The HertzsprungRussell Diagram

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The Hertzsprung-Russell Diagram
Hertzsprung and Russell had the idea of plotting
the luminosity of a star against its spectral
type. This works best for a cluster, where you
know the stars are all at the same distance. Then
apparent brightness vs spectral type is basically
the same as luminosity vs temperature. They found
that stars only appear in certain parts of the
diagram.
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Basics of the HR diagram
Size
Mass
Red dwarfs
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Visual Binary Stars
About half the stars in the sky have stellar
companions, bound together by gravity and in
orbit around each other. Some of these can be
seen by the eye or in a telescope, others are too
close to be resolved. You can see stars together,
but they must also share a common motion and be
at the same distance away (but not too far
away). If the orbital period is reasonable,
orbital motion can be measured. This allow us to
determine its tilt.
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Orbits and Masses of Binaries
The primary importance of binaries is that they
allow us to measure stellar parameters
(especially mass).
We get the sum of the masses unless we see both
stars moving.
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Visual Binary Star Images
Sirius the brightest star in the sky.
Mizar in the handle of the Big Dipper.
Albireo The Cal star
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Spectroscopic Binaries
If the stars are too close together to be
resolved, you may still be able to detect the
binary through the Doppler shift (in one or both
stars). They must be relatively close to each
other (short orbital period). The spectrum of the
system might also look like a combination spectrum
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Spectroscopic Binaries the tilt problem
One problem with spectroscopic binaries is that
you cant tell how badly the Doppler effect has
been reduced by the orbital tilt. Fully face on
orbits show no line-of-sight velocity at all. You
get a lower limit to the sum of the masses
(individual masses if both stars have visible
spectral lines).
Mizar A resolved by interferometry
Orbit face on small effect
Orbit edge on big effect
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Eclipsing Binaries
Sometimes the orbital plane is lined up so that
the stars pass in front of each other as seen
from the Earth. Each eclipse will cause the total
light from the system to decrease.
The amount of the decrease will depend on how
much of each star is covered up (they can have
different sizes) and on the surface brightness of
each star (they can have different temperatures).
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Eclipsing Binaries full information
Algol the demon star
You know the system is nearly edge on. Since you
also know the velocity (from Doppler shift) and
orbital period, you can get the true scale of the
system (including star sizes and masses). The
separation has to be pretty small for the odds to
be good this will happen.
The shape and timing of the eclipses gives the
shape and size of the stars.
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Stellar Parameters from Binaries
  The masses can be found from M1M2 (suns) 
a(AU)3 / P(yr)2 (individual masses can be gotten
if you have a signal from both stars) The orbital
period comes from watching the stars, or the
periodic variation of their velocity or
brightness. To get orbital semimajor axis, you
need either the parallax to a visual system or
the velocity from a spectroscopic system. In a
spectroscopic system, you only have a lower limit
unless you know the system tilt. In an eclipsing
system, you know everything, including the sizes
of the stars. Visual systems should be
relatively near the Earth, and have relatively
wide separations. Spectroscopic systems need not
be near to the Earth, but should have relatively
small separations. Eclipsing systems are likely
to have even smaller separations (and you have to
be lucky). Interferometry is converting some
spectroscopic systems into visual systems (and
resolving the tilt problem).
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The Mass-Luminosity Diagram
Main sequence stars
The payoff we can decode the HR diagram and
learn that the main sequence is a mass sequence
(and that off the main sequence things are more
complicated).
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HR Diagram - Properties
Stars in different parts of the HR Diagram are in
different phases of their life cycles. The Main
Sequence is set by hydrogen fusion.
Masses on the Main Sequence
Stellar Sizes
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Size/Luminosity
Hot stars are very bright but very rare. They can
affect the light, but not the mass of the Galaxy.
Red giants are more common. Most common are red
dwarfs.
O5
B0
A0
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The Structure of a Star
A star will take a size and luminosity which
balance the crush of gravity against the pressure
which fights it and holds up the star. The
pressure in a normal star is just thermal
pressure from heat.
The heat must constantly be replaced, as the star
radiates energy into space.
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How do Stars Shine?
The energy output of the Sun is 4x1033 erg/s
4x1020 megawatts If the Sun were burning coal or
gasoline, it could last a few thousand years
(which used to be OK) Gravitational contraction
is an energy source (gravitational potential
energy can be quite potent) could last 10
million years (this IS the source for young
stars, brown dwarfs, or black holes)
The required shrinkage would be barely noticeable
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Converting mass to energy
Professor Einstein found the secret to a stars
energy the equivalence of mass and energy
Emc2
This equation means that if you can manage it,
you can convert a little bit of mass into a lot
of energy
Units ergsgm(cm/s) 2 c21020 (assuming
perfect efficiency)
Actually, the hydrogen fusion the Sun uses is
only 0.7 efficient, so the fuel requirement to
power the Sun is 6x 1014 gm/s or 700 million
tons per sec! Since the Suns mass is 2x 1033
gm, it can last for 1012 years at that rate
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Elements and Isotopes
We define an element by the number of protons
in its nucleus. There can be isotopes with
different numbers of neutrons. The number of
protons and neutrons must be similar.
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Thermonuclear Fusion
In order to get fusion, you must overcome the
electric repulsion. But actually, you must also
have both a proton and a neutron. They stick
by the strong nuclear force which only works
on unlike particles.
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The Proton-Proton Cycle