DOI: 10.5281/zenodo.15783358
title: Spherical inspirals of spinning bodies into Kerr black holes

description: Dataset of gravitational-wave fluxes from spherical orbits in Kerr spacetime and mismatches of waveforms with spinning and nonspinning secondary. These data are part of the publication 

Viktor Skoupý, Gabriel Andres Piovano, Vojtěch Witzany, Spherical inspirals of spinning bodies into Kerr black holes (2025) arXiv:2506.20726 [gr-qc]

fluxes_spherical.zip contains files fluxes_a0.1000_v0.2000_x0.1000_r154.8100.dat etc. which contain all modes for given point in the parameter space. The columns are as follows:




$l$
multipolar number


$m$
azimuthal number


$k$
harmonic number of the polar motion


$n$
harmonic number of the radial motion


$\omega$
frequency


$\delta \omega$
linear part of the frequency


$d\omega/dr$
derivative of the frequency


$d\omega/dx$
derivative of the frequency


$Re\{C^+_{lmnk}\}$
real part of the infinity amplitude


$Im\{C^+_{lmnk}\}$
imaginary part of the infinity amplitude


 $Re\{C^-_{lmnk}\}$
real part of the horizon amplitude


$Im\{C^-_{lmnk}\}$
imaginary part of the horizon amplitude


$Re\{\delta C^+_{lmnk}\}$
real part of the linear-in-spin part of the infinity amplitude


$Im\{\delta C^+_{lmnk}\}$
imaginary part of the linear-in-spin part of the infinity amplitude


$Re\{\delta C^-_{lmnk}\}$
real part of the linear-in-spin part of the horizon amplitude


$Im\{\delta C^-_{lmnk}\}$
imaginary part of the linear-in-spin part of the horizon amplitude


$Re\{dC^+_{lmnk}/dr\}$
real part of the derivative of the infinity amplitude


$Im\{dC^+_{lmnk}/dr\}$
imaginary part of the derivative of the infinity amplitude


$Re\{dC^-_{lmnk}/dr\}$
real part of the derivative of the horizon amplitude


$Im\{dC^-_{lmnk}/dr\}$


imaginary part of the derivative of the horizon amplitude



$Re\{dC^+_{lmnk}/dx\}$
real part of the derivative of the infinity amplitude


$Im\{dC^+_{lmnk}/dx\}$
imaginary part of the derivative of the infinity amplitude


$Re\{dC^-_{lmnk}/dx\}$
real part of the derivative of the horizon amplitude


$Im\{dC^-_{lmnk}/dx\}$
imaginary part of the derivative of the horizon amplitude


$\alpha_{lmnk}$
constant for horizon fluxes


$d\alpha /d\omega$
$\omega$-derivative of $\alpha_{lmnk}$


$_{-2}S_{lm}^{a\omega}(\pi/2)$
spin-weighted spheroidal harmonic at $\pi/2$


$\mathcal{F}^{E+}_{lmnk}$
energy flux to infinity


$\mathcal{F}^{E-}_{lmnk}$
energy flux to the horizon


$\mathcal{F}^{L_z+}_{lmnk}$
angular momentum flux to infinity


$\mathcal{F}^{L_z-}_{lmnk}$
angular momentum flux to the horizon


$\delta\mathcal{F}^{E+}_{lmnk}$
linear-in-spin part of the energy flux to infinity


$\delta\mathcal{F}^{E-}_{lmnk}$
linear-in-spin part of the energy flux to the horizon


$\delta\mathcal{F}^{L_z+}_{lmnk}$
linear-in-spin part of the angular momentum flux to infinity


$\delta\mathcal{F}^{L_z-}_{lmnk}$
linear-in-spin part of the angular momentum flux to the horizon


$d\mathcal{F}^{E+}_{lmnk}/dr$
derivative of the energy flux to infinity


$d\mathcal{F}^{E-}_{lmnk}/dr$
derivative of the energy flux to the horizon


$d\mathcal{F}^{L_z+}_{lmnk}/dr$
derivative of the angular momentum flux to infinity


$d\mathcal{F}^{L_z-}_{lmnk}/dr$
derivative of the angular momentum flux to the horizon


$d\mathcal{F}^{E+}_{lmnk}/dx$
derivative of the energy flux to infinity


$d\mathcal{F}^{E-}_{lmnk}/dx$
derivative of the energy flux to the horizon


$d\mathcal{F}^{L_z+}_{lmnk}/dx$
derivative of the angular momentum flux to infinity


$d\mathcal{F}^{L_z-}_{lmnk}/dx$
derivative of the angular momentum flux to the horizon


$\lambda_{lmnk}$
Teukolsky eigenvalue


$d\lambda_{lmnk}/d\omega$
$\omega$-derivative of $\lambda_{lmnk}$


 
integration steps in $w_z$




 

grid.dat cotains the interpolation grid points. The columns are as follows:




$a$
Kerr parameter


$v$
interpolation parameter $v$ from Eq. (136)


$x$
inclination


$p$
radius




 

mismatches_secondary_spins.dat contains mismatches (unfaithfulnesses) for different secondary spins, mass ratios and polarizations (Fig. 9). The columns are as follows:




secondary spin


unfauihfullness for $q = 10^{-4}$, + polarization


unfauihfullness for $q = 10^{-4}$, x polarization


unfauihfullness for $q = 10^{-5}$, + polarization


unfauihfullness for $q = 10^{-5}$, x polarization




 

mismatches_primary_spins.dat contains mismatches (unfaithfulnesses) for different primary spins, mass ratios and polarizations (Fig. 10). The columns are as follows:




primary spin


unfauihfullness for $q = 10^{-4}$, + polarization


unfauihfullness for $q = 10^{-4}$, x polarization


unfauihfullness for $q = 10^{-5}$, + polarization


unfauihfullness for $q = 10^{-5}$, x polarization




 

mismatches_final_inclinations.dat contains mismatches (unfaithfulnesses) for different final inclinations, mass ratios and polarizations (Fig. 11). The columns are as follows:




final inclination


unfauihfullness for $q = 10^{-4}$, + polarization


unfauihfullness for $q = 10^{-4}$, x polarization


unfauihfullness for $q = 10^{-5}$, + polarization


unfauihfullness for $q = 10^{-5}$, x polarization