Starry, Starry Night

Hanging in the Museum of Modern Art (MoMA) in New York City, van Gogh’s remarkable The Starry Night is described in part by this MoMA excerpt:

In creating this image of the night sky — dominated by the bright moon at right and Venus at center left — van Gogh heralded modern painting’s new embrace of mood, expression, symbol, and sentiment. He was inspired by the view from his window at the Saint-Paul-de-Mausole asylum in Saint-Rémy, in southern France, where the artist spent twelve months in 1889–90 seeking reprieve from his mental illnesses.

By the way, at the bottom of the MOMA article, there is a marvelous 3–D interactive application to investigate the colors and brushstrokes at close quarters. Use the mouse wheel to zoom, click and drag to pivot. Try it, it’s amazing!

Many of us are also familiar with the Don McLean popular hit song Vincent, a paean to van Gogh from Don’s iconic American Pie album, which many think is entitled Starry, Starry Night, from the first stanza of the lyrics.

Starry, starry night.
Paint your palette blue and grey,
Look out on a summer’s day,
With eyes that know the darkness in my soul.

Back Down to Earth

Unlike van Gogh and his latter–day amanuensis Don, starry nights don’t imbue me with a sense of depression or dread; on the contrary, I can’t get enough of them. A significant fraction of my professional career has been devoted to astronomy, where my specialty is stellar astrophysics. I study the life and death cycles of stars much like our own Sun, with an emphasis on the late stages of their evolution. I sometimes tell my students I am a stellar necrologist, that is, I used to, having retired in full five weeks ago.

In what follows, I’ll narrate what is to me a spellbinding tale of how the Universe uses stars to take its two most abundant elements, hydrogen and helium, and from them synthesize all the other elements in chemistry’s periodic table. To me, this is an accomplishment of miraculous genesis. Once all the elements are in place, all that exists follows from well–established and largely well–understood principles.

All stars, with near–certainty, form planetary systems via the same processes that formed the stars themselves, and it is on exoplanets where we will find life beyond that on Earth. Whenever I reflect on the physical laws which govern the universe, laws which we are somehow able to understand through a working knowledge of creation’s native language of mathematics, I am filled with awe and wonder. If I can infect two or more of you with this sense of astonishment and delight, and you do the same, oh what a wonderful world this could be.

In the Beginning

1 When God began to create the heavens and the Earth,
2 the Earth was complete chaos, and darkness covered the face of the deep,
while a wind from God swept over the face of the waters.
3 Then God said, “Let there be light,” and there was light.
Genesis 1:1–3, New Revised Standard Version, Updated Edition.

Contemporary Western science leads us to believe that the Universe came into being about 13.7 billion years ago in a spontaneous, ex nihilo appearance of an unimaginably tiny, incomprehensively hot and dense region of space and time colloquially known as the Big Bang. At first, the temperature and density were so high that stable matter could not exist, and all that did exist was light in the form of high energy photons, and so–called virtual pairs of matter and antimatter that blinked into existence and almost immediately annihilated each other and vanished.

What Came Next?

Subsequently, the Universe expanded and cooled. When it was about 400,000 years old, the temperature and density became low enough for neutral atoms of hydrogen and helium to exist, along with very small traces of beryllium and lithium. Neutral atoms have the same number of electrons as the number of protons in the nucleus; these two types of charged particles are attracted to each other and are bound together by electrical forces. But no other elements were made at this time because the conditions that favored their formation lasted for only a very short time. This gaseous mixture was not uniformly distributed; it had very small fluctuations of about one part in 100,000 above and below the average density.

Regions which were slightly over–dense began to collapse under the influence of their own self–gravity, becoming more dense and hotter as they did so. The gas atoms, originally neutral, became completely ionized once again (a form of matter called a plasma), stripped of electrons and existing as bare atomic nuclei. For the most common form of hydrogen, this is just a single proton. For helium, this is a nucleus with two protons and two neutrons tightly bound together by what is called the strong nuclear force.

Eventually, such contracting balls of gas become sufficiently hot and dense in their centers to ignite the flame of nuclear fusion. In what is called the proton–proton chain, the primary source of energy in all but the most massive stars, collisions between two protons cause the particles to fuse (become bound to each other) and form deuterium, the second most common form of hydrogen, with one proton and one neutron in the nucleus. The transformation of a proton into a neutron is accomplished by the weak nuclear force and is accompanied by the release of a positron (an antimatter electron) and a neutrino, an almost massless particle that interacts with ordinary matter only very weakly.

Further collisions of deuterium and protons form nuclei of helium 3 (two protons and one neutron), and finally collisions of two helium 3 nuclei form one nucleus of helium 4 (two protons and two neutrons), releasing two protons back into the fusing plasma. Along the way, heat in the form of increased particle speeds and pressures, and energy in the form of gamma rays (high energy photons of light) are released.

Eventually, the rising temperature and pressure at the center of the star (which tends to make it expand) counterbalance its own self–gravity (which tends to make it contract), and the star achieves a state of stable equilibrium, with a size depending on its total mass. Fusion takes place only in the central core region, which for stars much like that of our own Sun contains about 10% of the total mass. The light released there makes its way to the surface, and the star shines with a total luminosity that also depends on its mass. The emission of light at the surface comes at a cost, namely, the steady conversion of hydrogen to helium in the core.

Hydrogen is the fuel supply of these stellar engines, and like all finite supplies it must eventually become exhausted. The engine sputters, then stops entirely, and the star dies. Stellar lifetimes depend strongly on the total mass, which lies between about 8% of the mass of our own Sun for tiny stars known as red dwarfs, up to about 250 times the mass of our Sun for stellar behemoths known as blue supergiants.

Objects with masses less than 8% of our Sun never get hot or dense enough in their centers for nuclear fusion to get started, and those with masses above the upper limit generate so much heat, light, and pressure that they literally blow themselves apart and cannot achieve a stable equilibrium. Our own Sun will have a lifetime of about 10 billion years, and at a current age of about 4.6 billion years, it is just entering middle age.

As I have written elsewhere, the low mass stars outnumber the high mass stars by a very large margin. It’s like a riverbed. There is a lot of fine mud, a fair amount of sand, fewer pebbles, even fewer stones, and hardly any boulders. Stars like our own Sun, or enough like it to support life as we know it, exist in a narrow range of about 0.5–1.5 solar masses and comprise less than 10% of all the stars in the universe. But these stars are not massive enough to create elements heavier than carbon, nitrogen, and oxygen (CNO) in subsequent stages of nuclear fusion.

The CNO elements are of course the basic building blocks of life. In the presence of hydrogen, these form molecular compounds such as methane (CH₄), carbon dioxide (CO₂), ammonia (NH₃), and of course water (H₂O), the universal solvent without which no organic chemistry can take place at all. These organic molecules in turn are the basis for the chemistry of life, including proteins, carbohydrates (sugars), lipids (fats), and nucleic acids (the steps on the ladder of DNA).

But these molecules by themselves are insufficient to sustain life. Trace quantities of many of the higher elements are necessary, among them sodium (Na), potassium (K), iron (Fe), zinc (Zn), copper (Cu), selenium (Se), chromium (Cr), cobalt (Co), iodine (I), manganese (Mn), and molybdenum (Mo). If stars like our Sun cannot make these, which stars do?

Big ones! After being synthesized in the cores of stars having masses larger than about 9–10 times that of our Sun, these elements, collectively known as “metals”, are spewed by supernova explosions back into the interstellar medium (ISM) from which all stars form, thus seeding the original mixture of about 90% hydrogen and 10% helium. Subsequent generations of stars forming from this enriched material incorporate these metals.

As a consequence, not only did planets and life not exist in the early Universe, they could not have done. In the beginning, with the very first stars lacking elements heavier than hydrogen and helium, no Earth–like planets could exist since there would have been no silicon to form rocks, nor any CNO for life. The earliest stars were massive and barren, planet–less and necessarily lifeless. Luckily, at least for us, massive stars have very short lifetimes, so enrichment of gas and dust in the ISM could begin almost immediately, as these things go.

Still, we note that our Sun is believed to be a “third–generation” star, formed from gas and dust enriched by two previous generations of massive stars via fatal supernova explosions. Since the ages of the Universe and Sun are 13.7 and 4.6 billion years, respectively, it evidently took about 2/3 of the lifetime of the Universe for the Sun to form. This is not to say that other Sun–like stars with enriched metals did not form elsewhere and earlier. See my previous article Is Anybody Out There? for a more detailed description of these processes and the implications for the existence of extraterrestrial lifeforms.

Live a Little, Die a Little

So much for the lives of stars. What about their deaths? As previously noted, all stars have a finite fuel supply and must “run out of gas”, both literally and figuratively. Now it happens that small stars burn their nuclear fuel at a much, much lower rate than massive stars. So even with a considerably smaller initial fuel supply, low–mass stars live much longer than massive stars.

Think of a race between a top fuel dragster vs. a Volkswagen Beetle. The dragster carries a supply of about 25 gallons of nitromethane fuel which it consumes at a rate of 77 gallons per minute at full throttle. It will consume almost all its fuel during warmup, burnout, staging, and the quarter-mile contest, for which the world record time is currently 5.09 seconds.

Conversely, the 2019 Beetle carries 14.5 gallons of Regular and gets 33 miles per gallon on the highway, giving it a range of about 480 miles. At a highway speed of, say, 65 mph, its fuel supply, about half of that of the dragster, will last for 7 hours and 20 minutes, almost 5,200 times as long than the dragster with its larger supply.

The smallest possible star, with less than one–tenth the mass of the Sun, will live for ten trillion years before it consumes all its hydrogen, while a leviathan with 200 times the mass of the Sun will die only 250,000 years after it is born. But beyond the time of death, what is the nature of those deaths? Again, like so much else, this is strongly dependent on the stellar mass.

Stars with up to about 8 Solar masses, including our own Sun of course, have cores that are only able to make elements up to oxygen, with perhaps a trace of neon. When the central fusion furnace is extinguished, the cores can no longer hold themselves up and slowly contract until they stabilize as remnant called a white dwarf. White dwarfs have masses between about 0.6 and 1.4 Solar masses and a radius about the same as the Earth. For comparison, the Sun has a radius about 110 times that of the Earth.

The matter in a white dwarf (mostly carbon and oxygen) is highly compressed, with an average density some 200,000 times that of the Earth. One sometimes hears the phrase “a teaspoon weighs a ton” as a description, and this turns out to be close, within a factor of two or three. As things astronomical go, this really is quite close.

Stars in the 10–20 Solar mass range have cores that cannot initially support themselves when nuclear fusion ceases. They go into freefall and collapse into a remnant called a neutron star, so named because the density is so high that protons and electrons are crushed together and become neutrons. They have masses about twice that of the Sun, but a radius of only about 10 km — this is about the same as the length of Manhattan, which despite my loathing of New York City somehow is always used as the comparison.

The density is another couple of million times larger than that of a white dwarf, about 100 trillion times that of the Earth. A piece of a neutron star the size of an average grain of sand would weigh about 2000 tons, if only one could find a scale that would not be destroyed in the process.

Stars larger than 20 Solar masses have cores that cannot be supported at all, at any density or size, when fusion ceases. When they go into freefall, nothing can stop it. All the remaining mass, up to several Solar masses worth of material, theoretically collapses into a singularity, a mathematical point with formally zero volume and infinite density. This violates all known laws of classical and quantum physics, so clearly there is something desperately missing in our current understanding.

The escape velocity (the velocity at which a projectile fired straight up would not turn around and come back) at the surface of a mass depends on the mass and radius:

where G is Newton’s constant of Universal Gravitation (a number), M is the mass, and R is the radius. Plugging in some numbers, for the Earth this is about 11.2 kilometers per second (km/s) or about 25,000 mph. For a neutron star the value is very large and is best expressed as about 3/4 of the speed of light.

As the equation suggests, for a given mass, the smaller the radius the larger the escape velocity, and if that radius becomes too small the escape velocity will exceed the speed of light. This is called the Schwarzschild Radius and is what we use to define a black hole. For a 3 Solar mass remnant this has a value of about 9 km, again about the length of despised Manhattan.

A black hole does not have a surface, per se. Rather, the Schwarzschild Radius is a boundary in space inside of which the gravity is so strong that nothing can get out, not even light. It’s like the Hotel California – once you check in you can check out, but you can never leave.

What Does It All Mean?

Well, that is probably enough about that, perhaps more than enough. Pulling back from the esoterica of stellar astrophysics and trying to regain a global, no, a Universal perspective, I find the cosmos to be a thing simultaneously bizarre and beautiful, awe–full and worthy of praise and devotion. Let us return to the beginning of this article, where like the mythical ouroboros, a symbol depicting a snake or dragon devouring its own tail and representing the eternal cycle of destruction and regeneration, we can come full circle, from stellar birth to life to death to rebirth.

After 13.6 years of existence, and 4.6 billion years since the birth of our Sun, the Universe has somehow managed through the agency of stars to evolve intelligent life on our planet. Well, if not strictly intelligent, then self–aware at the very least. In a process that we still do not understand, not even in its broadest strokes, conscious mind has arisen in the three–pound blob of neuron–packed jelly we carry around in our skulls. Of all the mysteries in the Universe, this might be one of the hardest nuts to crack, if ever.

The human brain is arguably the most complex object in the known Universe, with upwards of 100 billion neurons. Each neuron may have as many as 10,000 connections to other neurons, for a total of perhaps 1,000 trillion (one quadrillion) synapses. This exceeds the number of stars in the Milky Way Galaxy by a multiplicative factor of at least 1,000. With this organic supercomputer, we have managed to puzzle out significant details of the workings of the physical Universe, although as black holes and other exotica show, there is much that remains mysterious. Science deals with the physical, observable, computable aspects of the Universe.

Science also has integrated within it the means to recognize its limitations, many of which make it difficult, even impossible, to reconcile things we indisputably observe to exist with an understanding of those same things. The Universe is not a closed logical system. Kurt Gödel’s First Incompleteness Theorem demonstrates that we can make certain valid statements (propositions) within a consistent, formal system of logic that cannot be proved to be true or false within that same system. We can ask questions that cannot be answered, even in principle. The Second Incompleteness Theorem makes things much worse; any such formal system cannot even prove that the system itself is logically consistent.

Horatio:
O day and night, but this is wondrous strange.

Hamlet:
And therefore as a stranger give it welcome.
There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.

Long before Gödel, Shakespeare understood and eloquently expressed that there are things in this Universe that exist beyond the boundaries of rational cognition and cannot be known. There does exist such a thing as transcendence, yet its existence does not invalidate the methods or conclusions of science. This is precisely because science respects its own built–in boundaries, beyond which it is not competent. Science and Religion (or better for me, Faith) are what Steven Jay Gould described as Non–Overlapping Magisteria, two almost completely exclusive domains of expertise and method which are authoritative within those domains, but not outside them.

Science concerns itself with determining what the universe is (ontology), using certain methods for how that might be known (epistemology). Faith concerns itself with moral and ethical values and the spiritual meaning of our lives. If we are to live as happy, fulfilled, and wise beings, we should embrace both magisteria. Although separate, each exists in contact with the other, and valid exchanges of information can take place across the boundary. In Gould’s words,

Many of our deepest questions call upon aspects of both for different parts of a full answer — and the sorting of legitimate domains can become quite complex and difficult. To cite just two broad questions involving both evolutionary facts and moral arguments: Since evolution made us the only earthly creatures with advanced consciousness, what responsibilities are so entailed for our relations with other species? What do our genealogical ties with other organisms imply about the meaning of human life?

If science has taught me anything, it is how little I know about the most important things, and how vital it is that I keep an open mind about almost everything. It is humbling but not humiliating to know this, for humiliation is injured pride, while humility is a lack of false pride, a painfully learned distinction. Alas, if only I could better practice what I know to be true. But as I often remark about results in the bridge games I play, I’m not responsible for the outcome, only the effort.

All the best,
On Thursday, June 16, 2022 at 5 PM EDT
Rex

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Rex Saffer the AstroDoc

Rex Saffer the AstroDoc

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Retired Physics Professor, Motorcyclist, Bridge Player, Voracious Reader, Philosopher, Essayist, Science/Culture Utility Infielder