Viscous Stars Can Reflect Gravitational Waves like Black Holes Do
The detection of gravitational waves from mergers of black holes and neutron stars has opened a window onto the strong-gravitational-field regime, allowing physicists to put constraints on various gravitational theories [1, 2]. These observations also have the power to probe the ways in which such compact objects interact with gravitational waves hitting their boundaries or, in the case of neutron stars, passing through their interiors [3]. Valentin Boyanov at the University of Lisbon in Portugal and his colleagues have now investigated such interactions in detail, analyzing how an object’s response to passing gravitational waves is influenced by its viscosity [4]. Their results could allow researchers to extract information about the internal structure of neutron stars from future gravitational-wave measurements.
Boyanov and colleagues tackle the following questions: Under what conditions do viscous compact objects such as neutron stars reflect or absorb gravitational waves? And to what extent do these interactions mimic those of black holes? At first, it might seem that black holes in particular cannot be reflective―after all, their defining feature is that they absorb everything that falls on them. But in practice, whether a black hole absorbs or reflects gravitational waves depends on the frequency of those waves. High-frequency gravitational waves cross the event horizon and are absorbed, adding to the black hole’s mass and angular momentum. For low-frequency waves, on the other hand, the curved space time around the black hole constitutes a potential barrier to the wave propagation: The waves are “reflected,” meaning that they scatter off this region with their phase or their propagation direction altered.
For neutron stars, the situation is different. A neutron star has an interior through which gravitational waves can penetrate and in which oscillatory modes can be excited. These oscillations involve dynamic rearrangements of the neutron star’s mass distribution, which themselves generate gravitational waves. Therefore, the key property of these objects relevant to their interactions with gravitational waves is their shear viscosity. In a neutron star consisting of a perfect (zero-viscosity) fluid, the oscillatory modes excited by the gravitational waves would be undamped, meaning none of the gravitational-wave energy would be absorbed. As a result, zero-viscosity neutron stars should be highly reflective to gravitational waves at all frequencies. But while superfluids with such properties are thought to be present within some neutron stars, most neutron stars should consist of fluids with finite viscosity. The question then becomes: How does this viscosity affect the way neutron stars interact with gravitational waves?
As the viscosity of a neutron star’s fluid interior increases, the star absorbs more energy from incoming gravitational waves, dissipating it as internal heat. In particular, high-frequency modes are the most strongly damped, causing the neutron star to become less reflecting at high gravitational-wave frequencies. This frequency–reflectivity relationship begins to mirror that predicted for black holes. But how far does the similarity go? A black hole’s event horizon is strictly a one-way barrier, prohibiting the reemission of any gravitational wave that crosses it. In contrast, even a highly viscous neutron star will sustain internal oscillatory modes to some extent, allowing incoming gravitational waves to be scattered. Since the viscosity of a neutron star cannot be so high as to violate causality―a shear perturbation cannot propagate faster than light―one might expect that a neutron star must be significantly more reflective to high-frequency gravitational waves than a black hole.
The extent to which objects can mimic black holes in terms of their interactions with gravitational waves has been studied for a decade, since it is relevant to the measurement of astrophysical observables [5]. So far, proposed candidates for such black hole mimickers are made of exotic-matter fields or require subtle quantum-gravity effects, neither of which are well supported theoretically [6]. This is precisely the gap filled by Boyanov and colleagues [4]. Their study shows that a neutron star can indeed mimic a black hole, exhibiting high reflectivity at low gravitational-wave frequencies and low reflectivity at high frequencies. For this to happen, the viscosity of the star can only live on a restricted parameter space: Its shear viscosity—when scaled by appropriate powers of the radius, pressure, and density of the star—must be less than 3/4, and the effective velocity of perturbations within the fluid must be less than the speed of light. It is very gratifying that both of these conditions are within the region permitted by the causality constraint [7].
Adding to our excitement, Boyanov and colleagues have also analyzed what happens when one chooses the viscosity to be larger than 3/4, violating the causality bound. In this case, perturbations within the neutron star propagate faster than light. The star’s reflectivity can then actually become much larger than that of a black hole, meaning that the star acts as a waveguide for gravitational waves [8]; that is, it transmits gravitational waves of all frequencies without attenuation. If we assume an even larger viscosity, then the reflectivity at low frequencies becomes larger than unity, implying that gravitational waves incident upon the star can be amplified. Such gravitational-wave amplification relies on the extraction of energy from the star’s rotation. This extraction can have a cascading effect, leading to a very large amplitude for the reflected gravitational wave―a phenomenon known as a superradiant instability [9].
Returning to the observational significance of the work, the presence of viscosity can potentially be observed using future gravitational-wave detectors. During the late inspiral of two stars (Fig. 1), viscosity will modify the stars’ dynamical tidal deformabilities. It will also introduce dissipative effects, which will heat up the stars. Both the tidal deformability changes and the heating effects could measurably affect the emitted gravitational-wave waveform. In addition, the characteristic frequencies of these viscous stars, which one hopes to capture at the last moment of the coalescence, will carry the signatures of rapidly oscillating modes. Finally, one should also note that any accretion disk around a compact object is also made out of a viscous fluid and hence will itself absorb gravitational waves. Dissipation of gravitational-wave energy should lead to a brightening of the electromagnetic emission from the disk, which might also be detectable.
Boyanov and colleagues carried out their analysis in the linear regime since linear relativistic hydrodynamics is much more tractable than nonlinear relativistic hydrodynamics [7]. However, it is possible that, had they worked in the nonlinear regime, they would have derived modified causality bounds on the viscosity parameters and obtained different results. Such a nonlinear analysis of the gravity and the viscous fluid is an extremely challenging task, but it will be necessary for a complete understanding of the role of viscosity in stellar and gravitational-wave astrophysics. Irrespective of the outcome of tackling that challenge, it is clear that there will be many more surprises lying ahead of this adolescent phase of gravitational-wave astrophysics, in particular, regarding the waves’ interactions with matter.
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