Ask Ethan: When do stars turn the most mass into energy?

Deep inside every star in the Universe, an incredible process occurs: the nuclear fusion of light elements and isotopes into heavier ones. Because heavier elements (at least, up to iron) have slightly lower rest masses than the sum of the light elements masses that fuse into them, the act of nuclear fusion in stars releases energy via Einstein’s most famous equation: E = mc². That energy powers the stars and causes them to shine, and as stars run out of a particular type of fuel in their cores, they evolve into the next stage of their lives until they run out of fuel entirely.

At least, that’s the conventional story you’ve likely heard. But it turns out that the tale I just related, although simplified, contains a number of common misconceptions that are present even among professional astronomers. I got the motivation to look a little deeper and clear some of these up after being prompted by a question from our reader Greg Hallock, who wrote to ask:

“I would like to know:
-how much mass typical stars convert to energy (Relative to their total mass),
-[at] what points in stellar evolution the mass to energy conversion is the greatest,
-and, for supermassive stars, how much each of the fusion shells converts (And the efficiency thereof.)”

These sound like simple, straightforward questions, but they rely on an interesting assumption: that nuclear fusion, and the radiation that gets released from those fusion reactions, is what primarily determines the lifetime, evolution, brightness, and rate of energy emission from the star. That’s not necessarily true! Let’s go through the life cycle of stars in a little bit more detail than you’re used to, and perhaps that will help paint a better picture of what truly occurs inside of them.

This animation switches between an optical view of the dark molecular cloud that houses protostar L1527 (red circle), and infrared data from the WISE mission that showcases the protoplanetary system and its outflows directly. Frangmented, contracting molecular clouds are where (and how) new stars will form. Many protostars are analogues of Sun-like stars, except they show us what our Sun may have been like 4.6 billion years ago: back when it was first forming.

The story of stars and how they shine begins long before they ever form: back when you have a giant molecular cloud of gas that will, under the force of its own gravity, contract. With plenty of molecules inside — including hydrogen, water, carbon monoxide, carbon dioxide, methane, cyanide, ammonia, and more — plus inert helium, these high mass, low density, low temperature clouds will inevitably contract. The reason is simple: the (inward pulling) gravitational force is far greater than the (outward pushing) gas pressure, and so the cloud contracts. This contraction creates pressure differences in the cloud, which leads to fragmentation into hundreds or even thousands of clumps, and those clumps will eventually become stars.

But not yet! First, the gas density rises, which causes that clump within the cloud to become opaque (i.e., the opposite of transparent) to light. Because the cloud is opaque to light, the contracting cloud can no longer radiate heat away, and so its interior heats up: hotter towards the center, where the gravitational field is the strongest. This leads to a clump within a cloud becoming a protostar, where:

• the center is a few hundreds of thousands of K,
• and decreases in temperature as we move out towards the edge,
• all the way to its surface/photosphere, which sits at just a few thousand K.

Given the large, diffuse nature of this protostar (in comparison to the modern Sun), but also given its high surface temperature, it might surprise you to learn that this protostar is more luminous (about 30 times as luminous as the current Sun) even at this early stage: before any nuclear fusion has occurred at all.

This image shows the Orion Molecular Clouds, the target of the VANDAM survey. Yellow dots are the locations of the observed protostars on a blue background image made by Herschel. Side panels show nine young protostars imaged by ALMA (blue) and the VLA (orange). Protoplanetary disks not only are rich in organic molecules, but contain species that are not often seen in typical interstellar dust clouds. For several million years after fusion in the star’s core ignites, circumstellar gas-rich material persists.

Fusion won’t begin in the core until temperatures rise into the millions of K, but this takes a very long time to happen. Gravity works to further contract the protostar, but there’s a problem: the majority of the star’s interior is completely opaque to radiation, and the gas particles inside the star are now moving around very quickly: with lots of kinetic energy. Just as the moving air molecules inside a sealed balloon hold it up against the external pressure from the atmosphere (where the balloon will deflate if immersed in an ice bath, but will inflate further if left in direct sunlight), the moving gas molecules inside the star create a substantial amount of gas pressure. It is this gas pressure, not radiation, that primarily opposes the gravitational contraction of the protostar.

Eventually — on timescales of around 25-50 million years for a protostar of the equivalent mass of the Sun (shorter for more massive protostars; longer for less massive protostars) — the star does slowly contract, causing it to become smaller, hotter (both on the interior and on the surface), and overall less luminous. That last part surprises many, but the radius of the protostar changes (and shrinks) by a much greater amount than the surface temperature increases by. At every step along the way, the gas pressure opposes the gravitational force at all radii inside the protostar. At last, the temperatures inside the core of the protostar cross a critical threshold, and nuclear fusion officially ignites, transforming this entity from a protostar to a full-fledged young star.

This composite JWST image of the object Herbig-Haro 30 in the Taurus Molecular Cloud shows many features common to young, massive stars: a dusty disk (seen edge-on here), reflective dust grains above and below the disk, bipolar jets running perpendicular to the central disk, and conical outflows dovetailing into tail-like ejecta. Inside, planets are suspected to be forming around the central young star, which has only recently transitioned from the protostellar phase into the fusion-driven main sequence phase of its life.

Now, with nuclear fusion occurring in the core of the star, there’s an additional ingredient at play: the core of the star is fusing light elements (protons, or hydrogen nuclei) into heavier elements (deuterium, tritium, helium-3, and ultimately helium-4), with each such fusion reaction releasing a net amount of energy.

What is it, then, that determines how much fusion occurs? What determines the rate of fusion?

Believe it or not, it’s the brightness of that star at the moment fusion ignites. Initially, in the protostar-to-star transition, the star’s brightness starts to decrease as the protostar makes gradual adjustments to an equilibrium (or quasi-equilibrium) state, as the center of the star is now the location of its ultimate source of energy. The gas pressure — from the heated, moving particles inside the star — is still the dominant effect in terms of pushing back against the gravitational force trying to collapse the star, with radiation pressure representing less than 0.1% of the outward-pushing force (for a star the mass of the Sun) compared to gas pressure.

When it achieves equilibrium, and does not contract any further, it’s that equilibrium state:

• where the gas pressure opposes gravity,
• and where the brightness of the star, determined by its temperature and radius, determines the rate of fusion in the core,

that achieves the energy balance within the star.

This cutaway showcases the various regions of the surface and interior of the Sun, including the core, which is the only location where nuclear fusion occurs. As time goes on and hydrogen is consumed, the helium-containing region in the core expands and the maximum temperature increases, causing the Sun to “cross the main sequence” as its energy output increases. The balance between the inward-pulling gravity and the outward-pushing gas pressure, only slightly augmented by radiation pressure (and mostly in higher-mass stars), determines the size and stability of a star, while the core’s temperature and element abundance determines the rate and species of fusion inside.

The diagram above, known as the Hertzsprung-Russell (or color-magnitude) diagram, is a plot of a star’s color (on the x-axis, where blue/high temperature stars are towards the left and red/low temperature stars are towards the right) versus its brightness (on the y-axis, where brighter stars are higher up and fainter stars are lower down). The long, snake-like line from the top-left to the bottom-right is known as the main sequence: the stage of a star’s life where it fuses hydrogen into helium, just like our Sun is doing right now and has been for ~4.56 billion years.

When a star first ignites nuclear fusion in its core, it starts off at the bottom of the main sequence: where its color determines its temperature, and its brightness is the lowest value for stars of that particular mass/color that are fusing hydrogen into helium. If there were no nuclear fusion in the star’s core, the star would:

• expand,
• become slightly cooler,
• but more luminous (and brighter),
• and would do so relatively rapidly: on timescales of about tens of millions of years.

What nuclear fusion basically does is slow that evolution down. Instead of tens of millions of years, this evolution, for a star the mass of the Sun, takes about ~10 billion years instead. We often tell a naive story — as astronomers — that the brightness of a star scales as its mass cubed: that a star twice as massive as the Sun would be eight times as bright, while a star half as massive would only be one-eighth as bright.

This graph shows the brightness of a star (y-axis) versus the mass of a star (x-axis) over the course of its main sequence lifetime. Less massive stars get much fainter (as a function of mass) very swiftly, proportional to the mass ratio to the 5th power, while the most massive stars increase in luminosity more slowly, as mass to the 4/3 power. The gradual change in the relationship is shown by the blue curve.

But as you can see, above, the actual situation is far, far more severe. The “luminosity scales as mass cubed” approximation works: for stars that are about ten times as massive as our own Sun. But for a low-mass star like our Sun, the relation is more like “mass to the fifth power” for luminosity, while for the most massive stars, luminosity only goes as mass to the four-thirds power. A star half as massive as the Sun might only have ~2% of our Sun’s energy output; a star 100 times as massive as our Sun will have ~2 million times our Sun’s energy output. It’s only for these very massive stars, the most massive ones of all, that radiation pressure is actually important in determining the evolution of a star.

Still, the energy source for the star really is from nuclear fusion happening in the core, and the rate of fusion is determined by the temperature within the core: higher temperatures mean higher rates of fusion. For any star that begins its life on the main sequence, it doesn’t just stay there — with a constant brightness and a constant rate of fusion — over its lifetime. Instead:

• nuclear fusion of hydrogen into helium changes the core’s composition,
• replacing “light” atomic nuclei (protons) with “heavier” atomic nuclei (helium-4 nuclei),
• which increases the average mass-per-particle,
• which increases the average temperature within the star’s core,
• which increases the rate of fusion over the star’s main sequence lifetime.

As a result, stars increase their luminosities over their lifetimes, moving “up” the main sequence on the Hertzsprung-Russell diagram.

This color-magnitude (or Hertzsprung-Russell) diagram shows a “snapshot” of color vs. magnitude of a wide variety of stars. When stars ignite nuclear fusion in their cores for the first time, they begin life at the bottom of the main sequence (vertically) for whatever their color is. Over their hydrogen-burning lifetimes, they migrate upwards, becoming brighter but remaining at approximately the same color/temperature, before they run out of hydrogen in their cores and begin evolving into subgiants.

When the Sun first began its life on the main sequence, it’s brightness was only about ~75% of its present day value. In another 4.5 billion years, it will be about 50% more luminous than it is today: double its initial value. And another 1.5 billion years after that, roughly, it will reach double its current brightness: right around the time that its core begins to run out of hydrogen fuel to continue the nuclear fusion reactions that have powered it for so long. Stars that are born more massive will evolve in this fashion more quickly; stars that are born less massive will evolve in this fashion more slowly. The heaviest stars might burn through all of their core’s hydrogen in just 1-2 million years; the lowest-mass stars will take over 100 trillion years to do the same! All of these changes are coincident with increased rate-of-fusion outputs.

Yet, if you were to take the Sun’s initial mass and compare it with the Sun’s mass once it runs out of hydrogen in its core, you’d find something remarkable: the mass difference over those ~10-12 billion years adds up to just about 1.5 times the mass of Jupiter, or 0.15% of the Sun’s total mass. Only this tiny conversion of mass into energy, via E = mc², is sufficient to power the Sun at roughly its current power levels for the entirety of its main sequence life.

When a main sequence star, like the Sun, runs out of hydrogen in its core, its core becomes inert and the star expands into a subgiant, while hydrogen fusion continues in a shell surrounding the core. Eventually, the core contracts and heats up, where it can initiate helium fusion if the star’s core gets hot enough, which will only happen for sufficiently massive stars. During the red giant phase, the Sun’s brightness will increase to be hundreds, or at times a factor of 1000+, of times as bright as our Sun is today.

And then, something important happens: the core, now exhausted of hydrogen fuel, no longer has that central source of energy. All it has to hold the star up against gravitational collapse is gas pressure, which still outstrips radiation pressure by a great amount (which is good, as there’s no longer a source of new radiation), and this leads to a few important changes.

• The core of the star slowly begins to contract, as the gas pressure needs to remain constant to hold it up against gravity.
• This contraction causes either the density of particles or the temperature (or both) to increase within the core.
• That increased temperature propagates outward, enabling a “shell” of fusion to begin around the (inert) core: reigniting hydrogen fusion.
• And these changes propagate to the outer layers of the star, which begins to expand.

Therefore, the star’s luminosity (or brightness) increases as the star evolves. The star first transforms into a subgiant, with a shell of hydrogen burning around a core of inert helium as its temperature drops while its internal rate of fusion increases: to ~10 and then ~100 times its earlier rate of fusion. Later on, the core contracts and heats up sufficiently in an event known as a helium flash: where the temperatures achieve such heights that the helium in the core ignites, triggering a new phase of nuclear fusion.

The evolution of a solar-mass star on the Hertzsprung-Russell (color-magnitude) diagram from its pre-main-sequence phase to the end of fusion. Every star of every mass will follow a different curve, but the Sun is only a star once it begins hydrogen burning, and ceases to be a star once helium burning (in both the core and in all shells) is completed. Stars on the upper-left of the diagram (on the main sequence) are more massive, hotter, and more luminous than our Sun, but are also the shortest-lived.

Now, the star has become a full-fledged red giant star. During this phase, there’s a core that fuses helium surrounded by a shell that fuses hydrogen, and the star evolves in color (moving along the horizontal branch) to become hotter, while decreasing slightly in brightness (or luminosity). Less massive stars (like the Sun, and all stars below about 2.3 solar masses) have a degenerate helium core that fuses, while heavier-mass stars ignite helium fusion before the core becomes degenerate. Stars can ascend the red giant branch multiple times, but again: their rate of fusion is determined by the gas properties (pressure, density, and temperature) within the core, not the other way around.

Stars that were born with more than about 8-10 solar masses will go on to have their cores rise up in temperature and begin fusing:

• carbon into neon,
• neon into magnesium (which does not fuse) and oxygen,
• oxygen into silicon,
• and silicon into iron,

before dying. It’s very difficult to determine what the relative contributions are of the various shells and cores are to these red supergiant stars; we cannot tell what phase of life a supergiant star is in, internally, by observing its exterior. In these very massive stars, radiation pressure actually becomes an important contributor to holding up the star against gravitational collapse. While we can calculate temperature-based rates of fusion and energy production, these are based on interior models of such stars that do not teach us the answer to the rate of fusion or the rate of energy production in each layer inside such a star. We simply do not know for certain; we are only certain about the total amount of luminosity released by the star at its photosphere.

When stars run out of hydrogen in their cores, they evolve off of the main sequence, becoming subgiants, then red giants, then igniting helium in their cores, and then evolving onto the horizontal branch and eventually into supergiants (for high-mass stars) or into the asymptotic giant branch (for non-high-mass stars) before dying. The mass of a star determines its ultimate fate, but the rate of fusion is set by other internal properties.

But for Sun-like stars, the greatest rates of fusion occur in the final, post-red-giant phase: the asymptotic giant branch phase of a star’s life. The helium core, now inert (after the red giant phase completes), contracts and heats up, reaching temperatures of hundreds of millions of K. A shell around the core begins fusing helium: the primary source of energy for these stars. Fusion can be ~10-100 times the rate of red giant stars and ~1000-10,000 times the rate of Sun-like stars: representing the greatest rates of fusion for any Sun-like stars. (Stars born above ~8-10 solar masses achieve their greatest total rates of fusion in the supergiant phases, burning carbon and beyond.)

The biggest takeaway is that while nuclear fusion plays a vital role inside these stars — it provides the main source of energy that powers them throughout their lives — it isn’t the answer to all questions you might have about a star’s properties.

• What determines the size of a star? Not nuclear fusion, but the balance between gas pressure and gravity.
• What determines the temperature of a star? The internal energy balance as propagated out to the outermost layers, not nuclear fusion.
• What determines the rate of fusion inside a star? The temperature, density, and elemental composition of a star at each “shell radius” inside of it, as opposed to fusion determining those other properties.

If it weren’t for nuclear fusion, stellar evolution would still occur; it would just occur more quickly and without long, steady phases where the star’s properties appear constant. All told, stars lose about 0.3%-1% of their total mass (depending on their initial mass) due to nuclear fusion over their lifetimes, but lose much more of their mass due to the ejection of their outer layers in the giant phases of their life: 50% or even more. Nuclear fusion is a key aspect of stars and stellar evolution, but the internal balance between gravity and gas pressure — at a fundamental level — is what actually determines the rate of fusion itself.

Send in your Ask Ethan questions to startswithabang at gmail dot com!