Amateur Astronomers Association of Princeton

by Abhinav Sukla

Most of us will only be around for less than a century. With a lifespan that short, even the times of ancient civilizations feel unimaginably far away. When the frame of reference shifts to cosmic objects, the sheer scale of their age and longevity is completely unfathomable. There is little difference between a million, a billion, and a trillion years to someone who will live for less than 100. To better understand the differences between these numbers, we can use the classic example of equating one year to a second. 1 million seconds is about 12 days, while a billion seconds is almost 32 years. 1 trillion seconds is close to 32 millennia, over 10% of the total time humans have existed for. With this in mind, we can look at the lifespans of all sorts of cosmic objects with a comprehensive idea of just how long they will be around. 

The Sun:
The Sun is a G-type star, or yellow dwarf. These kinds of stars typically last a few billion years before they run out of hydrogen to fuse for energy, as it all fuses into helium. The gravitational forces will win for a moment, contracting and heating up the core of the Sun, resulting in more nuclear fusion in order to fight these forces, expanding the outside of the star drastically. Once the helium runs out, the star will slowly fade away, losing mass until it becomes a white dwarf.

Red dwarfs:
Red dwarfs are stars that are less massive, cooler, and smaller than our Sun, and consequently live much longer, up to 10 trillion years. When these stars run out of hydrogen fuel, most swell just as our Sun does, and they also collapse into white dwarfs once they run out of helium.

White dwarfs:
When a star collapses and becomes a white dwarf, it still has a staggering 10 trillion years or more left to live. White dwarfs are small, about the size of a city, but hold up to half the mass of the Sun, making them one of the densest objects in the universe. Because the gases are far more densely concentrated, these stars are extremely hot, around 10^5 degrees Celsius. Eventually, however, their heat radiates away, and they turn into black dwarves at the end of their lives, the longest lasting objects in the universe.

Black holes:
From here on out, the numbers begin to get a little fuzzy. The total number of years that every single human to ever exist has lived isn’t even close to a trillionth of a thousandth of a percent of the lifespan of a blackhole. Black holes were once thought to be eternal, but it was fairly recently discovered that they actually lose mass through a process called Hawking radiation. This happens when energy fluctuations near the edge of a black hole create a particle and antiparticle pair. Quantum mechanics states that space is never truly empty, which is what allows for the temporary creation of these pairs using “borrowed” energy from the black hole. Normally, these particles will annihilate each other, returning the borrowed energy. However, if the particle with positive energy escapes while the one with a negative energy density is consumed by the black hole, the black hole will lose mass(since e=mc^2). Hawking radiation is a painstakingly slow process, which is why it takes around 10^100 years for a decent sized black hole to finally die. Even this astronomical amount of time, however, pales in comparison to the lives of black dwarfs.

Black Dwarfs:
The universe is not nearly old enough to house any black dwarfs, but much is theorized about their existence and functions. Black dwarfs are extremely cold, close to absolute zero(-273°C). Their fusion is extremely weak, hardly enough to fight against the crushing gravity of these massive objects. When atoms are packed as tightly as they are in a black dwarf, the nuclei begin to press so close together that they no longer have a hold on their individual electrons. The matter inside of a black dwarf looks like multitudes of these nuclei pressed tightly together, with all of their electrons moving around between them. Because these electrons have the same charge, they repel each other, and as the gravity of the star pushes them closer together, the repulsive electromagnetic forces increase drastically in magnitude due to Coulomb’s law. It is this electromagnetic force that holds up black dwarfs. Their downfall comes about when these electrons begin to disappear. In order to understand how this happens, we must first understand how fusion occurs in general. Normally, overcoming the repulsive forces between two positively charged nuclei requires a large amount of energy, which even the Sun’s core is not hot enough to provide. However, due to the particle-wave duality of particles, there is a small chance that protons overcome these energy barriers between them, making fusion much more likely and powering stars for billions of years. When fusion occurs, a proton often has to be converted into a neutron in order to stabilize the new atom, which releases positrons, the antimatter particle of electrons. These positrons then go and annihilate the closest electrons. In normal stars, this is of little concern, but it is a crucial part of the deaths of black dwarfs. At absolute zero, this process still happens, but at a miniscule fraction of the pace. Two particles may fuse every trillion years or so, but when they do, positrons are released, and they detract from the overall number of electrons in the star. Since electrons are the ones holding up the black dwarf, each time fusion occurs, the electrons are pushed more tightly together as they begin to lose the battle against gravity. After around 10^1000 years, there are too few electrons to support the weight of the star, and it collapses in on itself in a violent explosion. These explosions will mark the end of light in our universe as it descends into darkness forever, nothing more than a cesspool of random particles in the far, far future. 

The incredible timescales of cosmic evolution stretch far beyond human comprehension. From the relatively short-lived existence of G-type stars like our Sun to the near-eternal life spans of black dwarfs and black holes, the lives of these objects unfold over periods that make human existence seem like a mere blink in comparison. Even the most enduring celestial objects, black dwarfs, will eventually succumb to the still mysterious forces of quantum mechanics rendering our universe dark and empty forever.