Select publications with significant personal contribution are highlighted below. A full list of my short-author work can be found on the ADS.
Observation of Gravitational Waves from the Coalescence of a 2.5−4.5 M☉ Compact Object and a Neutron Star
Abac et. al, (LIGO-Virgo-KAGRA Collaboration; including S. Biscoveanu as paper manager)
We report the observation of a coalescing compact binary with component masses 2.5−4.5 M☉ and 1.2−2.0 M☉ (all measurements quoted at the 90% credible level). The gravitational-wave signal GW230529_181500 was observed during the fourth observing run of the LIGO-Virgo-KAGRA detector network on 2023 May 29 by the LIGO Livingston Observatory. The primary component of the source has a mass less than 5 M☉ at 99% credibility. We cannot definitively determine from gravitational-wave data alone whether either component of the source is a neutron star or a black hole. However, given existing estimates of the maximum neutron star mass, we find the most probable interpretation of the source to be the coalescence of a neutron star with a black hole that has a mass between the most massive neutron stars and the least massive black holes observed in the Galaxy. We estimate a merger rate density of 55+127−47 Gpc−3yr−1 for compact binary coalescences with properties similar to the source of GW230529_181500; assuming that the source is a neutron star-black hole merger, GW230529_181500-like sources constitute about 60% of the total merger rate inferred for neutron star-black hole coalescences. The discovery of this system implies an increase in the expected rate of neutron star-black hole mergers with electromagnetic counterparts and provides further evidence for compact objects existing within the purported lower mass gap.
Probing Correlations in the Binary Black Hole Population with Flexible Models
J. Heinzel, S. Biscoveanu, S. Vitale
The astrophysical formation channels of binary black hole systems predict correlations between their mass, spin, and redshift distributions, which can be probed with gravitational-wave observations. Population-level analysis of the latest LIGO-Virgo-KAGRA catalog of binary black hole mergers has identified evidence for such correlations assuming linear evolution of the mean and width of the effective spin distribution as a function of the binary mass ratio and merger redshift. However, the complex astrophysical processes at play in compact binary formation do not necessarily predict linear relationships between the distributions of these parameters. In this work, we relax the assumption of linearity and instead search for correlations using a more flexible cubic spline model. Our results suggest a nonlinear correlation between the width of the effective spin distribution and redshift. We also show that the LIGO-Virgo-Kagra collaborations may find convincing Bayesian evidence for nonlinear correlations by the end of the fourth observing run, O4. This highlights the valuable role of flexible models in population analyses of compact-object binaries in the era of growing catalogs.
An observational upper limit on the rate of gamma-ray bursts with neutron star-black hole merger progenitors
S. Biscoveanu, E. Burns, P. Landry, S. Vitale
Compact-object binary mergers consisting of one neutron star and one black hole (NSBHs) have long been considered promising progenitors for gamma-ray bursts, whose central engine remains poorly understood. Using gravitational-wave constraints on the population-level NSBH mass and spin distributions we find that at most 20 Gpc−3yr−1 of gamma-ray bursts in the local universe can have NSBH progenitors.
Spin it as you like: the (lack of a) measurement of the spin tilt distribution with LIGO-Virgo-KAGRA binary black holes
S. Vitale, S. Biscoveanu, C. Talbot
While much has been learned about black holes by analyzing the latest LVK catalog, GWTC-3, a measurement of the astrophysical distribution of the black hole spin orientations remains elusive. This is usually probed by measuring the cosine of the tilt angle (cosτ) between each black hole spin and the orbital angular momentum, cosτ=+1 being perfect alignment. Abbott et al. has modeled the cosτ distribution as a mixture of an isotropic component and a Gaussian component with mean fixed at +1 and width measured from the data. We want to verify if the data require the existence of such a peak at cosτ=+1. We use various alternative models for the astrophysical tilt distribution and measure their parameters using the LVK GWTC-3 catalog. We find that a) Augmenting the LVK model such that the mean μ of the Gaussian is not fixed at +1 returns results that strongly depend on priors. If we allow μ>+1 then the resulting astrophysical cosτ distribution peaks at +1 and looks linear, rather than Gaussian. If we constrain −1≤μ≤+1 the Gaussian component peaks at μ=0.48+0.46−0.99 (median and 90% symmetric credible interval). Two other 2-component mixture models yield cosτ distributions that either have a broad peak centered at 0.19+0.22−0.18 or a plateau that spans the range [-0.5, +1], without a clear peak at +1. b) All of the models we considered agree on the fact that there is no excess of black hole tilts at around -1. c) While yielding quite different posteriors, the models considered in this work have Bayesian evidences that are the same within error bars. We conclude that the current dataset is not sufficiently informative to draw any model-independent conclusions on the astrophysical distribution of spin tilts, except that there is no excess of spins with negatively aligned tilts.<\p>
Population properties and multimessenger prospects of neutron star-black hole mergers following GWTC-3
S. Biscoveanu, P. Landry, S. Vitale
Neutron star-black hole (NSBH) mergers detected in gravitational-waves have the potential to shed light on supernova physics, the dense matter equation of state, and the astrophysical processes that power their potential electromagnetic counterparts. We use the population of four candidate NSBH events detected in gravitational waves so far with a false alarm rate ≤1 yr−1 to constrain the mass and spin distributions and multimessenger prospects of these systems. We find that the black holes in NSBHs are both less massive and more slowly spinning that those in black hole binaries. We also find evidence for a mass gap between the most massive neutron stars and least massive black holes in NSBHs at 98.6% credibility. We consider both a Gaussian and a power-law pairing function for the distribution of the mass ratio between the neutron star and black hole masses but find no statistical preference between the two. Using an approach driven by gravitational-wave data rather than binary simulations, we find that fewer than 15% of NSBH mergers detectable in gravitational waves will have an electromagnetic counterpart. Finally, we propose a method for the multimessenger analysis of NSBH mergers based on the nondetection of an electromagnetic counterpart and conclude that, even in the most optimistic case, the constraints on the neutron star equation of state that can be obtained with multimessenger NSBH detections are not competitive with those from gravitational-wave measurements of tides in binary neutron star mergers and radio and X-ray pulsar observations.
Constraining white dwarf tides from gravitational waves with LISA
S. Biscoveanu, K. Kremer, E. Thrane
Double white dwarf (DWD) systems are unique among gravitational-wave sources because their evolution is governed not just by general relativity, but also by mass transfer and tides. While the black hole and neutron star binaries observed with ground-based gravitational-wave detectors are driven to inspiral due to the emission of gravitational radiation - manifesting as a "chirp"-like gravitational-wave signal - the astrophysical processes at work in DWDs can cause the inspiral to stall and even reverse into an outspiral. The dynamics of the DWD outspiral thus encode information about tides, which tell us about the behaviour of electron-degenerate matter. We carry out a population study to determine the effect of the strength of tides on the distributions of the DWD binary parameters that the Laser Interferometer Space Antenna (LISA) will be able to constrain. We find that the strength of tidal coupling leaves a unique signature in the distribution of gravitational-wave frequencies and frequency derivatives for detectably mass transferring DWD systems. By measuring the population properties of DWDs, LISA will be able to probe the behavior of electron-degenerate matter.
The Binary Black Hole Spin Distribution Likely Broadens with Redshift
S. Biscoveanu, T.A. Callister, C.-J. Haster, K.K.Y. Ng, S. Vitale, W.M. Farr
The population-level distributions of the masses, spins, and redshifts of binary black holes (BBHs) observed using gravitational waves can shed light on how these systems form and evolve. Because of the complex astrophysical processes shaping the inferred BBH population, models allowing for correlations among these parameters will be necessary to fully characterize these sources. We hierarchically analyze the BBH population detected by LIGO and Virgo with a model allowing for correlations between the effective aligned spin and the primary mass and redshift. We find that the width of the effective spin distribution grows with redshift at 98.6% credibility. We determine this trend to be robust under the application of several alternative models and additionally verify that such a correlation is unlikely to be spuriously introduced using a simulated population. We discuss the possibility that this correlation could be due to a change in the natal black hole spin distribution with redshift.
Evidence of Large Recoil Velocity from a Black Hole Merger Signal
V. Varma, S. Biscoveanu, T. Islam, F.H. Shaik, C.-J. Haster, M. Isi, W.M. Farr, S.E. Field, S. Vitale
The final black hole left behind after a binary black hole merger can attain a recoil velocity, or a "kick," reaching values up to 5000 km /s . This phenomenon has important implications for gravitational wave astronomy, black hole formation scenarios, testing general relativity, and galaxy evolution. We consider the gravitational wave signal from the binary black hole merger GW200129_065458 (henceforth referred to as GW200129), which has been shown to exhibit strong evidence of orbital precession. Using numerical relativity surrogate models, we constrain the kick velocity of GW200129 to vf∼1542-1098+747 km /s or vf≥698 km /s (one-sided limit), at 90% credibility. This marks the first identification of a large kick velocity for an individual gravitational wave event. Given the kick velocity of GW200129, we estimate that there is a less than 0.48% (7.7%) probability that the remnant black hole after the merger would be retained by globular (nuclear star) clusters. Finally, we show that kick effects are not expected to cause biases in ringdown tests of general relativity for this event, although this may change in the future with improved detectors.
The orientations of the binary black holes in GWTC-3
S. Vitale, S. Biscoveanu, C. Talbot
It is expected that the orbital planes of gravitational-wave (GW) sources are isotropically distributed. However, both physical and technical factors, such as alternate theories of gravity with birefringence, catalog contamination, and search algorithm limitations, could result in inferring a non-isotropic distribution. Showing that the inferred astrophysical distribution of the orbital orientations is indeed isotropic can thus be used to rule out some violations of general relativity, as a null test about the purity of the GW catalog sample, and as a check that selection effects are being properly accounted for. We augment the default mass/spins/redshift model used by the LIGO-Virgo-KAGRA Collaboration in their most recent analysis to also measure the astrophysical distribution of orbital orientations. We show that the 69 binary black holes in GWTC-3 are consistent with having random orbital orientations. The inferred distribution is highly symmetric around π/2, with skewness Spost=0.01+0.17−0.17. Meanwhile, the median of the inferred distribution has a Jensen-Shannon divergence of 1.4×10−4 bits when compared to the expected isotropic distribution.
The effect of spin mismodelling on gravitational-wave measurements of the binary neutron star mass distribution
S. Biscoveanu, C. Talbot, S. Vitale
The binary neutron star (BNS) mass distribution measured with gravitational-wave observations has the potential to reveal information about the dense matter equation of state, supernova physics, the expansion rate of the universe, and tests of General Relativity. As most current gravitational-wave analyses measuring the BNS mass distribution do not simultaneously fit the spin distribution, the implied population-level spin distribution is the same as the spin prior applied when analyzing individual sources. In this work, we demonstrate that introducing a mismatch between the implied and true BNS spin distributions can lead to biases in the inferred mass distribution. This is due to the strong correlations between the measurements of the mass ratio and spin components aligned with the orbital angular momentum for individual sources. We find that applying a low-spin prior which excludes the true spin magnitudes of some sources in the population leads to significantly overestimating the maximum neutron star mass and underestimating the minimum neutron star mass at the population level with as few as six BNS detections. The safest choice of spin prior that does not lead to biases in the inferred mass distribution is one which allows for high spin magnitudes and tilts misaligned with the orbital angular momentum.
An Infrared Search for Kilonovae with the WINTER Telescope. I. Binary Neutron Star Mergers
D. Frostig, S. Biscoveanu et al.
The Wide-Field Infrared Transient Explorer (WINTER) is a new 1 deg2 seeing-limited time-domain survey instrument designed for dedicated near-infrared follow-up of kilonovae from binary neutron star (BNS) and neutron star-black hole mergers. WINTER will observe in the near-infrared Y, J, and short-H bands (0.9-1.7 microns, to JAB=21 magnitudes) on a dedicated 1-meter telescope at Palomar Observatory. To date, most prompt kilonova follow-up has been in optical wavelengths; however, near-infrared emission fades slower and depends less on geometry and viewing angle than optical emission. We present an end-to-end simulation of a follow-up campaign during the fourth observing run (O4) of the LIGO, Virgo, and KAGRA interferometers, including simulating 625 BNS mergers, their detection in gravitational waves, low-latency and full parameter estimation skymaps, and a suite of kilonova lightcurves from two different model grids. We predict up to five new kilonovae independently discovered by WINTER during O4, given a realistic BNS merger rate. Using a larger grid of kilonova parameters, we find that kilonova emission is ≈2 times longer lived and red kilonovae are detected ≈1.5 times further in the infrared than the optical. For 90% localization areas smaller than 150 (450) deg2, WINTER will be sensitive to more than 10% of the kilonova model grid out to 350 (200) Mpc. We develop a generalized toolkit to create an optimal BNS follow-up strategy with any electromagnetic telescope and present WINTER's observing strategy with this framework. This toolkit, all simulated gravitational-wave events, and skymaps are made available for use by the community.
Hints of spin-orbit resonances in the binary black hole population
V. Varma, S. Biscoveanu, M. Isi, W. Farr, S. Vitale
Binary black hole spin measurements from gravitational wave observations can reveal the binary's evolutionary history. In particular, the spin orientations of the component BHs within the orbital plane, φ1 and φ2, can be used to identify binaries caught in the so-called spin-orbit resonances. In a companion paper, we demonstrate that φ1 and φ2 are best measured near the merger of the two black holes. In this work, we use these spin measurements to constrain the distribution of φ1 and Δφ = φ1 - φ2 over the astrophysical population of merging binary black holes. We find that there is a preference for Δφ∼±π in the population, which can be a signature of spin-orbit resonances. We also find a preference for φ1∼−π/4 with respect to the line of separation near merger, which has not been predicted for any astrophysical formation channel. However, the strength of these preferences depend on our prior choices, and we are unable to constrain the widths of the φ1 and Δφ distributions. Therefore, more observations are necessary to confirm the features we find. Finally, we derive constraints on the distribution of recoil kicks in the population, and use this to estimate the fraction of merger remnants retained by globular and nuclear star clusters.
Measuring binary black hole orbital-plane spin orientations
V. Varma, M. Isi, S. Biscoveanu, W. Farr, S. Vitale
Binary black hole spins are among the key observables for gravitational wave astronomy. Among the spin parameters, their orientations within the orbital plane, φ1, φ2 and Δφ = φ1 - φ2, are critical for understanding the prevalence of the spin-orbit resonances and merger recoils in binary black holes. Unfortunately, these angles are particularly hard to measure using current detectors, LIGO and Virgo. Because the spin directions are not constant for precessing binaries, the traditional approach is to measure the spin components at some reference stage in the waveform evolution, typically the point at which the frequency of the detected signal reaches 20 Hz. However, we find that this is a poor choice for the orbital-plane spin angle measurements. Instead, we propose measuring the spins at a fixed \emph{dimensionless} time or frequency near the merger. This leads to significantly improved measurements for φ1 and φ2 for several gravitational wave events. Furthermore, using numerical relativity injections, we demonstrate that Δφ will also be better measured near the merger for louder signals expected in the future. Finally, we show that numerical relativity surrogate models are key for reliably measuring the orbital-plane spin orientations, even at moderate signal-to-noise ratios like ∼30−45.
Inference with finite time series: Observing the gravitational Universe through windows
C. Talbot, E. Thrane, S. Biscoveanu, R. Smith
Time series analysis is ubiquitous in many fields of science including gravitational-wave astronomy, where strain time series are analyzed to infer the nature of gravitational-wave sources, e.g., black holes and neutron stars. It is common in gravitational-wave transient studies to apply a tapered window function to reduce the effects of spectral artifacts from the sharp edges of data segments. We show that the conventional analysis of tapered data fails to take into account covariance between frequency bins, which arises for all finite time series -- no matter the choice of window function. We discuss the origin of this covariance and show that as the number of gravitational-wave detections grows, and as we gain access to more high signal-to-noise ratio events, this covariance will become a non-negligible source of systematic error. We derive a framework that models the correlation induced by the window function and demonstrate this solution using both data from the first LIGO--Virgo transient catalog and simulated Gaussian noise.
Measuring the spins of heavy binary black holes
A.S. Biscoveanu, M. Isi, V. Varma, S. Vitale
An accurate and precise measurement of the spins of individual merging black holes is required to understand their origin. While previous studies have indicated that most of the spin information comes from the inspiral part of the signal, the informative spin measurement of the heavy binary black hole system GW190521 suggests that the merger and ringdown can contribute significantly to the spin constraints for such massive systems. We perform a systematic study into the measurability of the spin parameters of individual heavy binary black hole mergers using a numerical relativity surrogate waveform model including the effects of both spin-induced precession and higher-order modes. We find that the spin measurements are driven by the merger and ringdown parts of the signal for GW190521-like systems, but the uncertainty in the measurement increases with the total mass of the system. We are able to place meaningful constraints on the spin parameters even for systems observed at moderate signal-to-noise ratios, but the measurability depends on the exact six-dimensional spin configuration of the system. Finally, we find that the azimuthal angle between the in-plane projections of the component spin vectors at a given reference frequency cannot be well-measured for most of our simulated configurations even for signals observed with high signal-to-noise ratios.
Measuring the primordial gravitational-wave background in the presence of astrophysical foregrounds
A.S. Biscoveanu, C. Talbot, E. Thrane, R. Smith
Primordial gravitational waves are expected to create a stochastic background encoding information about the early Universe that may not be accessible by other means. However, the primordial background is obscured by an astrophysical foreground consisting of gravitational waves from compact binaries. We demonstrate a Bayesian method for estimating the primordial background in the presence of an astrophysical foreground. Since the background and foreground signal parameters are estimated simultaneously, there is no subtraction step, and therefore we avoid astrophysical contamination of the primordial measurement, sometimes referred to as "residuals". Additionally, since we include the non-Gaussianity of the astrophysical foreground in our model, this method represents the statistically optimal approach to the simultaneous detection of a multi-component stochastic background.
A new spin on LIGO-Virgo binary black holes
A.S. Biscoveanu, M. Isi, S. Vitale, V. Varma
Gravitational waves from binary black holes have the potential to yield information on both of the intrinsic parameters that characterize the compact objects: their masses and spins. While the component masses are usually resolvable, a measurement of the component spins is generally elusive. This is partially a consequence of asking about the spins of the most and least massive objects in each binary, a question which becomes ill-defined for equal-mass systems. In this paper we show that one can ask a different question of the data: what are the spins of the most-spinning object, and of the least-spinning object, in the binary? We show that this can significantly improve estimates of the individual spins, especially for binary systems with comparable masses. When applying this parameterization to the first 13 gravitational-wave events detected by the LIGO-Virgo collaboration, we find that the most-spinning object is constrained to have nonzero spin and to have significant support at the Kerr limit for GW151226 and GW170729. A joint analysis of the first ten binary black-holes shows that the configuration where all of the spins in the population are aligned with the orbital angular momentum is excluded from the 90% credible interval, regardless of the parameterization used, reinforcing indications from previous analyses.
Bayesian inference for compact binary coalescences with BILBY: Validation and application to the first LIGO--Virgo gravitational-wave transient catalogue
I.M. Romero-Shaw, C. Talbot, A.S. Biscoveanu, et al.
Gravitational waves provide a unique tool for observational astronomy. While the first LIGO--Virgo catalogue of gravitational-wave transients (GWTC-1) contains eleven signals from black hole and neutron star binaries, the number of observations is increasing rapidly as detector sensitivity improves. To extract information from the observed signals, it is imperative to have fast, flexible, and scalable inference techniques. In a previous paper, we introduced BILBY: a modular and user-friendly Bayesian inference library adapted to address the needs of gravitational-wave inference. In this work, we demonstrate that BILBY produces reliable results for simulated gravitational-wave signals from compact binary mergers, and verify that it accurately reproduces results reported for the eleven GWTC-1 signals. Additionally, we provide configuration and output files for all analyses to allow for easy reproduction, modification, and future use. This work establishes that BILBY is primed and ready to analyse the rapidly growing population of compact binary coalescence gravitational-wave signals.
Constraining the delay time distribution of compact binary objects from the stochastic gravitational wave background searches
M. Safarzadeh, A.S. Biscoveanu, A. Loeb
The initial separation of massive star binaries sets the timescale over which their compact remnants merge through the emission of gravitational waves. We show that the delay time distribution (DTD) of binary neutron stars or black holes can be inferred from the stochastic gravitational wave background (SGWB). If the DTD of a population is long, most of the mergers take place at low redshifts and the background would be rather quiet compared to a scenario in which the DTD is short leading to few individual detections at low redshift but a rather loud background. We show that different DTDs predict a factor of 5 difference in the magnitude of the gravitational wave background energy density (ΩGW) and have the dominant effect on (ΩGW) over other factors such as the mass function of the primary BH mass, p(m1), the maximum considered BH mass (Mmax), and the effective spin of the black hole. A non-detection of such a background can rule out the short DTD scenario. We show that SGWB searches can rule out the short DTD scenario for the BBHs within about four years of observing time at advanced LIGO design sensitivty for a local merger rate of 30 Gpc-3yr-1 assuming p(m1)∝m1-1, and Mmax=50 solar masses.
Quantifying the Effect of Power Spectral Density Uncertainty on Gravitational-Wave Parameter Estimation for Compact Binary Sources
A.S. Biscoveanu, C.-J. Haster, and S. Vitale
In order to perform Bayesian parameter estimation to infer the source properties of gravitational waves from compact binary coalescences (CBCs), the noise characteristics of the detector must be understood. It is typically assumed that the detector noise is stationary and Gaussian, characterized by a power spectral density (PSD) that is measured with infinite precision. We present a new method to incorporate the uncertainty in the power spectral density estimation into the Bayesian inference of the binary source parameters. We calculate the PSD for the first 11 gravitational-wave detections reported by LIGO and Virgo with an on-source method, using only data from the analysis segment to obtain posterior samples for the PSD, which is modeled analytically using the BayesLine algorithm [1] as a sum of a set of Lorentzians and a broadband spline. We demonstrate how to marginalize over the uncertainty encompassed in the full PSD posterior for these first 11 CBC detections and find that incorporating the PSD uncertainty only leads to variations in the positions and width of the binary parameter posteriors on the order of a few percent.
Constraining short gamma-ray burst jet properties with gravitational waves and gamma rays
A.S. Biscoveanu, E. Thrane, S. Vitale
Gamma-ray burst (GRB) prompt emission is highly beamed, and understanding the jet geometry and beaming configuration can provide information on the poorly understood central engine and circum-burst environment. Prior to the advent of gravitational-wave astronomy, astronomers relied on observations of jet breaks in the multi-wavelength afterglow to determine the GRB opening angle, since the observer's viewing angle relative to the system cannot be determined from the electromagnetic data alone. Gravitational-wave observations, however, provide an independent measurement of the viewing angle. We describe a Bayesian method for determining the geometry of short GRBs using coincident electromagnetic and gravitational-wave observations. We demonstrate how an ensemble of multi-messenger detections can be used to measure the distributions of the jet energy, opening angle, Lorentz factor, and angular profile of short GRBs; we find that for a population of 100 such observations, we can constrain the mean of the opening angle distribution to within 10 degrees regardless of the angular emission profile. Conversely, the constraint on the energy distribution depends on the shape of the profile, which can be distinguished.
The reliability of the low-latency estimation of binary neutron star chirp mass
A.S. Biscoveanu, S. Vitale, C.-J. Haster
The LIGO and Virgo Collaborations currently conduct searches for gravitational waves from compact binary coalescences in real-time. For promising candidate events, a sky map and distance estimation are released in low-latency, to facilitate their electromagnetic follow-up. Currently, no information is released about the masses of the compact objects. Recently, Margalit and Metzger (2019) have suggested that knowledge of the chirp mass of the detected binary neutron stars could be useful to prioritize the electromagnetic follow-up effort, and have urged the LIGO-Virgo collaboration to release chirp mass information in low-latency. One might worry that low-latency searches for compact binaries make simplifying assumptions that could introduce biases in the mass parameters: neutron stars are treated as point particles with dimensionless spins below 0.05 and perfectly aligned with the orbital angular momentum. Furthermore, the template bank used to search for them has a finite resolution. In this paper we show that none of these limitations can introduce chirp mass biases larger than 10-3 solar mases. Even the total mass is usually accurately estimated, with biases smaller than 6%. The mass ratio and effective inspiral spins, on the other hand, can suffer from more severe biases.
Polarization-Based Tests of Gravity with the Stochastic Gravitational-Wave Background
T. Callister, A.S. Biscoveanu, et al.
The direct observation of gravitational waves with Advanced LIGO and Advanced Virgo offers novel opportunities to test general relativity in strong-field, highly dynamical regimes. One such opportunity is the measurement of gravitational-wave polarizations. While general relativity predicts only two tensor gravitational-wave polarizations, general metric theories of gravity allow for up to four additional vector and scalar modes. The detection of these alternative polarizations would represent a clear violation of general relativity. The LIGO-Virgo detection of the binary black hole merger GW170814 has recently offered the first direct constraints on the polarization of gravitational waves. The current generation of ground-based detectors, however, is limited in its ability to sensitively determine the polarization content of transient gravitational-wave signals. Observation of the stochastic gravitational-wave background, in contrast, offers a means of directly measuring generic gravitational-wave polarizations. The stochastic background, arising from the superposition of many individually unresolvable gravitational-wave signals, may be detectable by Advanced LIGO at design sensitivity. In this paper, we present a Bayesian method with which to detect and characterize the polarization of the stochastic background. We explore prospects for estimating parameters of the background and quantify the limits that Advanced LIGO can place on vector and scalar polarizations in the absence of a detection. Finally, we investigate how the introduction of new terrestrial detectors like Advanced Virgo aid in our ability to detect or constrain alternative polarizations in the stochastic background. We find that, although the addition of Advanced Virgo does not notably improve detection prospects, it may dramatically improve our ability to estimate the parameters of backgrounds of mixed polarization.