poly: speeding up a star's burn rate

I've been off this list for a few weeks, visiting my relations in a village
in England, eating delicious English food, watching the rain, and
considering how to speed up a star's burn rate. What a coincidence that my
fellow polymaths were considering the same question at the same time! I
haven't reached any definite conclusions, but in this message I will
blather about what I've come up with. Warning: this message will be
disorganized.

1. Why?

Why do we want to speed up the burning of stars? Two reasons: energy and
heavy elements.

1.1 Energy:

One might want to extract the energy from the star faster than the natural
rate because one has a discount rate higher than 1/(stellar lifetime).
Also, natural burning will not extract 100% of the energy inherent in the
fuel. With correct control, one can do better than nature. Finally,
controlled fusion of hydrogen is possibly only feasible using stars rather
than magnetic or inertial confinement.

1.2 Heavy elements:

The universe is grossly oversupplied with hydrogen and helium and short of
everything else. Stars can be used to transform light elements into heavy
ones, and, to some extent, to reprocess heavy elements into other heavy
ones. Conveniently, stars in a certain mass range can be designed to be
self-demolishing when their job is done, speading their matter conveniently
across interstellar space. This is called a 'Type Ia supernova' when it
occurs accidentally.

2. Limits

The ultimate limit to the luminosity/mass ratio of a star is the 'Eddington
limit', which is 30,000 (luminosity of the sun)/(mass of the sun). At this
limit, the light pressure of the light from the star will begin to blow
matter off its surface. This limit is reached by large stars near the end
of their life, and by accreting neutron stars and black holes. This is
750,000 times larger than the present luminosity/mass ratio of the galaxy,
so there is plenty of room for improvement.

The nuclear energy released by converting hydrogen to iron is released
about 80% in the hydrogen->helium reaction, 10% in the helium->carbon
reaction, and 10% in all subsequent reactions. Burning elements heavier
than helium causes much of the energy to be released as neutrinos rather
than photons, which is an annoying waste, since there's no way to catch the
neutrinos. The hydrogen->helium process has an ignition temperature around
20 MK, the helium->carbon process around 200 MK, and the carbon->iron
process around 800 MK. The carbon->iron process is actually a complex
sequence of processes that build heavier and heavier elements, but each
step provides enough heat to ignite the next one, so for
back-of-the-envelope purposes it can be considered a single process. It is
very rapid and tends to blow up the stars in which it occurs in a matter of
seconds.

The total energy released in the entire hydrogen->iron process is only 1%
of the rest mass energy of the matter.

For stars heavier than the Sun, the main hydogen-burning reaction is
catalyzed by the elements C, N, O and F. It doesn't matter which one you
use initially; they equilibrate fairly fast. The reaction rate is
proportional to the product of the hydrogen concentration and the CNOF
concentration.

The time scales required to substantially reconstruct stars are on the
order of a few hundreds of thousands of years. This is the so called
'Kelvin-Helmholtz time', and is the time required to produce by fusion an
energy equal to that needed to dismantle the star against gravity.

There is an annoying feedback mechanism that keeps most stars from burning
very hot. If they start to burn faster, they expand, which reduces the
central pressure, which decreases the burn rate. This keeps their core
temperature low enough that the reactions are just barely occuring. At the
moment, the sun is burning hydrogen to produce helium. In a few billion
years, the core will be depleted in hydrogen, and it will begin to burn
helium into carbon. This requires a higher temperature in the core, hence
higher heat conduction out of the core, hence higher solar luminosity.
This is the stage at which the Sun will expand into a red giant. The Sun
will never get hot enough to ignite the carbon, so after it uses up the
helium it will cool and contract to a black dwarf.

There are two ways around this annoying feedback process, both of which are
used by very massive stars. One is to increase the pressure at the center
until the matter becomes degenerate, which considerably reduces its
tendency to expand when heated. This requires large pressures, and hence
only occurs in large stars. The other is to make the core out of a
harder-to-ignite material than the periphery. Then the hot core can be
burning at the same time as the cooler shell. Just before supernova, some
stars have a carbon-buring core, a helium-burning shell, and a
hydrogen-burning shell.

3. Methods

As Amara points out, the easiest way to increase the burn rate of a star is
to increase its mass. Hence, a good first step toward reconstructing the
universe is to dismantle small stars, move the parts across interstellar
space, and put them into big stars. You don't want to make the big stars
too big, unless you are willing to lose heavy elements for good when they
collapse into a neutron star or black hole. The upper limit to avoid this
problem seems to be about 10 solar masses, at which the luminosity per unit
mass is 1000 times better than the Sun, or 25,000 times the present
galactic average.

We can do better than to just dump all the raw materials for a star
together higgledy-piggledy as nature does it. What we want is a helium
core, surrounded by a shell of hydrogen and CNOF catalyst, surrounded by a
pure hydrogen shell. The core will burn helium to carbon, the inner shell
will burn hydrogen to helium, and the outer shell will merely provide
weight to hold things in. You can build a Dyson sphere around the star
using all the elements left over. As burning proceeds, the helium core
will be gradually converted to carbon, and the helium burn zone will move
outward to consume the helium produced in the hydrogen burn zone. At some
point, the core will undergo carbon detonation, and scatter its processed
materials.

I'm not sure how bright such a carefully layered star would be, or how long
its lifetime would be. At least 10000 times solar luminosity, and at most
3,000,000 years seem like reasonable limits.

One problem with Dyson spheres is that a Dyson sphere around any single
star will have a hard time collecting the energy of the star going
supernova. It is possible to put a shell around an entire galaxy, which
would not have that probem, but that's a topic for another message...

4. References

The references I have found useful are

"Stellar Interiors" by Hansen and Kawaler: extremely clear and well
written. Discusses the physical effects that occur inside stars; not as
much on the phenomenology of stellar behavior. Good chapter on white dwarves.

"Supernovae and Nucleosynthesis" by Arnett: reasonably well written. Runs
through physical effects in about 1/3 the detail of the above, then talks
about the behavior of massive stars at length, concentrating on the stages
immediately before and after they explode, and on how they synthesize heavy
elements.

At 01:22 PM 12/30/97 -0800, Amara Graps wrote:
>
>----------------------------------
>Getting the carbon into the star.
>----------------------------------
>
>How to get material into the star considering convection?
>
>...
>Since the Sun's convective layer is the outer 30% of its radius,
>if you added any mass to the Sun, it would only reach the outer 30% of
>the radius and not reach the core.

Actually, if you drop a suffciently large mass of material into a star, and
it is denser than the material of the star (not hard if the star is made of
hydrogen), the new material will fall through the star to the center.
Calculating the precise value of 'sufficiently large' is beyond our present
astrophysical ability, but for getting helium to the center of the Sun, it
looks like a Luna-sized ball will be sufficient.

--CarlF
Received on Wed Jan 7 16:46:27 1998