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_Hertzsprung Russell Diagram
And Stellar Evolution_
_________________________________________________________________

_Introduction_

If this webpage looks different than it did the last time you saw it,
that's because I changed it! I have removed all reference to the
electric sun hypothesis, which I now take to task in great detail on
another page: [1]On the "Electric Sun" Hypothesis. I have also
radically altered the text and descriptions, hopefully for the better.

What follows is not an exhaustive study of stellar evolution. But it
is, I hope, an introduction to stellar evolution, through the
intermediary services of the Hertzsprung-Russel (HR) diagram. Simply
put, the HR diagram is a plot of brightness versus color, for as many
stars as you want to plot. The fact that this simple plot is highly
non-random is a hint that something is going on that we may want to
know about. That something turns out to be stellar evolution. As it
turns out, by building mathematical models of stars, based on straight
forward physics, and allowing those models to evolve naturally in time
as a star ages, we can recreate the HR diagram as it is observed. The
fidelity of the agreement between theory & observation is far greater
than I can communicate in this one webpage. Even small details are now
the stuff of intense study in astrophysics. The ability of the theory
of stellar evolution to explain the HR diagram in its finest details,
singles out stellar evolution as one of the most successful and
productive of scientific theories.

More details about stellar structure and evolution are available from
my companion webpage, [2]Solar Fusion and Neutrinos, including a much
larger bibliography, and lists of books and webpages.
_________________________________________________________________

_The HR Diagram in General_

_figure 1
A schematic Hertzsprung-Russell (HR) Diagram_

All stars have two properties that are fairly easy to see: Brightness
and color. Some stars look red (like [3]Betelgeuse), some look more
yellow (like the sun), and some look blue or blue-white (like
[4]Sirius). Color, as it turns out, is directly related to
temperature; things that look red are relatively cool, compared to
things that look yellow, which in their own turn are relatively cool
compared to things that look blue or white.

[5]Figure 1 above shows a schematic plot of temperature (X-axis) vs
brightness (Y-axis) [_temperature increases to the left for historical
reasons; the HR diagrams were originally based on color, left to right
being blue to red_]. This plot is called a Hertzsprung-Russell (or HR)
diagram, after the two astronomers who developed the concept in the
late 1800's, [6]Henry Norris Russell and [7]Ejnar Hertzsprung.

The HR diagram is important because it is the graphical interface
between observation and theory in stellar evolution. One can compute
the surface temperature and brightness of a star, based on the physics
of stellar structure, and from that derive an expected color based on
the temperature. Or, one can observe the brightness and color,
deriving the surface temperature from the observed color (we can now
use spectroscopy to derive temperatures in a manner not readily
available to Hertzsprung & Russell).

[8]Figure 1 is of particular interest, because we can see at a glance
that the diagram is not random. If you observe lots and lots of stars,
and plot a point for each star observed, the points are not scattered
freely around the page, as one might think. Instead, a specific
pattern emerges. Stars tend to concentrate along a curve that angles
down across the plot, from left to right, which is called the _main
sequence_, because that's where Hertzsprung & Russell saw the most
stars. There are clumps of bright red stars to the upper right, as
well as the dim red stars along the bottom of the main sequence. The
bright red stars are called _red giants_, because they must be very
large to be simultaneously cool (red) and bright. Likewise, the dim
blue stars that hang around the lower left are called _white dwarfs_,
since they must be very small in order to be simultaneously hot
(white) and dim.

_figure 2
Schematic Stellar Evolution_

A star is not a static thing, it changes with time. The process of
aging in stars is called _stellar evolution_. As a star ages, it goes
through changes reminiscent of the life cycles of living things, the
details of which depend on the star's overall mass. Massive stars live
short but exciting lives, whereas small stars live long, quiescent
lives. We can build a model of a star using physics & mathematics, and
then turn that model loose in time and watch it evolve. At any given
time the star will always have a brightness and a temperature (both of
which are as seen at the surface of the star). We can plot those
points at lots of different times, and then connect the points
together in order of time, and we get a curve (or _trajectory_ across
the HR diagram.

[9]Figure 2 shows examples of stellar evolution curves for stars of
1.6 and 2.0 solar masses. The blue curves represent the track followed
by the collapsing protostar, and are called _Hayashi Tracks_. The
green line represents the main sequence, where the star spends most of
its lifetime sitting around fusing hydrogen into helium. Once the star
stops burning hydrogen in its core, it begins to expand, and moves off
the main sequence towards the upper right (the _giant_ region). The
more massive stars sit on the hotter portion of the main sequence,
live shorter lives than the less massive stars, and become larger
giants. Less massive stars sit on the cooler portion of the main
sequence, live much longer lives, and may never become giant stars at
all. Our sun should remain essentially as we see it now, on the main
sequence, for a total of about 8,000,000,000 years. A supermassive hot
star, say in the 20,000 degree and hotter range, may sit on the main
sequence for only 1,000,000 years or less. A cool red star, down in
the 3000 degree and cooler range would be expected to sit on the main
sequence for as long as an astounding 100,000,000,000,000 years.
_________________________________________________________________

_The HR Diagram for a Specific Case_

_figure 3
HR Diagram for
Globular Cluster M5_

In figure 3 above, we see an HR plot of the stars in [10]globular
cluster M5 (I shamelessly confess that I took this diagram from that
page). The X-axis plots "B-V", which is the _color index_, and "B-V"
means "B minus V", where B and V are the relative brightness of the B
and V colors, in the system of _magnitudes_ normally used in
astronomy. This can be quite confusing, because astronomical
magnitudes run "backwards", the smaller the magnitude, the brighter
the object. So, if B-V is positive, then B is biffer than V, which
means that B is dimmer than V, and the object is relatively red,
compared to an object with a smaller value of B-V. So the scale is
relative in color, or temperature. So red is to the right, and blue is
to the left on this scale, just as it was in the previous figures. The
color index and temperature are directly related, so it is a matter of
convenience which one chooses to plot. In practice, this kind of plot,
called a _color-magnitude diagram_, is more common, since the color
index is derived directly from the photometer data.

Now, back up a paragraph or two, and remember the bit about stellar
evolution curves, like those in [11]figure 2. If you drew 100 curves
at once, it would be pretty confusing. But, you could select a point
from each of those 100 curves, all of them at the same time, and plot
100 points instead. If you do that, you get something that looks just
like [12]figure 3 above. The figure has several features labeled with
letters, which can be identified by stellar evolution, and the
assumption that all of the stars in the cluster are about the same age
(i.e., the cluster formed together).

The [13]main sequence is labeled _A_ in [14]figure 3. But it does not
run all the way across the image, as the schematic in [15]figure 1
shows it. That's because the massive, bright stars live shorter lives.
So, as the cluster ages, the stars beginning with the upper right
portion of the HR diagram, will peel off to the right, becoming red
giants. The main sequence in [16]figure 3 goes up a bit to the left,
and then disappears, with a sharp turn to the right (that unlabeled
point is called the _main sequence turn off_ or the _turn off point_).

The _red giant branch_ is labeled _B_ in [17]figure 3. Those are the
stars which have evolved off of the main sequence, and are now
becoming red giants. The stars that were bigger in the beginning, are
already up at the tip of the red giant branch. The stars that form the
line heading back towards the main sequence, are the smaller (less
massive) stars. The ones that are still on the main sequence are even
less massive. Stars that sit on the main sequence are fusing hydrogen
into helium in the core of the star. But once the star runs out of
hydrogen in the core, fusion moves away from the core, and into an
expanding shell around the core. When that happens the star expands,
and becomes a red giant.

The _tip of the red giant branch_ is labeled _C_ in [18]figure 3. As
time goes by on the red giant branch, the helium created in the shell
around the core, drops onto the core, causing it to heat up. When that
core gets hot enough (say about 100,000,000 Kelvins), it suddenly
begins to fuse helium into carbon, which generates a lot of new energy
flowing from the core. This sudden event is called the _helium flash_,
and occurs about the point labeled _C_ in the diagram. The new source
of energy from the core pushes the hydrogen fusing shell outwards,
forcing it to cool and shut off. Now that the star is generating new
energy in the core instead of a shell, it shrinks back to a smaller
size, and the star winds up on the horizontal branch.

The _horizontal branch_ (HB) is labeled _D_ in [19]figure 3. Stars
with a brightness and temperature that put them on the HB are fusing
helium into carbon, in the core of the star. The HB has some structure
of its own, the _Schwarzschild space_ is labeled _E_ in the diagram,
and the _red clump_ (not labeled), is immediately to the right of the
Schwarzschild space. The horizontal extent of the HB is determined by
_metalicity_. In the jargon of astronomers, everything heavier than
helium is a _metal_ by definition. The ratio of metal abundance to
hydrogen abundance is called _metalicity_. Stars with a higher
metalicity will look redder, because the metals absorb the bluer
light. The red clump is formed by the higher metalicity stars, while
the lower metalicity stars string out to the blue (left) end of the HB
(which also turns down here, for reasons not yet fully understood).
The Schwarzschild space (_E_) is peculiarly empty, because any star
that winds up in that spot is unstable, and becomes an _RR-Lyra_ type
variable star. Since these variable brightness stars cannot be plotted
with a single point, they are usually left off the diagram. So it's
not that there aren't any stars, it's just that they are variable in
brightness. This small detail is one of the many satisfying
consistencies between theory (which predicts instability), and
observation (which verifies instability).

The _asymptotic giant branch_ (AGB) is not labeled, but lies along the
left side of the red giant branch (_B_), essentially parallel to it.
Stars on the HB will run out of helium in their cores eventually, just
as they ran out of hydrogen before. And just as that sent the stars to
the giant realm once before, it will do so again. Once an HB star runs
out of core helium, it begins to fuse helium into carbon in a shell,
and the star expands once again. The expansion takes the evolutionary
track of the star asymptotically towards the red giant branch (hence
the monicker _asymptotic giant branch_). Stars on the AGB that are
smaller than maybe 8 solar masses will age more or less gracefully,
into _planetary nebulae_, and eventually into _white dwarf stars_.
Those that are heavier will not manage such a peaceful end, and
terminate in supernova explosions.

The _white dwarf branch_ is labeled _F_ in [20]figure 3. After making
it to the asymptotic giant branch, the track for the further evolution
of stars moves up and out of the diagram, way off to the left, and
then swings around under the diagram to the white dwarf branch. Once
the stars that are too small to blow up as supernova explosions have
finished all the nuclear fusion they can do, they wind up as small
intensely hot white dwarf stars. All they do after that is cool, which
takes a long time. The disk of our Milky Way galaxy is only about 9 or
10 billion years old, still too young for any of its white dwarf stars
to have cooled beyond visibility. That's how long it takes.

_figure 4
HR Diagram #2 for
Globular Cluster M5_

Figure 4 (shamelessly swiped from [21]COSMOS Project on Globular
Clusters) shows us yet another HR diagram for M5. This one is more
complete than the one in [22]figure 3, it has a lot more stars plotted
(all those little dots). But it also has an _isochrone_ on it, the
dark curve through the main sequence and red giant branch. An
isochrone is a line of constant age. It's a theoretical ideal, the
line along which all of the little dots would sit, in a perfect
universe, if M5 was 11 billion years old. In fact, the COSMOS folks
decided that anything from 9 billion to 13 billion fit pretty well, so
they set the age of the cluster at 11 ± 2 billion years (uncertainty
is a fact of life in science, you might as well get used to it now).
That isochrone is created by allowing a mathematical model of the
cluster and its stars to age, constrained as best we can by the laws
of phsyics. It tells us that there is good reason to believe that the
age of this cluster really is 11 ± 2 billion years.

[23]Figure 4 is just one example of an isochrone, the literature on
stellar evolution is packed with isochrones (unfortunately, the WWW is
not). The literature on stellar evolution is also packed with
_evolutionary tracks_ (another item missing from the WWW). An
[24]evolutionary track looks superficially like an isochrone, but
tracks the "life history" of a single star, so it makes a pretty
convoluted looking curve as it goes up & down & up the giant branch,
loops through the HB, and so forth.

The connectikon to the HR diagram is by now obvious (I hope). As the
star ages, the color-brightness point that identifies it moves around
on the HR diagram, drawing out the evolutionary track. The real beauty
of it all is that the tracks and isochrones, derived from the pure
physics models of stars, can recreate the essential features for HR
diagrams of real star clusters.
_________________________________________________________________

_Appendix - Relevant Websites_

* [25]Stellar Evolution and Death - A [26]NASA website
* [27]Stellar Evolution - A [28]University of Oregon website
* [29]The HR Diagram - And stellar evolution, from the [30]Univ of
Massachusetts Amherst
* [31]How Hot is that Star? - From the [32]Science Museum of
Virginia
* [33]Energy Production in Stars - From the [34]University of
Tennessee - [35]Physics and Astronomy Department
[36]Astronomy 162 - Stars, Galaxies and Cosmology
[37]Temperature and Pressure in Stars
[38]The Proton-Proton Chain
[39]The CNO Cycle
[40]The Solar Neutrino Problem
* [41]Stellar Evolution with the Hubble Space Telescope
* [42]Astronomy Unbound - A virtual Astronomy Text from the
University of Hertfordshire, England
* [43]Our Sun and Stellar Structure - A chapter out from
[44]Astronomy Notes, an online textbook.
* [45]Star Light, Star Bright, the stellar evolution & structure
module from the [46]Physics 4213 Cosmology Course, taught by
[47]Jeff Robertson at [48]Arkansas Tech University.
* [49]The Stanford Solar Center
* [50]National Solar Observatories
* [51]Big Bear Solar Observatory
* [52]150 foot solar tower - Mt Wilson, CA ([53]UCLA)
* [54]60 foot solar tower - Mt Wilson, CA ([55]USC)
* [56]Mees Solar Observatory - From the [57]University of Hawaii
_________________________________________________________________

_Appendix - Relevant Books_

* _[58]Stellar Interiors - Physical Principles, Structure and
Evolution_
C.J. Hansen & S.D. Kawaler
Springer (Astronomy & Astrophysics Library) - 1994
ISBN 0-387-94138-X
ISBN 3-540-94138-X
QB808.H36
* _[59]Astrophysical Concepts_
Martin Harwit
Springer (Astronomy & Astrophysics Library) - 1998 (3rd edition)
ISBN 0-387-94943-7
I used the 1973 1st edition (John Wiley) as the textbook for my
astrophysics course., and i also have the 1998 3rd edition linked
here. An excellent book for basic, college level astrophysics.
_________________________________________________________________

_Page last Modified on December 19, 2001_
[60]Tim Thompson's Home Page
[61]Tim Thompson's Collected Writings
[62]Solar Fusion & Neutrinos

setstats 1

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