GRB051103 LIGO data release

Data properties

As a simple check for any data corruption in your download, you are advised to take a look at the scripts plot_data.py and plot_data.m, modify them if needed to point to the data you've downloaded, and compare the output with what is posted here.

Printout from plot_data.py:

Contents of H2-STRAIN_4096Hz-815045078-256.hdf5
IFO, Npoints = H2, 1048576
Duration = 1.0 * 4096 * 256
min,max,mean,std = -1.83198e-17, 1.83661e-17, 8.40797613955e-23, 4.00000168617e-18

Contents of H2-STRAIN_16384Hz-815043278-2190.hdf5
IFO, Npoints = H2, 35880960
Duration = 1.0 * 16384 * 2190
min,max,mean,std = -7.1032527817e-16, 6.93651633689e-16, -1.80783501127e-21, 1.52450665622e-16

Contents of L1-STRAIN_4096Hz-815045078-256.hdf5
IFO, Npoints = L1, 1048576
Duration = 1.0 * 4096 * 256
min,max,mean,std = -2.5425e-18, 2.53164e-18, -1.86235564404e-25, 5.01073506755e-19

Contents of L1-STRAIN_16384Hz-815043278-2190.hdf5
IFO, Npoints = L1, 35880960
Duration = 1.0 * 16384 * 2190
min,max,mean,std = -1.23971151496e-16, 1.2349742552e-16, 9.44711599361e-23, 2.47410881493e-17

Data time series

Time series for the first ~10000 points in the files; made by plot_data.py:
Time series H2 Time series L1

Data histograms

Histogram of data points, compared with Gaussian.
Comments: These histograms are dominated by the low frequency (~<30 Hz) peaks that are evident in the ASDs (below). The data are only calibrated above 40 Hz. LIGO detector operations and data processing endeavor to achieve "in-band" strain noise (between 40 Hz and 2000 Hz) as stationary and Gaussian as possible.

Data from H2-STRAIN_4096Hz-815045078-256.hdf5 and L1-STRAIN_4096Hz-815045078-256.hdf5:
4096Hz Histogram H2 4096Hz Histogram L1

Data from H2-STRAIN_16384Hz-815043278-2190.hdf5 and L1-STRAIN_16384Hz-815043278-2190.hdf5:
16384Hz Histogram H2 16384Hz Histogram L1

ASDs

Noise amplitude spectral densities (noise ASDs) from H2-STRAIN_4096Hz-815045078-256.hdf5 and L1-STRAIN_4096Hz-815045078-256.hdf5, compared with the ones stored in H2-SPEC-815043278-2190.hdf5 and L1-SPEC-815043278-2190.hdf5, made by plot_data.py.
Comment: The data are only calibrated in the sensitive band between 40 Hz and 2000 Hz. The most prominent spectral lines are at harmonics of the power main 60 Hz, the mirror suspension violin modes at 340 Hz, or calibration lines. The difference between the spectrum in the (256 s @ 4096 Hz) data and the (2190 s @ 16384 Hz) data at mid-frequencies are indicative of the non-stationarity of the detector over the 2190 s. The difference starting at ~2000 Hz is due to the different sampling rate. ASD H2 ASD L1

Spectrograms

Spectrograms from H2-STRAIN_4096Hz-815045078-256.hdf5 and L1-STRAIN_4096Hz-815045078-256.hdf5,
made by plot_data.py:
Comment: One can see the spectral features evident in the ASDs above, running across the plot in time. There are no prominent short-duration periods of enhanced noise evident in these spectrograms (above 40 Hz); it's a relatively quiet period of detector operation. Periods of enhanced noise are present, but they're hard to see in these plots; they can be seen in omegagrams. LIGO detector operations and data processing endeavor to achieve "in-band" strain noise (between 40 Hz and 2000 Hz) as stationary and Gaussian as possible.
Spectrogram H2 Spectrogram L1

ASD comparison

As an illustration of how to interpret the noise amplitude spectral densities, we plot the ASDs from several places:

The Initial LIGO Science Requirements Document (iLIGO SRD), from LIGO Document E950018, and here.
The Advanced LIGO high-power, zero-detuned noise model, from LIGO Document T0900288.
The Enhanced LIGO (S6) representative (mode) noise spectrum from H1, starting at 40 Hz, from LIGO Document T1100338.
The noise spectra from H2 and L1 around GRB051103, from H2-SPEC-815043278-2190.hdf5 and L1-SPEC-815043278-2190.hdf5, respectively.

We also overlay the signal from a binary neutron star (BNS) inspiral at 3.6 Mpc from GRB051103 (with antenna factor 0.49; see below), plotted in the same units as the ASDs. The waveform is plotted up to the nominal end of the inspiral phase (innermost stable circular orbit, or ISCO), which is where the waveform templates used in the Compact Binary Coalescence search end.

This plot is made with the script asd_ranges.py.
ASD ranges

Sensitive distances

At these noise levels, an binary neutron star (BNS) inspiral signal (averaged over sky location and orientation) is expected to give a matched-filter signal-to-noise ratio (SNR) of 8 at distances of 3.6 and 8.0 Mpc in H2 and L1, respectively. This is one of our most useful measures of detector sensitivity.

Antenna factors: The response of a detector to a BNS signal depends not only on its noise spectrum, but also its quadrupole antenna response factor, which in turn depends on the source's sky location and the binary orientation with respect to our line-of-sight. The detection sensitivity is reduced by a factor 0.442 when one averages over source sky location and orientation. In this case, we are considering our sensitivity to a population of sources which we assume to be distributed uniformly in our sensitive volume; so we compute the average of the sensitive distance cubed, then take the cube root.

However, we know the sky location (and time) of GRB051103, so we can compute antenna factors associated with that source. If we assume that the binary is optimally oriented (the orbit is face-on, as one might expect for a beamed GRB), the antenna factors are 0.726 for H2, and 0.657 for L1. If instead we averaged over binary orientation (inclination angle and polarization azimuth) the antenna factors are 0.431 for H2, and 0.389 for L1. In this case we are averaging the sensitive distance, not the sensitive distance cubed.

See the publication describing the analysis (arXiv) as well as this page for more details.

The table below lists, for the noise spectra around GRB051103 ("H2 SPEC" and "L1 SPEC"), four distances:

D_hor = "inspiral horizon distance": the distance in Mpc at which an optimally located and oriented BNS inspiral signal would be observed in that detector with expected SNR = 8;
D_avg = "inspiral average distance": the distance in Mpc at which an BNS inspiral signal, averaged over location and orientation, would be observed in that detector with expected SNR = 8 (D_avg = D_hor * 0.442) ;
D_Gopt = "inspiral distance for GRB051103, optimally oriented": the distance in Mpc at which an BNS inspiral signal, at the sky location and time of GRB051103, optimally oriented (face on, as expected for a beamed GRB) would be observed in that detector with expected SNR = 8. (D_Gopt = D_hor * 0.726 for H2, and D_hor * 0.657 for L1) .
D_Gavg = "inspiral distance for GRB051103, average over orientation": the distance in Mpc at which an BNS inspiral signal, at the sky location and time of GRB051103, and (median) averaged over orientation (inclination angle and polarization azimuth) would be observed in that detector with expected SNR = 8. (D_Gavg = D_hor * 0.431 for H2, and D_hor * 0.389 for L1) .

Detector	D_hor	D_avg	D_Gopt	D_Gavg
iLIGO SRD	31.2	13.8
aLIGO HP 0-detune	445.1	196.9
S6 H1	40.7	18.0
H2 SPEC	8.1	3.6	5.9	3.5
L1 SPEC	18.0	8.0	11.8	7.0

Since M81 is at ~3.6 Mpc, we see that both H2 and L1 would have BNS signals with SNR of ~8 (or in the case of L1, much larger), making them much louder than the detector noise and easily detectable.