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.)
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.
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
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
AU’s and another common unit of distance,
the light year: 1 parsec = 3.26 lt. yrs =
200,000 AU’s.
Parallax
The nearest star has a parallax angle of about
¾ of a second of arc, and so is about 4/3 =
1.3 parsecs away (about 4 light years away, or
about 266,000 AU’s away). Recall that Pluto was
about 40 AU’s away, and the Oort Cloud is
thought to be about 50,000 AU’s away.
We can effectively measure distances this way
for about several thousand stars that are
within about 90 parsecs (300 light years)
from the earth.
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.
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.
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.
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.
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”.
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.
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 can’t 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).
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.
What we can measure
1.
2.
3.
4.
5.
Parallax (but only for the nearer stars)
Brightness
Spectra - how much red versus blue
Spectra - emission and absorption lines
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)
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  A*T4
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  A*T4 to get area (A).
For the nearer stars, we then know their
surface temperature and size.
Farther stars
For the farther stars, we cannot use parallax to
determine the distance.
Since we don’t know the distance, we can’t
determine their luminosity.
Since we don’t know their luminosity, we
can’t determine their area.
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  A*T4 to get their areas.
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.)
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.
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.
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.
Spectral Classification
(due to temperature)
We measure temperature of the star’s 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)
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).
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.
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.
H-R Diagram
expected results
-10
L
u
m
i
n
o
s
i
t
y
-5
0
Sun = G2 at +4.8 Magnitude
+5
+10
+15
O0
B0
A0
F0
G0
Temperature / Color
K0
M0
H-R Diagram
results for nearest stars
-10
L
u
m
i
n
o
s
i
t
y
-5
0
sun
+5
+10
+15
O0
B0
A0
F0
G0
Temperature / Color
K0
M0
H-R Diagram
brightest stars
-10
L
u
m
i
n
o
s
i
t
y
-5
0
sun
+5
+10
+15
O0
B0
A0
F0
Temperature / Color
G0
K0
M0
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. We’ll 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.
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.
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.
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.
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.
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.
Brightest stars in North – basic info
Star constellation class App. Mag Abs. Mag dist in ly
Sirius Canus Major A1 V -1.46
Arcturus Bootes K2 III 0
Vega Lyra
A0 V
0
Capella Auriga G8 III 0.1
Rigel Orion
B8 Ia
0.1
Procyon Canus Minor F5 IV 0.4
Betelgeuse Orion M2 Iab 0.5
Altair Aquila
A7 IV-V 0.8
+1.4
-0.2
+0.5
+0.3
-7.1
+2.6
-5.6
+2.2
9
36
26
42
900
11
310
16