The Cosmic Distance LadderMethods 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.

pp

d

3.26 lyd

p

•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) Parallax B) Radar DistancesC) 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

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 = 4d2B•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

Cepheid Variable Stars

•Simple relationship between period and luminosity•Period tells you luminosity

Cepheid Variable StarsHow it works•Measure the brightness•Measure the period

•From which we deduce the luminosity•Slow pulses = more luminous

•Deduce distance from: L = 4d2B

•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 A B) Star BA) Equally distantB) 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 Supernovae20 Mly – 10 GlyHow it works:

•Measure (peak) brightness of white dwarf supernova •Compare to reference luminosity of known supernovae•Deduce distance from: L = 4d2B

•They are rare – onlyworks occasionally•They are extremely bright

•You can see themhalf way across theuniverse

Hubble’s Law•Measure the distance to galaxies by various methods•Measure their velocity by Doppler shift of spectral lines•Nearby galaxies are movingtowards or away from us, notvery fast•Distant galaxies alwaysmoving away from us•The farther away they are, thefaster they are moving away.

•The universe is expanding

Hubble’s Law•The velocity is proportional to the distance•Hubble’s Law:

•H0 is a constant called Hubble’s Constant: •In addition, smaller motionscalled peculiar velocities

•Typically 300 km/s or soHow to to determine distances:•Measure v using Doppler shift•Deduce the distance from:

v = H0d

v = H0d

H0 = 21 km/s/Mly

According to Hubble’s Law, how far away is a galaxy thatis moving away from us at 2100 km/s?A) 1 Mly D) 484 MlyB) 10 Mly E) 4,840 MlyC) 100 Mly F) 48,400 Mly

Hubble’s LawLimitations•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