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Measuring the Properties of
Stars
Warm Up
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Where are bright, cool stars located on the HR Diagram?
Where are bright, hot stars located on the H-R
Diagram?
Where are dim, cool stars located on the H-R
Diagram?
Where are dim, hot stars located on the H-R
Diagram?
What is the H-R Diagram?
What is the H-R Diagram used for?
What are the seven spectral classes of stars?
What is luminosity?
Warm Up
1.
2.
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4.
5.
What is parallax?
What is an arc second?
What is a parsec?
How long is a parsec?
One degree of arc equals the thickness
on a penny on its side from how far
away?
Warm Up-11/04/12
1.
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The angular shift from January to June of the
star Rigel is 0.25 arc seconds. How far away is
Rigel in parsecs? How far away is Rigel in light
years?
The angular shift from January to June of the
star Alhambra is 0.345 arc seconds. How far
away is Alhambra l in parsecs? How far away is
Alhambra in light years?
What is a standard candle?
Comet ISON Site
http://blogs.discovermagazine.com/outthere/
2013/10/25/novice-observers-guidecomet-ison/
Warm Up
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Name two ways to determine the distance to a
star.
Wein’s Law equates temperature with what?
What is luminosity?
What is apparent brightness?
What is magnitude?
List the 7 spectral classes and tell which
direction stars are getting hotter?
Wondering as You Look at the Stars
It’s impossible not to wonder as you look at
the stars. What would that star look like if
you were close to it? How hot is that star?
What is that star made of?
Yet, scientists have developed ways to answer
many of these questions. Kepler gives us
star’s masses, Wein’s Law gives us their
temperature and Newton gives us spectra
which is their chemical composition.
How far away is that star?
But, one of the most fundamental questions about a
star is…how far away is that star?
Measuring Distance
Astronomers have several methods for
estimating a stars distance.
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Parallax
Triangulation
Method on standard candles
Triangulation
Using simple geometry, the distance of
stars can be determined given that you
know the
Parallax
Parallax is the change in an object apparent
position caused by a change in the observers
position.
Parallax
The shift in stars closer to us is greater
than for those far away. Regardless, the
amount of shift is very small. Because
of this, these shifts are measured in arc
seconds which 1/3600th of a degree.
Parallax
By definition:
Dpc = 1/parc seconds
Where:
D = distance in parsecs
P = measure of angular shift in
arc seconds
One parsec equals 3.26 light-years or 3.09
X 1013 kilometers
Parallax
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A shift of one degree of arc is what you’d
see of a penny’s edge from 4 kilometers
(2.5 miles)
How Far is Sirius?
Using the formula:
R
=
p
where R = 1 AU
2pd
360
p = in arc seconds
P for Sirius is 0.377 arc seconds, so….
How Far is Sirius?
d = 360 / 2pp
yields d = 360 AU/2p(.377) =
Express p in arc seconds and d in parsecs
and both cancel, leaving
d = 1/p, therefore Sirius is 1/.377 or 2.65
parsecs away. Multiply times 3.26 to
convert into light-years. The answer is
8.6 light-years away.
Method of Standard Candles
Imagine having two 100-watt light bulbs
in front of you. One is close and one is
far away. You can learn to tell about
how far away the distant light is.
Indeed, driving at night, you use this to
tell how far another car or a traffic light
is away.
Standard Candle
 Astronomers
use the concept of the
standard candle to estimate distance.
They assign a given luminosity (or
brightness) as a reference. This
reference is called a “standard
candle”.
Measuring Properties of Stars
from Their Light: Temperature
The temperature of a star is often
indicated by its color. Just like you look
are a stove eye to determine how hot it
is.
Measuring Properties of Stars
from Their Light: Temperature
Wein’s Law states that:
T = 3 x 106/lm where T = temperature and
lm is the frequency the star radiates at
most strongly (in nanometers).
Measuring Properties of Stars
from Their Light: Temperature
So, how hot is Sirius?
T = 3 x 106 / lm
Given that Sirius
radiates most strongly
at 300 nanometers (lm)
T = 3 x 106 / 300 nm, therefore
T = 10,000 K
Measuring Properties of Stars
from Their Light: Luminosity
Luminosity is the amount of energy a
star radiates each second. Our Sun has
a luminosity of about 4 X 1026 watts.
This a star’s luminosity is an indicator
of how quickly it is consuming fuel.
Astronomers use stars luminosity to
determine their distance and radius.
The Inverse Square Law and a Star’s
Luminosity
The inverse square law relates an
object’s luminosity to its distance and
apparent brightness. Like a shotgun
pattern, the farther away from an object
the fewer number of photons hit in a
particular area.
The Inverse Square Law and a Star’s
Luminosity
Astronomers have determined that the
relationship between brightness and
distance is an inverse square law:
B = L / 4pd2
where B is the apparent
brightness, L is luminosity
and d is the object’s distance.
Measuring Properties of Stars
from Their Light: Radius
If two stars have the same temperature,
but one is more luminous than the other,
then the brighter star must have a
larger radius.
The Stephen-Boltzmann Law
The Stephen-Boltzmann Law states that a
star’s luminosity equals its surface area times
sT4:
L = 4pR2sT4
where L=luminosity, R =
radius and sT4 is the
relationship between temperature and surface
area. You increase the temperature or radius
and you increase the star’s luminosity.
s = 5.6686 x 10- 6 (Watts/meters2Kelvins4).
The Stephen-Boltzmann Law
So, what is the radius of Sirius?
LSun =
4pRs2sTs4 where R and T are
LSirius
4pRSr2sTSr4
the Sun and Sirius
values respectively.
Solved for RSirius (25/1)1/2/(6,000k/10,000k)2
RSirius = 5(0.6)2
RSirius = 1.8 Solar radii
Page 359 text
What is a Parsec Anyway?
By definition, one arc second spans 1 AU
at the distance of one parsec.
Aah, but I digress…
So, back to Hipparcus. He wants to
classify stars. The characteristic he
decides to use is apparent brightness (or
how bright a star looks to you and me).
It’s All About Magnitude
Hipparcus calls this apparent (or how
bright a star appears) brightness,
magnitude. It is, with a few changes,
the same classification system used
today.
Magnitude
The system does have some problems.
First, it’s backwards, meaning that the
more positive the number, the fainter
the star. So, bright stars are like -1 or -2
and really dim stars are magnitude 10.
Our Sun is something whacked like -27
(I think).
Magnitude
Hipparcus didn’t start out with negative
numbers on his scale. He did, however,
seriously misjudge how bright the
brightest stars actually are. This
pushed the scale negative or brighter.
Magnitude
Here’s the part you’re going to hate.
Magnitude differences correspond to
brightness ratios. Now, this whole
system is based on the first magnitude
1. This is half a ratio. The other half of
the ratio is 2.512 (or the fifth root of
100).
Magnitude
Now naturally your first thought is, hell,
why didn’t I think of that. The idea is
that a magnitude 1 star is 100 times
brighter than a magnitude 6 star, so the
5th root of 100, see?
Magnitude
So, a magnitude 1 star’s ratio is:
2.5121 = 2.512 : 1
A magnitude 2 star’s is 2.5122 = 6.31 : 1
A magnitude 3 star’s ratio is 2.5123 = 15.85:1
A magnitude 4 star’s ratio is 2.5124 = 39.8:1
Yada, yada, yada…
Absolute Magnitude
Still, given all this, we’re still comparing
apples to oranges. The magnitude of a
star is related to its distance away from
us. Astronomers needed a better system
to level the playing field where stars
could be compared directly.
Absolute Magnitude
A new scale was invented that places
stars at a standard distance from us.
That distance is 10 parsecs (pc).
Absolute magnitude is a true measure of
a star’s luminosity.
The Dumbing it Down Slide
or it Gets Way Too Boring!
Now, very quickly. Stars give off light that
can be divided into spectra. The spectra
indicate a star’s temperature. People have
studied these spectra since the early 1800’s.
One man, Henry Draper (1870’s) studied the
classification of spectra. He died and his wife
gave a fortune to Harvard to compile a book of
these spectra called the Henry Draper catalog.
Remember the HD catalog numbers from the
constellations. This is a way to reference the
spectra of stars in a constellation. Cool, eh?
Oh Boy, A Fine Girl Kissed Me!
Star’s fit into one of seven distinct
spectral classes. Spectral classes convey
information on a star’s composition and
temperature. The seven spectral classes
are: O, B, A, F, G, K and M. From O to
M temperatures decline.
Spectral Classes
Other mnemonics include: Only Brilliant
Artistic Females Generate Killer
Mnemonics and my personal favorite:
Oh Big And Furry Gorilla, Kill My
Roommate. Four other very rare
spectral classes exist called R, N, S and
W. Can you include them in a
mnemonic?
Summary of Stellar Properties
Quantity
Distance
Temperature
Luminosity
Composition
Radius
Mass
Radial Velocity
Method
Parallax (up to about
250 parsecs
Wien’s Law
Spectral class (O- M)
B = L / 4pd2
Spectral lines
Stephen-Boltzmann law
Interferometer
Eclipsing binaries
Kepler’s third law
Doppler shift of spectral lines
Warm Up
1.
2.
3.
4.
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6.
7.
8.
Define a parsec.
Who had the idea for apparent brightness?
What is another name for apparent
brightness?
Which is brighter, a magnitude 1 star or a
magnitude 6 star.
How much brighter is a magnitude 3 star than
a magnitude 1 star.
What number is the base for the magnitude
system? (Hint for number 5)
What is absolute magnitude?
What are the 7 stellar classifications. What do
they mean?
The Hertzsprung-Russell
Diagram
While scientists could calculate the
mass, temperature, radius, luminosity
and other characteristics of stars, they
still understood practically nothing
about how they worked. This changed
in 1912 with the work of Ejnar
Herstzsprung and Henry Norris Russell.
The H-R Diagram
In a nearly simultaneous discovery, both
men found that if you plotted stars’
luminosities against their temperatures
(or spectral classes) that the vast
majority lay on a single line.
The H-R Diagram
Traditionally, on the H-R diagram, brighter stars
appear at the top and hotter stars appear on the left
axes.
The H-R Diagram
This line that most (90%) stars fall on is called
the “main sequence”. A minority of stars
appear in the upper right-hand and lower lefthand corners.
Looking at the H-R diagram brings several
questions to mind. How can stars of different
temperature have the same magnitude?
Conversely, how can stars with the same
temperatures have different magnitudes?
The answer lies in the Stephan-Boltzmann
law.
Analyzing The H-R Diagram
When you look at the H-R diagram and see for one
temperature that luminosities can range from 10-3 to
106, you get some idea of the great variety is the sizes
of stars.
The Stephen-Boltzmann Law
Stephen-Boltzmann (L = 4pR2sT4) relates
luminosity with a star’s temperature and
radius. So, if two stars, A and B, have the
same luminosity , but the temperature of star
A is higher, then the radius of star B must be
greater. Conversely, if stars A and B have the
same luminosity but star A is larger than star
B, then star B must have a higher
temperature. It’s all about total luminous
output.
Analyzing The H-R Diagram
To produce the same luminosity as very hot, smaller
stars, cooler star must be 1000’s of times larger.
These stars are termed “giants” and appear at the top
of the H-R diagram.
Analyzing The H-R Diagram
A similar look at the H-R diagram shows that some
stars that lie below the main sequence are very hot,
but have very small luminosities. These stars by
contrast must be very small. They are called “dwarf”
stars.
Other Differences in Stars
Giants, main sequence stars and dwarfs differ
in more ways than just temperature and
luminosity. They also differ greatly in
density. For a given mass, a larger body must
have a lower density, so giants have densities
millions of times less than main sequence
stars. Smaller stars must therefore have
much greater densities than main sequence
stars.
Other Relationships Revealed by the
H-R Diagram
The H-R diagram reveals relationships
between stars other than just
temperature and luminosity. It also
reveals the stars’ radii and masses as
well.
The Luminosity-Radius Relation
I relationship can be inferred by the H-R
diagram between the luminosity of a star and
its radius. The greater the star’s luminosity
the greater the star’s radius,
The Luminosity-Radius Relation
The Mass-Luminosity Relationship
Luminosity vs. mass is plotted for the Sun and all Main Sequence stars
that have good mass measurements shows that a Main Sequence star's
luminosity is very strongly correlated with its mass:
The masses are
written in terms
of solar masses.
The relationship
is defined as:
L = M3, where
L= luminosity in
solar units and
M= solar masses.
Summary of the H-R Diagram
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It offers a simple, pictorial summary of stellar
properties.
Most stars lie on the main sequence with the hotter
stars being more luminous.
Blue stars are hottest while red stars are the coolest
A star’s mass determines its location along the main
sequence with more massive stars located at the top.
Stars masses range from about 30 solar masses to
about 0.1 solar masses.
It shows that stars fall within three main regions of
the diagram: main sequence, giants and white
dwarves.
Variable Stars
Not all stars have constant luminosity. Some
stars, called variable stars, change brightness
over time. The time between the intervals of
maximum brightness is called the star’s
period. The graph of the star’s brightening
and darkening cycle is called its light curve.
The Instability Strip
Variable stars cluster together in the H-R
diagram in a region known as the instability
strip.
Analyzing The H-R Diagram
The H-R diagram shows the evolution of
stars. In the next section, we will
explore how and why stars evolve.