Testing waveform models using angular momentum

The anticipated enhancements in detector sensitivity and the corresponding increase in the number of gravitational wave detections will make it possible to estimate parameters of compact binaries with greater accuracy assuming general relativity(GR), and also to carry out sharper tests of GR itself. Crucial to these procedures are accurate gravitational waveform models. The systematic errors of the models must stay below statistical errors to prevent biases in parameter estimation and to carry out meaningful tests of GR. Comparisons of the models against numerical relativity (NR) waveforms provide an excellent measure of systematic errors. A complementary approach is to use balance laws provided by Einstein's equations to measure faithfulness of a candidate waveform against exact GR. Each balance law focuses on a physical observable and measures the accuracy of the candidate waveform vis a vis that observable. Therefore, this analysis can provide new physical insights into sources of errors. In this paper we focus on the angular momentum balance law, using post-Newtonian theory to calculate the initial angular momentum, surrogate fits to obtain the remnant spin and waveforms from models to calculate the flux. The consistency check provided by the angular momentum balance law brings out the marked improvement in the passage from \texttt{IMRPhenomPv2} to \texttt{IMRPhenomXPHM} and from \texttt{SEOBNRv3} to \texttt{SEOBNRv4PHM} and shows that the most recent versions agree quite well with exact GR. For precessing systems, on the other hand, we find that there is room for further improvement, especially for the Phenom models

(ÿ)-Fern-7-en-3a-ol from Sebastiania brasiliensis

The structure of a fernane isolated from S. brasiliensis was established as fern-7en-3[alpha]-ol, C30H50O. Rings A and D assume a chair conformation, while rings B and C adopt a twist-boat conformation. Rings A/B, C/D, and D/E are trans fused. The relative orientation of the hydroxy group and that of the iso­propyl group is [alpha].This structure was determined in the Molecular Structure Laboratory of the Department of Chemistry, University of Arizona, Tucson, AZ 85721, USA. The SMART1000 diffractometer was gratefully obtained with funds provided by NSF grant CHE9610374. This study was supported by NIH grant 5U01TW00316-10 awarded to BNT. This study was undertaken as part of the required course work for the class CHEM 517 offered by Dr J. H. Enemark at the University of Arizona. The authors thank Liliya Yatsunyk for her help in this study

(4R,4aR,6S,7S,7aS)-6-Hydroxy-7-hy- droxymethyl-4-methylperhydrocyclo- penta[c]pyran-1-one chloroform solvate from Valeriana laxiflora

The structure of an iridolactone isolated from Valeriana laxiflora was established as (4R,4aR,6S,7S,7aS)-6-hydroxy-7-hydroxy­methyl-4-methyl­per­hydro­cyclo­penta­[c]­pyran-1-one chloro­form solvate, C10H16O4·CHCl3. The two rings are cis-fused. The [delta]-lactone ring adopts a slightly twisted half-chair conformation with approximate planarity of the lactone group and the cyclo­pentane ring adopts an envelope conformation. The hydroxy group, the hydroxymethyl group and the methyl group all have [beta] orientations. The absolute configuration was determined using anomalous dispersion data enhanced by the adventitious inclusion of a chloro­form solvent mol­ecule. Hydro­gen bonding, crystal packing and ring conformations are discussed in detail.The structure of the title compound was determined in the Molecular Structure Laboratory of the Department of Chemistry, University of Arizona. The diffractometer was obtained with funds provided by the NSF (grant No. CHE9610374). This study was supported by NIH grant No. 5U01TW00316-10 awarded to BNT

Fixing the BMS Frame of Numerical Relativity Waveforms

Understanding the Bondi-Metzner-Sachs (BMS) frame of the gravitational waves produced by numerical relativity is crucial for ensuring that analyses on such waveforms are performed properly. It is also important that models are built from waveforms in the same BMS frame. Up until now, however, the BMS frame of numerical waveforms has not been thoroughly examined, largely because the necessary tools have not existed. In this paper, we show how to analyze and map to a suitable BMS frame for numerical waveforms calculated with the Spectral Einstein Code (SpEC). However, the methods and tools that we present are general and can be applied to any numerical waveforms. We present an extensive study of 13 binary black hole systems that broadly span parameter space. From these simulations, we extract the strain and also the Weyl scalars using both SpECTRE's Cauchy-characteristic extraction module and also the standard extrapolation procedure with a displacement memory correction applied during post-processing. First, we show that the current center-of-mass correction used to map these waveforms to the center-of-mass frame is not as effective as previously thought. Consequently, we also develop an improved correction that utilizes asymptotic Poincar\'e charges instead of a Newtonian center-of-mass trajectory. Next, we map our waveforms to the post-Newtonian (PN) BMS frame using a PN strain waveform. This helps us find the unique BMS transformation that minimizes the $L^{2}$ norm of the difference between the numerical and PN strain waveforms during the early inspiral phase. We find that once the waveforms are mapped to the PN BMS frame, they can be hybridized with a PN strain waveform much more effectively than if one used any of the previous alignment schemes, which only utilize the Poincar\'e transformations

Multipole moments on the common horizon in a binary-black-hole simulation

We construct the covariantly defined multipole moments on the common horizon of an equal-mass, non-spinning, quasicircular binary-black-hole system. We see a strong correlation between these multipole moments and the gravitational waveform. We find that the multipole moments are well described by the fundamental quasinormal modes at sufficiently late times. For each multipole moment, at least two fundamental modes of different $\ell$ are detectable in the best model. These models provide faithful estimates of the true mass and spin of the remnant black hole. We also show that by including overtones, the $\ell=m=2$ mass multipole moment admits an excellent quasinormal-mode description at all times after the merger. This demonstrates the perhaps surprising power of perturbation theory near the merger

Adding Gravitational Memory to Waveform Catalogs using BMS Balance Laws

Accurate models of gravitational waves from merging binary black holes are crucial for detectors to measure events and extract new science. One important feature that is currently missing from the Simulating eXtreme Spacetimes (SXS) Collaboration's catalog of waveforms for merging black holes, and other waveform catalogs, is the gravitational memory effect: a persistent, physical change to spacetime that is induced by the passage of transient radiation. We find, however, that by exploiting the Bondi-Metzner-Sachs (BMS) balance laws, which come from the extended BMS transformations, we can correct the strain waveforms in the SXS catalog to include the missing displacement memory. Our results show that these corrected waveforms satisfy the BMS balance laws to a much higher degree of accuracy. Furthermore, we find that these corrected strain waveforms coincide especially well with the waveforms obtained from Cauchy-characteristic extraction (CCE) that already exhibit memory effects. These corrected strain waveforms also evade the transient junk effects that are currently present in CCE waveforms. Lastly, we make our code for computing these contributions to the BMS balance laws and memory publicly available as a part of the python package $\texttt{sxs}$, thus enabling anyone to evaluate the expected memory effects and violation of the BMS balance laws

High Precision Ringdown Modeling: Multimode Fits and BMS Frames

Quasi-normal mode (QNM) modeling is an invaluable tool for studying strong gravity, characterizing remnant black holes, and testing general relativity. To date, most studies have focused on the dominant $(2, 2)$ mode, and have fit to standard strain waveforms from numerical relativity. But, as gravitational wave observatories become more sensitive, they can resolve higher-order modes. Multimode fits will be critically important, and in turn require a more thorough treatment of the asymptotic frame at $\mathscr{I}^+$. The first main result of this work is a method for systematically fitting a QNM model containing many modes to a numerical waveform produced using Cauchy-characteristic extraction, which is known to exhibit memory effects. We choose the modes to model based on their power contribution to the residual between numerical and model waveforms. We show that the all-angles mismatch improves by a factor of $\sim 10^5$ when using multimode fitting as opposed to only fitting $(2, \pm2, n)$ modes. Our second main result addresses a critical point that has been overlooked in the literature: the importance of matching the Bondi-van der Burg-Metzner-Sachs (BMS) frame of the simulated gravitational wave to that of the QNM model. We show that by mapping the numerical relativity waveforms to the super rest frame, there is an improvement of $\sim 10^5$ in the all-angles strain mismatch, compared to using the strain whose BMS frame is not fixed. We illustrate the effectiveness of these modeling enhancements by applying them to families of waveforms produced by numerical relativity, and comparing our results to previous studies