Goal: To understand the HR
diagram
Objectives:
1)
To explore the Magnitude scale
2)
To understand the differences between Absolute vs
Apparent Magnitude
3)
To understand the Relationship between Temperature,
color, and color magnitude differences
4)
To learn how to recognize the Main sequence on an HR
diagram
5)
Red giants, Super giants, White Dwarfs, oh my!
6)
To understand how to use the HR diagram for Clusters of
stars
Magnitude scale
• magnitude scale allows us to compare
stars of vastly (a factor of a trillion)
different brightnesses on a single scale.
• Bigger numbers mean dimmer, smaller
brighter.
• Each “color” has its own scale – and all
are calibrated to Vega.
Apparent Magnitude
•
•
•
•
The most common
Observed
The brightness as viewed from Earth
The apparent Magnitude of our sun from
Earth is -26
• The brightest star in the sky Sirius is about
a -1
• The dimmest star you can see in country
with naked eye is about a 7 or 8.
Absolute Magnitude
•
•
•
•
Mv
Based on Absolute brightness
That is the actual power of the object.
Mv is what the star would appear to be if it
was a distance of 10 Parsec away.
• The Absolute Magnitude of our sun is
about +5
Magnitudes of a different color
• What happens if you compare magnitudes
of different colors?
• You get the temperature of the object!
• You also get the COLOR of the object.
• How?
Brightness via the black body
• (draw Blackbody spectrum on board).
• At different temperatures, the blackbody
spectrum peaks out at a different part of
the spectrum.
• Hot stars peak in the blue – so they
appear to be blue.
• Moderate stars peak in the middle, so
appear to be yellow to white.
• Cooler stars peak in the red, so appear to
be orange to red.
Color vs. color
• What happens if I were to compare the
magnitudes of two different colors?
Suppose I took the Blue color magnitude
(B) and subtracted the brightness
magnitude in the middle of the visual
spectrum (V).
• For a hot star, will this value (B-V) be
value be positive or negative?
B-V vs. color
• For a hot star, this value is NEGATIVE!
• Reason, brighter means LOWER
magnitude.
• The object is blue, so the B will be lower
than the V.
• Will B-V increase or decrease as the
temperature of a star decreases?
B-V vs. temperature
• As the temperature drops, the B value
drops.
• Meanwhile the V value does not change
much.
• Therefore B-V increases as temperatures
drop.
• In fact, a B-V value is the indicator of a
specific temperature of star!
Color vs. temperature
• Since the color of a star depends on
temperature, it turns out that Color,
temperature, and B-V are ALL connected!
• But wait, there’s MORE!
Main sequence stars
• Ask you this again…
• Over the course of its lifetime, how much
do the color and brightness of a main
sequence star change?
• A) not much (maybe by 0.3 magnitudes)
• B) moderate amount (0.5-1 magnitude)
• C) considerable amount (2-3 magnitudes)
• D) they go all over the place (> 4
magnitudes)
What determines the absolute
brightness (and therefore
temperature) of a main sequence
star?
•
•
•
•
A) its age
B) its distance from us
C) its mass
D) its spin rate
Therefore:
• Any position on the Main Sequence has a
one to one relationship with the mass,
brightness, and color of the star.
• So, you can plot the Main Sequence as a
line on a chart which compares the
brightness to the color/temperature/color
magnitude difference of ANY star!
HR Diagram
• HR Diagram is a log-log plot.
• It plots brightness (either absolute or
apparent) vs. color or temperature or B-V.
http://outreach
.atnf.csiro.au/e
ducation/senio
r/astrophysics/
stellarevolutio
n_hrintro.html
Clusters of stars
• Stars form in clusters.
• If we plotted all the stars from a single
cluster what might we get?
• First we should ask 2 questions:
• 1) How do the distances from us compare
to all the stars in the cluster (close to
same, or not close)?
• 2) How do the ages of the stars in the
cluster compare?
http://www.sh
ef.ac.uk/physi
cs/teaching/p
hy103/hrclust
er.html
•
•
•
•
This is a VERY
young cluster!
All the stars are
main sequence
stars.
As the cluster
ages, the biggest
stars peel off
(like peeling
layers of an
onion) and die.
So, this chart
evolves with
time.
AGE!
• If you know the
age of the stars
that are
starting to die,
you know the
age of the
cluster!
• This point I
called the “turn
off point”.
• This cluster
does not have
a turn off point,
which is very
rare.
Distance
• You can also
find the
distance to this
cluster.
• First, lets figure
out what our
sun would look
like if it were in
this cluster.
• From the earth
the B-V of the
sun is 0.68.
• Will that
change with
distance?
Distance
• B changes,
and V change.
• With distance
each get bigger
(bigger =
dimmer).
• However, they
change by the
same amount,
so B-V is a
CONSTANT!
• Therefore, we
just need to
compare V to
the absolute
magnitude of a
star to find the
distance!
Distance
• If the sun
was in this
cluster, what
would it’s V
value be?
• B-V from
Earth is
0.68.
Distance from magnitude shift
• A shift in magnitude gives us a factor.
• The square root of this factor gives us the factor
in distance (since light spreads out over the
radius squared).
• Since magnitudes are logarithmic, the equation
is an exponential.
• To do this, find the V of the sun in the cluster.
• The absolute magnitude of the sun is +5.0.
• Find the difference between the two and call this
X (so X = V of sun if in cluster – 5.0)
• Distance = 10 parsecs * 10X/5
For Pleiades
• Vsun would
be about 10.
• So X = 10-5
• X=5
D = 10 pc * 10(X/5)
D = 10 pc * 10(5/5)
• D = 100 parsec
Conclusion
• On the main sequence you have a 1 to 1
relationship between color and mass.
• Color = B-V = temperature
• Since the top left stars on the main sequence die
first the top left is always peeling off of the main
sequence.
• The position where there is turn off tells you the
age of the cluster
• The comparison of absolute to apparent
magnitudes tells you the distance to the cluster.