Distances
Parallax
• Near objects appear to move
more than far objects against a
distant horizon.
• Trigonometric parallax is used
to measure distance to near
stars.
d
r
r

tan  
time A
Earth’s
orbit
time B
r

d
near stars
distant stars
Parsec
• Stellar distances are inversely
proportional to the parallax
angle.
– Earth’s radius fixed
– Define distance by angle
• The parsec (pc) is the distance
that would result in one arc
second of parallax.
– 1 pc = 3.086  1016 m
– 1 pc = 2.06  105 AU
d
r


d (pc) 
1 pc 
1

1
 (arc sec)
60  60  360
AU
2
Near Stars
• The Hipparcos satellite measured parallax of 118,000 stars.
– Resolution: 0.001 arc-second and 0.2% luminosity.
• Gaia launches in 2011 to measure 109 stars in the galaxy
Arcturus 11.3 pc (ESA)
Spectroscopic Parallax
• The Hipparcos data provides
very precise distances.
– Use for absolute
magnitudes
– Precise HR diagram
• Distant stars can be fit on the
main sequence.
– Measure luminosity and
apparent magnitude
Star Clusters
• Spectroscopic parallax assumes
stars on the main sequence.
– Better to average stars at the
same distance
• Globular clusters are dense with
100,000 stars in a 20-100 pc
region with less than 0.3 pc
separating the stars.
• Open clusters tend to be smaller
and younger.
Cluster Types
Type I Clusters
– Hot young stars
– Lots of gas and dust
– Abundant in heavy
elements
• Active star formation
Type II Clusters
– Old red stars
– No gas and dust
– Few heavy elements
• No star formation, just old stars
Standard Candle
• Up to 30 pc distance is measured with parallax.
– Less certainty to 300 pc
– Longer distances by spectroscopic parallax
• The best measure of large distances are variable stars.
– Luminosity directly related to the period.
Vibrational Modes
GMm
2
 2 K  mvs
r
2R
2R
4R3
T


vs
GM
GM R
T
1
G
• Thermal motion in a star relates
the speed to potential energy.
• Radial pressure waves move at
the speed of sound.
• The period of vibration is
inversely proportional to the
square root of the density.
Cepheid Variables
• Cepheid variables are massive
relatively cool stars.
– ~ 4 to 15 M
– Color classification F to K
• The period and apparent
luminosity determine the
distance.
• Density ~ 10-3 kg/m3
• Vibrational period ~ 106 s
RR Lyrae Variables
• RR Lyrae variables are short
period white variables.
– ~ 1 M
– Color classification A
• These are type I stars.
– Found in globular clusters
– Useful for galactic distances
• Density ~ 10 kg/m3
• Vibrational period ~ 4  104 s
Variables in M3
RR Lyrae stars in
one night time
lapse
Instability Strip
• Cepheid and RR Lyrae stars fall
in a narrow band on the HR
diagram.
– Instability strip
– Not on main sequence
• As stars pass through band they
oscillate.
Band of Stars
• The sun is in a galaxy called the
Milky Way.
– Observed as a diffuse band
– Millions of stars in a
telescope
• The Milky Way is thicker in
some directions.
– Appears as a band across
the sky
Disk
• The band of the Milky Way is the same view a viewer
would have sitting inside a disk of stars.
• This disk has type I stars with gas and dust.
sun
sun
top view
side view
Halo
•
•
•
•
Astronomers measure the distance to globular clusters.
Type II globular clusters are in a sphere around one point.
This sphere is the galactic halo.
The center of the sphere is the center of the galaxy.
sun
globular
clusters
Size and Shape
• To view the galaxy from inside,
we
– measure the distance to
globular clusters
– measure distributions of
hydrogen gas in the disk.
• The Milky Way is 50,000 pc
across with a central bulge.
• The stars group in arms.
Galactic Structure
• The galactic nucleus is bright and massive.
• It is obscured by the dust of the galactic disk.
• The Milky Way is probably similar to M83.