Download Lecture Ten - The Sun Amongst the Stars Part II

Last time we talked about telescopes, and the advantages to
be gained by making them very large:
1. More light-collecting
area, which lets us see
fainter objects.
Chandra X-ray Observatory
2. Greater angular
resolution, which lets us see
objects in greater detail.
Hubble Space Telescope
We finished noted the benefits of being above the atmosphere: the
availability of light which doesn’t reach the Earth’s surface, the
freedom from weather and light pollution, and the complete lack
of distortive effects from the Earth’s turbulent atmosphere.
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But the costs, we noted, are quite high. The 6.5m James Webb
Space Telescope, scheduled for launch in 2018, will have cost
almost 9 billion dollars – far more than the 1-2 billion dollars it
would cost to build a 100m telescope on the ground!
We also discussed what
we can observe from stars
– Apparent Brightness,
Position and Motion,
Colors (in all kinds of
light), and Absorption and
Emission Lines – and how
to use that information to
learn other things we want
to know about stars like
their Luminosity,
Distance, Temperature,
Radius, Mass, and Age.
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How do we go from that first list to the second?
Distance
by measuring the star’s parallax;
by knowing the luminosity and measuring apparent
brightness (standard candle method).
Luminosity
by knowing the distance and measuring apparent
brightness.
Apparent Brightness = L / 4d2
Temperature, we noted, could be estimated in a relative way
by the visual colors of stars. Redder stars have colder
atmospheres while bluer stars have hotter atmospheres.
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But a far better
approach is to
use the
spectral type
of a star –
what patterns
of absorption
lines appear in
light coming
from the star.
Those patterns do tell us something about the elements in a
star’s atmosphere, but that’s not as important as you might
think. As it turns out, all stars are made primarily of
Hydrogen & Helium, with only very minor differences
(<1%) in the amounts of other elements they possess.
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The differences in spectral types are actually caused by differences
in the temperature of the atmospheres of different types of stars –
spectral type tells you temperature.
O B A F G K M (L,T)
50,000 K
3,000 K
Temperature
Sirius
Spectral Type A
Alpha Centauri
Spectral Type G
(so is our Sun!)
Proxima Centauri
Spectral Type M
A star’s temperature sets which types of ions or molecules can
exist in its atmosphere, and the energy states of the electrons and
atoms in those ions and molecules. These energy states dictate how
the ions and molecules interact with light, and the number and the
relative ‘darkness’ of the absorption lines in the star’s spectrum.
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O-type stars have very few lines because they are so hot that
most of their elements have been stripped of electrons – while
in cooler, M-type stars, far more atoms retain their electrons.
Patterns of absorption lines can reveal the temperatures of the
stars to a precision within 50 degrees K – a factor of 10 better
than what can be done by looking at “colors” alone.
Ok, that’s distance, luminosity, and temperature – what about
mass? That can only be measured directly by observing the effect
that gravity has on the star. This is most easily done in binary star
systems, in which two stars orbit each other. Newton’s version of
Kepler’s laws can then tell you the masses of each.
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Sample of
multiple star
systems from
Stassun, 2012.
Fortunately such systems tend to be quite common – almost
half of all stars like the Sun are in multiple star systems!
Putting It All Together – the Hertzsprung-Russell Diagram
This plot, first developed in 1910, turns out to be very useful for
understanding stars. It shows two major physical properties:
Temperature (x) and Luminosity (y)
-- or to put it another way --
Spectral Type (x) and “Absolute Brightness” (y)
bright
MV
faint
hot
Spectral type
cool
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BRIGHT
H-R Diagrams
– and the many
patterns of
stars seen it –
reveal a great
deal about how
stars work.
HOT
COOL
FAINT
O B A
F
G
K
M
Perhaps the most
obvious feature in an
H-R diagram is the
Main Sequence (MS).
Over 90% of all stars
lie on the MS, which
suggests that most
stars spend most of
their lives generating
their luminosity in a
similar, temperature
dependent manner.
O B A
F
G
K
M
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The importance of
the Main
Sequence is hard
to overstate, and
we’ll be back to it
soon – but there’s
something else
going on here too.
Notice that many
stars have the
same temperature,
but vastly different
luminosities. How
can that be?
O B A
F
G
K
M
Well, the luminosity of a star depends primarily on its
surface temperature – at a fixed size, hotter is brighter.
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But a star’s luminosity also depends on its surface area (and
therefore its radius) – at a fixed temperature, a bigger star is
brighter than a smaller star.
So if the temperature of two stars is the same, but they have
different luminosities, then those stars must have different sizes.
L = 4πR2σT4
If we know the luminosity and the temperature of a star
(which we must if we can put it on an H-R diagram!), we can
estimate its radius by assuming that luminosity is based on the
star’s temperature and using well-known laws of thermal
radiation. Mind you – the uncertainties can be high, especially
if the temperature is poorly constrained!
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Low T,
High L =
BIG
High T,
Low L =
SMALL
O B A
F
G
K
M
But there’s one more
point that needs to be
made before we press
on, because an H-R
diagram like this one
disguises another key
characteristic of the
stars in our galaxy…
From this figure, what
would you guess is the
most common type of
MS star?
O B A
F
G
K
M
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Proper counting reveals that over half of all stars are M dwarfs!
A more revealing look at the HR Diagram!
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Think about what this
means – remember
this map of the
nearby universe?
That closest star –
Proxima Centauri –
is a spectral type M,
main sequence star,
and you can’t see it
with your naked eye!
Such dim red stars represent the overwhelming majority of stars in
our galaxy, yet even the nearest is completely invisible to you! That
dimness is why they do not appear clearly on many HR diagrams.
So why are there so many M dwarfs? Does the star formation
process strongly favor the production of such stars? Or is there
some other process at work ‘removing’ hotter and more
luminous stars from the populations we observe?
The answer requires us to know how stars change over time,
and therefore the ages of different stars – but this is by no
means easy. All stars “live” a very long time (billions of years
in most cases!), and their observed properties generally do not
change significantly on human timescales – so it’s not possible
to watch any one star “age” in any meaningful way.
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To uncover how stars are changing during their ‘lives’, we
study large populations of stars and perform ‘demographic’
studies of those populations. With large enough samples, we
can be confident we’re seeing both young and old stars –
and then work to find a way to determine which is which!
Just as in human
demographics, this can
be simplified by
studying unique,
isolated populations –
which yield insights
into both the
similarities and
differences that can
occur in populations.
Fortunately, nature
provides these
specialized groups to
astronomers in the form
of star clusters.
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There are two types of these clusters: “Open Clusters”…
• Hundreds to
thousands of stars
• irregular shapes
• gas and dust is
sometimes seen
amongst the stars
in the cluster
Pleaides
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… and “Globular Clusters”
• 105 stars or more
• pronounced
spherical shape
• very little gas or dust
seen between stars
M80
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Omega Centauri
47 Tucanae
Both types of cluster are very useful for studying stellar properties!
~ 30,000 light-years
~ 48 light-years
Since all the stars in the cluster are at (roughly) the same distance
from us, we can compare their apparent brightnesses to each other
as though they were true luminosities. This allows us to plot a
reliable H-R diagram of the cluster, knowing that the brighter stars
in the cluster really are brighter, and not just closer to us!
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Further, since all the
stars in a cluster form
within ~ 100 million
years of each other, they
are very approximately
the same age, at least in
stellar terms. So our H-R
diagram of a cluster is a
“snapshot” of what a
group of stars – all of
very nearly the same age
– look like.
Open Cluster
H-R Diagram – the Pleiades
Globular Cluster
H-R Diagram – Palomar 3
In general, the H-R Diagrams of globular and open clusters are
very different from each other – suggesting very different ages.
Where are the bright B and A-type main sequence stars in the
Globular Cluster on the right?
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The key to this agerelated difference is
found in another trend
seen amongst stars in
our H-R diagrams – the
mass-luminosity
relationship. Brighter
main sequence stars are
much, much more
massive than the less
luminous stars on the
main sequence.
The mass-luminosity relationship for
main sequence stars.
The reason behind this relationship between mass and
luminosity in stars first began to become clear in the early 20 th
century, when physicists like Einstein revealed that atoms
possess a type of potential energy based only on how massive
they are. This mass energy can be changed by altering the
atom’s mass, via the processes of fission and fusion.
Fission – Heavier element split into multiple lighter elements.
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Fusion – Lighter elements merge
to form a heavier element.
Note that the atoms that go
into either of these reactions
will not have the same
overall mass energy as the
atoms that come out –
depending on which types of
atoms go into the process, the
new atoms produced can
have less mass energy, or
more. This means either
fusion or fission can require
energy to be put in (because
you’re adding mass)…
…or can possibly give “energy out” (if you’re losing mass).
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In the early 1920’s, it was suggested that deep in a star’s
core, 4 H nuclei could be forced to fuse into 1 He nucleus via
a process called the proton-proton chain. This natural process
generates energy because the He nucleus has less mass than
the 4 H nuclei – that ‘lost’ mass energy is converted
primarily into high-energy photons and tiny particles called
neutrinos which stream away from the star’s core.
The process in a bit more gory detail. There are actually a few more
subtleties to this that are far beyond the scope of this course!
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Fortunately, only a small amount of mass is transformed into energy –
and the Sun is crazy huge! Despite ‘losing’ over 4 million tons of
mass per second, every second for over 5 billion years, the Sun has
still only used up less than 0.1% of its total mass.
For a star of the Sun’s mass, this process provides enough energy
to keep it stable and shining for a total of 10 billion years.
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