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The Nature of Stars
Distance and Magnitude
Black body Curves & Color
HR Diagrams
Choose Something Like a Star
O Star (the fairest one in sight),
We grant your loftiness the right
To some obscurity of cloud-It will not do to say of night,
Since dark is what brings out your light.
Some mystery becomes the proud.
But to be wholly taciturn
In your reserve is not allowed.
Say something to us we can learn
By heart and when alone repeat.
Say something! And it says, 'I burn.'
But say with what degree of heat.
Talk Fahrenheit, talk Centigrade.
Use language we can comprehend.
Tell us what elements you blend.
It gives us strangely little aid,
But does tell something in the end.
And steadfast as Keats' Eremite,
Not even stooping from its sphere,
It asks a little of us here.
It asks of us a certain height,
So when at times the mob is swayed
To carry praise or blame too far,
We may choose something like a star
To stay our minds on and be staid.
~Robert Frost
Distances
• Nothing can prepare people for the
distances to the stars.
• The nearest star (Alpha Centauri) is 40
trillion kilometers away.
– The fastest spacecraft ever built would take
800,000 years to reach it.
– Space in the solar neighborhood is
99.99999999999999999% empty
How Does One Measure Distance?
• The foundation of all distance measurements
is a simple geometric method called
Parallax or Stellar Parallax
tan(0.5q) = 0.5r/d
q
0.5q = 0.5r/d
q = r/d
.5q
d = r/q
d
.5r
1
r
2
Stellar Parallax
• Earth is on the
opposite side of the
sun every 6 months.
• Close stars appear to
shift because of this.
– The amount of shifting
is inversely
proportional to
distance
Proper Motion
• Stars have their own drift motions through space called
proper motions.
• Most stars are so distant we cannot measure this drift. But
the ones close enough for a parallax measure are also close
enough to detect proper motion!
• We must observe them for several years to first measure
proper motion before getting a parallax.
Inverse Square Law
• To measure to greater distances, we use
more indirect methods which are
calibrated by stellar parallax.
• All other methods, except cosmological
redshift, use the 1/r2 dimming of light.
– We measure apparent brightness or
magnitude and compare it with absolute
brightness or magnitude.
• We can get absolute brightnesses from
HR diagrams. These are a fundamental
tool that will reappear throughout the
semester. It is critical that you
understand how they work!
HR
Diagram
It is stellar
magnitude
plotted against
spectral type.
So what,
exactly, is a
magnitude?
What exactly
is a spectral
type?
Apparent Magnitude
• The measure of how bright a star appears in the nighttime sky.
• Symbolized by m or m.
• This is the system given to us by Hipparchus
–
–
–
–
The brightest stars are 1st magnitude.
The faintest stars visible to the naked eye are 6th magnitude.
1st to 6th magnitude is a factor of 100 times in brightness.
It is a logarithmic scale just like the response of the human eye.
m = -2.5log(brightness)
– Each step in magnitude is 2.512 times brighter.
Examples
• When carefully calibrated, a few stars ended
up being brighter than 1st magnitude.
–
–
–
–
–
–
–
Sirius A
Canopus
Arcturus
Alpha Centauri
Vega
Capella
Rigel
-1.44 (brightest in the sky)
-0.62
-0.05
-0.01
+0.03
+0.08
+0.18
Other Objects
•
•
•
•
•
Sun = -26.7
Full Moon = -12.6
Eye Limit = +6.0
Pluto = +14.0
Faintest object
seen with Keck
10m telescope =
+30.0
What Affects Apparent Magnitude?
1) How bright it really is
2) Its distance
– Examples
•
•
•
•
Sirius A
Canopus
Alpha Centauri
Rigel
m
Distance
-1.44
-0.62
-0.05
+0.18
8.61 ly
313 ly
4.4 ly
773 ly
– If we can measure the apparent magnitude of a
star and somehow discover what its real
brightness is, we can infer its distance!
Absolute Magnitude
• The measure of how bright a star really is.
• Symbolized by M or M.
• We define absolute magnitude as being the
brightness an object would have if it were placed 10
parsecs away.
• Some examples are:
–
–
–
–
–
–
The Faintest Stars = +20.0
The Sun = +4.8
The Brightest stars = -9.0
Exploding stars = -16.0
Average galaxies = -20.0
Giant galaxies = -23.0
Colors
• A Color Index is the difference between two
magnitudes taken in two different filters
– Examples: (B-V), (U-B), (b-y)
• Color measures the shape of the blackbody curve.
– This gives us the star’s temperature! That is the main goal!
– The more negative the index, the bluer the light.
– The bluer the light, the hotter the object.
Star Colors
Spectroscopy
• But if we want the blackbody curve, would it
be better to just measure the entire spectrum?
– A good idea! But it takes a lot of telescope time.
• Photometry is the study of magnitudes and is
best for studies of lots of objects at once.
• Spectroscopy is the detailed study of the entire
spectrum and is best for Doppler shifts,
chemical analysis, and exploring weirdos.
Temperature Sequence
• No. All stars have essentially the same amount
of hydrogen. Temperature greatly affects the
strength of spectral lines.
• In time the spectral sequence was rearranged
according to other line strengths and redundant
types were eliminated to end up with a
temperature sequence going hot to cool as:
– “OBAFGKM” (LT)
– ‘Oh Be a Fine Girl, Kiss Me’
HR Diagrams (finally!)
• Using the earliest distance determinations from
parallax, in 1911 Ejnar Hertzsprung (Danish)
plotted the absolute magnitude of stars versus a
color index for each star.
• In 1913 Henry Norris Russell (U.S.) plotted the
absolute magnitude versus the spectral type.
• The results were the same, the HertzsprungRussell diagram.
Nearby
Stars
• Notice how
the stars do
NOT distribute
randomly.
• We can infer a
great deal from
where they are
located.
Diameters
• If a star is
intrinsically
bright but cool, it
must be large.
• If it is
intrinsically faint
but hot, it must
be small.
• Most of the stars
are on the main
sequence: a line
from the upper
left to the lower
right on the
diagram.
• Red Giants and
Supergiants are in
the upper right.
Blue Giants to the
upper left.
• White Dwarfs are
in the lower left.
Masses
• Mass increases from
lower right to upper
left along the main
sequence.
• Found from binary
star systems.
M1+M2 = a3/P2
Luminosity Class
• In the 1930’s Morgan and Keenan developed a
system to help define the regions within the HR
diagram.
• The system was based on subtle differences in
the spectral features caused by different surface
gravity strength.
– Giants have lower surface gravity
– Dwarfs have higher surface gravity
Luminosity
Classes
• Ia - Luminous
Supergiants
• Ib - less Luminous
Supergiants
• II - Bright Giants
• III - Giants
• IV - Subgiants
• V - Main Sequence
or Dwarfs
• VI - Subdwarfs
By carefully examining a star’s spectral lines,
astronomers can determine whether that star is a mainsequence star, giant, supergiant, or white dwarf
The Sun
• The Sun is a G2 V star
• Any star which is a G2 V will …
–
–
–
–
have the same absolute magnitude as the Sun
have a surface temperature of about 5800º K
have the same radius as the Sun
have the same mass as the Sun.
• By the same token, all stars of the same spectral
type and class will have the same absolute
magnitude, surface temperature, radius and mass.
Back to Distance
• Suppose we take the spectrum of a star and
find it is a K5 II. We then know it
– is a red giant with a surface temperature of 4000º K
– has a luminosity about 1100x that of the Sun or an
absolute magnitude of about -2.0
• We then can measure the apparent magnitude
and find the distance.
– This is called “spectroscopic parallax” (although
perhaps spectroscopic distance would have been a
better name).