Phenomenological model for the gravitational-wave signal from precessing binary black holes with two-spin effects

Sebastian Khan, Katerina Chatziioannou, Mark Hannam, and Frank Ohme

Phys. Rev. D 100, 024059 – Published 29 July 2019

Abstract

The properties of compact binaries, such as masses and spins, are imprinted in the gravitational waves (GWs) they emit and can be measured using parametrized waveform models. Accurately and efficiently describing the complicated precessional dynamics of the various angular momenta of the system in these waveform models is the object of active investigation. One of the key models extensively used in the analysis of LIGO and Virgo data is the single-precessing-spin waveform model IMRPhenomPv2. In this article we present a new model IMRPhenomPv3, which includes the effects of two independent spins in the precession dynamics. Whereas IMRPhenomPv2 utilizes a single-spin frequency-dependent post-Newtonian rotation to describe precession effects, the improved model, IMRPhenomPv3, employs a double-spin rotation that is based on recent developments in the description of precessional dynamics. Besides double-spin precession, the improved model benefits from a more accurate description of precessional effects. We validate our new model against a large set of precessing numerical-relativity simulations. We find that IMRPhenomPv3 has better agreement with the inspiral portion of precessing binary-black-hole simulations and is more robust across a larger region of the parameter space than IMRPhenomPv2. As a first application we analyze the gravitational-wave event GW151226 with an efficient frequency-domain waveform model that describes two-spin precession. Within statistical uncertainty our results are consistent with published results. IMRPhenomPv3 will allow studies of the measurability of individual spins of binary black holes using GWs and can be used as a foundation upon which to build further improvements, such as modeling precession through merger, extending to higher multipoles, and including tidal effects.

Received 8 October 2018

DOI:https://doi.org/10.1103/PhysRevD.100.024059

Physics Subject Headings (PhySH)

Gravitational wave sources Gravitational waves

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Sebastian Khan ^1,2, Katerina Chatziioannou³, Mark Hannam⁴, and Frank Ohme^1,2

¹Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Callinstr. 38, 30167 Hannover, Germany
²Leibniz Universität Hannover, D-30167 Hannover, Germany
³Canadian Institute for Theoretical Astrophysics, 60 St. George Street, University of Toronto, Toronto, Ontario M5S 3H8, Canada
⁴School of Physics and Astronomy, Cardiff University, The Parade, Cardiff CF24 3AA, United Kingdom

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 100, Iss. 2 — 15 July 2019

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Comparison of leading-order (IMRPhenomPv2, leading order), NNLO (IMRPhenomPv2), full-PN (IMRPhenomPv3, all terms), and the version we adopt in the final model (IMRPhenomPv3) expressions for the precession angle, $α$ . First panel, $q = 1$ , $M_{tot} = 10 M_{⊙}$ $χ_{eff} = 0$ , $χ_{p} = 0.9$ ; second panel, $q = 8$ , $M_{tot} = 10 M_{⊙}$ $χ_{eff} = 0$ , $χ_{p} = 0.9$ ; third panel, $q = 10$ , $M_{tot} = 10 M_{⊙}$ $χ_{eff} = - 0.8$ , $χ_{p} = 0.1$ ; fourth panel, same configuration as third panel, but zoom of nonphysical behavior of $α_{v 2} (f)$ . All cases are generated from a frequency of 2 Hz. See the text for discussion.
Reuse & Permissions
Figure 2
Composite figure comparing the various models for the precession angles and their overall effect on the waveform. We generate the gravitational waveform from a BBH system with the following parameter: $q = 10$ , $M = 20$ , $S_{1} = (0.4, 0, 0.4)$ , $S_{2} = (0.3, 0, - 0.3)$ , $f_{start} = 10 Hz$ . The top row shows $h_{\times}$ polarization evaluated at $ι = π / 2$ (here $ι$ is the angle between $\vec{L}$ and the line of sight). In all panels the dashed blue line corresponds to IMRPhenomPv2 and the solid orange line corresponds to IMRPhenomPv3. Top left: The full waveform generated from 10 Hz. Top right: Zoom in around merger. We observe early-time agreement and late-time disagreement caused by the different precession models. The bottom row shows the precession angles as a function of GW frequency. Bottom left: $α$ . Bottom middle: $ε$ . Bottom right: $β$ . The solid black line is the hybrid-MECO frequency [64], the dashed black line is the Schwarzschild ISCO frequency and the dot-dashed black line is the ringdown frequency for this system. The legend in the bottom left plot applies to the bottom middle plot as well and shows to what $n$ order (see text) the $α$ and $ε$ angles were expanded. The legend in the bottom right figure indicates if aligned spins were included in the calculation of the magnitude of the orbital angular momentum.
Reuse & Permissions
Figure 3
The precessing parameter space we probe using the SXS public catalogue. The x axis is the SXS catalogue number. The four panels (from top to bottom) show the mass ratio $q = m_{1} / m_{2}$ , the dimensionless spin magnitudes $| {\vec{χ}}_{i} |$ , the polar angle between the Newtonian orbital angular momentum and the individal BH spin vectors $θ_{i}$ where $i = 1$ , 2 for the larger and smaller BH respectively and finally the last panel plots the start GW frequency for each simulation when scaled to a total mass of $50 M_{⊙}$ , where the primary and secondary BHs are plotted as blue diamonds and orange circles respectively.
Reuse & Permissions
Figure 4
The results of the comparison between IMRPhenomPv2 (first row), IMRPhenomPv3 (second row) and SEOBNRv3 (third row) and the precessing NR simulations from the public SXS catalogue. Each column shows the results for $ι = (0, π / 3, π / 2)$ , from left to right, where $ι$ is the angle between the Newtonian orbital angular momentum $\vec{L}$ and the line of sight, at the start frequency. The figure shows the orientation-averaged mismatch ( $1 - \bar{M}$ ) as a function of the total mass (log scale). Cases which have a maximum mismatch greater than 3% are colored and presented in Table 1.
Reuse & Permissions
Figure 5
Posteriors probability densities for $χ_{eff} - χ_{p}$ (left) and $χ_{eff} - q$ (right) for GW151226 using IMRPhenomPv2 and IMRPhenomPv3. Despite the more accurate description of two-spin dynamics of IMRPhenomPv3 the posteriors are consistent, demonstrating the difficulty of measuring two-spin dynamics.
Reuse & Permissions

Physical Review D

covering particles, fields, gravitation, and cosmology