Data Columns
| Column |
Description |
| ID |
A unique identification string for a simulation. It identifies the
collaboration, type of binary, and number. |
| Data |
Link to the metadata and downloadable data for a simulation. |
| m1/m2 |
Ratio of the Christodoulou masses at the relaxation time. We use $m_1>m_2$. |
| χ1,2 |
Dimensionless spin magnitudes at the relaxation time. |
| χ{1,2}{X,Y,Z} |
Dimensionless spin vector components at the relaxation time. |
| Ecc |
Eccentricity estimated by fitting $d\omega_{orb}/dt$ for 2.5 orbits after
the relaxation time. |
| Mωorb |
Orbital frequency multiplied by the total Christodoulou mass at the
relaxation time. |
| Orbits |
Number of orbits from $t=0$ until the region inside the common horizon is
excised. |
| Email |
Link to e-mail the SXS Collaboration about a particular simulation. |
Columns that can be added by the dropdown menu are described in the Metadata file.
File Descriptions
rhOverM_Asymptotic_GeometricUnits.h5, rMPsi4_Asymptotic_GeometricUnits.h5
These two files contain spin-weighted spherical-harmonic coefficients for the
gravitational radiation extrapolated to infinite radius, as described in
arXiv:0905.3177 and
arXiv:1302.2919. The coefficients are
given as functions of extrapolated proper time. All quantities have been rescaled to
units in which the total Christodoulou mass is 1, where the mass of each black hole is
measured at the relaxation time as reported in metadata.txt.
Various extrapolation orders are provided. The optimal choice depends on the
application. For example, the extrapolation with order $N=4$ is usually most useful for
data from early in the inspiral; during merger very little extrapolation is needed, so
$N=4$ becomes noisy. Convergence tests are generally the best way to decide which
extrapolation order to use.
For each extrapolation order, the datasets are contained in an h5-group labeled
"Extrapolated_Nx.dir", where "x" is the order of the extrapolating polynomial used.
There is also an h5-group labeled "OutermostExtraction.dir", for which no extrapolation
was done, though all relevant rescalings were applied. The following datasets are
provided in each group:
| Dataset |
Columns |
Description |
| Y_l[L]_m[M].dat |
$(t/M_{\text{Ch}}, \Re[R_{\text{areal}}Q_{\ell m}],
\Im[R_{\text{areal}}Q_{\ell m}])$ |
$Q_{\ell m}$ is the expansion coefficient in the spin-weight $s=-2$
spherical-harmonic decomposition of the gravitational-wave strain
($h/M_{\text{Ch}}$) or Penrose scalar ($M_{\text{Ch}}\Psi_4$). |
rhOverM_Asymptotic_GeometricUnits_CoM.h5, rMPsi4_Asymptotic_GeometricUnits_CoM.h5
These two files contain the same spin-weighted spherical-harmonic coefficients for the
gravitational radiation extrapolated to infinite radius as the files above, except that
they have been adjusted to correct the systems' center-of-mass motion, following the
method described in
arxiv:1509.00862. Briefly, each system
is given a translation and boost to minimize the average of the squared distance between
the origin and the system's center of mass. The center of mass is measured naively,
using the Newtonian formula along with the coordinate trajectories of the apparent
horizons. This average is taken over a range of times $(t_i, t_f)$, where $t_i$ is
fixed here as the relaxation time reported in metadata.txt, and $t_f$ represents 90% of
the total inspiral time during which the separate apparent horizons could be found.
The groups and datasets in these files are exactly the same as in the corresponding
files above; the only difference is the addition of the "_CoM" suffix in the file names.
rh_FiniteRadii_CodeUnits.h5, rPsi4_FiniteRadii_CodeUnits.h5
NOTE: These files contain
raw output from SpEC simulations, which have dimensions
that are related to the total mass of the corresponding SpEC simulation ("code units").
You should prefer data from the files labeled with "GeometricUnits_CoM" unless you need
the raw output and are familiar with all the caveats of SpEC.
These two files contain spin-weighted spherical harmonic coefficients for the
gravitational radiation (and related quantities) extracted at various finite radii as a
function of coordinate time $t$ in code units (
not retarded time). For a
specific extraction radius, the datasets are contained in an h5-group labeled
"Rxxxx.dir", where "xxxx" is the coordinate radius rounded to the nearest integer. The
following datasets are provided:
| Dataset |
Columns |
Description |
| ArealRadius.dat |
$(t, R_{\text{areal}})$ |
$R_{\text{areal}}$ is the radius computed from the proper area of the
extraction sphere. |
| AverageLapse.dat |
$(t, \bar{N})$ |
$\bar{N}$ is the angular average of the lapse function across the extraction
sphere. It is computed from the (L,M)=(0,0) mode of a scalar spherical
harmonic decomposition of the lapse function on the extraction sphere. |
| CoordRadius.dat |
$(t, R_{\text{coord}})$ |
$R_{\text{coord}}$ is the exact coordinate radius of the extraction sphere. |
| Y_l[L]_m[M].dat |
$(t, \Re[R_{\text{coord}}Q_{\ell m}], \Im[R_{\text{coord}}Q_{\ell m}])$ |
$Q_{\ell m}$ is the expansion coefficient in the spin-weight $s=-2$
spherical harmonic decomposition of the gravitational wave strain ($h$) or
Penrose scalar ($\Psi_4$). |
Horizons.h5
NOTE: This file contains raw output from SpEC simulations. Coordinates $t,x,y,z$ and
dimensionful quantities in this file are in "code units", which are related to the total
mass of the corresponding SpEC simulation. We use geometrized units, where $G=c=1$.
This HDF5 file contains information about the black holes' apparent horizons as a
function of coordinate time $t$ in code units (
not
retarded time). We call the individual apparent horizons AhA and AhB, and we call the
common apparent horizon AhC. Horizons.h5 contains one h5-group for each apparent
horizon: AhA.dir, AhB.dir, and AhC.dir.
The following datasets are provided:
| Dataset |
Columns |
Description |
| CoordCenterInertial.dat |
$(t, x,y,z)$ |
$x$,$y$,$z$ are the Cartesian coordinates of the center of the apparent
horizon, in the "inertial frame," the asymptotically inertial frame in which the
gravitational waves are measured. |
| ArealMass.dat |
$(t, M_{\text{irr}})$ |
$M_{\text{irr}}$ is the areal (irreducible) mass $\sqrt{A/16\pi}$, where $A$
is the horizon surface area. |
| DimensionfulInertialSpin.dat |
$(t, S_x, S_y, S_z)$ |
$S_i$ are the Cartesian vector components of the spin angular momentum
measured on the apparent horizon in the "inertial frame". The spin is measured
using approximate rotational Killing vectors (see Appendix A in
arXiv:0805.4192 for details of the
method used to measure the spin). |
| DimensionfulInertialSpinMag.dat |
$(t, S)$ |
$S$ is the Euclidean magnitude of the black-hole spin angular momentum given
in DimensionfulInertialSpin.dat, $S^2=S_x^2+S_y^2+S_z^2$. |
| ChristodoulouMass.dat |
$(t, M)$ |
Christodoulou mass $M$, where $M^2 = M_{\text{irr}}^2 +
S^2/4{M_{\text{irr}}^2}$ and $S$ is the magnitude of the spin angular
momentum of the black hole (as given in DimensionfulInertialSpinMag.dat). |
| chiInertial.dat |
$(t, \chi_x, \chi_y, \chi_z)$ |
$\chi_i = S_i/ M^2$, i.e., the Cartesian components of the spin angular
momentum measured in the "inertial frame", made dimensionless by dividing by the
square of the Christodoulou mass. |
| chiMagInertial.dat |
$(t, \chi)$ |
$\chi$ is the Euclidean magnitude of the dimensionless spin angular momentum
measured on the apparent horizon, $\chi^2 = \chi_x^2+\chi_y^2+\chi_z^2$. |
HorizonsDump.h5
Some simulations contain HorizonsDump.h5. This HDF5 file contains datasets describing
the apparent horizon surfaces and quantities measured on those surfaces, which (e.g.)
can be converted to VTK format for visualization.
HorizonsDump.h5 contains one h5-group for each apparent horizon: AhA.dir, AhB.dir, and
AhC.dir. The following datasets are provided:
| Dataset |
Description |
| CoordsMeasurementFrame.tdm |
Inertial Cartesian coordinates of the apparent horizon surface. |
| RicciScalar.tdm |
The dimensionful Ricci scalar on the hypersurface, given by Eq. B3 in
arXiv:0805.4192. |
| DimlessRicciScalar.tdm |
RicciScalar.tdm scaled by the Christodoulou mass, $M_{Ch}^2R$ |
| SpinFunction.tdm |
Curl of the angular momentum density. |
| WeylB_NN.tdm |
Magnetic Weyl tensor normal to the hypersurface, $B_{ij}n^in^j$. This
quantity is known as the horizon vorticity. It should be negative at the
north pole of a spinning black hole using the current conventions on
$B_{ij}$, which are given by (2.2b) in
arXiv:1108.5486. The horizon
vorticity was first introduced in
arXiv:1012.4869, and the physical
interpretation of the vorticity can be found in the cited texts. See also
arXiv:1208.3034 for its
connection to measures of the angular momentum of the horizon. NOTE: The
sign convention used for this quantity was switched in SpEC revision
08ac47f4 (Feb. 8, 2016), so all earlier catalog entries will differ by an
overall minus sign. |
| WeylE_NN.tdm |
Electric Weyl tensor normal to the hypersurface, $E_{ij}n^in^j$. This
quantity is known as the horizon tendicity, and describes tidal stretching
(negative values of WeylE_NN) and compression (positive values) normal to
the horizon. It was introduced in
arXiv:1012.4869. Our conventions
on $E_{ij}$ are given in
arXiv:1108.5486, and note that it
should be negative at the horizon of a Schwarzschild black hole. See also
arXiv:1208.3034
for its connection to the Ricci curvature of the horizon.
|
EvID
Files in the EvID directory contain initial data in a format that SpEC can evolve,
including the initial spatial metric, extrinsic curvature, lapse, and shift.
Astronomers should not need to look at these files, as the relevant initial data
parameters (masses, spins, and orbital parameters) are also included in the metadata.
The following files are provided:
| File |
Description |
| ID_Ah{A,B}Coefs.dat |
Coefficients characterizing the spectral expansion of the horizon surfaces. |
| ID_Init_FuncLambdaFactor{A,B,A0,B0}.txt |
Initial deformations of the spatial coordinates to conform to the black-hole
shapes. These files also include initial velocities of the excision surfaces,
which are sometimes nonzero in order to avoid incoming characteristic fields at
the beginning of the evolution. |
| Domain.input and SpatialCoordMap.input |
Specify the initial spatial computational domain. |
| Vars*.h5 |
HDF5 files containing the initial spatial metric $g$, extrinsic curvature
$K$, lapse $N$, and shift $\beta_i$. |