How big can mountains be on a neutron star?

Neutron stars are one of the densest stellar objects, with a density roughly five times that of the atomic nuclei. While the atomic nucleus is held together by nuclear forces, the neutron star is kept under gravity. They are so dense that a teaspoon full of neutron star mass could weigh around a trillion kilograms. And the most recent news on neutron stars has come from the University of Southampton, where the study lead by Ph.D. Student Fabian Gittins showed even the tallest ‘mountains’ on the surface of a neutron star could only be fractions of a millimetre high.

A typical neutron star weighs about 1.5 times the solar mass, while its radius is just over 10 km. And hence, the gravitational field on neutron stars is about 2 billion times stronger than that on earth. This extreme gravity squeezes the neutron star leading it to acquire a near-perfect spherical shape. But nothing in nature is perfect, and scientists have been trying to quantify the irregularity of the surface of the neutron star for almost several decades. The surface irregularities on the neutron star —quadrupole deformations from a perfect sphere are often termed as ‘mountains’ even though they are several orders smaller than the mountains on the earth.

The neutron star’s crust, about a kilometre thick, has the least density but is extremely hard and smooth. The neutron star mountains, which could more appropriately be called ‘hills’ or ‘bumps’ as quoted by Gittins, are found on this crust. They are formed when the star changes shape, usually under strain and begin to crack. The reasons for the formation of these mountains could be many. This could be the increased pressure due to the electromagnetic radiations surrounding the star or the changes in the spinning rate of the neutron star. The sudden increase in its rotational speed is often called glitching.

Whatever be the reason for the mountain formation, the size of the neutron star mountains is always limited by the amount of strain it can withstand before it breaks. “The stronger the crust is, the larger the mountains it can support”, said Gittins. The strength of the crust enables the star to hold large mountains, but the strong gravity counteracts with about a billion times stronger downward force. The enormous gravitational pull of neutron stars, thus, makes sure that the mountains are never higher than about a hundredth of a millimetre.

The Study on Mountains formation

The studies presented on July 19 at the National Astronomy Meeting 2021 in the U.K. reveal the maximum possible height of the mountains to be a hundred times smaller than the previous estimates. Ushomirsky et al. (2000) first carried out a maximum-mountain calculation in the context of Newtonian gravity using Cowling approximation of pulsating neutron stars. They assumed that the crust was subjected to an evenly distributed strain over the entire crust rather than at the point of mountain formation. This is what lead to the gross overestimation of the maximum size of the mountains. This overestimation was seen even in future relativistic calculations by other groups.

While the previous calculations were based on specifying the strain on the crust, the research led by Fabian Gittins chose a different approach. Instead of starting with the strain, they began with a description of the perturbing force that causes mountain formation. Also, in this approach, the neutron star crust was not maximally strained at all points, instead only at one point where the mountain was located. This provided for a more realistic calculation. The perturbing force deforms the star to give it a non-spherical shape. The maximum mountain size was then calculated considering the star’s evolutionary history, composition, and other factors.

This deforming force is often an abstract force, the form of which we are sure of. Hence many different forms of force were considered in the calculation. The three sources for the perturbations used in calculation by Gittins were: (i) a potential that satisfies Laplace’s equation, (ii) a potential that satisfies Laplace’s equation but does not act in the core, and (iii) a thermal pressure perturbation. All these three different calculations produced similar results for the upper limit on the size of the neutron star mountains.

This newly determined upper limit on the size of these mountains also impacts the detection of gravitational waves from the neutron stars. Owing to their small size, it is challenging to detect neutron stars using their light, and gravitational waves come to our rescue. Gravitational waves are the ripples in the space-time fabric around an accelerating body. A perfectly symmetric spinning body will never emit these radiations. The rotation of the neutron star that is deformed asymmetrically can create gravitational waves. And higher the deformation, the higher the chances to detect these waves.

Scientists have not been able to detect gravitational waves from spinning neutron stars so far. The smaller the deformations, the more difficult it is to detect the gravitational waves emanating from the star. Detecting a millimetre-sized bump on a 10 km wide object is quite a task! This lack of detection also confirms the findings of Gittins on the size of the mountains.

With the development of third-generation gravitational wave detectors such as those at LIGO, VIRGO, etc. we hope to detect these waves from neutron stars soon enough.

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