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# The Cosmological Distance Ladder - PowerPoint PPT Presentation

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

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Presentation Transcript

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

Paris

Ø

Cayenne (in French Guiana)

This angle was measured simultaneously

Measuring Earth-Mars:

In 1672:

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:

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…

Variable Stars:

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

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:

• 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…