Properties
of Stars
Mass
Size
Distance
Age
Brightness
Temperature
We can measure distance to the nearest stars using
parallax
Only for the nearest stars can that
angle be measured from Earth – out
to maybe 200 ly
From space, the parallax angle can
be measured for over 100,000 stars –
out to about 1500 ly.
The GAIA spacecraft will extend
that to up to 1 billion stars!
The relationship between
distance and parallax angle is
extremely simple:
1
d
p
Distance in parsecs
(1 parsec = 3.26 lightyears)
Angle in arcseconds
Example: Sirius, the brightest star in our sky, shows a parallax angle of 0.379
arcseconds. How far away is it?
1
d
p
Example: Sirius, the brightest star in our sky, shows a parallax angle of 0.379
arcseconds. How far away is it?
1
1
d 
 2.64 pc
p 0.379
What is that in lightyears?
Example: Sirius, the brightest star in our sky, shows a parallax angle of 0.379
arcseconds. How far away is it?
1
1
d 
 2.64 pc
p 0.379
What is that in lightyears?
ly
d (ly)  d (pc)  3.26
pc
ly
 2.64 pc  3.26
pc
 8.60 ly
If star A shows twice as much parallax as star B, then…
A) Star A is four times further away than star B
B) Star A is twice as far away as star B
C) They’re the same distance – star A just moves more
D) Star B is twice as far away as star A
E) Star B is four times further away than star A
1
d
p
Two different measures
of brightness:
Luminosity
Apparent Brightness
Apparent brightness
depends one two things:
Luminosity
Distance
luminosity
apparent brightness 
4  distance 2
This relationship is at the heart of how we
measure distance to many objects!
Which star would appear brighter to us, Fred or Barney?
Luminosity
Distance
Fred:
100 LSun
20 ly
Barney:
200 LSun
40 ly
A. Fred would appear brighter.
B. Barney would appear brighter.
C. Fred and Barney would appear equally bright to us on Earth.
luminosity
apparent brightness 
4  distance 2
We measure apparent brightness on the “magnitude scale”
Based on the system
devised by Hipparchus in
ancient Greece, where the
brightest stars were of the
“first magnitude”
(Sort of like the best seats
are “first class”)
The scale is defined so that a magnitude difference of 5 represents a difference in brightness
of a factor of 100
For example, a star of magnitude -1 is 100 times brighter than a star of magnitude 4.
We measure apparent brightness on the “magnitude scale”
Each individual step on the magnitude scale is a change in brightness of a factor of 100 1/5 ≈ 2.512
This is a logarithmic scale
brightness difference factor  2.512m2  m1 
How many times brighter is
Venus than Jupiter?
How many times brighter is
Sirius than Deneb?
Apparent magnitudes
Sun
– 26.8
Full Moon
– 12.6
Venus
–4
Jupiter
–2
Sirius
– 1.46
Rigel
0.14
Deneb
1.26
Polaris
2.1
Faintest naked eye stars
~6
Absolute magnitude:
How bright a star would appear IF it were 10 pc away
It’s the same magnitude scale, we just imagine moving the star to a standard distance.
Absolute magnitude:
How bright a star would appear IF it were 10 pc away
It’s the same magnitude scale, we just imagine moving the star to a standard distance.
Star
Distance (ly)
Sun
0.000016
Apparent
magnitude (mv)
Absolute
Magnitude (Mv)
-26.8
4.7
Sirius
8.6
-1.46
1.4
Rigel
772
0.14
-6.7
Deneb
2600
1.25
-8.38
Absolute magnitude:
How bright a star would appear IF it were 10 pc away
It’s the same magnitude scale, we just imagine moving the star to a standard distance.
Star
Distance (ly)
Sun
0.000016
Apparent
magnitude (mv)
Absolute
Magnitude (Mv)
-26.8
4.7
Sirius
8.6
-1.46
1.4
Rigel
772
0.14
-6.7
Deneb
2600
1.25
-8.38
This gives us a way to
compare stars’
luminosities directly
The mathematical connection is also going to prove very useful…
General form of the relationship:
mv  M v  5  5 logd 
(d in parsecs)
Solved for absolute visual magnitude:
M v  mv  5  5 log d 
Solved for distance:
d  10
 mv  M v  5 


5


Example: Deneb is 2600 ly away from
Earth. It’s apparent visual magnitude is
1.25. What is its absolute visual magnitude?
(d in parsecs)
Solved for absolute visual magnitude:
M v  mv  5  5 logd 
Solved for distance:
d  10
 mv  M v  5 


5


Example: Procyon has an apparent
visual magnitude of 0.34 and an
absolute visual magnitude of 2.66. How
far away from us is it?
(d in parsecs)
Solved for absolute visual magnitude:
M v  mv  5  5 log d 
Solved for distance:
d  10
 mv  M v  5 


5


The color of a star is related to its temperature
Astronomers go further…
Astronomers look at the star’s spectrum to see what is in its atmosphere
Hot stars have no molecules
Cool stars can’t excite hydrogen
Oh Be A Fine Girl/Guy Kiss Me
Only Bungling Astronomers Forget Generally Known Mnemonics
Each spectral type is further divided into numbers 0 – 9
Hottest B0 B1 B2 B3 … B8 B9 Coolest
Most
massive
Least
massive
It’s mass that determines temperature.
Actually, mass determines EVERYTHING!
Which spectral type signifies the hottest star?
A) G2
B) O2
C) B8
D) F1
E) O9
Binary stars allow us to determine the mass of the stars involved.
There are several kinds of binaries…
Visual Binaries
Both stars can be seen with a telescope
Spectroscopic Binaries
We can see Doppler shifts in the spectrum
Mizar and Alcor may be a true binary pair
Mizar is a visual binary.
Each star in the visual pair is itself a spectroscopic binary.
Recent update: Alcor has recently been discovered to have a binary partner.
Eclipsing Binaries
We can see a dip in its brightness that repeats regularly
These are both called eclipses
It takes more than just period to determine mass…
Newton’s version of
Kepler’s Third Law
Kepler’s Third Law
p 2  a3
(This is specific to the Sun)
2
4

p2 
a3
G M 1  M 2 
(This applies to any two masses)
You also need average distance between the stars (a).
That can be measured directly in a few cases, but
more often it has to be calculated from orbital velocity
(Which can be done most precisely with eclipsing binaries)
Which of these statements is true?
A) All eclipsing binaries are spectroscopic binaries
B) All spectroscopic binaries are eclipsing binaries
C) All visual binaries are spectroscopic binaries
D) All spectroscopic binaries are visual binaries
E) All visual binaries are eclipsing binaries
Astro-Cash Cab!
Connor
Alejandro
Tabitha
Jessica
1) Calculation
How far away is a star that shows 0.1 arcseconds of parallax?
(specify your units!)
2) If you moved a star to twice its current distance, it would appear…
Four times brighter
Twice as bright
The same brightness, just smaller
Half as bright
One quarter as bright
3) Which spectral classification indicates the coolest star?
M6
F2
O9
K3
G2
4) A double star in which we see the brightness dip in a regularly repeating pattern is
called a(n) ____________ binary.