Factorization and resummation: A new paradigm to improve gravitational wave amplitudes. II. the higher multipolar modes

The factorization and resummation approach of Nagar and Shah [Phys. Rev. D 94, 104017 (2016)PRVDAQ2470-001010.1103/PhysRevD.94.104017], designed to improve the strong-field behavior of the post-Newtonian (PN) residual waveform amplitudes fm's entering the effective-one-body, circularized, gravitational waveform for spinning coalescing binaries, is improved and generalized here to all multipoles up to =6. For a test particle orbiting a Kerr black hole, each multipolar amplitude is truncated at relative 6 PN order, both for the orbital (nonspinning) and spin factors. By taking a certain Padé approximant (typically the P24 one) of the orbital factor in conjunction with the inverse Taylor (iResum) representation of the spin factor, it is possible to push the analytical/numerical agreement of the energy flux at the level of 5% at the last-stable orbit for a quasimaximally spinning black hole with dimensionless spin parameter +0.99. When the procedure is generalized to comparable-mass binaries, each orbital factor is kept at relative 3+3 PN order; i.e., the globally 3 PN-accurate comparable-mass terms are hybridized with higher-PN test-particle terms up to 6 PN relative order in each mode. The same Padé resummation is used for continuity. By contrast, the spin factor is only kept at the highest comparable-mass PN order currently available. We illustrate that the consistency between different truncations in the spin content of the waveform amplitudes is more marked in the resummed case than when using the standard Taylor-expanded form of Pan et al. [Phys. Rev. D 83, 064003 (2011)PRVDAQ1550-799810.1103/PhysRevD.83.064003]. We finally introduce a method to consistently hybridize comparable-mass and test-particle information also in the presence of spin (including the spin of the particle), discussing it explicitly for the =m=2 spin-orbit and spin-square terms. The improved, factorized and resummed, multipolar waveform amplitudes presented here are expected to set a new standard for effective one body-based gravitational waveform models.