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## Stars

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### Stars Comparison of ground-based observation of the globular cluster M4 with an HST image showing white dwarfs. (Produced with the Wide-Field Planetary Camera 2 ... – PowerPoint PPT presentation

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Title: Stars

1
Stars
Comparison of ground-based observation of the
globular cluster M4 with an HST image showing
white dwarfs. (Produced with the Wide-Field
Planetary Camera 2, Hubble Space Telescope.)
2
Stars
• The stars in the sky appear to be objects much
like the sun although much, much further away.
Can we get some kind of idea of how far away?
• In the lab we will do an experiment demonstrating
the parallax method for determining distances.
This method actually works for the nearer
stars.

3
Parallax
• The basic idea behind parallax is trig using
known distances and angles to get unknown
distances

Line of sight to background stars very, very far
away
2 AUs
Change in angle of star from 6 months previous
Line of sight to background stars very, very far
away
4
Parallax
• We actually have a unit of distance defined by
the parallax method. It is called a parsec. A
parsec is the distance a star is away if it has a
change of angle of 1 arc second (which is 1/60th
of an arc minute, which is 1/60th of a degree).
A parsec can be converted into AUs and another
common unit of distance, the light year 1
parsec 3.26 lt. yrs 200,000 AUs.

5
Parallax
• The nearest star has a parallax angle of about ¾
of a second of arc, and so is about 4/3 1.3
266,000 AUs away). Recall that Pluto was about
40 AUs away, and the Oort Cloud is thought to be
• We can effectively measure distances this way for
about several thousand stars that are within
about 90 parsecs (300 light years) from the earth.

6
Binary Stars Get Mass
• Because gravity is the force that keeps smaller
objects going around bigger objects, we can
determine the mass of the bigger object by
measuring the radius and period of the smaller
orbiting objects.
• We use this in determining the masses of the
planets by looking at their moons or by putting
our own moons (satellites) in orbit around them.

7
Binary Stars Get Mass
• We use this same system to get the mass of the
sun since we have the planets orbiting the sun.
• We are only now being able to see other planets
orbit other stars since those stars are so far
away.
• However, we notice that there are lots of stars
that orbit each other and we can use that to
get the mass of the bigger (central) star.

8
Binary Stars
• The most direct way of seeing binary stars is to
really see them. This is possible for the nearer
stars. We can actually see both stars
individually and watch one orbit the other.
These are called visual binaries.
• We need to be careful here, since some stars only
appear to be close due to our perspective. These
are called optical doubles and not real binary
systems at all. We can tell the difference by
watching these over time or by noting that the
distance to each of the two is quite a bit
different.

9
Binary Stars
• A second way is to look at the spectra. When the
orbiting star comes toward us, its spectral lines
are shifted (Doppler effect) a little towards the
blue, and when it goes around and away from us,
the spectral lines are shifted a little towards
the red. This works well for binary systems that
we view edge on.

10
Binary Stars
• A third way of detecting binary stars is to
notice the brightness of a star over time (light
curves). When the orbiting star goes in front of
the more massive central star, a bit of the
central star will be covered by the orbiting
star and the total light from the star system
will decrease. A similar thing happens when the
orbiting star goes behind the central star.
These are called eclipsing binaries.

11
Binary Stars
• For these eclipsing binary star systems, we can
then determine it as binary and get some
interesting information about the systems from
these light curves.

12
Binary Systems
• A fourth way of detecting binary systems is to
notice that a star is wobbling as if it is
swinging another heavy object around it even if
the heavy object cant be seen. This can occur
if the star is swinging a dark star or perhaps
a burned out star. These are called
astrometric binaries. This will have to be
considered when looking at the birth and death of
stars (stellar evolution).

13
Binary and Multiple Star Systems
• By having these various methods available to
detect binary systems, we notice that most stars
are not single stars like the sun, but instead
are either binary star systems or are in star
groups with multiple stars mutually orbiting each
other. We will have to take this fact of
multiple star systems into consideration in
looking at theories of stellar formation and
evolution.

14
What we can measure
• 1. Parallax (but only for the nearer stars)
• 2. Brightness
• 3. Spectra - how much red versus blue
• 4. Spectra - emission and absorption lines
• 5. Binary systems orbits of less massive stars
around more massive stars
• a) by direct viewing (seeing the stars orbit)
• b) by spectroscopy (seeing alternating blue and
red shifts)
• c) by light curves (seeing dips in light output
due to stars eclipsing one another).
• d) astrometric (by observing the wobble of a
star)

15
Relations between quantities
• Spectra amount of red versus blue gives surface
temperature (T)
• Brightness (B) depends on luminosity (L) and
distance (d) B ? L/d2
• (Here the symbol ? means proportional to.)
• Luminosity (L) depends on temperature (T) and
area (A) L ? AT4

16
For the nearer stars
• 1. Get distance (d) from parallax.
• 2. Get temperature (T) from amount of red versus
blue in spectra.
• 3. From brightness (B) and distance (d), use
• L ? B/d2 to get luminosity (L).
• 4. From luminosity (L) and temperature (T), use
L ? AT4 to get area (A).
• For the nearer stars, we then know their surface
temperature and size.

17
Farther stars
• For the farther stars, we cannot use parallax to
determine the distance.
• Since we dont know the distance, we cant
determine their luminosity.
• Since we dont know their luminosity, we cant
determine their area.

18
Stellar Classifications
• Since there are several thousand stars close
enough to use parallax, perhaps we can classify
these stars, and then apply these classifications
to further stars to try and get their
luminosities based on their classifications.
• If we can determine their luminosities, we can
use B ? L/d2 to determine their distances, and
we can use L ? AT4 to get their areas.

19
The H-R diagram
• One way to try and see relations between
quantities for the purpose of developing a
classification system is to plot one quantity
versus another and see what it looks like.
• It turns out that plotting Luminosity versus
Temperature gives a very useful graph. This is
called an H-R diagram. (The diagram name is
actually the Hertzsprung-Russell diagram, but it
is called the H-R diagram for short.)

20
Luminosity
• Apparent Magnitude is a measure of brightness and
came from the attempt to classify stars by their
brightness 1 brightest, 5 dimmest (to the
unaided eye).
• Luminosity is often expressed in terms of
Absolute Magnitude the brightness (in Apparent
Magnitude) a star would have if it were located
at a standard distance of 10 parsecs away.

21
Luminosity
• When we started using the telescope, we had to
extend the apparent magnitude system to cover
even lower brightnesses. In doing so and in
using more sophisticated measuring devices than
the eye, we noted that the original five units of
apparent magnitude corresponded to 100 times in
brightness. Thus we could extend the brightness
system (apparent magnitude) down in brightness
but up in value from 1 to 5 all the way to 1 to
15. (At this point, we about reach the limit of
telescopes based on the light scatter in the
atmosphere.) With the Hubble, we can extend it
even lower still.

22
Luminosity
• But after we started using this scale for
Absolute Magnitude (Luminosity) we saw that we
needed even higher luminosities and so we needed
even lower numbers. This meant we had to go
below 1 (and even below 0) to reach as low (as
high a luminosity) as -10 !
• On this scale, our sun is rated as 4.8 . That
is, at 10 parsecs (about 32 light years away), it
would be just barely visible to the naked eye.

23
Spectral Classification (due to temperature)
• We measure temperature of the stars surface by
measuring how much red versus how much blue there
is in the spectra of the star. Thus we refer to
the cooler stars as red stars and the hotter
stars as blue stars. But we have developed a
letter scale for this as well From hotter to
cooler we have
• O B A F G K M (O stars are the hottest and
bluest, M stars are the coolest and reddest).
• (Memory device Oh Be A Fine Guy/Girl Kiss Me)

24
Temperature
• We even got good enough that we could identify
subclasses of these temperatures, with 0 being
the hottest and 9 being the coolest in any letter
category. According to this, an O0 star is the
hottest and an M9 star is the coolest.
• According to this scale, our sun is a G2 star (as
far as temperature/color is concerned).

25
The H-R diagram
• The vertical axis of the H-R diagram is
Luminosity, with the lower luminosity at the
bottom (15 in Absolute Magnitude) and the higher
luminosity at the top (-10 in Absolute
Magnitude).
• The horizontal axis of the H-R diagram is
temperature/color, with the hottest/bluest stars
(O) on the left and the coolest/reddest stars (M)
on the right.

26
The H-R Diagram
• Everything else being equal, we might expect that
the stars would fall on a diagonal line from the
upper left (high luminosity and high temperature)
to the lower right (low luminosity and low
temperature).
• Detailed H-R diagrams can be found on the web if
you search for H-R diagrams. Many stars do fall
on a more or less diagonal line like we expected,
and this line is called the Main Sequence.

27
H-R Diagramexpected results
-10

Luminosi ty
-5
0
Sun G2 at 4.8 Magnitude
5
10
15
O0
B0
A0
F0
G0
K0
M0
Temperature / Color
28
H-R Diagramresults for nearest stars
-10

Luminosi ty
-5
0
sun
5
10
15
O0
B0
A0
F0
G0
K0
M0
Temperature / Color
29
H-R Diagrambrightest stars
-10

Luminosi ty
-5
0
sun
5
10
15
O0
B0
A0
F0
G0
K0
M0
Temperature / Color
30
H-R diagram
• The nearest stars should give us a good
representation since it should count all the
stars in the area. We can see that many if not
most of the stars do fall on the predicted line.
Well call this predicted line the Main
Sequence.
• There are significant number of stars that fall
below the Main Sequence. Since they have lower
luminosities than their temperature would
normally suggest, we infer that they are much
smaller. We call them white dwarfs.

31
H-R diagram
• When we add in the brightest stars, we realize
that this is NOT a representative sample because
we can see those brighter stars at much greater
distances.
• Some of the bright stars do seem to fall on the
expected Main Sequence line. But many of these
stars have much higher luminosities than their
temperature suggests, they much be much larger
stars. We call these stars giant stars.

32
Size classification
• The stars furthest above the Main Sequence are
called Super Giants, and are classified as I or
II (with I being the biggest).
• The stars above but close to the Main Sequence
are called Giants, and are classified as III (or
IV for sub-giants).
• The stars on the Main Sequence are classified as
V.
• Stars below the Main Sequence are sometimes
called Dwarf stars, but they have low
luminosities and so are hard to see.
• Hence our sun is a G2-V star since it is on the
Main Sequence.

33
Mass-Luminosity Relation
• By using binary stars, we can get the mass of the
central star. As we noted earlier, over half of
the stars in the sky are part of binary or
multiple star systems, so we have lots of stars
to relate luminosity with brightness.
• We find that higher mass stars on the main
sequence also have higher luminosities.

34
Mass and Luminosity
• This makes sense
• higher mass means more gravity
• more gravity means more compactness and more
heat
• more heat and compactness means more energy
production by fusion
• more energy production means more luminosity.

35
Mass and Main Sequence Stars
• The place a star has on the main sequence can be
related to its mass.
• We still have the problem with the stars that are
off of the main sequence why would they have
different temperatures and different sizes when
they have the same mass as other stars? Is this
related to their age or development? This leads
to the next topic stellar evolution.

36
Brightest stars in North basic info
• Star constellation class App. Mag Abs. Mag
dist in ly
• Sirius Canus Major A1 V -1.46 1.4 9
• Arcturus Bootes K2 III 0 -0.2 36
• Vega Lyra A0 V 0 0.5 26
• Capella Auriga G8 III 0.1 0.3 42
• Rigel Orion B8 Ia 0.1 -7.1 900
• Procyon Canus Minor F5 IV 0.4 2.6 11
• Betelgeuse Orion M2 Iab 0.5 -5.6 310
• Altair Aquila A7 IV-V 0.8 2.2 16