Computes the quasi-normal modes of a black hole.

Synopsis

lalsim-bh-qnmode [-h] [-L] [-M Msolar] [-a a] -l l -m m -s s

Description

The lalsim-bh-qnmode utility prints the eigenvalues of a black hole quasinormal mode with spin weight s (use -2 for gravitational quasinormal modes) and mode numbers l and m for given black hole dimensionless spin if the spin a is specified using the argument -a; or prints a table of mode eigenvalues if a is not specified; or prints frequency and quality factor if mass Msolar is specified.

The utility uses Leaver's conventions (G = c = 2M = 1) if the option --leaver is used

Options

-h, --help: print a help message and exit
-L, --leaver: use Leaver's conventions: G = c = 2M = 1
-M Msolar: (optional) set black hole mass (solar masses)
-a a: (optional) set value of dimensionless spin parameter a/M, |a/M|<1 (Leaver: |a/M|<0.5)
-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-qnmode. 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-qnmode utility exits 0 on success, and >0 if an error occurs.

Example

The command:

lalsim-bh-qnmode -a 0.97 -M 10 -l 2 -m 2 -s -2

outputs the freqeuency and quality factor for black hole ringdown gravitational radiation in the l = m = 2 quasinormal mode for a M = 10 solar mass hole with Kerr spin parameter a = 0.97 M.

The command:

lalsim-bh-qnmode -L -l 2 -m 0 -s -2

prints a table of Kerr quasinormal frequencies and angular separation constants for the fundamental mode corresponding to l = 2 and m = 1 for gravitational perturbations (s = -2) in Leaver's conventions:

# quasinormal mode table for l=2 m=0 s=-2 (Leaver's conventions)
#  a            A                       omega
0.0000  (4.00000,+0.00000)      (+0.747343,-0.177925)
0.1000  (3.99722,+0.00139)      (+0.750248,-0.177401)
0.2000  (3.98856,+0.00560)      (+0.759363,-0.175653)
0.3000  (3.97297,+0.01262)      (+0.776108,-0.171989)
0.4000  (3.94800,+0.02226)      (+0.803835,-0.164313)
0.4500  (3.93038,+0.02763)      (+0.824009,-0.156965)
0.4900  (3.91269,+0.03152)      (+0.844509,-0.147065)
0.4999  (3.90770,+0.03227)      (+0.850231,-0.143650)

0.0000  (4.00000,-0.00000)      (-0.747343,-0.177925)
0.1000  (3.99722,-0.00139)      (-0.750248,-0.177401)
0.2000  (3.98856,-0.00560)      (-0.759363,-0.175653)
0.3000  (3.97297,-0.01262)      (-0.776108,-0.171989)
0.4000  (3.94800,-0.02226)      (-0.803835,-0.164313)
0.4500  (3.93038,-0.02763)      (-0.824009,-0.156965)
0.4900  (3.91269,-0.03152)      (-0.844509,-0.147065)
0.4999  (3.90770,-0.03227)      (-0.850231,-0.143650)

Compare with Table 3 of E. W. Leaver, "An analytic representation of quasi-normal modes of Kerr black holes", Proc. R. Soc. Lond. A 402 285 (1985).