Compact Binaries Research Articles

Gravitational waves and kicks from the merger of unequal mass, highly compact boson stars

Boson stars have attracted much attention in recent decades as simple, self-consistent models of compact objects and also as self-gravitating structures formed in some dark-matter scenarios. Direct detection of these hypothetical objects through electromagnetic signatures would be unlikely because their bosonic constituents are not expected to interact significantly with ordinary matter and radiation. However, binary boson stars might form and coalesce emitting a detectable gravitational wave signal which might distinguish them from ordinary compact object binaries containing black holes and neutron stars. We study the merger of two boson stars by numerically evolving the fully relativistic Einstein-Klein-Gordon equations for a complex scalar field with a solitonic potential that generates very compact boson stars. Owing to the steep mass-radius diagram, we can study the dynamics and gravitational radiation from unequal-mass binary boson stars with mass ratios up to $q\approx23$ without the difficulties encountered when evolving binary black holes with large mass ratios. Similar to the previously-studied equal-mass case, our numerical evolutions of the merger produce either a nonspinning boson star or a spinning black hole, depending on the initial masses and on the binary angular momentum. We do not find any evidence of synchronized scalar clouds forming around either the remnant spinning black hole or around the remnant boson stars. Interestingly, in contrast to the equal-mass case, one of the mechanisms to dissipate angular momentum is now asymmetric, and leads to large kick velocities (up to a few $10^4\,{\rm km/s}$) which could produce wandering remnant boson stars. We also compare the gravitational wave signals predicted from boson star binaries with those from black hole binaries, and comment on the detectability of the differences with ground interferometers.

Gravitational wave surrogates through automated machine learning

We analyze a prospect for predicting gravitational waveforms from compact binaries based on automated machine learning (AutoML) from around a hundred different possible regression models, without having to resort to tedious and manual case-by-case analyses and fine-tuning. The particular study of this article is within the context of the gravitational waves emitted by the collision of two spinless black holes in initial quasi-circular orbit. We find, for example, that approaches such as Gaussian process regression with radial bases as kernels, an approach which is generalizable to multiple dimensions with low computational evaluation cost, do provide a sufficiently accurate solution. The results here presented suggest that AutoML might provide a framework for regression in the field of surrogates for gravitational waveforms. Our study is within the context of surrogates of numerical relativity simulations based on reduced basis and the empirical interpolation method, where we find that for the particular case analyzed AutoML can produce surrogates which are essentially indistinguishable from the NR simulations themselves.

Improved early-warning estimates of luminosity distance and orbital inclination of compact binary mergers using higher modes of gravitational radiation

ABSTRACTThe pre-merger (early-warning) gravitational-wave (GW) detection and localization of a compact binary merger would enable astronomers to capture potential electromagnetic (EM) emissions around the time of the merger, thus shedding light on the complex physics of the merger. While early detection and sky localization are of primary importance to the multimessenger follow-up, improved estimates of luminosity distance and orbital inclination could also provide insights on the observability of EM emission. In this work, we demonstrate that the inclusion of higher modes of gravitational radiation, which vibrate at higher multiples of the orbital frequency than the dominant mode, would significantly improve the early-warning estimates of the luminosity distance and orbital inclination of asymmetric compact binaries, in particular, neutron-star black hole mergers. This will help astronomers to better determine their follow-up strategy of such systems. Focusing on future observing runs of the ground-based GW detectors, we show that for neutron-star black hole binaries that are potentially EM-bright, the inclusion of higher modes improves the luminosity distance estimates by a factor of ∼1 − 1.5 (1.1 − 2) [1.1 − 5] for the O5 (Voyager) [3G] observing scenario, 45 (45) [300] s before the merger. There are significant improvements in orbital inclination estimates as well. We also investigate these improvements with varying sky-location and polarization angle. Combining the luminosity distance uncertainties with localization skyarea estimates, we find that the number of galaxies within localization volume is reduced by a factor of ∼1 − 2.5 (1.2 − 4) [1.2 − 10] with the inclusion of higher modes in O5 (Voyager) [3G].

Unicorns and giraffes in the binary zoo: stripped giants with subgiant companions

ABSTRACT We analyse two binary systems containing giant stars, V723 Mon (‘the Unicorn’) and 2M04123153+6738486 (‘the Giraffe’). Both giants orbit more massive but less luminous companions, previously proposed to be mass-gap black holes. Spectral disentangling reveals luminous companions with star-like spectra in both systems. Joint modelling of the spectra, light curves, and spectral energy distributions robustly constrains the masses, temperatures, and radii of both components: the primaries are luminous, cool giants ($T_{\rm eff,\, giant} = 3800$ and $4000\, \rm K$, $R_{\rm giant}= 22.5$ and $25\, {\rm R}_{\odot }$) with exceptionally low masses ($M_{\rm giant} \approx 0.4\, {\rm M}_{\odot }$) that likely fill their Roche lobes. The secondaries are only slightly warmer subgiants ($T_{\rm eff,\, 2} = 5800$ and $5150\, \rm K$, $R_2= 8.3$ and $9\, {\rm R}_{\odot }$) and thus are consistent with observed UV limits that would rule out main-sequence stars with similar masses ($M_2 \approx 2.8$ and ${\approx}1.8\, {\rm M}_{\odot }$). In the Unicorn, rapid rotation blurs the spectral lines of the subgiant, making it challenging to detect even at wavelengths where it dominates the total light. Both giants have surface abundances indicative of CNO processing and subsequent envelope stripping. The properties of both systems can be reproduced by binary evolution models in which a $1{-}2\, {\rm M}_{\odot }$ primary is stripped by a companion as it ascends the giant branch. The fact that the companions are also evolved implies either that the initial mass ratio was very near unity, or that the companions are temporarily inflated due to rapid accretion. The Unicorn and Giraffe offer a window into into a rarely observed phase of binary evolution preceding the formation of wide-orbit helium white dwarfs, and eventually, compact binaries containing two helium white dwarfs.

Linear momentum flux from inspiralling compact binaries in quasielliptical orbits at 2.5 post-Newtonian order

Emission of anisotropic gravitational radiation from compact binary system leads to a flux of linear momentum. This results in the recoil of the system. We investigate the rate of loss of Linear momentum flux in the far zone of the source using various mass type and current type multipole moments for inspiralling compact binary mergers in quasi-elliptical orbits at 2.5 Post Newtonian order. We compute the linear momentum flux accurate up to $\mathcal{O}(e_t)$ in harmonic coordinate. A 2.5 Post Newtonian Quasi-Keplarian representation of the parametric solution to the Post Newtonian equation of motion for the compact binary system has been adopted here. We also provide a closed-form expression for the accumulated linear momentum from the remote past through the binary evolution.

Chaotic dynamics of wide triples induced by galactic tides: a novel channel for producing compact binaries, mergers, and collisions

ABSTRACT Recent surveys show that wide (>104 AU) binaries and triples are abundant in the field. We study the long-term evolution of wide hierarchical triple systems and the role played by the Galactic tidal (GT) field. We find that when the time-scales of the secular von–Ziepel–Lidov–Kozai and the GT oscillations are comparable, triple evolution becomes chaotic which leads to extreme eccentricities. Consequently, the close pericentre approaches of the inner-binary components lead to strong interactions, mergers, and collisions. We use a novel secular evolution code to quantify the key parameters and carry out a population-synthesis study of low and intermediate-mass wide-orbit triples. We find that in $\sim 9{{\ \rm per\ cent}}$ of low-mass wide-triples the inner main-sequence binaries collide or tidally-inspiral within $10\ \rm Gyr$, with direct collisions are 6 times more likely to occur. For the intermediate-mass sample, $\sim 7.6{{\ \rm per\ cent}}$ of the systems merge or inspiral with roughly equal probabilities. We discuss the relative fractions of different stellar merger/inspiral outcomes as a function of their evolutionary stage (Main Sequence, MS; Red Giant, RG; or White Dwarf, WD), their transient electromagnetic signatures and the final products of the merger/inspiral. In particular, the rate of WD–WD direct-collisions that lead to type-Ia Supernovae is comparable to other dynamical channels and accounts for at most $0.1{{\ \rm per\ cent}}$ of the observed rate. RG inspirals provide a novel channel for the formation of eccentric common-envelope-evolution binaries. The catalysis of mergers/collisions in triples due to GT could explain a significant fraction, or even the vast majority, of blue-stragglers in the field, produce progenitors for cataclysmic-variables, and give-rise to mergers/collisions of double-RG binaries.

Interplay of spin-precession and higher harmonics in the parameter estimation of binary black holes

Gravitational-wave (GW) signals from coalescing compact binaries carry enormous information about the source dynamics and are an excellent tool to probe unknown astrophysics and fundamental physics. Though the updated catalog of compact binary signals reports evidence for slowly spinning systems and unequal mass binaries, the data so far cannot provide convincing proof of strongly precessing binaries. Here, we use the GW inference library parallel Bilby to compare the performance of two waveform models for measuring spin-induced orbital precession. One of the waveform models incorporates both spin-precession effects and sub-dominant harmonics. The other model accounts for precession but only includes the leading harmonic. By simulating signals with varying mass ratios and spins, we find that the waveform model with sub-dominant harmonics enables us to infer the presence of precession in most cases accurately. In contrast, the dominant model often fails to extract enough information to measure precession. In particular, it cannot distinguish a face-on highly precessing binary from a slowly precessing binary system irrespective of the binary's mass ratio. As expected, we see a significant improvement in measuring precession for edge-on binaries. Other intrinsic parameters also become better constrained, indicating that precession effects help break the correlations between mass and spin parameters. However, the precession measurements are prior dominated for equal-mass binaries with face-on orientation, even if we employ waveform model including subdominant harmonics. In this case, doubling the signal-to-noise ratio does not help to reduce these prior induced biases. As we expect detections of highly spinning binary signals with misaligned spin orientations in the future, simulation studies like ours are crucial for understanding the prospects and limitations of GW parameter inferences.

Generalized quasi-Keplerian solution for eccentric, nonspinning compact binaries at 4PN order and the associated inspiral-merger-ringdown waveform

We derive fourth post-Newtonian (4PN) contributions to the Keplerian-type parametric solution associated with the conservative dynamics of eccentric, non-spinning compact binaries. The solution has been computed while ignoring certain zero-average, oscillatory terms arising due to 4PN tail effects. We provide explicit expressions for the parametric solution and various orbital elements in terms of the conserved energy, angular momentum and symmetric mass ratio. Canonical perturbation theory (along with the technique of Pade approximant) is used to incorporate the 4PN nonlocal-in-time tail effects within the action-angles framework. We then employ the resulting solution to obtain an updated inspiral-merger-ringdown (IMR) waveform that models the coalescence of non-spinning, moderately eccentric black hole binaries, influenced by arXiv:1709.02007. Our updated waveform is expected to be valid over similar parameter range as the above reference. We also present a related waveform which makes use of only the post-Newtonian equations and thus is valid only for the inspiral stage. This waveform is expected to work for a much larger range of eccentricity ($e_t \lesssim 0.85$) than our full IMR waveform (which assumes circularization of the binaries close to merger). We finally pursue preliminary data analysis studies to probe the importance of including the 4PN contributions to the binary dynamics while constructing gravitational waveform templates for eccentric mergers.

Detectability of the Cross-Correlation between CMB Lensing and Stochastic GW Background from Compact Object Mergers

The anisotropies of the Stochastic Gravitational-Wave Background (SGWB), produced by merging compact binaries, constitute a possible new probe of the Large-Scale Structure (LSS). However, the significant shot noise contribution caused by the discreteness of the GW sources and the poor angular resolution of the instruments hampers the detection of the intrinsic anisotropies induced by the LSS. In this work, we investigate the potential of cross-correlating forthcoming high precision measurements of the SGWB energy density and the Cosmic Microwave Background (CMB) lensing convergence to mitigate the effect of shot noise. Combining a detailed model of stellar and galactic astrophysics with a novel framework to distribute the GW emitters in the sky, we compute the auto- and cross-correlation power spectra for the two cosmic fields, evaluate the shot noise contribution and predict the signal-to-noise ratio. The results of our analysis show that the SGWB energy density correlates significantly with the CMB lensing convergence and that the cross-correlation between these two cosmic fields reduces the impact of instrumental and shot noise. Unfortunately, the S/N is not high enough to detect the intrinsic SGWB anisotropies. Nevertheless, a network composed of both present and future generation GW interferometers, operating for at least 10 yrs, should be able to measure the shot noise contribution.

Gravitational radiation from binary systems in massive graviton theories

Theories with massive gravitons have peculiarity called the van Dam-Veltman-Zakharov discontinuity in that the massive theory propagator does not go to the massless graviton propagator in the zero graviton mass limit. This results in large deviation in Newtons law for massive graviton theories even when the graviton mass vanishes. We test the vDVZ in massive graviton theories for single graviton vertex process namely the gravitational radiation from a classical source.We calculate the gravitational radiation from compact binaries using the perturbative Feynman diagram method. We perform this calculation for Einstein's gravity with massless gravitons and verify that the Feynman diagram calculation reproduces the quadrupole formula. Using the same procedure we calculate the gravitational radiation for three massive graviton theories: (1) the Fierz-Pauli theory (2) the modified Fierz-Pauli theory without the vDVZ discontinuity and (3) the Dvali-Gabadadze-Porrati theory with a momentum dependent graviton mass. We put limits on the graviton mass in each of these theories from observations of binary pulsar timings.

Flexible and Accurate Evaluation of Gravitational-wave Malmquist Bias with Machine Learning

Abstract Many astronomical surveys are limited by the brightness of the sources, and gravitational-wave searches are no exception. The detectability of gravitational waves from merging binaries is affected by the mass and spin of the constituent compact objects. To perform unbiased inference on the distribution of compact binaries, it is necessary to account for this selection effect, which is known as Malmquist bias. Since systematic error from selection effects grows with the number of events, it will be increasingly important over the coming years to accurately estimate the observational selection function for gravitational-wave astronomy. We employ density estimation methods to accurately and efficiently compute the compact binary coalescence selection function. We introduce a simple pre-processing method, which significantly reduces the complexity of the required machine-learning models. We demonstrate that our method has smaller statistical errors at comparable computational cost than the method currently most widely used allowing us to probe narrower distributions of spin magnitudes. The currently used method leaves 10%–50% of the interesting black hole spin models inaccessible; our new method can probe >99% of the models and has a lower uncertainty for >80% of the models.

Host galaxy properties of quasi-periodically erupting X-ray sources

Context.Quasi-periodic X-ray eruptions (QPEs) are a recently discovered phenomenon, the nature of which remains unclear. Based on their discovery in active galactic nuclei (AGNs), explanations related to an AGN accretion disk or potentially a stellar tidal disruption event (TDE) have been put forward. Alternatives, including highly unequal mass compact object binaries, have also been proposed to explain their properties.Aims.We perform a systematic study of the five known QPE host galaxies with the aim of providing new insights as to their nature.Methods.We analysed new and archival medium resolution optical spectroscopy of the QPE hosts. We measured emission (and absorption) line fluxes, their ratios, and equivalent widths (EWs) to locate the QPE hosts on diagnostic diagrams. We also measured the velocity dispersion of the stellar absorption lines to estimate their black hole masses.Results.All QPE host galaxies show emission lines in their optical spectra. Based on their ratios and EWs, we find evidence for the presence of an AGN in all sources, including those previously reported as passive. We measure velocity dispersions between 36 and 90 km s−1, implying the presence of low mass (105−6.7 M⊙) black holes, consistent with literature findings. Finally, we find a significant over-representation (two out of the five sources, or a factor of 13−10+13) of quiescent Balmer strong (post-starburst) galaxies among QPE hosts.Conclusions.The presence of a narrow line region consistent with an AGN in all QPE host galaxies implies that a long-lived accretion flow likely plays an integral part in the QPE phenomenon. The strong over-representation of quiescent Balmer strong galaxies among QPE hosts can be naturally explained in both the TDE and interacting extreme mass ratio inspiral hypotheses.

A repeating fast radio burst source in a globular cluster.

Fast radio bursts (FRBs) are flashes of unknown physical origin1. The majority of FRBs have been seen only once, although some are known to generate multiple flashes2,3. Many models invoke magnetically powered neutron stars (magnetars) as the source of the emission4,5. Recently, the discovery6 of another repeater (FRB 20200120E) was announced, in the direction of the nearby galaxy M81, with four potential counterparts at other wavelengths6. Here we report observations that localized the FRB to a globular cluster associated with M81, where it is 2 parsecs away from the optical centre of the cluster. Globular clusters host old stellar populations, challenging FRB models that invoke young magnetars formed in a core-collapse supernova. We propose instead that FRB 20200120E originates from a highly magnetized neutron star formed either through the accretion-induced collapse of a white dwarf, or the merger of compact stars in a binary system7. Compact binaries are efficiently formed inside globular clusters, so a model invoking them could also be responsible for the observed bursts.

Gravitational wave constraints on Lorentz and parity violations in gravity: High-order spatial derivative cases

High-order spatial derivatives are of crucial importance for constructing the low energy effective action of a Lorentz or parity violating theory of quantum gravity. One example is the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity, in which one has to consider at least the sixth-order spatial derivatives in the gravitational action in order to make the theory power-counting renormalizable. In this paper, we consider the Lorentz and parity violating effects on the propagation of GWs due to the fifth and sixth-order spatial derivatives, respectively. For this purpose we calculate the corresponding Lorentz and parity violating waveforms of GWs produced by the coalescence of compact binaries. By using these modified waveforms, we perform the full Bayesian inference with the help of the open source software bilby on the selected GW events of binary black hole (BBH) and binary neutron stars (BNS) merges in the LIGO-Virgo catalogs GWTC-1 and GWTC-2. Overall we do not find any significant evidence of Lorentz and parity violation due to the fifth and sixth-order spatial derivatives and thus place lower bounds on the energy scales ${M}_{\mathrm{LV}}>2.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\text{ }\text{ }\mathrm{GeV}$ for Lorentz violation and ${M}_{\mathrm{PV}}>1.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\text{ }\text{ }\mathrm{GeV}$ for parity violation at 90% confidence level. Both constraints represent the first constraints on the fifth- and sixth-order spatial derivative terms respectively in the framework of spatial covariant gravity by using the observational data of GWs.

Gamma-radiation sky maps from compact binaries

We study sky maps and light curves of gamma-ray emission from neutron stars in compact binaries, and in isolation. We briefly review some gamma-ray emission models, and reproduce sky maps from a standard isolated pulsar in the Separatrix Layer model. We consider isolated pulsars with several variations of a dipole magnetic field, including superpositions, and predict their gamma-ray emission. Our results provide new heuristics on what can and cannot be inferred about the magnetic field configuration of pulsars from high-energy observations. We find that typical double-peak light curves can be produced by pulsars with significant multipole structure beyond a single dipole. For binary systems, we also present a simple approximation that is useful for rapid explorations of binary magnetic field structure. Finally, we predict the gamma-ray emission pattern from a compact black hole-neutron star binary moments before merger by applying the Separatrix Layer model to data simulated in full general relativity; we find that face-on observers receive little emission, equatorial observers see one broad peak, and more generic observers typically see two peaks.

Graviton Mass in the Era of Multi-Messenger Astronomy

The idea of massive graviton plays a fundamental role in modern physics as a landmark of most scenarios related to modified gravity theories. Limits on graviton mass can be obtained through different methods, using all the capabilities of multi-messenger astronomy available today. In this paper, we consider some emerging opportunities. In particular, modified relativistic dispersion relations of massive gravitons may lead to changes in the travel time of gravitational waves (GWs) emitted from distant astrophysical objects. Strong gravitational lensing of signals from a carefully selected class of extra-galactic sources such as compact object binaries (actually, binary neutron stars) is predicted to play an important role in this context. Comparing time delays between images of the lensed GW signal and its electromagnetic (EM) counterpart may be a new model-independent strategy (proposed by us in X.-L. Fan et al., 2017), which is especially promising in light of the fruitful observing runs of interferometric GW detectors, resulting in numerous GW signals. In addition to this direct, kinematic method, one can use an indirect, static method. In this approach, the non-zero graviton mass would modify estimates of the total cluster mass via a Yukawa term, influencing the Newtonian potential. In A. Piórkowska-Kurpas et al., 2022, using the X-COP galaxy cluster sample, we obtained mg<(4.99−6.79)×10−29 eV (at 95% C.L.), which is one of the best available constraints.

Deformed Schwarzschild horizons in second-order perturbation theory: Mass, geometry, and teleology

In recent years, gravitational-wave astronomy has motivated increasingly accurate perturbative studies of gravitational dynamics in compact binaries. This in turn has enabled more detailed analyses of the dynamical black holes in these systems. For example, Pound et al. [Phys. Rev. Lett. 124, 021101 (2020)] recently computed the surface area of a Schwarzschild black hole's apparent horizon, perturbed by an orbiting body, to second order in the binary's mass ratio. In this paper, we take that as the starting point for a comprehensive study of a perturbed Schwarzschild black hole's apparent and event horizon at second perturbative order, deriving generic formulas for the first- and second-order corrections to the horizons' radial profiles, surface areas, Hawking masses, and intrinsic curvatures. We find that the two horizons are remarkably similar, and that any teleological behavior of the event horizon is suppressed in several ways. Critically, we establish that at all orders, the perturbed event horizon in a small-mass-ratio binary is effectively localized in time. Even more pointedly, the event horizon is identical to the apparent horizon at linear order regardless of the source of perturbation, implying that the seemingly teleological "tidal lead", previously observed in linearly perturbed event horizons, is not genuinely teleological in origin. The two horizons do generically differ at second order, but their Hawking masses remain identical, implying that the event horizon obeys the same energy-flux balance law as the apparent horizon. At least in the case of a binary system, the difference between their surface areas remains extremely small even in the late stages of inspiral. In the course of our analysis, we also numerically illustrate puzzling behaviour in the black hole's motion around the binary's center of mass.

Constraints on the Nieh-Yan modified teleparallel gravity with gravitational waves

The discovery of gravitational waves (GWs) from the compact binary components by LIGO/Virgo Collaboration provides an unprecedented opportunity for testing gravity in the strong and highly dynamical field regime of gravity. Currently a lot of model-independent tests have been performed by LIGO/Virgo Collaboration and no any significant derivation from general relativity has been found. In this paper, we study the parity violating effects on the propagation of GWs in the Nieh-Yan modified teleparallel gravity, a theory which modifies general relativity by a parity violating Nieh-Yan term. We calculate the corresponding parity violating waveform of GWs produced by the coalescence of compact binaries. By comparing the two circular polarization modes, we find the effects of the velocity birefringence of GWs in their propagation caused by the parity violation due to the Nieh-Yan term, which are explicitly presented in the GW waveforms by the phase modification. With such phase modifications to the waveform, we perform the full Bayesian inference with the help of the open source software Bilby on the GW events of binary black hole merges (BBH) in the LIGO-Virgo catalogs GWTC-1 and GWTC-2. We do not find any significant evidence of parity violation due to the parity violating Nieh-Yan term and thus place an upper bound on the energy scale ${M}_{\mathrm{PV}}<6.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}42}\text{ }\text{ }\mathrm{GeV}$ at 90% confidence level, which represents the first constraint on the Nieh-Yan modified teleparallel gravity so far.

Ability of LISA to detect a gravitational-wave background of cosmological origin: The cosmic string case

We investigate the ability of the Laser Interferometer Space Antenna (LISA) to detect a stochastic gravitational-wave background (GWB) produced by cosmic strings, and to subsequently estimate the string tension $G\mu$ in the presence of instrument noise, an astrophysical background from compact binaries, and the galactic foreground from white dwarf binaries. Fisher Information and Markov Chain Monte Carlo methods provide estimates of the LISA noise and the parameters for the different signal sources. We demonstrate the ability of LISA to simultaneously estimate the galactic foreground, as well as the astrophysical and cosmic string produced backgrounds. Considering the expected astrophysical background and a galactic foreground, a cosmic string tension in the $G \mu \approx 10^{-16}$ to $G\mu \approx 10^{-15}$ range or bigger could be measured by LISA, with the galactic foreground affecting this limit more than the astrophysical background. The parameter estimation methods presented here can be applied to other cosmological backgrounds in the LISA observation band.

Constraining the orbital eccentricity of inspiralling compact binary systems with Advanced LIGO

The detection of ~50 coalescing compact binaries with the Advanced LIGO and Virgo detectors has allowed us to test general relativity, constrain merger rates, and look for evidence of tidal effects, compact object spins, higher waveform modes, and black hole ringdowns. An effect that has not yet been confidently detected is binary eccentricity, which might be present in a small fraction of binaries formed dynamically. Here we discuss general limits on eccentricity that can, in-principle, be placed on all types of compact object binaries by a detector operating at the design sensitivity of Advanced LIGO. Using a post-Newtonian model for gravitational-wave phasing valid in the small eccentricity regime, we assess the relative measurement error for eccentricity for a variety of spinning and non-spinning binaries. Errors and correlations involving the mass and spin parameters are also investigated. We find that decreasing the low frequency limit of a detector's observational frequency band is one of the key design factors for increasing the odds of measuring binary eccentricity. We also introduce and analytically explore the eccentric chirp mass parameter, which replaces the chirp mass as the key measurable parameter combination in eccentric gravitational waveform models. The eccentric chirp mass parameter explains a degeneracy between the chirp mass and the eccentricity. This degeneracy leads to a bias in the standard chirp mass parameter. We also investigate the systematic parameter bias that arises when eccentric systems are recovered using circular waveform templates. We use both Fisher matrix and Bayesian-inference-based Markov Chain Monte Carlo (MCMC) methods to investigate these parameter estimation issues, and we find good agreement between the two approaches (for both statistical and systematic errors) in the appropriate signal-to-noise ratio regime. (abridged)