# poly: speeding up a star's burn rate (was: frontier replicators et. al.)

From: Amara Graps <amara@amara.com>
Date: Tue Dec 30 1997 - 13:22:24 PST

Hello Everyone,

My first post to this really cool mailing list... (Thanks for
inviting me!)

From: "Richard Schroeppel" <rcs@cs.arizona.edu>
(Mon, 22 Dec 1997 10:32:34 MST)

>Some other thoughts inspired by the discussion ...

>Can you speed up a star's burn rate by dumping in carbon?

Do you have a particular reason why you choose carbon ??

And the answer is "Sort Of".

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Do you want the carbon to be:

1) extra mass for the star's main sequence evolution (burning
hydrogen to helium)?

or

2) fuel for the star's burning?

or

3) a catalyst for the star's burning?

Considering each one of these (there is overlap though).

The references for the following are lecture notes: "Stellar Structure and
Evolution" by Joergen Christensen-Dalsgaard (Institut for Fysik
og Astronomi, Aarhus Universitet, Denmark) and an email conversation
with Dana Backman, Franklin and Marshall College, Pennsylvania)

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1) Carbon as extra mass for the star's main sequence evolution ?

You can speed up a star's burn rate by adding any mass. It doesn't
matter what the substance is. Dana says that you can add hydrogen, or
water, or uranium, or begonias (!), the star will get more luminous if you
add more mass. The power law for stars around the sun's mass
is approx: Luminosity proportional to Mass^4. So, for example,
if you increased the sun's mass by 10% the luminosity would go up by
about 40%. This is just because the extra mass (even if added only at the
surface) results in the core being squeezed and heated so the
reactions run faster.

But you would need to add huge amounts, if you added only an earth mass,
which is 3 x 10^-6 solar masses, the sun's luminosity would only
increase by about 1.2 x 10^-5, which is pretty negligible.

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2) Carbon as fuel for the star's burning?

The two major ways that hydrogen is converted to helium in a
star on the main sequence are the nuclear reactions:

- the proton-proton chain and
- the CNO cycle.

In order to burn carbon at its core, the star would have to
be massive enough to go through that process. It is a late evolutionary
process, which occurs when the star is near the end of its lifetime.
After the star finishes burning hydrogen, then, as long as the
core is not degenerate, it begins to burn helium. When the helium
is exhausted, it has a core of carbon and oxygen, and it begins
burning that.

But carbon burning at the core only happens for massive stars. I couldn't
find an exact number of what mass the star would have to be- I believe
that it is on the order of 4 or 5 times the mass of the Sun
but I'm not sure (I found examples in my stellar evolution texts
describing carbon-burning in the star's core for stars of that mass.)

The Sun is not massive to ever do actual carbon burning, even in its
red giant stages.

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2) Carbon as catalyst for the star's burning?

Like I said previously, the two major ways that hydrogen is converted to
helium in a star on the main sequence are the nuclear reactions:

- the proton-proton chain and
- the CNO cycle.

Note that the carbon is a *catalyst* for the CNO cycle which
converts hydrogen to helium

(For details, I talk about the proton-proton chain here:
http://solar-center.stanford.edu/FAQ/Qfusion.html and you
can see details for the CNO cycle at the bottom of the
following Web page:
http://zebu.uoregon.edu/~soper/Sun/fusionsteps.html)

The energy generation rate from the CNO cycle is much more
temperature-dependent than the energy-generation rate for
the P-P chain. Hence the P-P chain dominates at relatively low
temperatures, and the CNO cycle dominates at relatively
high temperatures.

The CNO cycle is more important in massive stars (from the star's
internal temperature). This CNO mechanism also has bearing on how the
energy is transported out of the star. The CNO cycle becomes more dominant
for stars on the main sequence that are about 1.2 * the mass of the
Sun.

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Getting the carbon into the star.
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In any of these 3 cases, you also need to consider the structure
of the star, in order to get the carbon to the source.

So I have to mention two processes by which stars transport
their energy from fusion processes, but I should probably
first briefly describe the structure of our Sun, just so that
we are speaking the same language.

According to standard solar models, the solar structure looks like
the following. The Sun is a sphere of solar radius R* = 6.96^10^{10}
centimeters, initially composed by mass of about 70% hydrogen, 28%
helium and 2% heavier elements. About half of the mass and 98% of
the energy generation (where hydrogen fuses into helium) exists in a
core with a radius of about 0.25xR*. On top of the core is a stable
region called the "radiative zone," where the energy is transported
by radiation. At a solar radius of 0.713xR* and upwards to near the
solar surface, the temperature is low enough that convection is the
dominant mechanism for transporting energy. This zone is called the
"convection zone."

How to get material into the star considering convection?

Astrophysicists who specialize in stellar evolution have found
that stars of masses larger than a solar mass have convective
cores, the extent of which grow rapidly with increasing mass. The
convective core is a direct result of the CNO cycle being
so sensitive to temperature (the temperature instability causes
convection).

So if you want to get carbon (or any other mass) into a star, a
low mass star like of about .25 * R* has a completely convective envelope,
so it's well-mixed, and you can get your carbon in that way.

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.

Dana says that for stars more massive than about 1.2 times the mass Msun
of the Sun, the outer part of those stars is not convective, so for them,
whatever you added at "the top" would not reach the core.
But, if you could add carbon directly to their cores somehow,
then the reaction would be better catalyzed.

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Thanks for a thought-provoking post!

Amara

********************************************************************
Amara Graps email: amara@amara.com
Computational Physics vita: finger agraps@shell5.ba.best.com