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.
Basics of
the HR
diagram
Size
Mass
Red dwarfs
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.
Visual Binary
Stars
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.
Sirius – the brightest
star in the sky.
Visual Binary Star Images
Mizar – in the handle of the
Big Dipper.
Albireo –
The “Cal” star
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
Spectroscopic Binaries : the tilt problem
One problem with spectroscopic binaries is
that you can’t 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
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).
Eclipsing Binaries – full information
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.
Algol – the “demon” star
The shape and timing
of the eclipses gives
the shape and size of
the stars.
Stellar Parameters
from Binaries
The masses can be found from M1+M2 (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).
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).
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
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
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.
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…
Converting mass to energy
Professor Einstein found the secret to a star’s energy:
the equivalence of mass and energy
E=mc2
This equation means that if you can manage it, you
can convert a little bit of mass into a lot of energy:
Units: ergs=gm(cm/s) 2 ; c2~1020
(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 Sun’s mass is 2x
1033 gm, it can last for 1012 years at
that rate…
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.
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.
The Proton-Proton Cycle