Quantum vacuum may explain slowing of pulsar spin

Study points to friction caused by contact with "void" as one of the energy-loss mechanisms affecting these ultracompact astrophysical bodies.

By José Tadeu Arantes  |  Agência FAPESP – The resistance to movement offered by the vacuum of space may slow down the rapidly spinning neutron stars known as pulsars. This intriguing hypothesis has been put forward by Brazilian researchers in an article in The Astrophysical Journal entitled “The influence of quantum vacuum friction on pulsars” and was recently featured in the Journal Club blog of the US National Academy of Sciences under the heading “Friction of the vacuum could slow the rotation of pulsars”.

The article was authored by Jaziel Goulart Coelho, a postdoctoral fellow at the National Space Research Institute (INPE), Jonas Pedro Pereira, a postdoctoral fellow at the Federal University of the ABC (UFABC), and José Carlos Neves de Araújo, a full-time researcher at INPE. All three are involved in research projects supported by FAPESP. The study in question is most closely associated with Coelho’s postdoctoral research supervised by Araújo on “Magnetars and the highly magnetized, fast, very massive, strange white dwarf pulsars, and the generation of gravitational waves”. This research is linked to the FAPESP-funded Thematic Project “Superdense matter in the universe”, for which Manuel Máximo Bastos Malheiro de Oliveira is principal investigator.

“According to astronomical observations, a pulsar’s spin period slows down every second between one hundred trillionth (10^-14) and one ten trillionth (10^-13) of a second. The classical energy-loss mechanism due to magnetic dipole radiation isn’t sufficient to explain this deceleration. There must be something more. Our study led us to conclude that the additional component might be the braking action exerted by quantum vacuum friction,” Coelho told Agência FAPESP.

In quantum physics, a vacuum is not really empty but rather is permeated by fluctuations. It is an extremely dynamic medium in which local fluctuations of potential constantly produce pairs of particles and anti-particles, which then annihilate each other. Thus, however tenuous interstellar space may be, its effect on highly compact rotating bodies like neutron stars cannot be negligible.

Two thousand pulsars have been identified to date, but they are so hard to detect that only nine have well-established parameters. The three researchers compiled all the available data on these nine pulsars in the literature and revisited them using the concepts of fundamental physics. They concluded that pulsar spin deceleration could be caused not just by energy loss due to electromagnetic radiation but also by quantum vacuum friction (QVF).

“A pulsar’s spin period and its temporal variations are determined observationally,” Coelho said. “From these, it’s possible to calculate a braking index defined as a delay equivalent to 10^-14 to 10^-13 seconds per second. To explain this index, we combined two energy loss mechanisms: classical magnetic dipole radiation and quantum vacuum friction. We investigated the role of QVF as an additional mechanism. The study involved theoretical astrophysics applied to observables.”

Where does the energy sucked from pulsars by QVF go? According to Coelho, more studies are needed to work out a completely convincing answer, but in his view heat production is intimately associated with QVF. Heat is one of the consequences of the interaction between a very strong magnetic field and a supermagnetized medium. It is produced by friction between the vacuum, understood in this case as a material medium, and the pulsar’s surface, just as an outboard motor propeller heats water after churning for a time.

“It also seems important to achieve a better theoretical understanding of the consequences of the heat associated with QVF,” Coelho said. “How much does it influence the pulsar’s surface temperature? Is this heat’s presence important for other classes of stars?”

Electromagnetic emission

This is an appropriate point at which to summarize the current state of knowledge about pulsars. The first pulsar was observed in 1967 by Northern Irish astrophysicist Jocelyn Bell, who at the time was completing her PhD at Cambridge University. It was located in the Crab Nebula and detected as the source of electromagnetic emission in the radio frequency band. The pulses were so regular that Bell and her fellow astronomers initially thought they could be looking at a signal from an extraterrestrial civilization. However, the scientific community quickly realized that the pulses were produced by a rotating neutron star.

Pulsars are the terminal stage in the evolution of outsized stars, which begin their lives with between eight and 25 solar masses. At some point, they explode as supernovae, ejecting most of their matter into space.

Before the explosion, nuclear fusion reactions at the star’s core create outward pressure that counterbalances the inward pressure of gravity, but in a supernova this process can no longer take place, so the small dense remnant collapses and becomes increasingly compact under the force of gravity.

In this powerful gravitational contraction, electrons and protons fuse to form closely packed neutrons, creating a neutron star. Its density is on the order of 10¹⁵ g/cm³ (i.e., one cubic centimeter has a mass of 1 billion tons). Its radius is only about 20 km, even though its mass is one and a half times that of the Sun.

One of the consequences of this contraction is that the star spins faster and faster, thanks to a regularity in the behavior of matter that physicists refer to as the “angular momentum conservation principle”. The angular momentum of a solid sphere is the product of its mass, the square of its radius and its angular velocity. In the case of a neutron star, mass and radius are drastically reduced, and angular velocity must increase proportionally if angular momentum is to remain constant.

“There are very fast pulsars with rotation periods on the order of a millisecond (10^-3 s), intermediate pulsars with periods ranging from a hundredth to a tenth of a second (10^-2 to 10^-1 s), and slower pulsars with periods of one to ten seconds (10⁰ to 10¹ s),” Coelho said.

Another consequence of the contraction is that the star’s magnetic field intensifies enormously. “This is due to the flow conservation principle,” said Araújo said. “Because the star’s surface shrinks, in order for magnetic flow to remain constant, the magnetic field must grow in line with the square of the ratio between the previous radius and the resulting radius.”

The magnetic field of a neutron star can reach values on the order of 100 million (10⁸) to 1 quadrillion (10¹⁵) gauss. That compares to 0.25-0.65 gauss for Earth’s magnetic field measured at its surface.

Photon beam

Although the first pulsars were detected in the radio frequency band, neutron stars emit radiation at all frequencies of the electromagnetic spectrum: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays.

A neutron star cannot be observed as a pulsar – short for pulsating radio star – unless its magnetic axis does not coincide with its rotation axis. The reason is that the radiation is emitted from the star’s magnetic poles. When the axes are aligned, the beam of photons (particles responsible for electromagnetic interaction) always points in the same direction. When the axes are misaligned, the photon beam sweeps different regions of space as the star rotates. Whenever it points toward an observer on Earth, it is perceived as a pulse, like an interstellar lighthouse beam.

“What excited us most about this study of QVF was that, based on this effect, it might be possible to predict a pulsar’s magnetic inclination angle with respect to its rotation axis, as well as the magnetic field’s evolution over time,” Coelho said. “In the classical scenario involving pure magnetic dipole radiation, the field should expand so as to explain the braking indices observed. But the introduction of QVF and other ingredients inverts this tendency.”

It must be stressed that only observation can confirm or refute QVF. “Our analysis shows there are highly divergent physical quantities depending on whether QVF is inserted into a pulsar’s energy-loss mechanism. As a result, we have high hopes that definitive proof or falsification of QVF will be possible when these physical quantities can be measured,” said Pereira, one of the article’s three co-authors.

According to the researchers, QVF is especially relevant in pulsars that have very intense magnetic fields (10¹² to 10¹³ gauss) and have already lost energy, such that their rotation period has slowed (1 to 10 s).

“By taking QVF into account, our study added an important element to the classical pulsar energy-transfer model based solely on electromagnetic radiation,” Araújo concluded. “But we want to go further, and we’re now working on a third transfer mechanism involving gravitational wave emission.”