DOI: 10.5281/zenodo.16801267
title: Kerr Modes: Phase fixed gravitational QNMs and TTMs

description: These HDF5 files contain data for gravitational modes of the Kerr geometry.  Each file contains the complex mode frequency, angular separation constant, and spheroidal expansion coefficients along a sequences of solutions parameterized by the dimensionless angular momentum of the Kerr black hole.  For each mode along each sequence, the spheroidal expansion coefficients have been phase fixed using the SL-C phase choice to guarantee that the phase smoothly connects to the spherical limit along each sequence.

The spin-weight -2 Quasinormal Modes are contained in the files named KerrQNM_nn.h5, where nn is the 2-digit overtone number.  Each file for 0<=nn<=15 contains all the modes for 2<=l<=16, while the each file for 16<=nn<=32 contains all the modes for 2<=l<=4.  The QNM data was constructed using the methods outlined in Cook & Zalutskiy, Phys. Rev. D 90 (2014) pp. 124021 (DOI: https://doi.org/10.1103/PhysRevD.90.124021).

The spin-weight -2 Left Total-Transmission Modes are contained in the files named KerrTTML_nn.h5, and the spin-weight +2 Right Total-Transmission Modes are contained in the files named KerrTTMR_nn.h5.   The 2-digit overtone number nn is used to designate one of three known TTM families as described in Cook & Lu, Phys. Rev. D 107 (2023) pp. 044043 (DOI: https://doi.org/10.1103/PhysRevD.107.044043).  Each file contains all the modes for 2<=l<=8.

All of the data have been constructed using the publicly available KerrModes Mathematica paclets.

The publicly available HDF5KerrModes Mathematcia paclet can be used to read the data in all of these files, create plots of the mode frequencies and separation constants, and plots of the spin-weighted spheroidal function associated with the modes.

Data in this version (v4) have changed from v3 because of a change in the way that the angular eigenvalues are sorted.  This change causes some solutions along some sequences to have a different index.  When this index changes, this can change the included phase factor which is used to convert the spheroidal expansion coefficients to the SL-Ind phase choice.  Such changes are present in a small number of solutions along Quasinormal Mode sequences with overtones in the range 18<=nn<=32, and along all of the Total-Transmission Mode sequences.  However, no changes have been made to the complex mode frequencies, the angular separation constants, or the stored spheroical expansion coefficients stored in any file, with one exception.  The last 7 expansion coefficients for one solution along the l=8, m=6, n=2 Left Total-Transmission Mode sequence were removed for consistency with the corresponding Right Total-Transmission Mode.

Note that the data contained in each column of the original 2 versions of the data (Versions 1 and v2) are different from subsequent versions!  The first 5 columns of data are consistent between versions.  However, beginning in Version v3, 3 new columns were inserted before the expansion coefficients.  These new columns containt the 0-based index of the eigenvalue and the complex phase factor needed to convert the subsequent expansion coefficients from the stored SL-C phase choice to the SL-Ind phase choice.