Constraint violation in free evolution schemes: comparing BSSNOK with a conformal decomposition of Z4

We compare numerical evolutions performed with the BSSNOK formulation and a conformal decomposition of a Z4-like formulation of General Relativity. The important difference between the two formulations is that the Z4 formulation has a propagating Hamiltonian constraint, whereas BSSNOK has a zero-speed characteristic variable in the constraint subsystem. In spherical symmetry we evolve both puncture and neutron star initial data. We demonstrate that the propagating nature of the Z4 constraints leads to results that compare favorably with BSSNOK evolutions, especially when matter is present in the spacetime. From the point of view of implementation the new system is a simple modification of BSSNOK.Comment: Published in PR

Binary black hole merger in the extreme-mass-ratio limit: a multipolar analysis

Building up on previous work, we present a new calculation of the gravitational wave (GW) emission generated during the transition from quasi-circular inspiral to plunge, merger and ringdown by a binary system of nonspinning black holes, of masses $m_1$ and $m_2$, in the extreme mass ratio limit, $m_1 m_2\ll(m_1+m_2)^2$. The relative dynamics of the system is computed {\it without making any adiabatic approximation} by using an effective one body (EOB) description, namely by representing the binary by an effective particle of mass $\mu=m_1 m_2/(m_1+m_2)$ moving in a (quasi-)Schwarzschild background of mass $M=m_1+m_2$ and submitted to an \O(\nu) 5PN-resummed analytical radiation reaction force, with $\nu=\mu/M$. The gravitational wave emission is calculated via a multipolar Regge-Wheeler-Zerilli type perturbative approach (valid in the limit $\nu\ll 1$). We consider three mass ratios, $\nu={10^{-2},10^{-3},10^{-4}}$,and we compute the multipolar waveform up to $\ell=8$. We estimate energy and angular momentum losses during the quasi-universal and quasi-geodesic part of the plunge phase and we analyze the structure of the ringdown. We calculate the gravitational recoil, or "kick", imparted to the merger remnant by the gravitational wave emission and we emphasize the importance of higher multipoles to get a final value of the recoil $v/(c\nu^2)=0.0446$. We finally show that there is an {\it excellent fractional agreement} ($\sim 10^{-3}$) (even during the plunge) between the 5PN EOB analytically-resummed radiation reaction flux and the numerically computed gravitational wave angular momentum flux. This is a further confirmation of the aptitude of the EOB formalism to accurately model extreme-mass-ratio inspirals, as needed for the future space-based LISA gravitational wave detector.Comment: 20 pages, 12 figures. Version published in Phys. Rev.

Dynamical excitation of space-time modes of compact objects

We discuss, in the perturbative regime, the scattering of Gaussian pulses of odd-parity gravitational radiation off a non-rotating relativistic star and a Schwarzschild Black Hole. We focus on the excitation of the $w$-modes of the star as a function of the width $b$ of the pulse and we contrast it with the outcome of a Schwarzschild Black Hole of the same mass. For sufficiently narrow values of $b$, the waveforms are dominated by characteristic space-time modes. On the other hand, for sufficiently large values of $b$ the backscattered signal is dominated by the tail of the Regge-Wheeler potential, the quasi-normal modes are not excited and the nature of the central object cannot be established. We view this work as a useful contribution to the comparison between perturbative results and forthcoming $w$-mode 3D-nonlinear numerical simulation.Comment: RevTeX, 9 pages, 7 figures, Published in Phys. Rev.

Gravitational waves from pulsations of neutron stars described by realistic Equations of State

In this work we discuss the time-evolution of nonspherical perturbations of a nonrotating neutron star described by a realistic Equation of State (EOS). We analyze 10 different EOS for a large sample of neutron star models. Various kind of generic initial data are evolved and the corresponding gravitational wave signals are computed. We focus on the dynamical excitation of fluid and spacetime modes and extract the corresponding frequencies. We employ a constrained numerical algorithm based on standard finite differencing schemes which permits stable and long term evolutions. Our code provides accurate waveforms and allows to capture, via Fourier analysis of the energy spectra, the frequencies of the fluid modes with an accuracy comparable to that of frequency domain calculations. The results we present here are useful for provindig comparisons with simulations of nonlinear oscillations of (rotating) neutron star models as well as testbeds for 3D nonlinear codes.Comment: 17 pages, 9 figures. Small changes. Version published in Phys. Rev.

Black-hole remnants from black-hole-neutron-star mergers

Observations of gravitational waves and their electromagnetic counterparts may soon uncover the existence of coalescing compact binary systems formed by a stellar-mass black hole and a neutron star. These mergers result in a remnant black hole, possibly surrounded by an accretion disk. The mass and spin of the remnant black hole depend on the properties of the coalescing binary. We construct a map from the binary components to the remnant black hole using a sample of numerical-relativity simulations of different mass ratios q, (anti)aligned dimensionless spins of the black hole aBH, and several neutron star equations of state. Given the binary total mass, the mass and spin of the remnant black hole can therefore be determined from the three parameters (q,aBH,Λ), where Λ is the tidal deformability of the neutron star. Our models also incorporate the binary black hole and test-mass limit cases and we discuss a simple extension for generic black-hole spins. We combine the remnant characterization with recent population synthesis simulations for various metallicities of the progenitor stars that generated the binary system. We predict that black-hole-neutron-star mergers produce a population of remnant black holes with masses distributed around 7 M and 9 M. For isotropic spin distributions, nonmassive accretion disks are favored: no bright electromagnetic counterparts are expected in such mergers

Detectability of QCD phase transitions in binary neutron star mergers: Bayesian inference with the next generation gravitational wave detectors

We study the detectability of postmerger QCD phase transitions in neutron star binaries with next-generation gravitational-wave detectors Cosmic Explorer and Einstein Telescope. We perform numerical relativity simulations of neutron star mergers with equations of state that include a quark deconfinement phase transition through either a Gibbs or Maxwell construction. These are followed by Bayesian parameter estimation of the associated gravitational-wave signals using the $\tt{NRPMw}$ waveform model, with priors inferred from the analysis of the inspiral signal. We assess the ability of the model to measure the postmerger peak frequency $f_2^{\rm peak}$ and identify aspects that should be improved in the model. We show that, even at postmerger signal to noise ratios as low as 10, the model can distinguish (at the 90% level) $f_2^{\rm peak}$ between binaries with and without a phase transition in most cases. Phase-transition induced deviations in the $f_2^{\rm peak}$ from the predictions of equation-of-state insensitive relations can also be detected if they exceed $1.6\,\sigma$. Our results suggest that next-generation gravitational wave detectors can measure phase transition effects in binary neutron star mergers. However, unless the phase transition is ``strong'', disentangling it from other hadronic physics uncertainties will require significant theory improvements

Curcumin and Novel Synthetic Analogs in Cell-Based Studies of Alzheimer's Disease

Alzheimer's disease (AD) is a chronic neurodegenerative disorder that is associated with the most common type of dementia and is characterized by the presence of deposits of the protein fragment amyloid beta (A\u3b2) in the brain. The natural product mixture of curcuminoids that improves certain defects in innate immune cells of AD patients may selectively enhance A\u3b2 phagocytosis by alteration of gene transcription. In this work, we evaluated the protective effects of curcuminoids in cells from AD patients by investigating the effect on NF-\u3baB and BACE1 signaling pathways. These results were compared to the gene expression profile of the clearance of A\u3b2. The minor curcumin constituent, bisdemethoxycurcumin (BDC) showed the most potent protective action to decrease levels of NF-\u3baB and BACE1, decrease the inflammatory cascade and diminish A\u3b2 aggregates in cells from AD patients. Moreover, mannosyl-glycoprotein 4-beta-N-acetylglucosaminyltransferase (MGAT3) and vitamin D receptor (VDR) gene mRNAs were up-regulated in peripheral blood mononuclear cells from AD patients treated with BDC. BDC treatment impacts both gene expression including Mannosyl (Beta-1,4-)-Glycoprotein Beta-1,4-N-Acetylglucosaminyltransferase, Vitamin D and Toll like receptor mRNA and A\u3b2 phagocytosis. The observation of down-regulation of BACE1 and NF-\u3baB following administration of BDC to cells from AD patients as a model system may have utility in the treatment of asymptomatic AD patients

Sulforaphane rewires central metabolism to support antioxidant response and achieve glucose homeostasis

Cruciferous-rich diets, particularly broccoli, have been associated with reduced risk of developing cancers of various sites, cardiovascular disease and type-2 diabetes. Sulforaphane (SF), a sulfur-containing broccoli-derived metabolite, has been identified as the major bioactive compound mediating these health benefits. Sulforaphane is a potent dietary activator of the transcription factor Nuclear factor erythroid-like 2 (NRF2), the master regulator of antioxidant cell capacity responsible for inducing cytoprotective genes, but its role in glucose homeostasis remains unclear. In this study, we set to test the hypothesis that SF regulates glucose metabolism and ameliorates glucose overload and its resulting oxidative stress by inducing NRF2 in human hepatoma HepG2 cells. HepG2 cells were exposed to varying glucose concentrations: basal (5.5 mM) and high glucose (25 mM), in the presence of physiological concentrations of SF (10 μM). SF upregulated the expression of glutathione (GSH) biosynthetic genes and significantly increased levels of reduced GSH. Labelled glucose and glutamine experiments to measure metabolic fluxes identified that SF increased intracellular utilisation of glycine and glutamate by redirecting the latter away from the TCA cycle and increased the import of cysteine from the media, likely to support glutathione synthesis. Furthermore, SF altered pathways generating NADPH, the necessary cofactor for oxidoreductase reactions, namely pentose phosphate pathway and 1C-metabolism, leading to the redirection of glucose away from glycolysis and towards PPP and of methionine towards methylation substrates. Finally, transcriptomic and targeted metabolomics LC-MS analysis of NRF2-KD HepG2 cells generated using CRISPR-Cas9 genome editing revealed that the above metabolic effects are mediated through NRF2. These results suggest that the antioxidant properties of cruciferous diets are intricately connected to their metabolic benefits

On the Shear Instability in Relativistic Neutron Stars

We present new results on instabilities in rapidly and differentially rotating neutron stars. We model the stars in full general relativity and describe the stellar matter adopting a cold realistic equation of state based on the unified SLy prescription. We provide evidence that rapidly and differentially rotating stars that are below the expected threshold for the dynamical bar-mode instability, beta_c = T/|W| ~ 0.25, do nevertheless develop a shear instability on a dynamical timescale and for a wide range of values of beta. This class of instability, which has so far been found only for small values of beta and with very small growth rates, is therefore more generic than previously found and potentially more effective in producing strong sources of gravitational waves. Overall, our findings support the phenomenological predictions made by Watts, Andersson and Jones on the nature of the low-T/|W|.Comment: 20 pages; accepted to the Classical and Quantum Gravity special issue for MICRA200