From Ethan Siegel: “Ask Ethan: Can Failed Stars Eventually Succeed?”

Ethan Siegel
Jun 24, 2017

The closest brown dwarf system to Earth, Luhman 16, contains enough total mass to form a red dwarf star if everything within it were combined. The question of whether this will ever happen in our Universe is an interesting one. Janella Williams, Penn State University.

In the night sky, the most apparent thing of all are the stars, found in every direction we dare to look. But for every star that gathers enough mass to ignite nuclear fusion in its core, burning hydrogen into helium and turning matter into energy via E = mc2, there are many other objects that didn’t make it that far. Most collections of mass that start to form in a nebula never get big enough to become a star, and instead become fragmented gas clouds, asteroids, rocky worlds, gas giants, or brown dwarfs. The brown dwarfs are the “failed stars” of the Universe, having gathered enough mass to ignite some rare-isotope fusion reactions, but not enough to become true stars. But many brown dwarfs come in binary pairs, leading Ibnul Hussaini to wonder if they might, someday, merge:

“Will the orbit of these [brown dwarfs] over a long period of time, eventually become smaller and smaller from the loss of energy through gravitational waves? Will they then eventually end up merging? If so, what happens in a [brown dwarf] merger? Will they merge to become an actual star that goes through fusion? Or is it something else entirely?”

In astronomy, as in life, just because you didn’t make it on the first try doesn’t mean you’ll never get there. Let’s start by looking at the ones that make it.

An illustration of a giant planet around a red dwarf star. The difference between a planet, a failed star, and a true star comes down to one thing only: mass. ESO.

In order to ignite nuclear fusion in the core of a star — to get hydrogen nuclei to fuse — you need to reach a temperature of around 4,000,000 K. The gas that stars form from in interstellar space begins at relatively cold temperatures: just a few tens of degrees above absolute zero. But once gravitation kicks in, it causes this cloud of gas to collapse. When collapse occurs, the atoms inside gain speed, collide with each other, and heat up. If there were only a small number of atoms present, they’d emit that heat out into the interstellar medium, sending light streaming throughout the galaxy. But when you get large numbers of atoms together, they trap that heat, causing the interior of the gas cloud to heat up.

The constellation of Orion, along with the great molecular cloud complex and including its brightest stars. Many new stars are presently forming here due to the collapse of gas, which traps the heat from stellar formation. Rogelio Bernal Andreo.

If you form something very small, like of the mass of an asteroid, Earth, or even Jupiter, you might heat up to thousands or even tens of thousands of degrees in your core, but you’ll still be very far away from that fusion temperature. But if you hit a certain critical mass — about thirteen times the mass of Jupiter — you’ll achieve a temperature of about 1,000,000 K. That’s not enough to begin fusing hydrogen into helium, but is a critical temperature for a very specific reaction: deuterium fusion. About 0.002% of the hydrogen in the Universe doesn’t just have a single proton as its nucleus, but rather a proton and a neutron bound together, known as a deuteron. At temperatures of a million degrees, a deuteron and a proton can fuse together into helium-3 (an uncommon isotope of helium), a reaction which releases energy.

The proton-proton chain responsible for producing the vast majority of the Sun’s power is an example of nuclear fusion. In deuterium fusion, only the deuterium (H-2) + proton (H-1) going to helium-3 (He-3) reaction can occur. Borb / Wikimedia Commons.

This is important! This release of energy, particularly during the protostar (i.e., star-formation) phase, generates high-energy radiation that pushes back against internal gravitational collapse, preventing the very center from getting too hot and hitting that 4,000,000 K threshold. This buys you extra time — tens of thousands of years or more — allowing you to gather more and more mass. Once you start fusing pure hydrogen (i.e., protons) in your core, the energy release is so intense that stars don’t grow any larger, so those early, first stages are critical. If it weren’t for deuterium fusion, the most massive stars would cap out at only about three times the mass of our Sun, instead of the hundreds of solar masses they reach in our backyard.

A composite image of the first exoplanet ever directly imaged (red) and its brown dwarf parent star, as seen in the infrared. A true star would be much physically larger and higher in mass than the brown dwarf shown here. European Southern Observatory (ESO).

In order to ever reach that 4,000,000 K temperature in your core, and thereby become a true star, you need a minimum of about 7.5% the mass of our Sun: around 1.5 × 1029 kg of mass. To become a deuterium-fusing brown dwarf, also known as a failed star, you need somewhere between 2.5 × 1028 kg and 1.5 × 1029 kg of mass. And just as there are binary stars out there in great numbers, so, too, are there binary brown dwarfs.

These are the two brown dwarfs that make up Luhman 16, and they may eventually merge together to create a star. NASA/JPL/Gemini Observatory/AURA/NSF.

Gemini/North telescope at Mauna Kea, Hawaii, USA

Gemini South telescope, Cerro Tololo Inter-American Observatory (CTIO) campus near La Serena, Chile

NRAO/Karl V Jansky VLA, on the Plains of San Agustin fifty miles west of Socorro, NM, USA

In fact, the closest brown dwarf to us, the system Luhman 16, is a binary system, while other brown dwarfs have been known to have giant planets orbiting them. In the specific case of Luhman 16, the masses of the two brown dwarfs are determined to be:

Between 8.0 × 1028 kg and 1.0 × 1029 kg, for the primary, and
between 6.0 × 1028 kg and 1.0 × 1029 kg, for the secondary.

In other words, there’s an excellent chance that if these two failed stars, orbiting at about three times the Earth-Sun distance from one another, were to merge, they would form an actual star. In fact, any addition of mass that takes a failed star over that mass threshold to begin burning hydrogen in its core ought to do it.

The two brown dwarfs that make up Luhman 16 have been imaged twelve separate times by the Hubble Space Telescope, indicating their motion and relative orbits over a multi-year time period. Image credit: Hubble / ESA, L. Bedin / INAF.

Ibnul’s hunch is on the right track: yes, it’s true that orbiting masses do emit gravitational waves, and that the emission of these waves will cause orbits to decay. But for these masses and distances, we’re talking about decay times of somewhere in the neighborhood of 10200 years, which is much, much longer than the lifetime of the Universe. In fact, it’s much longer than the lifetime of any star at all, of the galaxy, or even of the galaxy’s central black hole. If you wait around for gravitational waves to turn this binary pair of brown dwarfs into a star, you’re going to be waiting a disappointingly long time.

The inspiral and merger scenario for brown dwarfs as well-separated as these two are would take a very long time due to gravitational waves. But collisions are quite likely. Just as red stars colliding produce blue straggler stars, brown dwarf collisions can make red dwarf stars. Melvyn B. Davies, Nature 462, 991-992 (2009).

Every once in a while, you get random collisions between objects in space. Just the fact that stars, failed stars, rogue planets and more move through the galaxy, primarily influenced by gravitation, means that there’s a finite chance that you’ll just randomly get a collision between two objects. This is a much better strategy than waiting for gravitational waves to take your orbits down, except in the most extreme cases. On timescales of about 1018 years, “only” about 100 million times older than the Universe presently is, brown dwarfs will randomly collide with either other brown dwarfs or stellar corpses, giving new life to a failed star. About 1% of brown dwarfs, according to current estimates, will meet that fate.

The Sun’s atmosphere is not confined to the photosphere or even the corona, but rather extends out for millions of miles in space, even under non-flare or ejection conditions. NASA’s Solar Terrestrial Relations Observatory.

NASA/STEREO spacecraft

But even if you can’t wait for gravitational radiation, and even if you don’t get lucky enough to collide with another brown dwarf in interstellar space, you still have a chance to merge. We normally think of stars as having a certain extent in space: that they take up a certain volume. For that matter, that’s how we think of Earth’s atmosphere, too: as a hard edge, with a boundary between what we consider the atmosphere and outer space. How foolish is that! In reality, atoms and particles extend outward for millions of miles (or kilometers), with flares from stars reaching well beyond the orbit of Earth. It was recently discovered that brown dwarfs emit flares, too, so just as a satellite in low-Earth orbit will fall back down to our planet, the friction from a brown dwarf in orbit around another will eventually draw them in. It won’t quite work for Luhman 16, but if the distance between the two failed stars were more like the Sun-Mercury distance, rather than the Sun-Ceres distance, this effect would have a shot.

Luigi Bedin’s multi-year study observing the motions of the failed stars in Luhman 16 has shown us how their positions and motions have changed over time, with the cycloid nature resulting from Earth’s motion during the year. Hubble / ESA, L. Bedin / INAF.

NASA/ESA Hubble Telescope

So what happens if you do get a merger or a collision? These events are rare and will, for the most part, take much longer than the present age of the Universe to occur. By that point, even a brown dwarf will have burned up all of its deuterium, while the corpse will have cooled off to just a few degrees above absolute zero at the surface. But the energy of a collision or merger ought to create enough heat and pressure in the core that we should — so long as we cross that critical mass threshold — still ignite nuclear fusion in the core. The star will be low-mass, red in color, and extremely long-lived, burning for more than 10 trillion years. When a failed star at last ignites, it will most likely be the only star shining in the galaxy for its entire life; these events will be that rare and spaced out in time. Yet the type of star you become is interesting in its own right.

When two brown dwarfs, far into the future, finally do merge together, they will likely be the only light shining in the night sky, as all other stars have gone out. The red dwarf that results will be the only primary light source left in the Universe at that time. user Toma/Space Engine; E. Siegel.

It will burn its fuel so slowly that the helium-4 which gets made — the product of the core’s hydrogen fusion — will eventually convect out of the core, enabling more hydrogen to fuse in the core. The convection is efficient enough that 100% of the star’s hydrogen should burn to completion, leaving a solid mass of helium atoms. There won’t be enough mass to burn that helium any further, so the stellar remnant will contract down to a type of star that doesn’t yet exist in the Universe today: a helium white dwarf. It will take roughly a quadrillion years for this white dwarf to cool down and stop emitting light, during which time other brown dwarfs in the galaxy will collide and ignite. By time a failed star finally succeeds and goes through its entire life cycle, becoming a black dwarf, another failed star will gets its opportunity.

An accurate size/color comparison of a white dwarf (L), Earth reflecting our Sun’s light (middle), and a black dwarf (R). When white dwarfs finally radiate the last of their energy away, they will all eventually become black dwarfs. BBC / GCSE (L) / SunflowerCosmos (R).

If you managed to achieve some type of immortality, you could, in theory, travel from failed star to failed star, continuing on by drawing your energy from the Universe’s final, rare successes. Most failed stars will remain failures forever, but the few that succeed will be burning long after all other lights have gone out. As Winston Churchill famous said, “Success is not final, failure is not fatal: it is the courage to continue that counts.” Perhaps that applies to even the stars, even moreso than to ourselves.

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“Starts With A Bang! is a blog/video blog about cosmology, physics, astronomy, and anything else I find interesting enough to write about. I am a firm believer that the highest good in life is learning, and the greatest evil is willful ignorance. The goal of everything on this site is to help inform you about our world, how we came to be here, and to understand how it all works. As I write these pages for you, I hope to not only explain to you what we know, think, and believe, but how we know it, and why we draw the conclusions we do. It is my hope that you find this interesting, informative, and accessible,” says Ethan