The Cosmological Distance Ladder

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

Measuring Earth - Geometry  = s/r Two wells E-W Measure s Time sun /2 = t/24 hr

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

Calculating Earth’s Orbit: 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. 1.5 x 108 km

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

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…

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

Variable Stars:

RR Lyrae Variables:

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

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 Polaris 466 Ly = Cepheid

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…

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

Type I Supernovae:

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

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…

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…