The motivation of this waveform catalog is to allow for rigorous
testing between Cauchy characteristic extraction (CCE) code in
SpECTRE and the extrapolation
code in
scri. Asymptotic
waveforms are provided for the gravitationalwave strain $h$ and the
complete set of Weyl Scalars $(\Psi_4, \Psi_3, \Psi_2, \Psi_1, \Psi_0)$.
Data Columns
Name 
Alt Name 
$M^{\text{ini,1}} / M^{\text{ini,2}}$ 
$\vec{\chi}^{\text{ini,1}}$ 
$\vec{\chi}^{\text{ini,2}}$ 
$N^{\text{orbits}}$ 
Files 
SXS:BBH_ExtCCE:0001 
q1_nospin 
1.0 
(0, 0, 0) 
(0, 0, 0) 
20.78 

SXS:BBH_ExtCCE:0002 
q1_aligned_chi0_2 
1.0 
(0, 0, 0.2) 
(0, 0, 0.2) 
18.99 

SXS:BBH_ExtCCE:0003 
q1_aligned_chi0_4 
1.0 
(0, 0, 0.4) 
(0, 0, 0.4) 
19.26 

SXS:BBH_ExtCCE:0004 
q1_aligned_chi0_6 
1.0 
(0, 0, 0.6) 
(0, 0, 0.6) 
19.35 

SXS:BBH_ExtCCE:0005 
q1_antialigned_chi0_2 
1.0 
(0, 0, 0.2) 
(0, 0, 0.2) 
18.84 

SXS:BBH_ExtCCE:0006 
q1_antialigned_chi0_4 
1.0 
(0, 0, 0.4) 
(0, 0, 0.4) 
18.84 

SXS:BBH_ExtCCE:0007 
q1_antialigned_chi0_6 
1.0 
(0, 0, 0.6) 
(0, 0, 0.6) 
18.77 

SXS:BBH_ExtCCE:0008 
q1_precessing 
1.0 
(0.487, 0.125, 0.327) 
(0.190, 0.051, 0.227) 
20.47 

SXS:BBH_ExtCCE:0009 
q1_superkick 
1.0 
(0.6, 0, 0) 
(0.6, 0, 0) 
18.78 

SXS:BBH_ExtCCE:0010 
q4_nospin 
4.0 
(0, 0, 0) 
(0, 0, 0) 
20.07 

SXS:BBH_ExtCCE:0011 
q4_aligned_chi0_4 
4.0 
(0, 0, 0.4) 
(0, 0, 0.4) 
19.00 

SXS:BBH_ExtCCE:0012 
q4_antialigned_chi0_4 
4.0 
(0, 0, 0.4) 
(0, 0, 0.4) 
18.76 

SXS:BBH_ExtCCE:0013 
q4_precessing 
4.0 
(0.487, 0.125, 0.327) 
(0.190, 0.051, 0.227) 
17.43 

Waveform Information
File Compression
The waveform files have been compressed using
scri's RPXM compression
format and can be opened with functions in that python module. See
the
scri documentation
for more information.
Mass Scaling
The asymptotic waveforms and corresponding values of time have been
made dimensionless by an appropriate factor of the system mass. The
system mass is the combined Christodoulou mass of the two black
holes measured at the reference time.
CenterofMass Correction
There is a known centerofmass (CoM) drift during the numerical
evolution in SpEC. We attempt to mitigate the resulting gauge effects
in the waveforms by applying the correction described in Woodford+
(2019)
[arXiv:1904.04842].
The spacetranslation and boost that have been applied can be found
in the JSON file accompanying each waveform.
Memory Correction
The asymptotic strain waveforms produced by extrapolation are missing
the contribution of displacement memory. This missing contribution
has been added using the correction described in Mitman+ (2021)
[arXiv:2011.01309].
CCE Waveforms
The characteristic evolution is performed by the CCE code in
SpECTRE. See Moxon+ (2020)
[arXiv:2007.01339]
for details about this CCE scheme. The worldtube data is extracted
at four different radii in the simulation, and there is a different
set of asymptotic CCE waveforms for each worldtube radius. Due to
the difficulty in choosing initial data, the asymptotic CCE strain
waveforms exhibit spurious oscillations that are entirely gauge
effects. The waveforms from the outermost worldtube radius have the
least gauge effects. However, the waveforms from the second smallest
worldtube radius satisfy the Bianchi identities best. For most
purposes then,
the waveforms from the second smallest worldtube
radius are recommended.
Extrapolated Waveforms
Extrapolation is performed by the
scri python module. See
Iozzo+ (2021)
[arXiv:2010.15200]
for details about this extrapolation scheme. The extrapolation
performed here is slightly different from the main SXS waveform database.
The optimal extrapolation order $N$ for each data type in this ExtCCE
waveform database is:
 $h$: $N=5$
 $\Psi_4$: $N=7$
 $\Psi_3$: $N=7$
 $\Psi_2$: $N=5$
 $\Psi_1$: $N=4$ for merger/ringdown and $N=3$ for early inspiral
 $\Psi_0$: $N=2$
These orders were determined by considering the convergence of the
extrapolation procedure and minimizing the violation of the Bondi
gauge Bianchi identities. We include waveforms from two orders lower
than the optimal order for convergence testing.