4.2 Identification and characterization of spectral lines
4.2.1 Finding spectral lines in the data
Stochmon is a tool developed by Thomas Callister that monitors certain diagnostic statistics relevant to the cross-correlation GW searches described in chapter 2. It gen- erally operates with a lag time of O(1 hour). Stochmon produces an estimate of the sensitivity of the isotropic search as a function time, an estimate of the contribution of correlated magnetic noise to GW searches, and the modulus of the coherence spectrum of the two LIGO interferometers, defined in equation (3.3). It is this last feature that is commonly used for detector characterization. We identify lines that are coherent between the interferometers using the method described in section 3.2.4. We construct a histogram of the coherence spectrum and compare that histogram to what one would expect for a coherence spectrum generated from Gaussian noise. This was shown in fig- ure 3.6. Any frequency bins found as outliers from that histogram require follow-up to see if they are caused by a known detector issue or if they could potentially be caused by GWs. This follow-up is often performed using STAMP-PEM or the coherence tool, which are discussed in section 4.2.2.
The comb seen with 1 Hz spacing and 0.5 Hz offset from the integer that was discussed in section 3.2 (colloquially referred to as the “0.5 Hz comb”) was observed first in stochmon coherences and FScans (discussed below) and eventually the source of this comb was found to be blinking LEDs on timing chips [51].
Time shifts of SGWB searches
As described in section 3.2.2, we often perform our cross-correlation searches with an unphysical time shift in an attempt to identify detector-related issues. For broadband searches for a Gaussian SGWB, this method is good at blinding our searches. When we use the data for individual frequency bins to try to detect signals from sources like rotating pulsars or to try to identify spectral artifacts, we must be careful because an unphysical time-shift will not remove correlations due to GWs. It will change the relative phase between the detectors (making it appear as though the signal is coming
from a different direction), but it does not remove the signal from the data. Therefore, we cannot simply notch narrow frequency bins that have excess cross-correlation just because they are outliers in a time-shifted search. We must treat them the same way we do lines we find from stochmon: we need compelling evidence that this noise is not caused by GWs.
Most of the lines marked “unknown” in appendix A were identified as issues for the O1 SGWB searches due to time shifted runs. We followed up on these lines with a combination of the coherence tool, STAMP-PEM, and FScans; all of which are discussed below.
Comb finder
Many stochastic searches integrate over frequency. While we need to remove obvious excess coherence, there are also cases where an integration over sub-threshold combs yield a broadband excess in coherence. By this we mean that there is not an obvious single frequency exceeding the typical levels of noise, but there is a set of frequencies with a specific spacing that, when summed together, gives something larger than expected if the same number of frequency bins were chosen from random noise and summed. To deal with this we developed a “comb-finder” which sums power over many possible tooth-spacings and offsets and checks whether that sum is larger than expected.
For a time-shifted isotropic SGWB search, we calculate the signal-to-noise-ratio (SNR) from the cross-correlation bin-by-bin estimator ˆY (fi) and the associated uncer-
tainty σY(fi), defined in equation (2.37), for a variety of different potential combs. We
then combine these bins using a weighted sum (the same weighted sum as in equa- tion (2.38) except over frequency bins instead of time segments). For a comb with N teeth, the combined statistic becomes
ˆ YcombN = PN i Yˆiσ−2Yi PN i σY−2i (4.1) σYNcomb = " N X i σY−2 i #−1/2 . (4.2)
We parameterize a specific comb by the offset of the first bin from the start of the search band and the frequency spacing between the teeth of the comb. The offset number of bins m and spacing n determine which frequency bins contribute to the comb in question. For a search over a given frequency band ∆f = fmax− fmin, with a
frequency resolution of df , the number of teeth in a comb with bin spacing n will be given by N = 1 + floorh∆fn i. We then define the combined SNR statistic using our optimal combination method
Sm,n = ˆ Ycomb(m,n) σY(m,n) comb = PN i Y (fˆ m+ni)σY−2(fm+ni) h PN i σY−2(fm+ni) i1/2 . (4.3)
Figure 4.1 shows an example output of the comb-finder tool demonstrating the 0.5 Hz comb found during O1. Excess SNR is visible at regular 1 Hz spacings and offsets of 0.5 Hz.
This tool also identified an 8 Hz comb in the observing run 2 (O2) time shifted SGWB results, which was eventually identified as a detector artifact using the coherence tool. FScans and FineTooth
FScans and FineTooth are tools that are used to identify narrow lines in the strain spectrum of the individual interferometers, as well as auxiliary channels. They are maintained by researches at the University of Michigan. FScans generates 1800 s am- plitude spectral densities for the strain channel and many auxiliary channels. The long-duration spectra allow for very narrow frequency resolution, which is often neces- sary when performing very sensitive searches for known rapidly rotating neutron stars. FineTooth then sorts and searches through the spectra produced by FScans to identify combs that are evident in the spectra and track the amplitude of those combs over time. It can be used to identify new combs, potentially introduced by changes in the inter- ferometers, as well as quantify the effect of efforts made by commissioners to mitigate sources of those combs and lines.
For SGWB searches, we commonly use the results of FScans and FineTooth as follow up tools to identify whether coherent lines that show up in time shifted results
Figure 4.1: Example output of the comb-finder. White pixels indicate strong SNR. The loudest pixels indicate a coherent 1 Hz comb with 0.5 Hz offset identified during O1. This comb is also discussed in section 3.2
or inter-site strain channel coherences appear in just a single interferometer, both in- terferometers, or are part of an obvious comb in one of the detectors. A source of GWs would be expected to have a measurable amplitude in both detectors and because the Earth rotates and moves relative to any prospective source of narrowband GWs, there is an expected Doppler broadening that should smear any real GW signals over multiple 1/1800 Hz frequency bins. Therefore, large lines that are seen in just a single frequency bin in one detector for spectra that have been averaged over several hundred days are very likely caused by digital noise in the detectors.
This analysis technique was very useful in removing several coherent lines identified by time shifted SGWB studies and recorded in appendix A.