Sources Of Gravitational Radiation Research Articles

Scalar gravitational waves can be generated even without direct coupling between Dark Energy and ordinary matter

We point out, the scalar sector of gravitational perturbations may be excited by an isolated astrophysical system immersed in a universe whose accelerated expansion is not due to the cosmological constant, but due to extra field degrees of freedom. This is true even if the source of gravitational radiation did not couple directly to these additional fields. We illustrate this by considering a universe driven by a single canonical scalar field. By working within the gauge-invariant formalism, we solve for the electric components of the linearised Weyl tensor to demonstrate that both the gravitational massless spin-2 (transverse-traceless) tensor and the (Bardeen) scalar modes are generated by a generic astrophysical source. For concreteness, the Dark Energy scalar field is either released from rest, or allowed to asymptote toward the minimum in a certain class of potentials; and we compute the traceless tidal forces induced by gravitational radiation from a hypothetical compact binary system residing in such a universe. Though their magnitudes are very small compared to the tensors', spin zero gravitational waves in such a canonical scalar driven universe are directly sensitive to both the Dark Energy equation of state and the eccentricity of the binary's orbit.

Dynamical Friction Models for Black Hole Binary Formation in Active Galactic Nucleus Disks

Stellar-mass black holes (sBHs) embedded in gaseous disks of active galactic nuclei (AGN) can be important sources of detectable gravitational radiation for LIGO/Virgo when they form binaries and coalesce due to orbital decay. In this paper, we study the effect of dynamical friction (DF) on the formation of BH binaries in AGN disks using N-body simulations. We employ two simplified models of DF, with the force on the BH depending on Δ v , the velocity of the sBH relative to the background Keplerian gas. We integrate the motion of two sBHs initially on circular orbits around the central supermassive black hole (SMBH) and evaluate the probability of binary formation under various conditions. We find that both models of DF (with different dependence of the frictional coefficient on ∣Δ v ∣) can foster the formation of binaries when the effective friction timescale τ satisfies ΩK τ ≲ 20–30 (where ΩK is the Keplerian frequency around the SMBH): prograde binaries are formed when the DF is stronger (smaller τ), while retrograde binaries dominate when the DF is weaker (larger τ). We determine the distribution of both prograde and retrograde binaries as a function of initial orbital separation and the DF strength. Using our models of DF, we show that for a given sBH number density in the AGN disk, the formation rate of sBH binaries increases with decreasing τ and can reach a moderate value with a sufficiently strong DF.

Multi-localized time-symmetric initial data for the Einstein vacuum equations

Abstract We construct a class of time-symmetric initial data sets for the Einstein vacuum equations modeling elementary configurations of multiple almost isolated systems. Each such initial data set consists of a collection of several localized sources of gravitational radiation, and lies in a family of data sets which is closed under scaling out the distances between the systems by arbitrarily large amounts. This class contains data sets which are not asymptotically flat, but to which nonetheless a finite ADM mass can be ascribed. The construction proceeds by a gluing scheme using the Brill–Lindquist metric as a template. Such initial data are motivated in part by a desire to understand the dynamical interaction of distant systems in the context of general relativity. As a by-product of the construction, we produce families of complete, scalar-flat initial data with trivial topology and infinitely many minimal spheres, as well as families of initial data with infinitely many Einstein–Rosen bridges.

Reversing the verdict: Cataclysmic variables could be the dominant progenitors of AM CVn binaries after all

Context. AM CVn binaries are potential progenitors of thermonuclear supernovae and strong sources of persistent gravitational wave radiation. For a long time, it has been believed that these systems cannot descend from cataclysmic variables (CVs), at least not in large numbers, because the initial conditions need to be fine-tuned and, even worse, the resulting surface hydrogen abundance would be high enough to be detected which contradicts a defining feature of AM CVn binaries. Aims. Here we show that both claimed weaknesses of the CV formation channel for AM CVn binaries are model-dependent and rely on poorly constrained assumptions for magnetic braking. Methods. We performed binary evolution simulations with the MESA code for different combinations of post-common-envelope white dwarf and companion masses as well as orbital periods assuming the CARB model for strong magnetic braking. Results. We found that AM CVn binaries with extremely-low surface hydrogen abundances are one natural outcome of CV evolution if the donor star has developed a non-negligible helium core prior to the onset of mass transfer. In this case, after hydrogen envelope exhaustion during CV evolution, the donor becomes degenerate and its surface hydrogen abundance substantially drops and becomes undetectable. Our simulations also show that the CV formation channel is able to explain the observed AM CVn binaries with very low mass and bloated donor stars (Gaia14aae and ZTF J1637+49). Conclusions. CVs with evolved donors are likely the progenitors of at least a fraction of AM CVn binaries.

A Roche lobe-filling hot subdwarf and white dwarf binary: possible detection of an ejected common envelope

ABSTRACTBinaries consisting of a hot subdwarf star and an accreting white dwarf (WD) are sources of gravitational wave radiation at low frequencies and possible progenitors of Type Ia supernovae if the WD mass is large enough. Here, we report the discovery of the third binary known of this kind: It consists of a hot subdwarf O (sdO) star and a WD with an orbital period of 3.495 h and an orbital shrinkage of 0.1 s in 6 yr. The sdO star overfills its Roche lobe and likely transfers mass to the WD via an accretion disc. From spectroscopy, we obtain an effective temperature of $T_{\mathrm{eff}}=54\, 240\pm 1840$ K and a surface gravity of log g = 4.841 ± 0.108 for the sdO star. From the light curve analysis, we obtain an sdO mass of MsdO = 0.55 M⊙ and a mass ratio of q = MWD/MsdO = 0.738 ± 0.001. Also, we estimate that the disc has a radius of $\sim\!0.41\ \mathrm{R}_\odot$ and a thickness of $\sim\!0.18\ \mathrm{R}_\odot$. The origin of this binary is probably a common envelope ejection channel, where the progenitor of the sdO star is either a red giant branch star or, more likely, an early asymptotic giant branch star; the sdO star will subsequently evolve into a WD and merge with its WD companion, likely resulting in an R Coronae Borealis (R CrB) star. The outstanding feature in the spectrum of this object is strong Ca H&K lines, which are blueshifted by ∼200 km s−1 and likely originate from the recently ejected common envelope, and we estimated that the remnant common envelope (CE) material in the binary system has a density $\sim\!6\times 10^{-10}\ {\rm g\, cm}^{-3}$.

Gravitational radiation from accelerating jets

Non-spherical rapid acceleration of mass (or energy) to a relativistic velocity is a natural source of gravitational radiation. Such conditions arise in both long and short gamma-ray bursts whose central engine ejects relativistic jets. The resulting gravitational wave signal is of a memory type, rising to a finite level (of order 4 G E/r) over a duration that corresponds to the longer of either the injection time and the acceleration time of the jet. We explore the properties of such signals and their potential detectability. Unfortunately, the expected signals are below the frequency band of Advanced LIGO-Virgo-Kagra, and above LISA. However, they fall within the range of the planned BBO and DECIGO. While current sensitivity is marginal for the detection of jet gravitational wave signals from GRBs, hidden relativistic jets that exist within some core collapse SNe could be detected. Such a detection would reveal the acceleration mechanism and the activity of the central engine, which cannot be explored directly in any other way

Numerical evolution of the center of mass and angular momentum for binary black holes

The asymptotic approach derived by Kozameh-Quiroga provides a modern framework to obtain the evolution of global variables of isolated sources of gravitational radiation. We test the Kozameh-Quiroga formalism evolving the equations of motion for the center of mass, the intrinsic angular momentum, and several other global variables, for black hole binary coalescence. First, we evolve the equations of motion using 777 simulations from the RIT catalog of numerical data of ${\ensuremath{\psi}}_{4}$ [J. Healy and C. O. Lousto, Third RIT binary black hole simulations catalog, Phys. Rev. D 102, 104018 (2020).]. We then analyze the trajectory of the center of mass and compute the final state of other physical variables after the coalescence has taken place. Finally, we show that the results obtained from our equations of motion are consistent with those in the Rochester metadata.

Gravitational tensor and acoustic waves in a radiation dominated universe: Weyl curvature and polarization patterns

We provide evidence that gravitational radiation in a 4D radiation-dominated universe, with equation-of-state $w=1/3$, consists of two components: helicity-2 gravitons and massless scalar acoustic waves. On physical grounds, we would expect the homogeneous solution of the Weyl tensor components to be a good approximation to its inhomogeneous counterparts, whenever the observer is located well in the far zone of an isolated astrophysical source of cosmological gravitational radiation. We show explicitly that these homogeneous and inhomogeneous solutions both receive contributions from the gauge-invariant tensor {\it and} the two Bardeen (acoustic) scalars. Comparison of these Weyl tensor computations thus allows us to not only identify, in the high frequency limit, the corresponding gravitational tensor and scalar radiation; but also their oscillatory polarization patterns.

Physics and evolution of the most massive stars in 30 Doradus

Context.The identification of stellar-mass black-hole mergers with up to 80 M⊙as powerful sources of gravitational wave radiation led to increased interest in the physics of the most massive stars. The largest sample of possible progenitors of such objects, very massive stars (VMS) with masses up to 300M⊙, have been identified in the 30 Dor star-forming region in the Large Magellanic Cloud (LMC). In this young starburst analogue, VMS were found to dominate stellar feedback. Despite their importance, the physics and evolution of VMS is highly uncertain, mainly due to their proximity to the Eddington limit.Aims.In this work, we investigate the two most important effects that are thought to occur near the Eddington limit: enhanced mass loss through optically thick winds and the formation of radially inflated stellar envelopes.Methods.We compute evolutionary models for VMS at LMC metallicity and perform a population synthesis of the young stellar population in 30 Dor. We adjust the input physics of our models to match the empirical properties of the single-star population in 30 Dor as derived in the framework of the VLT-Flames Tarantula Survey.Results.Enhanced mass loss and envelope inflation near the Eddington limit have a dominant effect on the evolution of the most massive stars. While the observed mass-loss properties and the associated surface He-enrichment are well described by our new models, the observed O-star mass-loss rates are found to cover a much larger range than theoretically predicted, with particularly low mass-loss rates for the youngest objects. Also, the (rotational) surface enrichment in the O-star regime appears to not be well understood. The positions of the most massive stars in the Hertzsprung-Russell diagram (HRD) are affected by mass loss and envelope inflation. For instance, the majority of luminous B supergiants in 30 Dor, and the lack thereof at the highest luminosities, can be explained through the combination of envelope inflation and mass loss. Finally, we find that the upper limit for the inferred initial stellar masses in the greater 30 Dor region is significantly lower than in its central cluster, R 136, implying a variable upper limit for the masses of stars.Conclusions.The implementation of mass-loss and envelope physics in stellar evolution models turns out to be essential for the modelling of the observable properties of young stellar populations. While the properties of the most massive stars (≳100 M⊙) are well described by our new models, the slightly less massive O stars investigated in this work show a much more diverse behaviour than previously thought, which has potential implications for rotational mixing and angular momentum transport. While the present models are a big step forward in the understanding of stellar evolution in the upper HRD, more work is needed to understand the mechanisms that regulate the mass-loss rates of OB stars and the physics of fast-rotating stars.

Spectroscopy of the helium-rich binary ES Ceti reveals accretion via a disc and evidence of eclipses

Context. Amongst the hydrogen-deficient accreting binaries known as the AM CVn stars are three systems with the shortest known orbital periods: HM Cnc (321 s), V407 Vul (569 s), and ES Cet (620 s). These compact binaries are predicted to be strong sources of persistent gravitational wave radiation. HM Cnc and V407 Vul are undergoing direct impact accretion in which matter transferred from their donor hits the accreting white dwarfs directly. ES Cet has the longest period of the three and is amongst the most luminous AM CVn stars, but it is not known whether it accretes via a disc or direct impact. ES Cet displays strong HeII 4686 line emission, which is sometimes a sign of magnetically controlled accretion. Peculiarly, although around one third of hydrogen accreting white dwarfs show evidence of magnetism, none have been found amongst helium accretors. Aims. We present the results of Magellan and VLT spectroscopic and spectropolarimetric observing campaigns dedicated to ES Cet with the aim of understanding its accretion structure. Methods. Based on the data collected, we derived trailed spectra, computed Doppler maps of the emission lines, and looked for circular polarisation and variability. Results. We find strong variability in our spectra on the 620 s period. The lines show evidence of double-peaked emission, characteristic of an accretion disc, with an additional component associated with the outermost disc, rather than a direct impact, which is broadly consistent with S-wave emission from the gas stream or disc impact region. This confirms beyond any doubt that 620 s is the orbital period of ES Cet. We find no significant circular polarisation (below 0.1%). The trailed spectra show that ES Cet’s outer disc is eclipsed by the mass donor, revealing at the same time that the photometric minimum coincides with the hitherto unrecognised eclipse. Conclusions. ES Cet shows spectroscopic behaviour consistent with accretion via a disc, and is the shortest orbital-period eclipsing AM CVn star known.

Detecting gravitational waves from cosmological phase transitions with LISA: an update

We investigate the potential for observing gravitational waves from cosmological phase transitions with LISA in light of recent theoretical and experimental developments. Our analysis is based on current state-of-the-art simulations of sound waves in the cosmic fluid after the phase transition completes. We discuss the various sources of gravitational radiation, the underlying parameters describing the phase transition and a variety of viable particle physics models in this context, clarifying common misconceptions that appear in the literature and identifying open questions requiring future study. We also present a web-based tool, PTPlot, that allows users to obtain up-to-date detection prospects for a given set of phase transition parameters at LISA.

Hot subdwarf B stars with neutron star components

Context. Subdwarf B stars (sdBs) play a crucial role in stellar evolution, asteroseismology, and far-UV radiation of early-type galaxies, and have been intensively studied with observation and theory. It has theoretically been predicted that sdBs with neutron star (NS) companions exist in the Galaxy, but none have been discovered yet. This remains a puzzle in this field. In a previous study (hereafter Paper I), we have studied the formation channels of sdB+NS binaries from main-sequence (MS) stars plus NS binaries by establishing a model grid, but it is still unclear how these binaries consisting of MS stars and NS binaries came to be in the first place. Aims. We systematically study the formation of sdB+NS binaries from their original zero-age main-sequence progenitors. We bridge the gap left by our previous study in this way. We obtain the statistical population properties of sdB+NS binaries and provide some guidance for observational efforts. Methods. We first used Hurley’s rapid binary evolution code BSE to evolve 107 primordial binaries to the point where the companions of NS+MS, NS+Hertzsprung gap star, and NS+Giant Branch star binaries have just filled their Roche lobes. Next, we injected these binaries into the model grid we developed in Paper I to obtain the properties of the sdB+NS populations. We adopted two prescriptions of NS natal kicks: the classical Maxwellian distribution with a dispersion of σ = 265 km s−1, and a linear formula that assumes that the kick velocity is associated with the ratio of ejected to remnant mass. Different values of αCE, where αCE is the common-envelope ejection efficiency, were chosen to examine the effect of common-envelope evolution on the results. Results. In the Galaxy, the birthrate of sdB+NS binaries is about 10−4 yr−1 and there are ∼7000 − 21 000 such binaries. This contributes 0.3−0.5% of all sdB binaries in the most favorable case. Most Galactic sdB+NS binaries (≳60%) arise from the channel of stable mass transfer. The value of αCE has little effect on the results, but when we use the linear formula prescription of NS natal kick, the number and birthrate doubles in comparison to the results we obtained with the Maxwellian distribution. The orbital periods of sdB+NS binaries from different formation channels differ significantly, as expected. This results in two peaks in the radial velocity (RV) semi-amplitude distribution: 100 − 150 km s−1 for stable mass transfer, and 400 − 600 km s−1 for common-envelope ejection. However, the two sdB+NS binary populations exhibit similar delay-time distributions, which both peak at about 0.2 Gyr. This indicates that Galactic sdB+NS binaries are born in very young populations, probably in the Galactic disk. The sdB+NS binaries produced from the common-envelope ejection channel are potential sources of strong gravitational wave radiation (GWR), and about ∼100 − 300 could be detected by the Laser Interferometer Space Antenna (LISA) with a signal-to-noise ratio of 1. Conclusions. Most sdB+NS binaries are located in the Galactic disk with small RV semi-amplitudes. SdB+NS binaries with large RV semi-amplitudes are expected to be strong GWR sources, some of which could be detected by LISA in the future.

Relativistic center of mass in general relativity

The center of mass and spin for isolated sources of gravitational radiation that move at relativistic speeds are defined. As a first step, we also present these definitions in flat space. This contradicts some general wisdom given in textbooks claiming that such definitions are not covariant and thus, have no physical meaning. We then generalize the definitions to asymptotically flat spacetimes giving their equations of motion when gravitational radiation is emitted by the isolated sources. The resulting construction has some similarities with the Mathisson-Papapetrou equations which describes the motion of the particle in an external field. We analyze the relationship between the center of mass velocity and the Bondi linear momentum and show they are not proportional to each other. A similar situation happens between the total and intrinsic angular momentum when the Bondi momentum vanishes. We claim that extra terms should be added in other approaches to adequately describe the time evolution of isolated sources of gravitational radiation.

Tests of gravity theories with Galactic Center observations

An active stage of relativistic astrophysics started in 1963 since in this year, quasars were discovered, Kerr solution had been found and the first Texas Symposium on Relativistic Astrophysics was organized in Dallas. Five years later, in 1967–1968 pulsars were discovered and their model as rotating neutron stars (NSs) had been proposed, meanwhile Wheeler claimed that Kerr and Schwarzschild vacuum solutions of Einstein equations provide an efficient approach for astronomical objects with different masses. Wheeler suggested to call these objects black holes. NSs were observed in different spectral band of electromagnetic radiation. In addition, a neutrino signal had been found for SN1987A. Therefore, multi-messenger astronomy demonstrated its efficiency for decades even before observations of the first gravitational radiation sources. However, usually, one has only manifestations of black holes in a weak gravitational field limit and sometimes a model with a black hole could be substituted with an alternative approach which very often looks much less natural, however, it is necessary to find observational evidences to reject such an alternative model. At the moment, only few astronomical signatures for strong gravitational field are found, including a shape of relativistic iron [Formula: see text] line, size and shape of shadows near black holes at the Galactic Center (GC) and M87, trajectories of bright stars near the GC. After two observational runs, the LIGO–Virgo collaboration provided a confirmation for a presence of mergers for 10 binary black holes and one binary NS system where gravitational wave signals were found. In addition, in the last years, a remarkable progress has been reached in a development of observational facilities to investigate a gravitational potential, for instance, the number of telescopes operating in the Event Horizon Telescope network is increasing and accuracy of a shadow reconstruction near the GC is improving, meanwhile largest VLT, Keck telescopes with adaptive optics and especially GRAVITY facilities observe bright IR stars at the GC with perfect accuracy. More options for precision observations of bright stars will be available with creating extremely large telescopes Thirty Meter Telescope (TMT) and E-ELT. It is clear that the GC (Sgr [Formula: see text]) is a specific object for observations. Our solar system is located at a distance around 8 kpc from the GC. Earlier, theorists proposed a number of different models including exotic ones for GC such as boson star, fermion ball, neutrino ball, a cluster of NSs. Later, some of these models were ruled out or essentially constrained with consequent observations and theoretical considerations. Currently, a supermassive black hole with mass around [Formula: see text] is the most natural model for GC. Using results of observations for trajectories of bright stars in paper [A. F. Zakharov, P. Jovanović, D. Borka and V. B. Jovanović, J. Cosmol. Astropart. Phys. 05 (2016) 045] the authors got a graviton mass constraint which is comparable and consistent with constraints obtained recently by the LIGO–Virgo collaboration. Later, we consider opportunities to improve current graviton mass constraints with future observations of bright stars [A. F. Zakharov, P. Jovanović, D. Borka and V. B. Jovanović, J. Cosmol. Astropart. Phys. 04 (2018) 050]. Similarly, from an analysis of bright star trajectories, one could constrain a tidal charge which was predicted by a gravity theory with an additional dimension [A. F. Zakharov, Eur. Phys. J. C 78 (2018) 689].

Primordial scalar gravitational waves produced at the QCD phase transition due to the trace anomaly

Relying only on the standard model of elementary particles and gravity, we study the details of a new source of gravitational waves whose origin is in quantum physics. Namely, it is well known that massless fields in curved backgrounds suffer from the so-called ‘trace anomaly’. This anomaly can be cast in terms of new scalar degrees of freedom which take account of macroscopic effects of quantum matter in gravitational fields. The linearized effective action for these fields describes scalar (as opposed to transverse) gravitational waves, which are absent in Einstein’s theory. Since these new degrees of freedom couple directly to the gauge field scalars in QCD, the epoch of the QCD phase transition in early universe is a possible source of primordial cosmological gravitational radiation. While the anomaly is most likely fully unsuppressed at the QCD densities (temperature is much higher than the u and d quark masses), just to be careful we introduced the window function which cuts-off very low frequencies where the anomaly effect might be suppressed. We then calculated the characteristic strain of the properly adjusted gravitational waves signal today. The region of the parameter space with no window function gives a stronger signal, and both the strain and the frequencies fall within the sensitivity of the near future gravitational wave experiments (e.g. LISA and The Big Bang Observer). The possibility that one can study quantum physics with gravitational wave astronomy even in principle is exciting, and will be of value for future endeavors in this field.

Binary white dwarfs as laboratories for extreme gravity with LISA

The observation of low-frequency gravitational waves with the Laser Interferometer Space Antenna will allow the study of new sources of gravitational radiation that are not accessible by ground-based instruments. Gravitational wave sources provide invaluable information both about their astrophysics, as well as the nature of the gravitational interaction in their neighborhoods. One low frequency source that has not received much attention regarding the latter are galactic binaries composed of two white dwarves or a white dwarf and a neutron star. We here show that, contrary to the common lore, such gravitational wave sources can indeed be used to constrain an important feature of the gravitational interaction: the absence of pre-Newtonian, dipolar dissipation. We propose a model-independent framework to carry out a null test for the presence of this feature in the data that is very much analogous to tests of general relativity with radio-observations of binary pulsars. We then go one step further and specialize this test to scalar–tensor theories to derive projected constraints on spontaneous scalarization. We find that these constraints can be comparable to current bounds with binary pulsars, and in some optimistic cases, they can be even stronger.

Theoretical and observed quality factor of gravitational quadrupoles

Useful insights into the complicated physics of gravitational waves can often be drawn from approximations to analogous physics of electromagnetic waves. Here, we present a gravitational form of the electromagnetic Chu limit that sets bounds on the achievable $Q$ (quality factor) relating the ratio of stored energy to radiated energy in the underlying fields. In particular, we answer two fundamental physics questions: (1) what is the theoretical $Q$ for gravitational quadrupole radiation sources, and (2) can gravitational $Q$ be observed from recent measured astronomical data? Gravitational $Q$ is shown to follow an inverse seventh-order power law, and gravitational-wave data is used to find observed values of $Q$ for GW170817. Inasmuch as electromagnetic $Q$ serves a central role in design and analysis of electrically-small antennas, the proposed gravitational $Q$ offers the potential for a similar utility in the design and analysis of gravitationally-small detectors and quadrupoles.

Physical properties of AM CVn stars: New insights fromGaiaDR2

AM CVn binaries are hydrogen deficient compact binaries with an orbital period in the 5–65 min range and are predicted to be strong sources of persistent gravitational wave radiation. UsingGaiaData Release 2, we present the parallaxes and proper motions of 41 out of the 56 known systems. Compared to the parallax determined using the HST Fine Guidance Sensor we find that the archetype star, AM CVn, is significantly closer than previously thought. This resolves the high luminosity and mass accretion rate which models had difficulty in explaining. Using Pan-STARRS1 data we determine the absolute magnitude of the AM CVn stars. There is some evidence that donor stars have a higher mass and radius than expected for white dwarfs or that the donors are not white dwarfs. Using the distances to the known AM CVn stars we find strong evidence that a large population of AM CVn stars has yet to be discovered. As this value sets the background to the gravitational wave signal of LISA this is of wide interest. We determine the mass transfer rate for 15 AM CVn stars and find that the majority has a rate significantly greater than expected from standard models. This is further evidence that the donor star has a greater size than expected.

Spin and center of mass comparison between the post-Newtonian approach and the asymptotic formulation

In this work we analyse the similarities and differences between the equations of motion for the center of mass and intrinsic angular momentum for isolated sources of gravitational radiation obtained by two different formulations. One approach is based on the asymptotic formulation of the GR whereas the other relies on Post- Newtonian methods. Several conclusions are obtained which could be useful for further developments in both approaches.

Graviatom of Superheavy Dark Matter as a Source of Gravitational Radiation

The nature of dark matter (DM) in modern physics is an important problem. We consider a quantum system consisting of two identical particles which are candidates for the role of DM.We call them graviatoms, and they could be formed in the early Universe. We find the energy spectrum of the gravitatom from DM particles, the Bohr radius, the intensity and frequency of gravitational radiation, and the lifetime of a state. This lifetime is large for superheavy particles. Estimates of these values for different masses of DM particles are given. The amplitude of a gravitational wave from a cloud of dark matter in the Milky Way is also estimated.