Mass Ratio Limit Research Articles

Analytical model of precessing binaries using post-Newtonian theory in the extreme mass-ratio limit: General formalism

Analytical model of precessing binaries using post-Newtonian theory in the extreme mass-ratio limit: General formalism

WISE J141530.7+592234: A Very Low Mass Ratio Contact Binary with Significant Light Curve Variations

Multi-band photometric observations and period investigations of the total eclipsing binary WISE J141530.7+592234 (hereinafter J141530), whose mass ratio close to the low mass ratio limit, were carried out for the first time. The stellar atmospheric parameters of the primary component were calculated by the spectral fitting, yielding the following results: T eff = 5890 ± 22 K, [Fe/H] = 0.01 ± 0.03 dex, log g = 4.53 ± 0.04 cm s−2. Our observations show that the light curve of V-band on May 2 is about 0.1 mag brighter than that observed in February and March at phase 0.6. Comparing with the small amplitude (about 0.2 mag), the variations are remarkable. Meanwhile, obvious light curve variations and quick reversal of O’Connell effects are found in Transiting Exoplanet Survey Satellite data, which is likely caused by magnetic activity. Photometric solutions derived from multi-band light curves indicate that J141530 has a high contact degree (f ∼ 70%) and a very low mass ratio (q ∼ 0.0546). Based on the O − C diagram, a long-term period increase was found. The period increase rate is calculated to be dP/dt = 3.90 × 10−7 day yr−1, which can be explained by mass transfer from the low mass component to the large mass component. By analyzing the merging criterion, such as the ratio of spin angular momentum (J spin) to the orbital angular momentum (J orb), the instability separation and the instability mass ratio, J141530 can be regarded as a potential progenitor of luminous red novae.

WISE J185503.7+592234: A particularly low mass ratio contact binary approaching merger

ABSTRACT In this paper, the total eclipsing binary WISE J185503.7+592234 (hereinafter J185503), whose mass ratio is around the mass ratio limit, was observed and investigated for the first time. The stellar atmospheric parameters of the primary (more massive) component were calculated by the spectral fitting, and the following results are obtained: Teff = 5747 ± 25 K, [Fe/H] = −0.16 ± 0.04 dex, logg = 4.78 ± 0.05 cm s−2. Although J185503 has a very small amplitude (∼ 0.17 mag in V band) and a short period (0.2800782 d), its light curves exhibit total eclipses (eclipse duration: ∼ 40 min, which is about 0.1 phase). The light curves derived from TESS exhibit some unusual behaviour, such as inversion of the O’Connell effect, exchange of occultation, and transit depths. Photometric solutions obtained from the multiband observations suggest that J185503 has a particularly low mass ratio (q = 0.0514) and a moderate contact degree of $26{{\ \rm per\ cent}}$. Based on 103 newly determined times of minimum spanning 14 yr, a secular period decrease was found, which is calculated to be dP/dt = −2.24 × 10−7 d yr−1. Through analysing the instability criterion, such as the instability separation, the instability mass ratio, and the ratio of spin angular momentum (Jspin) to the orbital angular momentum (Jorb), J185503 can be regarded as a progenitor of luminous red novae.

Extreme mass-ratio binary black hole merger: Characteristics of the test-particle limit

We study binary black hole mergers in the extreme mass-ratio limit. We determine the energy, angular momentum, and linear momentum of the post-merger, remnant black hole. Unlike previous works, we perform our analysis directly in the test-particle limit by solving the Regge-Wheeler-Zerilli wave equation with a source that moves along a geodesic. We rely on the fact that toward the merger, small mass-ratio binary systems follow a quasiuniversal geodesic trajectory. This formalism captures the final premerger stages of small mass-ratio binaries and thus provides a straightforward universal description in a region inaccessible to numerical relativity simulations. We present a general waveform template that may be used in the search for gravitational wave bursts from small and intermediate mass-ratio binary systems. Finally, this formalism gives a formal proof that the recoil velocity is quadratic in the symmetric mass ratio $\nu$. Specifically, the velocity is given by $V/c\approx 0.0467 \nu^2$. This result is about $4\%$ larger than previously estimated. Most of this difference stems from the inclusion of higher multipoles in our calculation.

Event horizon of a charged black hole binary merger

We analyze the formation and evolution of the event horizon of a black hole binary merger when the black holes are charged. We find that the presence of charge influences the properties of the merger and can be useful for investigating the validity of various theories of modified gravity and several proposals for dark matter candidates. It can moreover give insights into various aspects of astrophysical phenomena involving black holes, such as degeneracies in the gravitational wave parameter determination. We perform our analysis both analytically and numerically, in $D=4$ dimensions, in the extreme mass ratio (EMR) limit and compare the results. The development of analytical results in the EMR limit is of uttermost importance in view of the upcoming observations of the LISA interferometer. We then use our analysis to describe how the horizon evolves in time during the merger and to investigate the growth in the area of the event horizon and the duration of the merger. We moreover provide a numerical solution valid in arbitrary dimensions $D\ensuremath{\ge}4$ which could be of interest in the context of the $\mathrm{AdS}/\mathrm{CFT}$ correspondence or for examining possible extensions of general relativity.

A Bayesian Analysis of Physical Parameters for 783 Kepler Close Binaries: Extreme-mass-ratio Systems and a New Mass Ratio versus Period Lower Limit

Contact binary star systems represent the long-lived penultimate phase of binary evolution. Population statistics of their physical parameters inform an understanding of binary evolutionary pathways and end products. We use light curves and new optical spectroscopy to conduct a pilot study of ten (near) contact systems in the long-period (P > 0.5 days) tail of close binaries in the Kepler field. We use PHOEBE light-curve models to compute Bayesian probabilities on five principal system parameters. Mass ratios and third-light contributions measured from spectra agree well with those inferred from the light curves. Pilot study systems have extreme mass ratios q < 0.32. Most are triples. Analysis of the unbiased sample of 783 0.15 d < P < 2 days (near) contact binaries results in 178 probable contact systems, 114 probable detached systems, and 491 ambiguous systems for which we report best-fitting and 16th-/50th-/84th-percentile parameters. Contact systems are rare at periods P > 0.5 days, as are systems with q > 0.8. There exists an empirical mass ratio lower limit ≈ 0.05–0.15 below which contact systems are absent, supporting a new set of theoretical predictions obtained by modeling the evolution of contact systems under the constraints of mass and angular momentum conservation. Premerger systems should lie at long periods and near this mass ratio lower limit, which rises from q = 0.044 for P = 0.74 days to q = 0.15 at P = 2.0 days. These findings support a scenario whereby nuclear evolution of the primary (more massive) star drives mass transfer to the primary, thus moving systems toward extreme q and larger P until the onset of the Darwin instability at precipitates a merger.

Redshift factor and the small mass-ratio limit in binary black hole simulations

We present a calculation of the Detweiler redshift factor in binary black hole simulations based on its relation to the surface gravity. The redshift factor has far-reaching applications in analytic approximations, gravitational self-force calculations, and conservative two-body dynamics. By specializing to nonspinning, quasicircular binaries with mass ratios ranging from ${m}_{A}/{m}_{B}=1$ to ${m}_{A}/{m}_{B}=9.5$ we are able to recover the leading small-mass-ratio (SMR) prediction with relative differences of order ${10}^{\ensuremath{-}5}$ from simulations alone. The next-to-leading order term that we extract agrees with the SMR prediction arising from self-force calculations, with differences of a few percent. These deviations from the first-order conservative prediction are consistent with nonadiabatic effects that can be accommodated in an SMR expansion. This fact is also supported by a comparison to the conservative post-Newtonian prediction of the redshifts. For the individual redshifts, a reexpansion in terms of the symmetric mass ratio $\ensuremath{\nu}$ does not improve the convergence of the series. However we find that when looking at the sum of the redshift factors of both back holes, ${z}_{A}+{z}_{B}$, which is symmetric under the exchange of the masses, a reexpansion in $\ensuremath{\nu}$ accelerates its convergence. Our work provides further evidence of the surprising effectiveness of SMR approximations in modeling even comparable mass binary black holes.

Numerical-relativity validation of effective-one-body waveforms in the intermediate-mass-ratio regime

One of the open problems in developing binary black hole (BBH) waveforms for gravitational wave astronomy is to model the intermediate mass ratio regime and connect it to the extreme mass ratio regime. A natural approach is to employ the effective one body (EOB) approach to the two-body dynamics that, by design, can cover the entire mass ratio range and naturally incorporates the extreme mass ratio limit. Here we use recently obtained numerical relativity (NR) data with mass ratios $m_1/m_2=(7,15,\,32,\,64,\,128)$ to test the accuracy of the state-of-the-art EOB model TEOBResumS in the intermediate mass ratio regime. We generally find an excellent EOB/NR consistency around merger and ringdown for all mass ratios and for all available subdominant multipoles, except for the $\ell=m=5$ one. This mode can be crucially improved using the new large-mass ratio NR data of this paper. The EOB/NR inspirals are also consistent with the estimated NR uncertainties. We also use several NR datasets taken by different public catalogs to probe the universal behavior of the multipolar hierarchy of waveform amplitudes at merger, that smoothly connects the equal-mass BBH to the test-mass result. Interestingly, the universal behavior is strengthened if the nonoscillatory memory contribution is included in the NR waveform. Future NR simulations with improved accuracy will be necessary to further probe, and possibly quantitatively refine, the TEOBResumS transition from late inspiral to plunge in the intermediate mass ratio regime.

Precisely computing bound orbits of spinning bodies around black holes. I. General framework and results for nearly equatorial orbits

Very large mass ratio binary black hole systems are of interest both as a clean limit of the two-body problem in general relativity, as well as for their importance as sources of low-frequency gravitational waves. At lowest order, the smaller body moves along a geodesic of the larger black hole's spacetime. Accurate models of such systems require postgeodesic corrections to this motion. Postgeodesic effects that drive the small body away from the geodesic include the gravitational self-force, which incorporates the backreaction of gravitational-wave emission, and the spin-curvature force, which arises from coupling of the small body's spin to the black hole's spacetime curvature. In this paper, we describe a method for precisely computing bound orbits of spinning bodies about black holes. Our analysis builds off of pioneering work by Witzany which demonstrated how to describe the motion of a spinning body to linear order in the small body's spin. Exploiting the fact that in the large mass-ratio limit spinning-body orbits are close to geodesics (in a sense that can be made precise) and using closed-form results due to van de Meent describing precession of the small body's spin along black hole orbits, we develop a frequency-domain formulation of the motion which can be solved very precisely. We examine a range of orbits with this formulation, focusing in this paper on orbits which are eccentric and nearly equatorial (i.e., the orbit's motion is $\mathcal{O}(S)$ out of the equatorial plane), but for which the small body's spin is arbitrarily oriented. We discuss generic orbits with general small-body spin orientation in a companion paper. We characterize the behavior of these orbits, contrasting them with geodesics, and show how the small body's spin shifts the frequencies ${\mathrm{\ensuremath{\Omega}}}_{r}$ and ${\mathrm{\ensuremath{\Omega}}}_{\ensuremath{\phi}}$ which affect orbital motion. These frequency shifts change accumulated phases which are direct gravitational-wave observables, illustrating the importance of precisely characterizing these quantities for gravitational-wave observations.

Measuring quasinormal mode amplitudes with misaligned binary black hole ringdowns

In recent work, we examined how different modes in the ringdown phase of a binary coalescence are excited as a function of the final plunge geometry. At least in the large mass ratio limit, we found a clean mapping between angles describing the plunge and the amplitude of different quasi-normal modes (QNMs) which constitute the ringdown. In this study, we use that mapping to construct a waveform model expressed as a sum of QNMs where the mode amplitudes and phases are determined by the source plunge parameters. We first generate a large number of calibration waveforms and interpolate between fits of each mode amplitude and phase up to $\ell \leq 8$ and $\ell - |m| \leq 4$. The density of our calibration data allows us to resolve important features such as phase transition discontinuities at large misalignments. Using our ringdown waveform model, we then perform Bayesian parameter estimation with added white Gaussian noise to demonstrate that, in principle, the mode amplitudes can be measured and used to constrain the plunge geometry. We find that inferences are substantially improved by incorporating prior information constraining mode excitation, which motivates work to understand and characterize how the QNM excitation depends on the coalescence geometry. These results are part of a broader effort to map the mode excitation from arbitrary masses and spins, which will be useful for characterizing ringdown waves in upcoming gravitational-wave measurements.

Absolute parameters of four W UMa stars with extreme low mass ratios

Photometric observations of four extreme low mass ratio W UMa binaries with wide total eclipses, and their absolute parameters are presented. The main results are as follows: (i) ASAS J015429+2042.8 is of A subtype while V755 Cep, VESPA V22 and GSC 02800-01387 are of W subtype; (ii) The mass ratios are close to the lower mass-ratio limit and can be classified as Extreme Low Mass Ratio Binaries (ELMRB). (iii) The fill-out factors of ASAS J015429+2042.8 and VESPA V22 are 0.16 and 0.21 respectively, the one of GSC 02800-01387 is 0.63 while the one of V755 Cep is 0.83; (iv) The smaller in size (and less massive) components of all targets are located above the MS band of the evolutional diagrams while the bigger (and more massive) components are located around ZAMS; (v) Our ELMRB systems fall into the stability zone with Jspin/Jorb lower than the Darwin’s instability ∼1/3.

Extended electron tails in electrostatic microinstabilities and the nonadiabatic response of passing electrons

Ion-gyroradius-scale microinstabilities typically have a frequency comparable to the ion transit frequency. Due to the small electron-to-ion mass ratio and the large electron transit frequency, it is conventionally assumed that passing electrons respond adiabatically in ion-gyroradius-scale modes. However, in gyrokinetic simulations of ion-gyroradius-scale modes in axisymmetric toroidal magnetic fields, the nonadiabatic response of passing electrons can drive the mode, and generate fluctuations in narrow radial layers, which may have consequences for turbulent transport in a variety of circumstances. In flux tube simulations, in the ballooning representation, these instabilities reveal themselves as modes with extended tails. The small electron-to-ion mass ratio limit of linear gyrokinetics for electrostatic instabilities is presented, in axisymmetric toroidal magnetic geometry, including the nonadiabatic response of passing electrons and associated narrow radial layers. This theory reveals the existence of ion-gyroradius-scale modes driven solely by the nonadiabatic passing electron response, and recovers the usual ion-gyroradius-scale modes driven by the response of ions and trapped electrons, where the nonadiabatic response of passing electrons is small. The collisionless and collisional limits of the theory are considered, demonstrating parallels in structure and physical processes to neoclassical transport theory. By examining initial-value simulations of the fastest-growing eigenmodes, the predictions for mass-ratio scaling are tested and verified numerically for a range of collision frequencies. Insight from the small electron-to-ion mass ratio theory may lead to a computationally efficient treatment of extended modes.

Two Contact Binaries with Mass Ratios Close to the Minimum Mass Ratio

Abstract The cutoff mass ratio is under debate for contact binaries. In this paper, we present the investigation of two contact binaries with mass ratios close to the low mass ratio limit. It is found that the mass ratios of VSX J082700.8+462850 (hereafter J082700) and 1SWASP J132829.37+555246.1 (hereafter J132829) are both less than 0.1 (q ∼ 0.055 for J082700 and q ∼ 0.089 for J132829). J082700 is a shallow contact binary with a contact degree of ∼19%, and J132829 is a deep contact system with a fill-out factor of ∼70%. The O − C diagram analysis indicated that the two systems manifested long-term period decreases. In addition, J082700 exhibits a cyclic modulation which is more likely resulting from the Applegate mechanism. In order to explore the properties of extremely low mass ratio contact binaries (ELMRCBs), we carried out a statistical analysis on contact binaries with mass ratios of q ≲ 0.1 and discovered that the values of J spin/J orb of three systems are greater than 1/3. Two possible explanations can interpret this phenomenon. One explanation is that some physical processes, unknown to date, are not considered when Hut presented the dynamic stability criterion. The other explanation is that the dimensionless gyration radius (k) should be smaller than the value we used (k 2 = 0.06). We also found that the formation of ELMRCBs possibly has two channels. The study of evolutionary states of ELMRCBs reveals that their evolutionary states are similar with those of normal W UMa contact binaries.

Towards the merger of Hawking radiating black holes

We discuss the merger process of binary black holes with Hawking radiation taken into account. Besides the redshifted radiation to infinity, binary black holes can exchange radiation between themselves, which is first redshifted and then blueshifted when it propagates from one hole to the other. The exchange rate should be large when the temperature-divergent horizons are penetrating each other to form a single horizon with unique temperature. This will cause nonnegligible mass and angular momentum transfer between the black holes during the merging process of the horizons. We further argue in the large mass ratio limit that the light hole whose local evaporation is enhanced by the competing redshift–blueshift effects will probably evaporate or decay completely before reaching the horizon of the heavy one. We also discuss the possibility of testing Hawking radiation and even exploring the information loss puzzle in gravitational wave observations.

Flow-induced instabilities of springs-mounted plates in viscous flows: A global stability approach

The linear stability of a typical aeroelastic section, consisting in a rectangular plate mounted on flexion and torsion springs, is revisited here for low-Reynolds-number incompressible flows. By performing global stability analyses of the coupled fluid-solid equations, we find four types of unstable modes related to different physical instabilities and classically investigated with separate flow models: coupled-mode flutter, single-mode flutter, and static divergence at high reduced velocity U* and vortex-induced vibrations at low U*. Neutral curves for these modes are presented in the parameter space composed of the solid-to-fluid mass ratio and the reduced velocity. Interestingly, the flutter mode is seen to restabilize for high reduced velocities thus leading to a finite extent flutter region, delimited by low-U* and high-U* boundaries. At a particular low mass ratio, both boundaries merge such that no flutter instability is observed for lower mass ratios. The effect of the Reynolds number is then investigated, indicating that the high-U* restabilization strongly depends on viscosity. The global stability results are compared to a statically calibrated Theodorsen model: if both approaches converge in the high mass ratio limit, they significantly differ at lower mass ratios. In addition, the Theodorsen model fails to predict the high-U* restabilization of the flutter mode.

Late-time Observations of Calcium-rich Transient SN 2019ehk Reveal a Pure Radioactive Decay Power Source

Abstract We present multiband Hubble Space Telescope imaging of the calcium-rich supernova (SN) SN 2019ehk at 276-389 days after explosion. These observations represent the latest B-band to near-IR photometric measurements of a calcium-rich transient to date and allow for the first opportunity to analyze the late-time bolometric evolution of an object in this observational SN class. We find that the late-time bolometric light curve of SN 2019ehk can be described predominantly through the radioactive decay of 56Co for which we derive a mass of M(56Co) = (2.8 ± 0.1) × 10−2 M ⊙. Furthermore, the rate of decline in bolometric luminosity requires the leakage of γ-rays on timescale t γ = 53.9 ± 1.30 days, but we find no statistical evidence for incomplete positron trapping in the SN ejecta. While our observations cannot constrain the exact masses of other radioactive isotopes synthesized in SN 2019ehk, we estimate a mass ratio limit of M(57Co)/M(56Co) ≤ 0.030. This limit is consistent with the explosive nucleosynthesis produced in the merger of low-mass white dwarfs, which is one of the favored progenitor scenarios in early-time studies of SN 2019ehk.

Tidal Effects in the Post-Minkowskian Expansion.

Tools from scattering amplitudes and effective field theory have recently been repurposed to derive state-of-the-art results for the black hole binary inspiral in the post-Minkowskian expansion. In the present Letter, we extend this approach to include the tidal effects of mass and current quadrupoles on the conservative dynamics of nonspinning neutron star mergers. We compute the leading and, for the first time, next-to-leading order post-Minkowskian finite size corrections to the conservative Hamiltonian, together with their associated scattering amplitudes and scattering angles. Our expressions are gauge invariant and, in the extreme mass ratio limit, consistent with the dynamics of a tidally deformed test body in a Schwarzschild background. Furthermore, they agree completely with existing results at leading post-Minkowskian and second post-Newtonian orders.

Model independent tests of the Kerr bound with extreme mass ratio inspirals

An outstanding prediction of general relativity is the fact that the angular momentum S of an isolated black hole with mass μ is limited by the Kerr bound, S≤Gμ2/c. Testing this cornerstone is challenging due to the difficulty in modeling spinning compact objects that violate this bound. We argue that precise, model-independent tests can be achieved by measuring gravitational waves from an extreme mass ratio inspiral around a supermassive object, one of the main targets of the future LISA mission. In the extreme mass ratio limit, the dynamics of the small compact object depends only on its multipole moments, which are free parameters. At variance with the comparable-mass case, accurate waveforms are valid also when the spin of the small object greatly exceeds the Kerr bound. By computing the orbital dephasing and the gravitational-wave signal emitted by a spinning point particle in circular, nonprecessing, equatorial motion around a Kerr black hole, we estimate that LISA will be able to measure the spin of the small compact object at the level of 10%. Together with mass measurements, this will allow for theory-agnostic, unprecedented constraints on string-theory inspired objects such as “superspinars”, almost in their entire parameter space.

Logarithmic tail contributions to the energy function of circular compact binaries

We combine different techniques to extract information about the logarithmic contributions to the two-body conservative dynamics within the post-Newtonian (PN) approximation of General Relativity. The logarithms come from the conservative part of non linear gravitational-wave tails and their iterations. Explicit, original expressions are found for conservative dynamics logarithmic tail terms up to 6PN order by adopting both traditional PN calculations and effective field theory (EFT) methods. We also determine all logarithmic terms at 7PN order, fixing a sub-leading logarithm from a tail-of-tail-of-tail process by comparison with self-force (SF) results. Moreover, we use renormalization group techniques to obtain the leading logarithmic terms to generic power $n$, appearing at $(3n+1)$PN order, and we resum the infinite series in a closed form. Half-integer PN orders enter the conservative dynamics starting at 5.5PN, but they do not generate logarithmic contributions up to next-to-next-to-leading order included. We nevertheless present their contribution at leading order in the small mass ratio limit.

Global parameters of the totally-eclipsing W UMa stars NSVS 6673994, NSVS 4316778, PP Lac and NSVS 1926064

Photometric observations of four totally-eclipsing W UMa binaries, NSVS 6673994, NSVS 4316778, PP Lac and NSVS 1926064, are presented. Their global parameters were determined from the light curve solutions and GAIA distances. The main results are as follows: (i) NSVS 6673994, NSVS 4316778 and PP Lac are of W subtype while NSVS 1926064 is of A subtype; (ii) The mass ratios of NSVS 4316778 and NSVS 1926064 are close to the lower mass-ratio limit; (iii) NSVS 4316778 has double contact configuration while NSVS 1926064 is in deep contact; (iv) The changes of the PP Lac period seem cyclic and are accompanied with episodes of essentially constant value; (v) The relations between the global parameters of the four W UMa stars differ considerably from those of Main Sequence (MS) stars. The deviations of the radii, temperatures and luminosities of the stellar components from those of MS stars with the same masses are bigger for the two targets with extremely small mass ratio.