Re: Universe principles [was Re: Carbon in the grand scheme]

Amara Graps (
Sun, 24 Oct 1999 16:32:16 +0100

Robert J. Bradbury ( Thu, 21 Oct 1999 writes:

>Amara provided a nice condensed version of nucleosynthesis

I should have stated my references. Here they are.

(References to my previous Nucleosynthesis message)

Clayton, D. _Principles of Stellar Evolution and Nucleosynthesis_, U of Chicago Press, 1983. (this is the usual textbook for graduate Stellar Evolution courses)

Shu, F., _The Physical Universe_, University Science Books, 1982.

Christensen-Dalsgaard, J. _Lecture Notes on Stellar Structure and Evolution_ , 4th Edition: August 1995.

And _your_ coffee-table references ...

>Since I've been wrestling with the Dark Matter question since
>Extro3, my living room coffee table is buried under a number
>of references, including:

>100 Billion Suns, Rudolf Kippenhahn

Kippenhahn is a really good writer. I have his book on the Sun. You might like his _Stellar Structure and Evolution_ by Kippenhahn and Weigert, 1990, Springer Verlag.

>Structure and Evolution of the Stars, Martin Schwarzchild

A little bit strange book. It's dated (written 1958). His equations are not useful for helping one solve homework (practical?) problems because he states them in a nonstandard way that other texts don't use and he makes frequent use of parametric forms and approximations (which could, on the other hand, provide insight). His layout of the boundary value problem that is necessary to solve to arrive at the Standard Solar Model, is really clear, and I think that his presentation and approach was followed by many astrophysicists in the 60s and 70s, before computers got better and faster.

>Stars and Their Spectra, James B. Kaler

Great book. (I wish I had had it when I took most of my graduate astrophysics courses 15 years ago.)

>Stellar Evolution, Amos Harpaz

I don't know this one.

>Galactic Astronomy, James Binney & Michael Merrifield

This is probably a standard textbook. I have an earlier one: _Galactic Astronomy_ by Mihalas and Binney, Freeman, 1981.

>Dark Matter, Missing Planets & New Comets, Tom van Flandern

I don't know this book, but I would be skeptical of his writings.

>Nucleosynthesis and Chemcial Evolution of Galaxies,
>Bernared E. J. Pagel (which IMO is probably the best of
>the bunch).

I don't know that one. I'll have to take a look, next time I'm in a bookstore in the States.

In your message, you managed to put forth some of the big questions in astronomy.

First about the depletion of rare light elements: 2D, 3He, Li, Be, and B.

I wrote:

>So you see, an important feature in understanding
>nucleosynthesis is the energetics of fusion, as determined by
>the atomic mass excesses and the mean binding energy per
>nucleon. "boron" doesn't have the right atomic and binding
>energy to fit in the scheme of the nucleosynthesis processes
>(P-P chain, CNO chain), and so you see how carbon is a natural
>fusion product of heavier stars.

And you said:

>But *why* does B not have the proper binding energy?

>The question of why nucleosynthesis doesn't produce Li, B, or
>Be in much abundance is related to this.

To clarify, I think what you are asking. These rare light elements (2D, 3He, Li, Be, and B.) are primarily bypassed in stellar nucleosynthesis, and you are wondering why is that?

I thought that it was because that these elements are easily destroyed at the typical conditions inside of a main sequence star. And because of this fact (i.e. lithium et al. easily destroyed by thermonuclear processes), one can use lithium to find the age of the Sun and other stars.

Clayton (p 73-74) offers some comments to that: "The initial galactic abundances of these species are unknown, and it may be that their abundances are primarily remnants of an early cosmological phase of the universe or that they are synthesized in nonthermal events in a star's outer surface or they were produced and/or modified in the early history of the solar system."

There is something related to this, called the "Lithium Depletion Problem" in astronomy, that I'll try to summarize.

Lithium is easily destroyed by nuclear reactions with protons.

For 6Li:
6Li + 1H --> 4He + 3He T > 2E6 K

For 7Li:
7Li + 1H --> 2 4He T > 2.4E6 K

If one observes the lithium abundance in the atmosphere of the Sun, we don't see any 6Li, and we do observe a weak 7Li line, but the 7Li abundance is reduced by a factor of ~100 compared with the abundance observed in meteorites and the early-phase stars: T Tauri stars.

Therefore, in the outer (convective) regions of our Sun, mixing processes must carry all of the 6Li and most of the 7Li down to layers in the star, which are hot enough to destroy it. Since we don't see much of lithium in our observations, then we know how deep the star's convective layer is, that the lithium reached to, in order to be destroyed. And once we know the depth of the convection zone, then we know the time involved for the lithium to be destroyed, from theories of convective transport. In the Sun, material mixes through the convection zone in about one month.

Since we know that _all_ of the 6Li is destroyed, the convective zone must be able to do down to _at least_ 2 million degrees. However, we _do_ see some 7Li, so the convective zone does not reach all of the way down to 2.4 million degrees. Astronomers think that "slow overshoot" is the process that reduces the 7Li abundance on a time scale of 1 billion years.

It's certain that the Sun's lithium has been depleted over time. As a star ages, its convection zone becomes deeper, and hence the amount of lithium will be reduced in time, because the lithium is able to reach deeper to hot temperatures that destroy it. But for stars with supposedly shallow convection zones, such as F0-F5 stars, we also see severe lithium depletion, so the problem is: how did the lithium get destroyed? The astronomers have to come up with another process to convective mixing (such as "rotation induced mixing" or "diffusion") to explain the surface lithium depletion for F0-F5 stars.

I don't really know how "big" of a problem this lithium depletion is, since I'm not working in this field, and haven't followed closely all of the developments.

I do know from my previous job (working for a group of helioseismologists), that the helioseismology results (GONG/SOHO) during the last 5 years really nailed down the stellar evolution models. In fact, stellar evolution processes are among the things known best in astronomy. Helioseismologists routinely use numbers from the standard solar models that match observations that are in the 2nd decimal place (for example, the radius of the convective region of the Sun is known to that accuracy).

And these helioseismology results have shown that other explanations than a revision of the stellar evolution theories will be required to explain the "Solar Neutrino Problem." People like John Bahcall have invoked other things to explain it, such as some intrinsic neutrino properties being different from what they are currently thought.

Now about "Universe" Principles.

I wrote:

> Why is nucleosynthesis like this in our universe ?
> (I don't know the answer to that)

You said:

>This was really more the point of my previous comment. Dyson
>pointed out in several places the degree to which some of the
>fundamental constants & forces are constrained to produce the
>universe we see.


>Have any serious physicists sat down and designed universes
>with physical constants that would have much better or worse
properties than our own? [Sounds like a way to manufacture
>many Physics PhDs, just as "clone & explain" a gene is now
>doing in molecular biology...]

I don't know. I agree that it would be great PhD thesis material.

I know that some have worked on the "inverse problem", that is, given our current Universe, derive the relationships between the constants, leading to what we currently observe.

In the later part of his career, in the early 1930s, Arthur Eddington attempted to derive from pure mathematics and general principles of physics his "cosmical numbers", which were dimensional units which he hoped would unify quantum theory with gravitation through the apparent relationships among certain numbers such as: the radius of curvature of the earth, the recession velocity constants of the external galaxies, the number of particles in the Universe, and the physical constants such as the ratio of the mass of the proton to the electron, the ratio of the gravitational to the electrical force between a proton and an electron, the fine structure constant and the velocity of light.

This work was published in _The Expanding Universe_, Cambridge University Press, 1933, in a chapter called "The Constants of Nature". Some see this work as a "curious fall" from his standards as an astrophysicist because his efforts were seen to be more rationalization than deductions.

In 1938, Paul Dirac, also explored the physical constants. (Dirac, P., "A New Basis for Cosmolgy", Proceedings of the Royal Society, 1938, pp. 199-208). Dirac found that 10^{40} is particularly prominent as it represents the ratio of the force of electrostatic attraction between a proton and an electron to the force of gravitational attraction between the two particles. The known radius of the Universe is also about 10^{40} times the radius of an electron. And 10^{40} represents the square root of 10^{80} - the number of particles in the cosmos. So Dirac hypothesized a model of the Universe that relies extensively onthe number 10^{40}.

In more recent times, a nice description of the Cosmic Numbers was writen by Edward Harrison in _Cosmology_, Cambridge University Press, 1981, in a chapter called "The Cosmic Numbers". It's not even an "inverse" approach, in that he shows that there is nothing extraordinary about these numbers except the coincidental ways in which they appear in nature. Harrison explores in an interesting and entertaining way the entire range of natural units, from the radius of the nucleon (fermi), to the time required for light to travel across one fermi (which is known as a "jiffy").

I found the 3 references above in a 3 volume book series called _The World of Physics_ by Weaver, which has original physics papers from ancient times to the present. I recommend this small 3 volume series to anyone who wants to read the original writings from some of the great thinkers in the physics field. (I always learn something delightful when I open these books. Knowing the historical framework of concepts that are so often taken for granted, is really important, I think.)


Amara Graps                  email:
Computational Physics        vita:  finger
Multiplex Answers            URL:
     "Trust in the Universe, but tie up your camels first."
               (adaptation of a Sufi proverb)