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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 = 4d2B
•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d2B
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d2B
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 = 4d2B
•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 = 4d2B
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 = 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
•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