Lecture 25: The Cosmic
Distance Scale
Sections 25-1, 26-4 and Box
26-1
Key Ideas
The Distance Problem
Geometric Distances
Trigonometric
Parallaxes
Luminosity Distances
ÒStandard CandlesÓ
Spectroscopic
Parallaxes
Cepheid Variables
RR Lyrae Variables
Type I supernovae
The Distance Problem
Measuring accurate distances
remains the biggest problem in Astronomy
Distances are necessary for
estimating
Total energy
released by objects (Luminosity)
Physical sizes of
objects
Masses of objects
Distribution of
objects in space
Geometric Distances
Direct measurements of
distances using geometry
Solar System Distances:
Orbit Geometry
(Copernicus)
Radar Measurements
Stellar Distances
Method of
Trigonometric Parallax
Method of Trigonometric
Parallaxes
Parallax Limits
Ground-based parallaxes are
measured to a precision of ~0.01 arcsec
Good distances out
to 100 pc
< 1000 stars this
close
Hipparcos parallaxes have a
precision of ~0.001 arcsec (at best)
Good distances out
to 1000 pc
Measured for ~100,000
stars
INDIRECT DISTANCE
MEASUREMENTS
One of the most common ways
to measure distances without geometry is to assume that you know the luminosity
of the object you are observing. Then use the inverse square law that relates
brightness and luminosity. We will discuss guessing luminosities by the
Òstandard candleÓ (ÒbootstrapÓ) method below. Other methods of estimating are
possible, such as using theoretical models, but they are much less common.
Luminosity Distances
Indirect distance estimate
Measure the objectÕs
Apparent Brightness, B
Assume the objectÕs
Luminosity, L
Solve
for the objectÕs distance, d, by applying the Inverse Square Law of Brightness.
solving for the luminosity
distance, dL
Standard Candles
Objects whose Luminosity you
know ahead of time.
Bootstrap Method
Òpulling yourself up by your
bootstrapÓ ˆ help yourself, often through improvised means
Calibrate
the Luminosities of nearby objects for which you have a distance (ideally) from
Trigonometric Parallaxes
Identify
distant by similar objects, using a distance-independent property that they
share (color, pulsation period, spectrum)
Assume
that the distance objects have the same Luminosity as the nearby objects
Spectroscopic ÒParallaxesÓ
Distance-Independent
Property:
The observed
spectrum of the star
Physics
Spectral Type tells
you the starÕs Temperature
Luminosity
Class tells you which region of the H-R Diagram the star belongs in.
Together, give a
unique location on a calibrated H-R Diagram
Method
Build a calibrated H-R
Diagram for nearby stars with good parallax distances.
Get the Spectral Type &
Luminosity Class of the distant star from its spectrum
Locate the star on the
calibrated H-R Diagram
Read off the Luminosity and
Compute the Luminosity
Distance (dL) from the measured Apparent Brightness
NOTE: has NOTHING to do with
ÒparallaxesÓ
Spectroscopic Parallax
Limits
Distance Limit
Practical limit is a
few 100,000 pc
Works best for star
clusters
Problems
Luminosity classes
are only roughly defined
H-R diagram location
depends on composition
Faint spectra give
poor classifications
Periodic Variable Stars
Stars whose brightness varies
regularly with a characteristic, periodic patter
Distance-Independent
Property:
Period (repetition
time) of their cycle of brightness variations
Physics
Period-Luminosity
Relations exist for certain classes of periodic variable stars. On the
so-called Òinstability stripÓ
Measuring the Period gives
the Luminosity
Period-Luminosity Relationship
See Figure 25-4
Cepheid Variables
Rhythmically Pulsating
Supergiant Stars
Found in young star
clusters
Luminosities of ~103-4
Changes in
Brightness: few % to 2-3 times
Period Range: 1 day
to ~50 days
Period-Luminosity Relation
for Cepheids:
Longer Period = Higher Luminosity
P=3 days, L ~103
LSun
P=30 days, L~104
LSun
TYPICAL CEPHEID LIGHT CURVES
See Figure 21-16
Cepheid Variable
Limitations
Found only in young star
clusters
Distance Limit
30-40 Megaparsecs
(if you use the Hubble Space Telescope)
Crucial for
measuring distances to galaxies
Problems
Cepheid
parallax measurements at the edge of what is possible (need HST) Two types of
Cepheids with different P-L relations (d Cephei and
W
Virginis)
Young
star clusters often associated with gas/dust
RR Lyrae Variables
Pulsating Horizontal Branch
(=Low Mass) stars:
Luminosity of ~50 LSun
Change in
Brightness: factor of ~2-3
Period Range: Few
hours up to ~1 day
Relatives of Cepheid
Variables (also on the instability strip)
Period-Luminosity Relation
for RR Lyrae
Less strong than for
Cepheids
\
RR Lyrae Star Limitations
Found in old clusters,
Galactic bulge & halo
Distance Limit
~ 1 Megaparsec if
you use Hubble Space Telescope
Less
luminous than the Cepheids
Limited to our Galaxy,
Andromeda and other Local Group Galaxies
Problems
No RR Lyrae stars
with good Trigonometric Parallaxes
Less bright than
Cepheid stars, so useful only relatively nearby
Period-Luminosity
Relation depends on chemical composition
Type I Supernovae
Distance Limit
10 billion light
years (3 billion pc)
Disadvantages
Not quite a standard
candle
Can be confused with
novae and Type II Supernovae
Can be in galaxies
with gas and dust
Transient
The Cosmic Distance Scale
No single method will provide
distances on all cosmic scales:
Calibrate parallaxes
using the astronomical unit
Calibrate H-R
diagrams using parallaxes
Calibrate
Cepheid and RR Lyrae star distances using H-R diagrams of the clusters that
contain them.
Imprecision at each step carries
forward, making subsequent steps less precise
This is the challenge of
measuring distances.