The Cosmic Distance Ladder Methods for Measuring Distance Radar Distances Parallax Spectroscopic Parallax Main Sequence Fitting Cepheid Variable Stars White Dwarf Supernovae Hubble’s Law Standard Candles Geometric Methods

Radar Distance Earth Venus d 2d = ct, solve for d Radar distances We know what an AU is Effectively no error 0 - few AU

Parallax View a star from two different angles The difference in angle is the parallax p The smaller p is, the farther away the star is. p p d p in arc- seconds 1AU – 300 ly Which technique can be used to tell how far it is to the nearest galaxies (besides our own)? A) ParallaxB) Radar Distances C) Both A and BD) Neither A nor B

Standard Candles A standard candle is any object that is consistently the same luminosity Like 100 W light bulbs, or G2 main sequence stars How the technique works: Figure out how luminous your standard candles are If you know distance d and brightness B, you can figure this out from: L = 4  d 2 B To find the distance to another of the same class: It should have the same luminosity L Measure its brightness B Deduce distance from: L = 4  d 2 B

Spectroscopic Parallax Has nothing to do with parallax Works only on main sequence stars How it works: Observe the star – determine it’s brightness B Measure its spectral type from spectrum Deduce its luminosity from the Hertzsprung-Russell Diagram Find its distance from: L = 4  d 2 B

Spectroscopic Parallax Limitations: The main sequence is a band, not a line Because stars are different ages Causes significant error Main sequence stars are not the most luminous stars You can’t measure it if you can’t see it Limits maximum distance 10 ly – 200 kly

Cosmic Dist. Ladder: Why is it a Ladder? Parallax requires knowledge of the Earth-Sun distance, the AU Which we get from radar distances Spectroscopic parallax requires the Hertzsprung-Russell diagram Which requires parallax Radar Distances Parallax Spectroscopic Parallax Main Sequence Fitting Cepheid Variable Stars White Dwarf Supernovae Hubble’s Law

Main Sequence Fitting Spectroscopic parallax applied to a cluster of stars How it works: Measure brightness and spectral type of stars in a cluster Deduce age from turn off point Adjust H-R diagram accordingly Deduce distance from: L = 4  d 2 B Having multiple stars also reduces statistical errors Still limited by luminosity of main sequence stars 300 ly – 1 Mly

Cepheid Variable Stars Not all stars are stable In a portion of the H-R diagram, stars pulsate The “why” is a little complicated Star a little too small Heat builds up – increased pressure Star expands – too far Heat leaks out Star shrinks How fast a star pulsates depends on its luminosity Period of pulsation tells you the luminosity

Cepheid Variable Stars

Simple relationship between period and luminosity Period tells you luminosity

Cepheid Variable Stars How it works Measure the brightness Measure the period From which we deduce the luminosity Slow pulses = more luminous Deduce distance from: L = 4  d 2 B Because these stars are so bright, you can see them at vast distances But they are rare, so you can’t use this for nearby objects 100 kly – 100 Mly Star A and Star B are equally bright, and both are Cepheid variable stars. Star A pulses once a day, and star B once a week. Which one is farther away? A) Star AB) Star B A) Equally distant B) Insufficient information

White Dwarf Supernova During each cycle the white dwarf gains mass Shrinks slightly Reaches Chandrasekhar mass Star begins to collapse Heats up Fusion begins Whole star burns - explodes Star is completely destroyed Burns mostly to iron Since they all are at 1.4 solar masses, they should always explode the same way Should make a good standard candle Reality is more complicated

White Dwarf Supernovae 20 Mly – 10 Gly How it works: Measure (peak) brightness of white dwarf supernova Compare to reference luminosity of known supernovae Deduce distance from: L = 4  d 2 B They are rare – only works occasionally They are extremely bright You can see them half way across the universe

Hubble’s Law Measure the distance to galaxies by various methods Measure their velocity by Doppler shift of spectral lines Nearby galaxies are moving towards or away from us, not very fast Distant galaxies always moving away from us The farther away they are, the faster they are moving away. The universe is expanding

Hubble’s Law The velocity is proportional to the distance Hubble’s Law: H 0 is a constant called Hubble’s Constant: In addition, smaller motions called peculiar velocities Typically 300 km/s or so How to to determine distances: Measure v using Doppler shift Deduce the distance from: v = H 0 d v = H 0 d H 0 = 21 km/s/Mly According to Hubble’s Law, how far away is a galaxy that is moving away from us at 2100 km/s? A) 1 MlyD) 484 Mly B) 10 MlyE) 4,840 Mly C) 100 MlyF) 48,400 Mly

Hubble’s Law Limitations Peculiar velocities add error Makes technique worthless below 100 Mly At sufficiently large distances, you are looking at how things were in the past, not how they are now Universe may have been expanding faster/slower Still, faster always means farther away Can be corrected if you have a sample of white dwarf supernovae > 100 Mly

Hubble’s Law Interpretation Everyone sees the same thing The Universe is expanding It all began together The big bang

Summary of Distance Methods Parallax Spec. Parallax M.S Fitting Cepheids WD Super H Law AU ly kly Mly Gly Radar