Bad astronomy | Neutron star mountains can be very, very small

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The highest mountain on earth – measured from its base to its summit – is the Mauna Kea volcano with a height of 10,200 meters.

On a neutron star the highest mountain would be a millimeter high. Maybe up to an inch.

That’s what new research has shown into how these tiny but ridiculously powerful objects work. It might seem a little esoteric to wonder how high a mountain can be on the ultra-compact remnant of a massive star core, but it turns out that it has some pretty important implications for astronomy.

Neutron stars are formed when stars with 8 to 20 times the mass of the sun end their life. The outer layers of the star explode outward as a supernova, but the core collapses downward. The core is hundreds of thousands of kilometers in diameter, but contracts into a sphere less than 30 kilometers wide. All of the protons and electrons in the atomic elements in the nucleus (plus antineutrinos if you keep the score) combine to form neutrons, creating a neutron star.

They are incredible, almost inappropriately dense, with up to a hundred million tons in every cubic centimeter of material (called Neutronium). This crushes their surface gravity, about a billion times greater than that of the earth.

ON billion. On a neutron star, I would weigh as much as a small mountain.

But I wouldn’t be nearly that tall. Gravity is so strong that anything that tries to pile up will be shattered. This also applies on earth: Mountains can only get so high that they collapse under their own weight; the fabric on top presses on the fabric underneath, which then flows away. That is why high mountains are made of hard rock. Try making one out of mud and it won’t get very high before collapsing.

This problem is billions of times worse with a neutron star. Another problem is that a mountain must be supported by the crust below. The earth’s crust can only take so much weight until it is deformed by the pressure, which also limits the size of the mountains.

A neutron star also has a crust of material, and it’s much stronger than Earth’s. But with a hundred billion times the downward force, even a neutron star crust can only withstand a limited amount.

How much?

This problem has been addressed by scientists for several decades, but it is difficult. For one thing, gravity is so strong that using Isaac Newton’s simple math formulas won’t work. You have to use Einstein’s general theory of relativity which is much more complex but solves the equations more easily.

You also need to know how thick a neutron star crust is, and that is a quantum mechanical problem that is … difficult. However, approximations can be made to make the calculation easier. The common answer is that a mountain on a neutron star can get about four inches tall before it breaks through the crust.

However, the computational math makes a funny assumption: the mountain puts pressure on the entire crust, not just the place it sits on. This assumption makes the math a lot easier, but it seems clear that long before the entire crust breaks, you will have a big problem building a mountain locally on a neutron star.

This is what the new job is about. They find that the critical size of a mountain depends on many other factors, including how it was made (perhaps material is being pulled off a companion star, or the malevolently strong magnetic field helps lift matter from the surface). When they do their calculations, they find that the tallest mountain can be up to an inch high, but can go up to less than a millimeter, depending on specific local conditions.

A mountain that is less than a millimeter high! That is ten millionth the size of Mauna Kea. However, to scale it would still be billions of times more difficult to climb due to the strong gravity. I’m exhausted climbing a few thousand meters here on earth, so I’ll probably put my neutron star hiking plans on hold.

In other words: the height of Mauna Kea is 0.08% of the diameter of the earth. The height of a 1 mm high mountain on a neutron star is 0.000003% of its diameter. Tiny. Neutron stars are smooth.

All of this has interesting implications. Neutron stars tend to spin quickly, and it takes from a few seconds to sometimes as little as a handful of milliseconds to spin once. Over time, this speed slows down as the neutron star loses rotational energy due to various factors. For example, its strong magnetic field can carry away charged subatomic particles in space around it. This acts like a parachute and creates a drag that slows down the spin.

But they can also emit gravitational waves that literally shake the fabric of spacetime. A perfectly symmetrical, rotating object like a sphere or even a flattened sphere does not emit these waves, but any deviation from them does will create them. Let’s say a bump on the side of a neutron star. This raises the symmetry and creates the gravitational waves. These waves get their energy from the star’s spin, so the star’s rotation slows down as they are created.

We have never seen these waves from a spinning neutron star, but scientists hope to see them one day. The size of the mountain will determine how much energy the waves have. So if we are ever to discover them, we need to understand how mountains behave on neutron stars.

In addition, these calculations are interesting in and of themselves. Neutron stars are fascinating and terrifying, and the cause of many even more terrifying phenomena like magnetars (yes, read this about magnetars if you dare). So the better we understand them, the better.

And it’s just cool. A mountain smaller than a grain of sand, but one that weighs trillions times more! The universe is such a strange place, and the more we learn about it, the stranger and grander it gets.


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