Cosmic Dist. Ladder: Why Is it a Ladder? Radar Distances Parallax Spectroscopic Parallax Main Sequence Fitting Cepheid Variable Stars White Dwarf Supernovae Hubble’s Law 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

Main Sequence Fitting 300 ly – 1 Mly 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d2B Having multiple stars also reduces statistical errors Still limited by luminosity of main sequence stars Radar Distances Parallax Spectroscopic Parallax Main Sequence Fitting Cepheid Variable Stars White Dwarf Supernovae Hubble’s Law

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 Radar Distances Parallax Spectroscopic Parallax Main Sequence Fitting Cepheid Variable Stars White Dwarf Supernovae Hubble’s Law

Cepheid Variable Stars

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d2B 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 Q. 98: Cepheid Variable Stars Radar Distances Parallax Spectroscopic Parallax Main Sequence Fitting Cepheid Variable Stars White Dwarf Supernovae Hubble’s Law

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d2B 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 H0 = 21 km/s/Mly v = H0d Q. 99 Applying Hubble’s Law The velocity is proportional to the distance Hubble’s Law: H0 is a constant called Hubble’s Constant: In addition, smaller motions called peculiar velocities Typically 300 km/s or so How to determine distances: Measure v using Doppler shift Deduce the distance from: v = H0d H0 = 21 km/s/Mly v = H0d Q. 99 Applying Hubble’s Law

Hubble’s Law > 100 Mly 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

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

Summary of Distance Methods Radar Parallax Spec. Parallax M.S Fitting Cepheids Q. 100: Understanding the Cosmic Distance Ladder WD Super H Law AU ly kly Mly Gly