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Haystack and Owens Valley Radio Observatory (OVRO) observations recently revealed strong sinusoidal total flux density variations that maintained coherence between 1975 and 2021 in the blazar PKS 2131-021 ($z=1.283)$. This was interpreted as possible evidence of a supermassive black hole binary (SMBHB). Extended observations through 2023 show coherence over 47.9~years, with an observed period $P_\textrm{15 GHz}=(1739.3 \pm 1.2) \, {\rm days}$. We reject, with $p$-value = $5.3 \times 10^{-7}$, the hypothesis that the variations are due to random fluctuations in the red noise tail of the power spectral density. There is clearly a constant-period physical phenomenon in PKS 2131-021 producing coherent intermittent sinusoidal flux density variations. We find the coherent sinusoidal intensity variations extend from below 2.7 GHz to optical frequencies, from which we derive an observed period $P_\textrm{optical}=(1764 \pm 36)$ days. Across this broad frequency range there is a monotonic phase shift in the sinusoidal variations with frequency. The same coherent periodicity is possibly also observed at $\gamma$-ray energies. The importance of well-vetted SMBHB candidates to searches for gravitational waves is pointed out. We estimate the fraction of blazars that are SMBHB candidates to be $>1$ in 100. Thus monitoring programs covering tens of thousands of blazars could discover hundreds of SMBHB candidates., Comment: 23 pages, 17 figures, 5 tables, submitted to ApJ

We investigate the relationship between a galaxy cluster's hydrostatic equilibrium state, the entropy profile, $K$, of the intracluster gas, and the system's non-thermal pressure (NTP), within an analytic model of cluster structures. When NTP is neglected from the cluster's hydrostatic state, we find that the gas' logarithmic entropy slope, $k\equiv \mathrm{d}\ln K/\mathrm{d}\ln r$, converges at large halocentric radius, $r$, to a value that is systematically higher than the value $k\simeq1.1$ that is found in observations and simulations. By applying a constraint on these `pristine equilibrium' slopes, $k_\mathrm{eq}$, we are able to predict the required NTP that must be introduced into the hydrostatic state of the cluster. We solve for the fraction, $\mathcal{F}\equiv p_\mathrm{nt}/p$, of NTP, $p_\mathrm{nt}$, to total pressure, $p$, of the cluster, and we find $\mathcal{F}(r)$ to be an increasing function of halocentric radius, $r$, that can be parameterised by its value in the cluster's core, $\mathcal{F}_0$, with this prediction able to be fit to the functional form proposed in numerical simulations. The minimum NTP fraction, as the solution with zero NTP in the core, $\mathcal{F}_0=0$, we find to be in excellent agreement with the mean NTP predicted in non-radiative simulations, beyond halocentric radii of $r\gtrsim0.7r_{500}$, and in tension with observational constraints derived at similar radii. For this minimum NTP profile, we predict $\mathcal{F}\simeq0.20$ at $r_{500}$, and $\mathcal{F}\simeq0.34$ at $2r_{500}$; this amount of NTP leads to a hydrostatic bias of $b\simeq0.12$ in the cluster mass $M_{500}$ when measured within $r_{500}$. Our results suggest that the NTP of galaxy clusters contributes a significant amount to their hydrostatic state near the virial radius, and must be accounted for when estimating the cluster's halo mass using hydrostatic equilibrium approaches., Comment: 10 pages, 5 figures. Accepted for publication in PASA

PSR J2215+5135 (J2215) is a `redback' spider pulsar, where the intrabinary shock (IBS) wraps around the pulsar rather than the stellar-mass companion. Spider orbital light curves are modulated, dominated by their binary companion thermal emission in the optical bands and by IBS synchrotron emission in the X-rays. We report on new XMM-Newton X-ray and U-band observations of J2215. We produce orbital light curves and use them to model the system properties. Our best-fit optical light model gives a neutron star mass $M_{NS}=1.98\pm0.08$ M$_\odot$, lower than previously reported. However, uncertainty in the stellar atmosphere metallicity, a parameter to which J2215 is unusually sensitive, requires us to consider an acceptable systematic plus statistical range of $M_{NS}\sim1.85-2.3$ M$_\odot$. From the X-ray analysis, we find that the IBS wraps around the pulsar, but with a pulsar wind to companion wind momentum ratio unusually close to unity, implying a flatter IBS geometry than seen in other spiders. Estimating the companion wind momentum and speed from the X-ray light curve, we find a companion mass-loss rate of ${\dot M}_c\gtrsim10^{-10}$ M$_\odot$ yr$^{-1}$, so that J2215 may become an isolated millisecond pulsar in $\sim 1$ Gyr. Our X-ray analyses place constraints on the magnetization and particle density of the pulsar wind and support models of magnetic reconnection and particle acceleration in the highly magnetized relativistic IBS., Comment: 9 pages, 5 figures, 3 tables; Version to appear in ApJ

We investigate the connection between a cluster's structural configuration and observable measures of its gas emission that can be obtained in X-ray and Sunyaev-Zeldovich (SZ) surveys. We present an analytic model for the intracluster gas density profile: parameterised by the dark matter halo's inner logarithmic density slope, $\alpha$, the concentration, $c$, the gas profile's inner logarithmic density slope, $\varepsilon$, the dilution, $d$, and the gas fraction, $\eta$, normalised to cosmological content. We predict four probes of the gas emission: the emission-weighted, $T_\mathrm{X}$, and mean gas mass-weighted, $T_\mathrm{m_g}$, temperatures, and the spherically, $Y_\mathrm{sph}$, and cylindrically, $Y_\mathrm{cyl}$, integrated Compton parameters. Over a parameter space of clusters, we constrain the X-ray temperature scaling relations, $M_{200} - T_\mathrm{X}$ and $M_{500} - T_\mathrm{X}$, within $57.3\%$ and $41.6\%$, and $M_{200} - T_\mathrm{m_g}$ and $M_{500} - T_\mathrm{m_g}$, within $25.7\%$ and $7.0\%$, all respectively. When excising the cluster's core, the $M_{200} - T_\mathrm{X}$ and $M_{500} - T_\mathrm{X}$ relations are further constrained, to within $31.3\%$ and $17.1\%$, respectively. Similarly, we constrain the SZ scaling relations, $M_{200} - Y_\mathrm{sph}$ and $M_{500} - Y_\mathrm{sph}$, within $31.1\%$ and $17.7\%$, and $M_{200} - Y_\mathrm{cyl}$ and $M_{500} - Y_\mathrm{cyl}$, within $25.2\%$ and $22.0\%$, all respectively. The temperature observable $T_\mathrm{m_g}$ places the strongest constraint on the halo mass, whilst $T_\mathrm{X}$ is more sensitive to the parameter space. The SZ constraints are sensitive to the gas fraction, whilst insensitive to the form of the gas profile itself. In all cases, the halo mass is recovered with an uncertainty that suggests the cluster's structural profiles only contribute a minor uncertainty in its scaling relations., Comment: This paper has been accepted for publication with PASA

We investigate the relationship between a dark matter halo's mass profile and measures of the velocity dispersion of kinematic tracers within its gravitational potential. By predicting the scaling relation of the halo mass with the aperture velocity dispersion, $M_\mathrm{vir} - \sigma_\mathrm{ap}$, we present the expected form and dependence of this halo mass tracer on physical parameters within our analytic halo model: parameterised by the halo's negative inner logarithmic density slope, $\alpha$, its concentration parameter, $c$, and its velocity anisotropy parameter, $\beta$. For these idealised halos, we obtain a general solution to the Jeans equation, which is projected over the line of sight and averaged within an aperture to form the corresponding aperture velocity dispersion profile. Through dimensional analysis, the $M_\mathrm{vir} - \sigma_\mathrm{ap}$ scaling relation is devised explicitly in terms of analytical bounds for these aperture velocity dispersion profiles: allowing constraints to be placed on this relation for motivated parameter choices. We predict the $M_{200} - \sigma_\mathrm{ap}$ and $M_{500} - \sigma_\mathrm{ap}$ scaling relations, each with an uncertainty of $60.5\%$ and $56.2\%$, respectively. These halo mass estimates are found to be weakly sensitive to the halo's concentration and mass scale, and most sensitive to the size of the aperture radius in which the aperture velocity dispersion is measured, the maximum value for the halo's inner slope, and the minimum and maximum values of the velocity anisotropy. Our results show that a halo's structural and kinematic profiles impose only a minor uncertainty in estimating its mass. Consequently, spectroscopic surveys aimed at constraining the halo mass using kinematic tracers can focus on characterising other, more complex sources of uncertainty and observational systematics., Comment: This paper has been accepted for publication with PASA

Double lobe radio sources associated with active galactic nuclei represent one of the longest studied groups in radio astronomy. A particular sub-group of double radio sources comprises the compact symmetric objects (CSOs). CSOs are distinguished by their prominent double structure and sub-kpc total size. It has been argued that the vast majority of high-luminosity CSOs (CSO 2s) represent a distinct class of active galactic nuclei with its own morphological structure and life-cycle. In this work, we present theoretical considerations regarding CSO 2s. We develop a semi-analytic evolutionary model, inspired by the results of large-scale numerical simulations of relativistic jets, that reproduces the features of the radio source population. We show that CSO 2s may be generated by finite energy injections and propose stellar tidal disruption events as a possible cause. We find that tidal disruption events of giant branch stars with masses $\gtrsim1$ M$_\odot$ can fuel these sources and discuss possible approaches to confirming this hypothesis. We predict that if the tidal disruption scenario holds, CSO 2s with sizes less than 400 pc should outnumber larger sources by more than a factor of $10$. Our results motivate future numerical studies to determine whether the scenarios we consider for fueling and source evolution can explain the observed radio morphologies. Multiwavelength observational campaigns directed at these sources will also provide critical insight into the origins of these objects, their environments, and their lifespans., Comment: 9 pages, 4 figures; Accepted for publication in MNRAS

Gravitational-wave astronomy has developed enormously over the last decade with the first detections across different frequency bands, but has yet to access $0.1-10$ $\mathrm{Hz}$ gravitational waves. Gravitational waves in this band are emitted by some of the most enigmatic sources, including intermediate-mass binary black hole mergers, early inspiralling compact binaries, and possibly cosmic inflation. To tap this exciting band, we propose the construction of a detector based on pulsar timing principles, the Artificial Precision Timing Array (APTA). We envision APTA as a solar system array of artificial "pulsars"$-$precision-clock-carrying satellites that emit pulsing electromagnetic signals towards Earth or other centrum. In this fundamental study, we estimate the clock precision needed for APTA to successfully detect gravitational waves. Our results suggest that a clock relative uncertainty of $10^{-17}$, which is currently attainable, would be sufficient for APTA to surpass LISA's sensitivity in the decihertz band and observe $10^3-10^4$ $\mathrm{M}_\odot$ black hole mergers. Future atomic clock technology realistically expected in the next decade would enable the detection of an increasingly diverse set of astrophysical sources, including stellar-mass compact binaries that merge in the LIGO-Virgo-KAGRA band, extreme-mass-ratio inspirals, and Type Ia supernovae. This work opens up a new area of research into designing and constructing artificial gravitational-wave detectors relying on the successful principles of pulsar timing., Comment: 10 pages, 3 figures

In `spider' pulsars, the X-ray band is dominated by Intrabinary Shock (IBS) synchrotron emission. While the double-peaked X-ray light curves from these shocks have been well characterized in several spider systems (both black widows and redbacks), the polarization of this emission is yet to be studied. Motivated by the new polarization capability of the Imaging X-ray Polarization Explorer (IXPE) and the confirmation of highly ordered magnetic fields in pulsar wind nebulae, we model the IBS polarization, employing two potential magnetic field configurations: toroidal magnetic fields imposed by the pre-shock pulsar wind, and tangential shock-generated fields, which follow the post-shock flow. We find that if IBSs host ordered magnetic fields, the synchrotron X-rays from spider binaries can display a high degree of polarization ($\gtrsim50\%$), while the polarization angle variation provides a good probe of the binary geometry and the magnetic field structure. Our results encourage polarization observational studies of spider pulsars, which can distinguish the proposed magnetic models and better constrain unique properties of these systems., Comment: 10 pages, 6 figures; to appear in the Astrophysical Journal

Precursor emission has been observed seconds to minutes before some short gamma-ray bursts. While the origins of these precursors remain unknown, one potential explanation relies on the resonance of neutron star pulsational modes with the tidal forces during the inspiral phase of a compact binary merger. In this paper, we present a model for short gamma-ray burst precursors which relies on tidally resonant neutron star oceans. In this scenario, the onset of tidal resonance in the crust-ocean interface mode corresponds to the ignition of the precursor flare, possibly through the interaction between the excited neutron star ocean and the surface magnetic fields. From just the precursor total energy, the time before the main event, and a detected quasi-periodic oscillation frequency, we may constrain the binary parameters and neutron star ocean properties as never before. Our model can immediately distinguish neutron star-black hole mergers from binary neutron star mergers without gravitational wave detection. We apply our model to GRB 211211A, the recently detected long duration short gamma-ray burst with a quasi-periodic precursor, and explore the parameters of this system within its context. The precursor of GRB 211211A is consistent with a tidally resonant neutron star ocean explanation that requires an extreme-mass ratio NSBH merger and a high mass neutron star. While difficult to reconcile with the gamma-ray burst main emission and associated kilonova, our results constrain the possible precursor generating mechanisms in this system. A systematic study of short gamma-ray burst precursors with the model presented here can test precursor origin and could probe the possible connection between gamma-ray bursts and neutron star-black hole mergers., Comment: 9 pages, 2 figures, accepted in MNRAS

LIGO's mission critical timing system has enabled gravitational wave and multi-messenger astrophysical discoveries as well as the rich science extracted. Achieving optimal detector sensitivity, detecting transient gravitational waves, and especially localizing gravitational wave sources, the underpinning of multi-messenger astrophysics, all require proper gravitational wave data time-stamping. Measurements of the relative arrival times of gravitational waves between different detectors allow for coherent gravitational wave detections, localization of gravitational wave sources, and the creation of skymaps. The carefully designed timing system achieves these goals by mitigating phase noise to avoid signal up-conversion and maximize gravitational wave detector sensitivity. The timing system also redundantly performs self-calibration and self-diagnostics in order to ensure reliable, extendable, and traceable time stamping. In this paper, we describe and quantify the performance of these core systems during the latest O3 scientific run of LIGO, Virgo, and KAGRA. We present results of the diagnostic checks done to verify the time-stamping for individual gravitational wave events observed during O3 as well as the timing system performance for all of O3 in LIGO Livingston and LIGO Hanford. We find that, after 3 observing runs, the LIGO timing system continues to reliably meet mission requirements of timing precision below 1 $\mu$s with a significant safety margin., Comment: 11 pages, 8 figures

Neutron stars in astrophysical binary systems represent exciting sources for multi-messenger astrophysics. A potential source of electromagnetic transients from compact binary systems is the neutron star ocean, the external fluid layer encasing a neutron star. We present a groundwork study into tidal waves in neutron star oceans and their consequences. Specifically, we investigate how oscillation modes in neutron star oceans can be tidally excited during compact binary inspirals and parabolic encounters. We find that neutron star oceans can sustain tidal waves with frequencies between $0.01-20$ Hz. Our results suggest that tidally resonant neutron star ocean waves may serve as a never-before studied source of precursor electromagnetic emission prior to neutron star-black hole and binary neutron star mergers. If accompanied by electromagnetic flares, tidally resonant neutron star ocean waves, whose energy budget can reach $10^{46}$ erg, may serve as early warning signs ($\gtrsim 1$ minute before merger) for compact binary mergers. Similarly, excited ocean tidal waves will coincide with neutron star parabolic encounters. Depending on the neutron star ocean model and a flare emission scenario, tidally resonant ocean flares may be detectable by Fermi and NuSTAR out to $\gtrsim 100$ Mpc with detection rates as high as $\sim 7$ yr$^{-1}$ for binary neutron stars and $\sim0.6$ yr$^{-1}$ for neutron star-black hole binaries. Observations of emission from neutron star ocean tidal waves along with gravitational waves will provide insight into the equation of state at the neutron star surface, the composition of neutron star oceans and crusts, and neutron star geophysics., Comment: 16 pages, 3 figures, 3 tables; accepted for publication in MNRAS

With the inception of gravitational wave astronomy, astrophysical studies using interferometric techniques have begun to probe previously unknown parts of the universe. In this work, we investigate the potential of a new interferometric experiment to study a unique group of gravitationally interacting sources within our solar system: binary asteroids. We present the first study into binary asteroid detection via gravitational signals. We identify the interferometer sensitivity necessary for detecting a population of binary asteroids in the asteroid belt. We find that the space-based gravitational wave detector LISA will have negligible ability to detect these sources as these signals will be well below the LISA noise curve. Consequently, we propose a 4.6 AU and a 1 AU arm-length interferometers specialized for binary asteroid detection, targeting frequencies between $10^{-6}$ and $10^{-4}$ Hz. Our results demonstrate that the detection of binary asteroids with space-based gravitational wave interferometers is possible though very difficult, requiring substantially improved interferometric technology over what is presently proposed for space-based missions. If that threshold can be met, an interferometer may be used to map the asteroid belt, allowing for new studies into the evolution of our solar system., Comment: 17 pages, 18 figures, Accepted for Publication to Monthly Notices of the Royal Astronomical Society

We demonstrate that the rapidity and robustness of slow contraction in homogenizing and flattening the universe found in simulations in which the initial conditions were restricted to non-perturbative variations described by a single fourier mode along only a single spatial direction are in general enhanced if the initial variations are along two spatial directions, include multiple modes, and thereby have reduced symmetry. Particularly significant are shear effects that only become possible when variations are allowed along two or more spatial dimensions. Based on the numerical results, we conjecture that the counterintuitive enhancement occurs because more degrees of freedom are activated which drive spacetime away from an unstable Kasner fixed point and towards the stable Friedmann-Robertson-Walker fixed point., Comment: 5 pages, 2 figures

We study the detailed process by which slow contraction smooths and flattens the universe using an improved numerical relativity code that accepts initial conditions with non-perturbative deviations from homogeneity and isotropy along two independent spatial directions. Contrary to common descriptions of the early universe, we find that the geometry first rapidly converges to an inhomogeneous, spatially-curved and anisotropic ultralocal state in which all spatial gradient contributions to the equations of motion decrease as an exponential in time to negligible values. This is followed by a second stage in which the geometry converges to a homogeneous, spatially flat and isotropic spacetime. In particular, the decay appears to follow the same history whether the entire spacetime or only parts of it are smoothed by the end of slow contraction., Comment: 27 pages, 10 figures

The origin, environment, and evolution of stellar-mass black hole binaries are still a mystery. One of the proposed binary formation mechanisms is manifest in dynamical interactions between multiple black holes. A resulting framework of these dynamical interactions is the so-called hierarchical triple merger scenario, which happens when three black holes become gravitationally bound, causing two successive black hole mergers to occur. In such successive mergers, the black holes involved are directly related to each other, and hence this channel can be directly tested from the properties of the detected binary black hole mergers. Here we present a search for hierarchical triple mergers among events within the GWTC-1 and GWTC-2 catalogs of LIGO/Virgo, the eccentric localization of GW190521 and those found by the IAS-Princeton group. The search includes improved statistical quantification that also accounts for black hole spins. We perform our analysis for different upper bounds on the mass distribution of first generation BHs. Our results demonstrate the importance of the mass distributions' properties for constraining the hierarchical merger scenario. We present the individually significant merger pairs. The search yields interesting candidate families and hints of its future impact., Comment: 4 figures, 7 pages without references

Gravitational waves from neutron star mergers have long been considered a promising way to measure the Hubble constant, $H_0$, which describes the local expansion rate of the universe. While black hole mergers are more abundantly observed, their expected lack of electromagnetic emission and poor gravitational-wave localization make them less well suited for measuring $H_0$. Black hole mergers within the disks of Active Galactic Nuclei (AGN) could be an exception. Accretion from the AGN disk may produce an electromagnetic signal, pointing observers to the host galaxy. Alternatively, the low number density of AGNs could help identify the host galaxy of $1-5\%$ of mergers. Here we show that black hole mergers in AGN disks may be a sensitive way to determine $H_0$ with gravitational waves. If $1\%$ ($10\%$) of LIGO's observations occur in AGN disks with identified host galaxies, we could measure $H_0$ with $12\%$ ($4\%$) uncertainty in five years, possibly comparable to the sensitivity of neutron star mergers and set to considerably improve current gravitational wave measurements., Comment: 5 pages, 2 figures

We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to solve the full nonlinear modified Einstein's Equations on a two-dimensional grid with a Newton polynomial finite difference scheme. We validate this code by considering static and axisymmetric black holes in General Relativity. We obtain rotating black hole solutions in scalar-Gauss-Bonnet gravity with a linear (linear scalar-Gauss-Bonnet) and an exponential (Einstein-dilaton-Gauss-Bonnet) coupling and compare them to analytical and numerical perturbative solutions. From these numerical solutions, we construct a fitted analytical model and study observable properties calculated from the numerical results.

Shapiro time delay is one of the fundamental tests of general relativity and post-Newtonian theories of gravity. Consequently, its measurements can be used to probe the parameter $\gamma$ which is related to spacetime curvature produced by a unit mass in the post-Newtonian formalism of gravity. To date all measurements of time delay have been conducted on astronomical scales. It was asserted in 2010 that gravitational wave detectors on Earth could be used to measure Shapiro delay on a terrestrial scale via massive rotating systems. Building on that work, we consider how measurements of Shapiro delay can be made using next-generation gravitational wave detectors. We perform an analysis for measuring Shapiro delay with the next-generation gravitational wave detectors Cosmic Explorer and Einstein Telescope to determine how precisely the effect can be measured. Using a rotating mass unit design, we find that Cosmic Explorer and Einstein Telescope can measure the Shapiro delay signal with amplitude signal to noise ratios upwards of $\sim28 $ and $\sim43$ in 1 year of integration time, respectively. By measuring Shapiro delay with this technique, next-generation interferometers will allow for terrestrial measurements of $\gamma$ in the paramaterized post-Newtonian formalism of gravity with sub-percent precision., Comment: 15 pages, 5 figures, Version accepted to Classical and Quantum Gravity, includes modified figures

One of the proposed channels of binary black hole mergers involves dynamical interactions of three black holes. In such scenarios, it is possible that all three black holes merge in a so-called hierarchical merger chain, where two of the black holes merge first and then their remnant subsequently merges with the remaining single black hole. Depending on the dynamical environment, it is possible that both mergers will appear within the observable time window. Here we perform a search for such merger pairs in the public available LIGO and Virgo data from the O1/O2 runs. Using a frequentist p-value assignment statistics we do not find any significant merger pair candidates, the most significant being GW170809-GW151012 pair. Assuming no observed candidates in O3/O4, we derive upper limits on merger pairs to be $\sim11-110\ {\rm year^{-1}Gpc^{-3}}$, corresponding to a rate that relative to the total merger rate is $\sim 0.1-1.0$. From this we argue that both a detection and a non-detection within the next few years can be used to put useful constraints on some dynamical progenitor models., Comment: 7 pages, 4 figures

Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such observations requires detailed knowledge of the black hole spacetime, both within and outside of General Relativity. We present here a new numerical code that can be used to obtain stationary solutions that describe black hole spacetimes in a wide class of modified theories of gravity. The code makes use of a relaxed Newton-Raphson method to solve the discretized field equations with a Newton's polynomial finite difference scheme. We test and validate this code by considering static and spherically symmetric black holes both in General Relativity, as well as in scalar-Gauss-Bonnet gravity with a linear (linear scalar-Gauss-Bonnet) and an exponential (Einstein-dilaton-Gauss-Bonnet) coupling. As a by-product of the latter, we find that analytic solutions obtained in the small coupling approximation are in excellent agreement with our fully non-linear solutions when using a linear coupling. As expected, differences arise when using an exponential coupling. We then use these numerical solutions to construct a fitted analytical model, which we then use to calculate physical observables such as the innermost stable circular orbit and photon sphere and compare them to the numerical results. This code lays the foundation for more detailed calculations of black hole observables that can be compared with data in the future., Comment: 27 pages, 11 figures

We study slowly-rotating neutron stars in ghost-free massive bigravity. This theory modifies General Relativity by introducing a second, auxiliary but dynamical tensor field that couples to matter through the physical metric tensor through non-linear interactions. We expand the field equations to linear order in slow rotation and numerically construct solutions in the interior and exterior of the star with a set of realistic equations of state. We calculate the physical mass function with respect to observer radius and find that, unlike in General Relativity, this function does not remain constant outside the star; rather, it asymptotes to a constant a distance away from the surface, whose magnitude is controlled by the ratio of gravitational constants. The Vainshtein-like radius at which the physical and auxiliary mass functions asymptote to a constant is controlled by the graviton mass scaling parameter, and outside this radius, bigravity modifications are suppressed. We also calculate the frame-dragging metric function and find that bigravity modifications are typically small in the entire range of coupling parameters explored. We finally calculate both the mass-radius and the moment of inertia-mass relations for a wide range of coupling parameters and find that both the graviton mass scaling parameter and the ratio of the gravitational constants introduce large modifications to both. These results could be used to place future constraints on bigravity with electromagnetic and gravitational-wave observations of isolated and binary neutron stars., Comment: 15 pages, 6 figures

This paper presents an advanced DAG-based algorithm for datapath synthesis that targets area minimization using logic-level resource sharing. The problem of identifying common specification logic is formulated using unweighted graph isomorphism problem, in contrast to a weighted graph isomorphism using AIGs. In the context of gate-level datapath circuits, our algorithm solves the un- weighted graph isomorphism problem in linear time. The experiments are conducted within an industrial synthesis flow that includes the complete high-level synthesis, logic synthesis and placement and route procedures. Experimental results show a significant runtime improvements compared to the existing datapath synthesis algorithms., Comment: 6 pages, 8 figures. To appear in 2017 IEEE/ACM International Conference on Computer-Aided Design (ICCAD'17)