was measured simultaneously Measuring Earth-Mars: In 1672:

  4. 1.5 x 108 km If you know the Earth-Mars distance, Kepler’s law RE3 =RM3 TE2 TM2 now lets you figure out the radius of Earth’s orbit. Calculating Earth’s Orbit:

  5. Parsecs - Parallax Seconds You know that Tan(Ø ) = d/D Today we have accurate parallaxes for about 10,000 stars.

  6. 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…

  7. Variable Stars: - Generally - We can determine their absolute magnitude. • RR Lyrae (cluster variables) • Cepheids: (Very Bright)

  8. Variable Stars:

  9. RR Lyrae Variables:

  10. 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 < M < 1) • Use M = m - 5 log10(d/10) to find d

  11. Cepheid Variables: • Star contracts, heats up • Singly ionized He gets double ionized • Double ionized is opaque. • Absorbs energy, expands cools • Doubly ionized becomes singly • Goto 1

  12. 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:

  13. 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

  14. Type I Supernovae:

  15. 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 Supernovae…People vs. robots

  16. Type II Supernovae: • A Huge star • Runs out of fuel. • Kablooey • Kablooey has a different magnitude each time • Kablooey gives off most of its energy as Neutrinos. • Neutrinos are observable for a long long way • We’re still working on this one…

  17. 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…

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