The RIT binary black hole simulations catalog

TL;DR

The RIT catalog provides a comprehensive set of numerical relativity simulations of binary black holes, including precessing and non-precessing systems, to aid gravitational wave data analysis.

Contribution

This work introduces a publicly available catalog of 126 binary black hole simulations with detailed waveform data and remnant properties, expanding resources for gravitational wave research.

Findings

Includes 126 simulations covering various mass ratios and spins

Provides waveforms extrapolated to infinity for accurate analysis

Contains data on peak luminosity and remnant black hole properties

Abstract

The RIT numerical relativity group is releasing a public catalog of black-hole-binary waveforms. The initial release of the catalog consists of 126 recent simulations that include precessing and non precessing systems with mass ratios $q=m_1/m_2$ in the range $1/6\leq q\leq1$. The catalog contains information about the initial data of the simulation, the waveforms extrapolated to infinity, as well as information about the peak luminosity and final remnant black hole properties. These waveforms can be used to independently interpret gravitational wave signals from laser interferometric detectors and

Full text

I Introduction

The breakthroughs Pretorius (2005); Campanelli et al. (2006a); Baker et al. (2006) in numerical relativity allowed numerical relativists to make detailed predictions for the gravitational waves from the latest inspiral, plunge, merger and ringdown of black hole binary systems (BHB). Numerical relativity predictions were confirmed by the first direct detection Abbott et al. (2016a) of gravitational waves from such binary systems Abbott et al. (2016b, c, d) and by its comparison to targeted runs Abbott et al. (2016e); Lovelace et al. (2016). Those observations are consistent with general relativity as the correct theory for gravity as discussed in Abbott et al. (2016f, d).

The RIT group has been using numerical relativity techniques to explore the late dynamics of spinning black-hole binaries, beyond the post-Newtonian regime for many years. This includes simulations of the first generic, long-term precessing binary black hole evolution without any symmetry were performed in Ref. Campanelli et al. (2009a), where a detailed comparison with post-Newtonian $\ell=2,3$ waveforms was made, as well as studies of the hangup, i.e. the role individual black hole spins play to delay or accelerate their merger Campanelli et al. (2006b), the determination of the magnitude and direction of the recoil velocity of the final merged black hole Campanelli et al. (2007a, b); Lousto and Zlochower (2011a), and the flip-flop of individual spins during the orbital phase Lousto and Healy (2015); Lousto et al. (2016); Lousto and Healy (2016). Other numerical simulations have also explored the corners of parameter space, such as mass ratios $q=1/100$ in Ref. Lousto and Zlochower (2011b), and larger initial separations $R=100M$ in Lousto and Zlochower (2013). And also near extremal $\chi=0.994$ spinning black hole binaries in Lovelace et al. (2015) by the SXS collaboration.

There have been several significant efforts to coordinate numerical relativity simulations to support gravitational wave observations. These include the numerical injection analysis (NINJA) project Aylott et al. (2009a, b); Ajith et al. (2012); Aasi et al. (2014), the numerical relativity and analytical relativity (NRAR) collaboration Hinder et al. (2014), and the waveform catalogs released by the simulating extreme spacetimes (SXS) collaboration Mroue et al. (2013) and Georgia Tech. Jani et al. (2016).

The paper is organized as follows. Section II describe the methods and criteria for producing the numerical simulations. We next describe in Sec. III the use and content of the data in the public catalog. We conclude with a discussion in Sec. IV of the use and potential extensions to this work to precessing binaries.

II Full Numerical Evolutions

The runs in the RIT Catalog were evolved using the LazEv Zlochower et al. (2005) implementation of the moving puncture approach Campanelli et al. (2006a) with the conformal function $W=\sqrt{\chi}=\exp(-2\phi)$ suggested by Ref. Marronetti et al. (2008). In all cases we use the BSSNOK (Baumgarte-Shapiro-Shibata-Nakamura-Oohara-Kojima) family of evolutions systems Nakamura et al. (1987); Shibata and Nakamura (1995); Baumgarte and Shapiro (1998). For the runs in the catalog, we used a variety of finite-difference orders, Kreiss-Oliger dissipation orders, and Courant factors Lousto and Zlochower (2008); Zlochower et al. (2012); Healy and Lousto (2017). Note that we do not upwind the advection terms. All of these are given in the metadata included in the catalog and the references associated with each run.

The LazEv code uses the EinsteinToolkit Löffler et al. (2012); ein / Cactus cac / Carpet Schnetter et al. (2004) infrastructure. The Carpet mesh refinement driver provides a “moving boxes” style of mesh refinement. In this approach, refined grids of fixed size are arranged about the coordinate centers of both holes. The Carpet code then moves these fine grids about the computational domain by following the trajectories of the two BHs.

We use AHFinderDirect Thornburg (2004) to locate apparent horizons. We measure the magnitude of the horizon spin using the isolated horizon (IH) algorithm detailed in Ref. Dreyer et al. (2003) and as implemented in Ref. Campanelli et al. (2007c). Note that once we have the horizon spin, we can calculate the horizon mass via the Christodoulou formula ${m_{H}}=\sqrt{m_{\rm irr}^{2}+S_{H}^{2}/(4m_{\rm irr}^{2})}\,,$ where $m_{\rm irr}=\sqrt{A/(16\pi)}$, $A$ is the surface area of the horizon, and $S_{H}$ is the spin angular momentum of the BH (in units of $M^{2}$). In the tables below, we use the variation in the measured horizon irreducible mass and spin during the simulation as a measure of the error in computing these quantities, since the levels of gravitational wave energy and momentum absorbed by the holes is orders of magnitude smaller. We measure radiated energy, linear momentum, and angular momentum, in terms of the radiative Weyl Scalar $\psi_{4}$, using the formulas provided in Refs. Campanelli and Lousto (1999); Lousto and Zlochower (2007). However, rather than using the full $\psi_{4}$, we decompose it into $\ell$ and $m$ modes and solve for the radiated linear momentum, dropping terms with $\ell>6$. The formulas in Refs. Campanelli and Lousto (1999); Lousto and Zlochower (2007) are valid at $r=\infty$. We extract the radiated energy-momentum at finite radius and extrapolate to $r=\infty$. We find that the new perturbative extrapolation described in Ref. Nakano et al. (2015) provides the most accurate waveforms. While the difference of fitting both linear and quadratic extrapolations provides an independent measure of the error. Studies of the finite difference errors, and verification that the waveforms provided in this catalog are computed at a numerical resolution in the convergence regime can be found in the appendices of Refs. Healy et al. (2014) and  Healy and Lousto (2017). Although higher multipoles modes [beyond $(\ell,m)=(2,\pm 2)$] are not provided in the catalog for the sake of simplicity, they are used (typically up to $\ell=4$ or $\ell=6$) in the computation of radiative quantities such as the energy and linear and angular momenta.

To compute the initial low eccentricity orbital parameters we use the post-Newtonian techniques described in Healy et al. (2017). To compute the numerical initial data, we use the puncture approach Brandt and Brügmann (1997) along with the TwoPunctures Ansorg et al. (2004) thorn.

We measure the distance between the two BHs using the simple proper distance or SPD. The SPD is the proper distance, on a given spatial slice, between the two BH apparent horizons as measured along the coordinate line joining the two centers. As such, it is gauge dependent, but still gives reasonable results (see Ref. Lousto and Zlochower (2013) for more details).

III Catalog

The RIT Catalog can be found at http://ccrg.rit.edu/~RITCatalog. Figure 1 shows the distribution of non-precessing runs in the catalog in terms of $\chi_{12}$ and $q$ ($\chi$ here is the $z$-component of the dimensionless spin). The information currently in the catalog consists of the metadata describing the runs and $(\ell=2,m=\pm 2)$ modes of $r\psi_{4}$. The extrapolations of $r\psi_{4}$ to $r=\infty$ are performed using the perturbative approach of Nakano et al. (2015). The associated metadata include the initial orbital frequencies, ADM masses, initial waveform frequencies, black hole masses, momenta, spins, separations, and eccentricities, as well the black-hole masses and spins once the initial burst of radiation has left the region around the binary. These relaxed quantities are more accurate for modeling purposes than the initial masses and spins. In addition, we also include the final remnant masses and spins.

The catalog is organized using an interactive table that includes an identification number, resolution, type of run (nonspinning, aligned spins, precessing), the initial simple proper distance between the two black holes, the coordinate separation, the mass ratio of the two black holes, the components of the dimensionless spins of the two black holes, the starting waveform frequency, time to merger, number of gravitational wave cycles, remnant mass, remnant spin, recoil velocity, and peak luminosity. The final column gives the appropriate bibtex keys for the relevant publications where the waveforms were first presented. The table can be sorted (ascending or descending) by any of these columns.

The initial waveform frequency, denoted by $Mf_{22,{\rm start}}$ in the table gives the starting frequency in units of $2.03\times 10^{5}\left(\frac{M_{\odot}}{M}\right){\rm Hz},$ where $M$ is the mass of the binary and $M_{\odot}$ is one solar mass (e.g., $Mf_{22,{\rm start}}=0.01$ corresponds to 34 Hz for a 60 $M_{\odot}$ binary). Note that $2\pi f_{22}=\omega_{22}$. The runs in the catalog span initial frequencies from 0.003 to 0.012, with a corresponding initial proper separations of 10.59M to 25.18M. Times from the start of the simulation to merger range from 556M to 19 219M, and the number of inspiral cycles in the $(\ell=2,m=2)$ mode of $\psi_{4}$ range from 8.3 to 89.9.

Resolutions are given in terms of the gridspacing of the refinement level where the waveform is extracted (which is typically two refinement levels below the coarsest grid) with $R_{obs}\sim 100M$. We use the notation nXYY, where the gridspacing in the wavezone is given by M/X.YY, e.g., n120 corresponds to $h=M/1.2$.

For each simulation in the catalog there are two files: one contains the metadata information in ASCII format, the other is a tar.gz file containing ASCII files with the $(\ell=2,m=\pm 2)$ modes of $r\psi_{4}$ (extrapolated to $r=\infty$).

Note that our catalog provides the Weyl scalar $r\psi_{4}$ extrapolated to infinity rather than the strain $\hat{h}$. We leave to the user to convert $r\psi_{4}$ to strain (e.g., along the lines of the method delineated in the NRAR collaboration  Hinder et al. (2014), for instance).

Figure 2 shows the distribution of the 120 non-precessing runs in the catalog in terms of $\chi_{1,2}$ and $q$ ($\chi$ here is the $L$ or $z$-component of the dimensionless spin).

IV Conclusions and Discussion

The breakthroughs Pretorius (2005); Campanelli et al. (2006a); Baker et al. (2006) in numerical relativity were instrumental in identifying the first detection of gravitational waves Abbott et al. (2016a) with the merger of two black holes. The direct comparison of numerical waveforms with observations also allows one to determine the parameters of such binary Abbott et al. (2016e). The current catalog of waveforms as displayed in Fig. 3 can be used to perform independent analysis by the wider gravitational wave community and serves as a platform to deliver new sets of simulations as they become available.

Aside the interest in producing waveforms for direct comparison with observation, the simulations of orbiting black hole binaries produce information about the final remnant of the merger of the two holes. This was already the subject of early studies using the Lazarus approach Baker et al. (2004); Campanelli (2005). With the advent of the breakthroughs that allowed for longer accurate computations, numerous empirical formulas relating the initial parameters $(q,\vec{\chi}_{1},\vec{\chi}_{2})$ (individual masses and spins) of the binary to those of the final remnant $(m_{f},\vec{\chi}_{f},\vec{V}_{f})$ have been proposed. These include formulas for the final mass, spin, and recoil velocity Barausse et al. (2012); Rezzolla et al. (2008); Hofmann et al. (2016); Jiménez-Forteza et al. (2016); Lousto et al. (2010); Lousto and Zlochower (2014); Healy et al. (2014); Zlochower and Lousto (2015), as well as algebraic properties of the final metric Campanelli et al. (2009b); Owen (2010). Recently, the computation of the peak luminosity has also been the subject of interest in relation to the observation of gravitational waves Abbott et al. (2016a, d); Healy and Lousto (2017); Keitel et al. (2016). The data in RIT catalog, along with the SXS Mroue et al. (2013) and Georgia Tech. Jani et al. (2016), can be used by other groups to develop and improve new empirical formulas for the remnant properties and approximate/phenomenological waveform models Babak et al. (2017); Khan et al. (2016).

Acknowledgements.

The authors thank N.K.J-McDaniel, H. Nakano, and R. O’Shaughnessy for discussions on this work. The authors gratefully acknowledge the NSF for financial support from NSF Grants No. PHY-1607520, No. ACI-1550436, No. AST-1516150, No. ACI-1516125, No. PHY-1305730, No. PHY-1212426, No. PHY-1229173, No. AST-1028087, No. PHY-0969855, No. OCI-0832606, and No. DRL-1136221. Computational resources were provided by XSEDE allocation TG-PHY060027N, and by NewHorizons and BlueSky Clusters at Rochester Institute of Technology, which were supported by NSF grants No. PHY-0722703, No. DMS-0820923, No. AST-1028087, and No. PHY-1229173.