Evaluates a spin-weighted spheroidal wave function.

Synopsis

lalsim-bh-sphwf [-h] [-i theta] -a a -l l -m m -s s

Description

The lalsim-bh-sphwf utility prints the value of the spin-weighted spheroidal wave function \( {}_{s}S_{\ell,m}(\cos\theta, a) \) for the specified dimensionless spin parameter a, spin weight s mode numbers l and m, and polar angle theta. If the parameter theta is not given, the utility prints a table of the values of the spin-weighted spheroidal wave function.

Options

-h, --help: print a help message and exit
-i theta: (optional) set the polar angle (degrees)
-a a: (required) set value of dimensionless spin parameter a/M, |a/M|<1
-l l: (required) set value of mode number l, l>=0
-m m: (required) set value of mode number m, abs(m)<=l
-s s: (required) set value of spin weight s, s<=0

Environment

The LAL_DEBUG_LEVEL can used to control the error and warning reporting of lalsim-bh-sphwf. Common values are: LAL_DEBUG_LEVEL=0 which suppresses error messages, LAL_DEBUG_LEVEL=1 which prints error messages alone, LAL_DEBUG_LEVEL=3 which prints both error messages and warning messages, and LAL_DEBUG_LEVEL=7 which additionally prints informational messages.

Exit Status

The lalsim-bh-sphwf utility exits 0 on success, and >0 if an error occurs.

Example

The command:

lalsim-bh-sphwf -a 0.97 -l 2 -m 2 -s -2

prints a table of the spin-weighted spheroidal harmonic for spin weight -2 (gravitational perturbations) in the l = m = 2 quasinormal mode for black hole with Kerr spin parameter a/M = 0.97:

# theta(deg)        Re(S)           Im(S)
       0        1.872344e+00    -6.463929e-02
      10        1.827823e+00    -6.206959e-02
      20        1.694394e+00    -5.225983e-02
      30        1.504102e+00    -4.281635e-02
      40        1.273225e+00    -3.208053e-02
      50        1.027770e+00    -2.170445e-02
      60        7.909086e-01    -1.294164e-02
      70        5.808472e-01    -6.804991e-03
      80        4.043798e-01    -2.360517e-03
      90        2.668276e-01    -8.673617e-19
     100        1.656352e-01    9.846400e-04
     110        9.604459e-02    1.063797e-03
     120        5.104255e-02    8.091283e-04
     130        2.420241e-02    4.838700e-04
     140        9.739511e-03    2.305645e-04
     150        3.034816e-03    8.061289e-05
     160        5.924425e-04    1.697014e-05
     170        3.675324e-05    1.099041e-06
     180        0.000000e+00    0.000000e+00