Stars
… how I wonder what you are.
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Goals
• Stars are Suns.
• Are they:
–
–
–
–
–
Near? Far?
Brighter? Dimmer?
Hotter? Cooler?
Heavier? Lighter?
Larger? Smaller?
• What categories can we place them in?
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Angular Size
• Linear size = how big something really is
– Meters, inches, light years, feet
• Angular size = how big something looks
– Degrees, arcminutes, arcseconds, milliarcseconds
Circle = 360 degrees
1 degree = 60 arcmin
1 arcmin = 60 arcsec
1 arcsec = 1000 mas
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Distance
• One proof of a heliocentric
Universe is stellar parallax.
– Tycho Brahe saw no parallax.
– Copernicus: stars too far away.
• Nearest star: Proxima Centauri
Parallax angle = 0.76 arcsec
– Tycho’s precision = 1 arcmin
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The Parsec
• What is the distance of an
object with a parallax angle
of 1 arcsec?
Distance = 206,265 AU
• This distance is 1 parsec (pc)
1 pc = 206,265 AU = 3.3 ly
• 1 lightyear = distance light
travels in one year.
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Concept Test
• If Star A has a parallax of 2 arcseconds, and
Star B has a parallax of 0.25 arcseconds:
a. Star A is closer to us than Star B. Both are farther
from us than 1 pc.
b. Star A is closer to us than Star B. Both are closer
to us than 1 pc.
c. Star A is closer to us than 1 pc. Star B is farther
than 1 pc.
d. Star B is closer to us than 1 pc. Star A is farther
than 1 pc.
e. Star B is closer to us than Star A. Both are farther
away than 1 pc.
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Distances
1
Distance (in parsecs) 
parallax (in arcsec)
• Closest star: Proxima Centauri
parallax = 0.76 arcsec
Distance = 1.3 pc or 4.3 lightyears
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Terms
• Brightness = How
intense is the light I
see from where I
am.
– Magnitude is
numerical term for
this.
• Luminosity = how
much light is the
thing really giving
off.
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Magnitude
Scale
• The SMALLER the
number the BRIGHTER
the star!
– Every difference of 1
magnitude = 2.5x brighter
or dimmer.
– Difference of 2
magnitudes = 2.5x2.5 =
6.3x brighter or dimmer
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Magnitude vs. Brightness
Mag.
Difference
1
Factors of 2.5
2.51 = 2.5
Brightness
Diff.
2.5
2
2.52 = 2.5 X 2.5
6.3
3
2.53 = 2.5 X 2.5 X 2.5
16
4
2.54 = 2.5 X 2.5 X 2.5 X 2.5
40
5
2.55 = 2.5 X 2.5 X 2.5 X 2.5 X 2.5
100
6
2.56 = 2.5 X 2.5 X 2.5 X 2.5 X 2.5 X 2.5
250
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Star light, star
bright
• Sirius is magnitude -1.5
Polaris is magnitude 2.5
• Is Sirius really more
luminous than Polaris?
• No, Sirius is just closer.
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Apparent and Absolute
• Apparent Magnitude = brightness (magnitude)
of a star as seen from Earth.  m
– Depends on star’s total energy radiated
(Luminosity) and distance
• Absolute Magnitude = brightness (magnitude)
of a star as seen from a distance of 10 pc.  M
– Only depends on a star’s luminosity
 distance
m  M  5log 10 
 10pc



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Concept Test
• Polaris has a an apparent magnitude of 2.5.
It’s absolute magnitude is 3.1. Polaris is:
a.
b.
c.
d.
e.
Closer to us than 10pc.
Farther from us than 10 pc.
Exactly 10 pc away.
Can’t know without the parallax angle.
None of these is correct.
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Concept Test
• Polaris has a parallax angle of 0.01 arcsconds.
Polaris is therefore:
a. Closer to us than 1pc.
b. Farther from us than 1pc.
c. Exactly 1pc away.
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Concept Test
• Polaris has a parallax angle of 0.01 arcsconds.
Polaris is therefore:
a.
b.
c.
d.
e.
1pc.
10pc.
100pc.
1000pc.
None of the above.
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example
 distance
m  M  5log 10 
 10pc



• Our Sun:
– m = -26.8,
– distance = 4.8 x 10-6 pc
So: M = 4.8
• Polaris:
– m = 2.5,
– distance = ~100 pc
So: M = -3.1
• Polaris is 1500 times more luminous than the
Sun!
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Concept Test
•
Star
Distance
m
A
5 pc
1.0
B
10 pc
2.5
C
20 pc
-1.0
M
The most likely absolute magnitudes (M) for each is:
a.
b.
c.
d.
e.
A = 2.5, B = -2.5, C = 2.5
A = 2.5, B = 2.5, C = -2.5
A = -2.5, B = 2.5, C = 2.5
A = 2.5, B = 2.5, C = 2.5
None of the above.
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A Spectrum
Emission lines
Continuum
Absorption lines
• A spectrum = the amount of light given off by
an object at a range of wavelengths.
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Three Reasons
All objects do one or more:
1. Reflect light because of color or smoothness (same
as scatter)
2. Emit light because of their temperature
(thermal radiation)
3.
Emit or absorb light because of their composition
(spectral lines)
A person, house, or the Moon: reflects visible light, and
because each is warm, emits infrared light.
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Temperature and
Light
• Warm objects emit light.
– Thermal radiation
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Stellar Temperatures
Hot
Stellar Spectra
How hot are stars?
• Thermal
radiation and
temperature.
• Different stars
have different
colors, different
stars are
temperatures.
• Different temp,
different trace
compositions
Cool
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Spectral
Classification
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Stellar Masses
How massive are stars?
• Kepler’s Laws – devised for the planets.
• Apply to any object that orbits another object.
• Kepler’s Third Law relates:
– Period: “how long it takes to orbit something”
– Semimajor axis: “how far you are away from that
something”
– Mass: “how much gravity is pulling you around in orbit”
3
a
P 
M
2
• Where M is the Total Mass.
• Can calculate the mass of stars this way.
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Binary Stars
• Most stars in the sky
are in multiple
systems.
• Binaries, triplets,
quadruplets, etc….
– Sirius
– Alcor and Mizar
– Tatooine
• The Sun is in the
minority by being
single.
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NPOI Observations of Mizar A
(1 Ursa Majoris)
0.005 arcsec
Orbital Phase: 000o
Mizar, 88 light years distant, is the middle star in the handle of
the Big Dipper. It was the first binary star system to be imaged
with a telescope. Spectroscopic observations show periodic
Doppler shifts in the spectra of Mizar A and B, indicating that they
are each binary stars. But they were too close to be directly
imaged - until 2 May 1996, when the NPOI produced the first
image of Mizar A. That image was the highest angular resolution
image ever made in optical astronomy. Since then, the NPOI has
observed Mizar A in 23 different positions over half the binary
orbit. These images have been combined here to make a movie
of the orbit. As a reference point, one component has been fixed
at the map center; in reality, the two stars are of comparable size
and revolve about a common central position.
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Stellar Masses
How massive are stars?
3
a
P 
M
2
• Most stars have masses calculated this way.
• Find:
– The more massive the star, the more luminous it is.
– The more massive the star, the hotter it is.
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Stellar Radii
How big are stars?
• We see stars have different
luminosities and different
temperatures.
• Stars have different sizes.
• If you know:
50 mas
– Distance
– Angular size
• Learn real size.
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Betelgeuse
• Angular size = 50 mas
• Parallax = 7.6 mas = 0.0076 arcsec
• Apparent mag = 0.6
• Distance = 1/parallax = 132 pc
• True size = distance * angular size = 1400 Rsol
– Model solar system: 97 yards in radius.
• Absolute Mag = m – 5log(d/10pc) = -5
– Our sun M ~5, Betelgeuse = 10,000x luminosity
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Angular versus Linear
Supergiants, Giants and Dwarfs
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H-R Diagram
• Can order the stars by:
– Temperature (or spectral type)
– Luminosity (or absolute magnitude).
• And see where other qualities fall:
– Mass
– Radius
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Luminosity Class
• The roman
numerals.
• Stars at same temp
can have different
luminosities.
• Corresponds to
different classes:
MS, giant,
supergiant.
I
V
III
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Concept Test
Which star is:
1. Hottest?
2. Coolest?
3. Faintest as seen
from Earth?
4. Most luminous?
Of Main Seq. Stars?
1. Most massive?
2. Most like the
Sun?
Star
Spec
Type
m
M
A
F0 V
0.0
0.0
B
G2 V
10.0
4.4
C
K5 III
0.0
-2.0
D
F7 I
-1.0
-5.0
E
K3 V
5.0
6.5
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The Main Sequence
• Stars characterized by
what holds them up.
• 90% held up by heat of
Hydrogen fusion?
4H  He + Energy
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