Kernel formats

To unpack the Regge-Wheeler tables execute the following command (and similarly for the Zerilli tables).

tar -zxvf TablesHeunRBC.tar.gz

This command creates a directory TablesHeunRBC within which there are 5 subdirectories: Rho15,Rho30,Rho60, Rho120, and Rho240. These names denote the boundary radius in terms of the dimensionless variable \( \rho_b \equiv r_b/(2M) \). For example, the Rho240 directory corresponds to RBCs imposed at \(r_b = 480M\).

The aformentioned subdirectories contain a collection of text and MATLAB files, each of which is a table. For example, the directory TablesHeunRBC/Rho060/ contains both FdCqRho0060L005D12_rw2.txt and FdCqRho0060L005D12_rw2.m each of specifies the same table. FdCq means Format in double precision and Computed in quad precision. The *.m file is suited for direct implementation in a MATLAB code, whereas the *.txt is a raw text file. Both tables specify the RBC for the Regge-Wheeler equation with \(\rho_b = 60\) and \(\ell=5\). Regarding the file names, the outer boundary \(\rho_b\) and multipole value \(\ell\) are those numbers following Rho and L, whereas the number following \(D\) denotes the number of poles in the kernel, in this case 12.

Additional information, such as the number of purely real and conjugate poles, is found inside each file. FdCqRho0060L005D12_rw2.txt is shown below. Evidently this kernel is comprised of 8 purely real poles (7 of which approximate the analytic kernel's branch cut profile) and 2 conjugate-pole pairs (these 4 genuinely complex poles, along with the fourth purely real pole correspond to direct propagation). One such pole is located at (-5.5420039751986106E-002 , 2.9541609939390942E-002) in the complex plane and has a strength of (-5.4972680329151328E-002 , 3.0039580430797788E-002). Here we use the format (real, imaginary). From the output below, the first 8 poles are seen to be purely real.

rhoBd:
  6.0000000000000000E+001
 ell:
   5
 Nsing:
   8
 Npair:
   2
 ====== timestamp: (D) 8- 7-2013 (T)17:49:28 =======
 
 Beta locations:
 1 -1.4240044173895337E-001  0.00E+000
 2 -1.0128919691677426E-001  0.00E+000
 3 -7.3170213043602224E-002  0.00E+000
 4 -6.0546419757577656E-002  0.00E+000
 5 -5.3891962173564062E-002  0.00E+000
 6 -3.7398357686381061E-002  0.00E+000
 7 -2.4845884406568458E-002  0.00E+000
 8 -1.4878395766597290E-002  0.00E+000
 9 -5.5420039751986106E-002  2.9541609939390942E-002
10 -3.8170434475033878E-002  5.9383926261453977E-002
11 -5.5420039751986106E-002 -2.9541609939390942E-002
12 -3.8170434475033878E-002 -5.9383926261453977E-002
 
 Gamma strengths:
 1  1.4461125855693138E-007  0.00E+000
 2  2.9783560995567696E-005  0.00E+000
 3  2.3849939725599964E-003  0.00E+000
 4 -7.1341757172001727E-002  0.00E+000
 5  4.4642039883901987E-003  0.00E+000
 6  1.4232463638236825E-005  0.00E+000
 7  5.9938437299092638E-008  0.00E+000
 8  8.8513860197518676E-011  0.00E+000
 9 -5.4972680329151328E-002  3.0039580430797788E-002
10 -3.7594817063411394E-002  5.9248936478593952E-002
11 -5.4972680329151328E-002 -3.0039580430797788E-002
12 -3.7594817063411394E-002 -5.9248936478593952E-002