The Cosmic Distance Ladder Methods for Measuring Distance
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The Cosmic Distance Ladder Methods for Measuring Distance •Radar Distances Geometric Methods •Parallax •Spectroscopic Parallax •Main Sequence Fitting Standard •Cepheid Variable Stars Candles •White Dwarf Supernovae •Hubble’s Law Radar Distance 0 - few AU Earth Venus d 2d = ct, solve for d Radar distances •We know what an AU is •Effectively no error 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. d p p 1AU – 300 ly 3.26 ly d p •p in arcseconds Which technique can be used to tell how far it is to the nearest galaxies (besides our own)? A) Parallax B) Radar Distances C) Both A and B D) 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 = 4d2B •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 = 4d2B 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 = 4d2B Spectroscopic Parallax 10 ly – 200 kly 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 Cosmic Dist. Ladder: Why is it a Ladder? •Parallax requires knowledge of the Earth-Sun distance, the AU •Radar Distances •Which we get from radar •Parallax distances •Spectroscopic Parallax •Main Sequence Fitting •Spectroscopic parallax requires •Cepheid Variable Stars the Hertzsprung-Russell diagram •White Dwarf Supernovae •Which requires parallax •Hubble’s Law 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 = 4d2B •Having multiple stars also reduces statistical errors Still limited by luminosity of main sequence stars 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 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 = 4d2B 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 •Because these stars are so bright, away? A) Star A B) Star B you can see them at vast distances A) Equally distant •But they are rare, so you can’t use B) Insufficient information this for nearby objects 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 = 4d2B •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: v = H0d •H0 is a constant called Hubble’s Constant: H0 = 21 km/s/Mly •In addition, smaller motions According to Hubble’s Law, called peculiar velocities how far away is a galaxy that •Typically 300 km/s or so How to to determine distances: is moving away from us at •Measure v using Doppler shift 2100 km/s? A) 1 Mly D) 484 Mly •Deduce the distance from: B) 10 Mly E) 4,840 Mly v = H0d C) 100 Mly F) 48,400 Mly 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 WD Super AU ly kly Mly H Law Gly
