S. Siddhant, A. M. Grant and D. A. Nichols. “Higher memory effects and the post-Newtonian calculation of their gravitational-wave signals,” (2024). arxiv:2403.13907
E. E. Flanagan and D. A. Nichols. “Fully nonlinear transformations of the Weyl-Bondi-Metzner-Sachs asymptotic symmetry group.” J. High Energy Phys. 03, 120 (2024) arxiv:2311.03130.
D. A. Nichols. “Center-of-mass angular momentum and memory effect in asymptotically flat spacetimes.” Phys. Rev. D 98, 064032 (2018), arXiv:1807.08767.
D. A. Nichols. “Spin memory effect for compact binaries in the post-Newtonian approximation.” Phys. Rev. D 95, 084048 (2017), arxiv:1702.03300.
E. E. Flanagan and D. A. Nichols. “Conserved charges of the extended Bondi-Metzner-Sachs algebra.” Phys. Rev. D 95, 044002 (2017), arxiv:1510.03386.
The Bondi-Metzner-Sachs (BMS) group is the symmetry group of asymptotically flat spacetimes, and it consists of the Lorentz transformations and the supertranslations (an infinite-dimensional commutative group that has the spacetime translations as a subgroup). There recently was a proposal that a larger symmetry algebra than the BMS algebra could be relevant. This new algebra was called the extended BMS algebra, and it included the infinite number of conformal Killing vectors on the two-sphere, not just the smooth six-parameter family of Lorentz transformations. Eanna Flanagan and I computed the conserved quantities corresponding to these new symmetries in a somewhat more general context than before, and we found that they are finite and that they have an electric- and a magnetic-parity part. These two parts are generalizations of the spin angular momentum and the center-of-mass parts of the relativistic angular momentum (the superspin and super-center-of-mass charges, respectively). The change in the superspin charges can be a source of a new kind of memory effect, which had been proposed earlier, called the spin memory effect.
Much later, Eanna Flanagan and I computed the transformation properties of the metric functions in the BMS formalism under different classes of fully nonlinear coordinate transformations. We were able to compute, and slightly generalize, the form of a vacuum solution under a new set of symmetry transformations known as the Weyl BMS group. These expressions for the transformations of the metric functions will prove useful in understanding how the conserved quantities in the BMS, generalized BMS and Weyl BMS transform under the respective class of symmetry transformations.
Returning to the spin memory effect, another source of it is the effective angular momentum per solid angle that is radiated in gravitational waves. I computed the expansion of this effective angular momentum flux in terms of radiative moments of the gravitational-wave strain, thereby deriving a quadrupole-like formula for the spin memory. I then specialized to compact binary sources in the post-Newtonian approximation. In this limit, I found that the spin memory has a substantial slow secular growth during the inspiral stage of a compact binary. In addition, the rate of accumulation of the spin memory is related to a non-hereditary, nonlinear, and non-oscillatory contribution to the gravitational waveform that appears at a high order in the post-Newtonian expansion. This rate of accumulation of the spin memory might be detectable by third-generation gravitational-wave detectors, such as the Einstein Telescope, by coherently adding the spin memory signals from hundreds of gravitational-wave observations of black-hole-binary mergers.
I also showed that changes in the super-center-of-mass charges can also produce a new type of memory effect, which I called the center-of-mass memory effect. Like the spin memory effect, it produces a lasting change in a quantity related to the time integral of the gravitational-wave strain. There are terms in the gravitational waves related to the center-of-mass memory effect. These gravitational-wave terms, however, will be weaker than those related to the spin memory effect. As a result, it is less likely that the next generation of gravitational-wave detectors will be able to find evidence for the effect. It should, however, appear in the post-Newtonian expansion of the gravitational waveform, when the gravtiational waveform is computed at fourth post-Newtonian order.
Most recently, Siddhant, Alex Grant and I completed an investigation of the gravitational-wave memory effects related to the higher temporal moments of the news tensor (the time derivative of the gravitational-wave strain). We identified gravitational-wave signals related to these moments of the news, and computed several properties of these so-called higher memory effects. First, we developed a systematic procedure to compute the higher memory effects from a sequence of nonlinear flux-type terms and a charge-type term. Next, we performed a multipolar expansion of the first three flux-type terms; the first two sets of flux terms reproduced the multipolar expansions of the displacement, spin and center-of-mass memory effects; the third set of flux terms had not been investigated before. These new terms, named the ballistic memory by Alex, were our main focus for performing computations from compact-binary sources. Finally, we worked in the post-Newtonian approximation, and we found that one such term flux term was of the same post-Newtonian order as the spin memory effect. Given that the spin memory could be detected by the next-generation of ground-based gravitational-wave detectors, this part of the gravitational-wave signal looked like the most promising signature of a new higher memory effect that could be detected.
]]>D. A. Nichols, B. Wade, and A. M. Grant. “Secondary accretion of dark matter in intermediate mass-ratio inspirals: Dark-matter dynamics and gravitational-wave phase.” Phys. Rev. D 108, 124062 (2023), arXiv:2309.06498.
A. Coogan, G. Bertone, D. Gaggero, B. J. Kavanagh, and D. A. Nichols. “Measuring the dark matter environments of black hole binaries with gravitational waves.” Phys. Rev. D 105, 043009 (2022), arXiv:2108.04154.
B. J. Kavanagh, D. A. Nichols, G. Bertone, and D. Gaggero. “Detecting dark matter around black holes with gravitational waves: Effects of dark-matter dynamics on the gravitational waveform.” Phys. Rev. D 102, 083006 (2020), arXiv:2002.12811.
Black holes that form in dark-matter halos can slowly grow in mass over long timescales as they accrete and capture matter. During this slow growth, the dark matter can redistribute around the black hole to produce a “spike” of high density close to the black hole that falls off rapidly with radius. If an intermediate mass (thousands to hundreds of thousands of solar masses) black hole with such a “dress” of dark matter around it, then it could capture a stellar mass (tens of solar masses) black hole or a neutron star to form an intermediate mass-ratio inspiral (IMRI). IMRIs with and without the surrounding dark-matter dress have quite different orbital dynamics. In particular, the dark matter adds an additional drag force (dynamical friction) that causes the small black hole or neutron star to inspiral much more rapidly than it would if gravitational waves were the only source of energy loss from the system. Previous work had shown that this allows the dark matter distribution to be mapped out precisely by the inspiralling neutron star or small black hole.
In the first paper (Kavanagh, Nichols, Bertone and Gaggero), however, we noted that previous estimates of the change in the rate of inspiral assumed that the distribution of dark matter was static throughout the process. This assumption is not a good one for large changes in the inspiral rate, because the amount of energy input into the distribution of dark matter can be much larger than the total binding energy of the dark-matter spike. Thus, to make accurate predictions of the orbital dynamics, one must simultaneously evolve the distribution of dark matter with the binary’s orbit. The paper describes a method to do this for dark-matter distributions that remain spherically symmetric throughout the inspiral. We found that the rate of inspiral was much slower when the dynamics of the dark matter was taken into account. This mean that estimates of how well the dark matter could be measured through gravitational waves would need to be revised.
In the second paper (Coogan et al.), we addressed this question about the possibilities for detecting, discovering, and measuring the presence of dark matter in these IMRI systems. Gravitational waves from IMRIs with and without dark matter can be detected out to nearly identical distances by the planned space-based detector LISA. We then showed that searches for systems with dark matter with waveform templates that do not include dark-matter effects would lead to systems with dark matter being missed, because of reductions in the signal to noise. Finally, after developing a faster approximant to compute the waveforms, it was possible to compute the posteriors for the dark matter parameters using Bayesian inference. The density could be distinguished from zero even for systems near the threshold for detection. The Bayesian evidence ratio also favored the dark-matter hypothesis, when such waveforms were taken as the mock LISA data. If such IMRIs with dark matter form within the detection horizon for LISA, then they will be able to be distinguished from systems without dark matter.
In the third paper (Nichols, Wade and Grant), we investigated the effects of accretion of dark matter onto the secondary when the secondary was a black hole. We found that previous calculations of the amount of accretion onto the secondary were overestimates when the dark matter was assumed to be non-evolving as the secondary inspirals (specifically, because the amount of dark matter accreted would exceed the dark matter enclosed within the secondary’s orbit in certain scenarios). Adding in feedback from dynamical friction and evolving the dark-matter distribution decreased the amount of overestimate, but still did not account for the mass loss from the dark-matter density from accretion onto the secondary. We then derived and implemented a procedure to remove dark-matter particles from the dark-matter distribution so that mass was conserved. This led to smaller gravitational-wave effects from the accretion process, but there still were scenarios in which the effects of accretion were large enough that they would likely be measurable by the LISA detector, if such a system were observed.
]]>LISA Consortium Waveform Working Group. “Waveform Modelling for the Laser Interferometer Space Antenna.” arXiv:2311.01300.
K. G. Arun, et al. “New Horizons for Fundamental Physics with LISA.” Living Rev. Relativ. 25, 4 (2022), arXiv:2205.01597.
L. Piro et al. “Multi-messenger Athena Synergy White Paper.” Exp. Astron. 54, 23-117 (2022), arXiv:2110.15677.
The first paper on Athena focused on what one can learn from multi-messenger observations of gravitational waves from binary neutron stars and black-hole–neutron-star binaries with future ground based detectors (such as Cosmic Explorer and Einstein Telescope) and x-ray observations of the electromagnetic emission from these mergers using the Athena mission. The most promising avenues were understanding the demographics of the x-ray afterglows from gamma-ray bursts. Measuring precursor flares or the prompt emission from the merger, as well as x-rays from the kilonova could even be possible.
The next two papers are related to the planned LISA gravitational-wave detector. The first on fundamental physics is a broad summary of the wide range of theoretical physics topics that can be studied with LISA. I contributed to the parts on gravitational-wave probes of dark matter and of measurements of gravitational-wave memory effects. The second on waveform modeling focused more on the analytical and numerical calculations of gravitational waves that will need to be performed to make detections of gravitational wave sources and to analyze the properties of these sources. I similarly contributed to the parts on dark-matter effects in the gravitational waves, and gravitational-wave memory-effect waveform models.
]]>A. M. Grant and D. A. Nichols. “Outlook for detecting the gravitational wave displacement and spin memory effects with current and future gravitational wave detectors.” Phys. Rev. D 107, 064056 (2023), arXiv:2210.16266. Erratum: Phys. Rev. D 108, 029901 (2023).
O. M. Boersma, D. A. Nichols, and P. Schmidt. “Forecasts for detecting the gravitational-wave memory effect with Advanced LIGO and Virgo.” Phys. Rev. D 101, 083026 (2020), arXiv:2002.01821.
The gravitational-wave luminosity of a black-hole binary at its peak can be as high as a few thousandths of the fundamental unit of luminosity—the speed of light to the fifth power divided by Newton’s constant (c^{5}/G)—the so-called Planck luminosity. One consequence of this high luminosity is that asymmetries in the distribution of energy radiated in gravitational waves produces secondary gravitational waves. Aspects of the gravitational waves produced through this mechanism are called the gravitational-wave memory effect, because they lead to a lasting change in the gravitational-wave strain that endures even after the gravitational-waves have passed. This lasting strain is typically a small fraction (around a twentieth) of the peak amplitude of the gravitation waves, and it is currently below the threshold of detection for individual binary-black-hole mergers. However, it had been shown previously that one could find statistical evidence for the gravitational-wave memory effect in a population of binary black holes like that of the first event detected, GW150914. For a population of these events, it was shown it would take fewer than one-hundred such events to find statistical evidence for the memory effect.
Subsequent gravitational-wave detections showed that the population of binary-black-hole mergers had a much wider range of distances and masses than the first event. Oliver Boersma in his MS thesis (supervised by Patricia Schmidt and me) then investigated how long it would take for advanced LIGO and Virgo to detect the memory effect from a population of binary black holes that was consistent with the population inferred from the first gravitational-wave catalog of events (GWTC-1). We found that the it would take closer to five years of observing runs (assuming the three detectors were operational in coincidence for half of the time) for LIGO and Virgo to detect the gravitational-wave memory effect. This is illustrated in the figure above, which shows how the signal to noise in the population (roughly the significance of the observation in units of standard deviations), accumulates as a function of time. Given the rate of events, it is then anticipated that it will take closer to one thousand detections to find evidence for the gravitational-wave memory effect. It is thus more likely to be discovered during the next upgrade of the LIGO and Virgo detectors after the detectors achieve their design sensitivity (when LIGO A+ and Advanced Virgo+ are operating).
In more recent work, Alex Grant and I revisited the forecasts for the detection of the gravitational-wave memory effect, because the rate of binary-black-hole mergers was determined more precisely after the many additional discoveries and improved modeling of the binary-black-hole population that occurred during LIGO’s third observing run. The LIGO A+ upgrade was also approved, which changed LIGO’s observing plans. We found that the memory effect would be likely to be detected for the population of black-hole mergers within a few years of LIGO A+ reaching its design sensitivity. For the next-generation gravitational-wave detector, Cosmic Explorer, this detector would likely detect the memory effect from a single, high signal-to-noise binary-black-hole observation. In addition, given the much larger number of detections of black-hole mergers, it could also detect the gravitational-wave spin memory effect from the large population of binary black holes measurable by Cosmic Explorer. These latter results for Cosmic Explorer highlighted the potential of the detector for making precision gravitational-wave measurements.
]]>A. M. Grant and D. A. Nichols. “Persistent gravitational-wave observables: Curve deviation in asymptotically flat spacetimes.” Phys. Rev. D 105, 024056 (2022), arXiv:2109.03832.
E. E. Flanagan, A. M. Grant, A. I. Harte, and D. A. Nichols. “Persistent gravitational-wave observables: Nonlinear plane wave spacetimes.” Phys. Rev. D 101, 104033 (2020), arXiv:1912.13449.
E. E. Flanagan, A. M. Grant, A. I. Harte, and D. A. Nichols. “Persistent gravitational-wave observables: General framework.” Phys. Rev. D 99, 084004 (2019), arXiv:1901.00021.
The gravitational-wave memory effect is often characterized by the lasting displacement it would cause between freely falling observers after a burst of gravitational waves pass by their locations. Subsequently, it was realized that there other types of memory effects that freely falling observers could measure, including lasting relative velocities, changes in proper time elapsed, and relative rotation of inertial gyroscopes. We were interested in determining procedures that observers could, in principle implement, by which observers could meaure all these memory effects (and potentially other new effects). We in fact found three such types of procedures, which encompass the known memory effects, and potentially other new ones. The first procedure involved measuring a type of deviation vector between two neary accelerating observers. The second involves transporting a certain kind of linear and angular momentum around a closed curve in spacetime. The third is based on measuring the location, linear momentum, and intrinsic angular momentum of a nearby spinning point particle. We called the outcome of these measurement procedures “persistent gravitational-wave observables,” and we are currently investigating their properties in specific gravitational-wave spacetimes.
The first class of spacetimes that we investigated were the so-called nonlinear plane-wave spacetimes. We found that several observables can be obtained from the values of tensors that solve the equation of geodesic deviation (specifically for observalbes that involved geodesic curves). Thus, these observables contain information that is equivalent to the displacement and subleading displacement (e.g., spin or center of mass) gravitational-wave memory effects. However, for observables involving worldlines with acceleration, the persistent observables were more nontrivial (and nonlocal) functions of the solutions to the equation of geodesic deviation and the acceleration of the curve. This implies that there are much wider range of possible persistent observables than the leading and subleading displacement memory effects (which will be investigated in greater detail in future work).
We then investigated the curve-deviation observable in asymptotically flat spacetimes. At leading order in distance from the source, we found that there is an infinite hierarchy of memory effects when the curve-deviation observable is measured by observers with a nontrival, time-dependent acceleration. The entire collection of memory effects are sourced by “charge” and “flux” terms, where the flux part vanishes in the absence of gravitational waves. This charge-flux decomposition is well known for the displacement and subleading displacement (spin and center of mass) effects, but it was shown to hold for all of the acceleration-dependent effects in this paper. For the effects that depend on higher derivatives of the initial acceleration, the charge and flux sources are more and more subleading parts of the expansion of the spacetime metric and curvature in a series in inverse distance. Thus, the curve deviation observable is capable of probing very high-order persistent changes in the spacetime through a measurement at large distances. This type of asymptotic reconstruction of the interior of a spacetime is reminiscent of the types of holography that appear in high-energy physics and string theory.
]]>S. Tahura, D. A. Nichols, and K. Yagi, “Gravitational-wave memory effects in Brans-Dicke theory: Waveforms and effects in the post-Newtonian approximation.” Phys. Rev. D 104, 104010, (2021), arXiv:2107.02208.
S. Tahura, D. A. Nichols, A. Saffer, L. C. Stein, and K. Yagi, “Brans-Dicke theory in Bondi-Sachs form: Asymptotically flat solutions, asymptotic symmetries and gravitationalwave memory effects.” Phys. Rev. D 103, 104026, (2021), arXiv:2007.13799.
The set of symmetries of asymptotically flat spacetimes in general relativity is the Bondi-Metzner-Sachs (BMS) group. This group consists of the rotations, boosts, and the infinite-dimensional group of supertranslations (“angle-dependent” translations around an isolated source). These symmetries have corresponding conserved quantites, and changes in the conserved quantities and their fluxes are responible for producing gravitational-wave memory effects. It was not known what the symmetries of asymptotically flat solutions are in modified theories of gravity, or if there is the same relationship between memory effects and conserved quantities in these theories. To investigate this topic in more detail, we focused on a well known and extensively studied theory called Brans-Dicke theory, which has a third (scalar-type) polarization of gravitational waves.
In work lead by UVA Physics graduate student Shammi Tahura, we constructed asymptotically flat solutions in Brans-Dicke theory, found the symmetries that preserve the asymptotic properties of these solutions, computed the corresponding conserved charges, and understood their relationship to gravitational-wave memory effects. Specifically, we found that the tensor polarizations of gravitational waves are related to the changes in the conserved quantities related to the asymptotic spacetime symmetries. The scalar polarizations are not (though it was shown elsewhere that they are related to large asymptotic gauge symmetries of a dual theory).
The fact that the tensor-polarized gravitational-wave memory effect is related to flux-balance laws allowed us to compute the effect in the post-Newtonian approximation for compact binaries. We found a few differences between the memory effects in general relativity and in Brans-Dicke theory for these sources. First, the scalar-polarized radiation produces a small effect of a negative post-Newtonian order. Second, this radiation also changes the sky pattern of the memory effect around the source. Because the size of these effects is small, it will be challenging to detect with current (and even future) gravitational-wave detectors. There is the possibility that these slight differences could be found in a population of events (if indeed Brans-Dicke theory describes the gravitational interaction in nature).
]]>A. Elhashash and D. A. Nichols. “Definitions of (super) angular momentum in asymptotically flat spacetimes: Properties and applications to compact-binary mergers.” Phys. Rev. D 104, 024020 (2021), arXiv:2101.12228.
G. Compere and D. A. Nichols. “Classical and Quantized General-Relativistic Angular Momentum,” (2021). arXiv:2103.17103.
Finding a definition of the angular momentum of an isolating gravitating system has a long and involved history. Over several decades of (sporadic) work on the topic, a number of different researches used different methods to converge on an expression for the quantity. However, there were still several different definitions used in different subfields, which were not clearly equivalent. It was subsequently noted that there are in fact a two-parameter family of angular momenta that generalize many of the existing definitions. This two parameter family satisfies a number of physically reasonable conditions.
With UVA graduate student Arwa Elhashash, we found that one condition that the two-parameter family did not satisfy was that it vanished in flat spacetime. Imposing this requirement forced the two parameters to be equal, which left a one-parameter family of angular momentum (and the different definitions used in the various subfields were all consistent with this one-parameter family). We then explored how large the difference in definitions is for binary-black-hole mergers. For nonspinning binaries, the difference in the (orbital) angular momentum for the definitions is illustrated in the figure above. The figure shows that the definitions agree at early times and after the gravitational waves pass, but there is a difference when the system is radiating gravitational wave most strongly. The difference is also largest for equal mass ratios (q=1). We also investigated a one-parameter family of super angular momentum, a kind of generalization of angular momentum. For the super angular momentum, there is again a difference between the definitions, but this difference lasts after the gravitational waves have passed (which occurs because of the graviational-wave memory effect). The amplitude of the differences in the (super) angular momentum are small, but they can be resolved by numerical simulations of binary-black-hole mergers.
I also wrote an essay for the 2021 Gravity Research Foundation Essays on Gravitation competition with Geoffrey Compere. The subject of the essay was the definition and transformation properties of angular momentum and its generalizations in asymptotically flat spacetimes. We discussed the fact that the most-frequently used value in the one-parameter family of angular momentum (that which reduces to the Komar formula when there is an exact rotational symmetry) is not the same value of the angular momentum that gives rise to the standard charge algebra for the super angular momentum. We also noted that there are a wider range of possible definitions of angular momentum and its generalizations beyond the one-parameter family discussed above, including those which behave like an intrinsic angular momentum that does not transform under (super)translations.
]]>The gravitational-wave (GW) event GW170817 was followed by electromagnetic (EM) observations of the system over a broad range of the EM spectrum from gamma rays to radio waves. The GWs were consistent with the merger of two objects with masses typical of neutron stars, and the EM observations were those expected if at least one of the objects were a neutron star. Thus, while a binary neutron star is the favored progenitor for the system, it has not been definitively shown that this is the only possible binary progenitor. In this paper, we investigated whether a binary composed of a low mass black hole and a neutron star could explain the observed GW and EM signals. Using new numerical relativity simulations of black-hole neutron-star binaries, we showed that both the GWs and kilonova emission from an unequal-mass binary could be consistent with the observed emission from GW170817. When we combined information from the GW measurements with predictions of the remaining mass around a black hole following its merger with a neutron star, we could put conservative constraints on the regions of parameter space in which the system could have been a black-hole neutron-star binary. Surprisingly, there was still a substantial region that could be consistent with a neutron-star black-hole system.
]]>I also took this as an opportunity to update my website to a more modern format. I have joined the many people who use Jekyll and the Minimal Mistakes theme.
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