Introduction The Patterns

Evidence for a Likely Lunar Role in LIGO Gravitational-Wave Detections

2017-09-04

Introduction The LIGO Scientific Collaboration and Virgo Collaboration have, up until this date, reported three confirmed Gravitational-Wave detections1,2,4 along with a candidate detection although too weak to confirm but generally discussed3. All four detections (confirmed and otherwise) will be examined in this paper. We start with the simple act of listing all for reported detections along with the date and times and shown in Table I. A cursory examination reveals multiple layers of patterns. The more these patterns are examined, the more patterns that emerge. It is some of these patterns, which will be examined here in detail. Everyone should agree that any sort of pattern should not appear in the dataset for independent and statistically random events such as Gravitational Wave generation and detection. Table I: Time and date of the GW detections reported by LIGO including the non-confirmed event (LVT151012).

LIGO Designation GW150914 LVT151012 GW151226 GW170104

Used in this paper GW1 LVT1 GW2 GW3

Date September 14, 2015 October 12, 2015 December 26, 2015 January 4, 2017

Time [UTC] 9:50:45 9:54:43 03:38:53 10:11:59

The Patterns The most obvious pattern (to this author) is the time of day the detections occurred. GW1, GW3 and LVT1 all occur within ±637 seconds (~10 minutes) of UTC 10:01:22. And though GW2 does not follow this pattern, the pattern itself is nonetheless troubling. The clustering of data around a particular time of day implies, in a way, a solar connection. And it should be pointed out that for all four detections, it is either late night or early morning with the Sun below the horizon at the time of detection. Another pattern and yet another possible solar connection is the clustering of data by seasons. GW1 and LVT1 both occurred very close to the Autumn Equinox. While GW2 and GW3 both occurred very close to Winter Solstice. There are no detections far from equinox and solstice. Not visible in Table I, but as shown in the appendix, is a lunar connection in the data. GW1 and LVT1 both happen very close in time to a New Moon. GW2 occurred close to a Full Moon and GW3 occurred close to a First Quarter Moon. New or Full Moons, which by implication are roughly in line with the Earth and the Sun are often described as near Syzygy (which means “in a line”). Syzygy produces strong tides. When the Moon is far from syzygy (First and Last Quarter Moons), the tidal forces are usually weaker6. The patterns that include solar and lunar influences implicate a Gravitational-Wave Observatory that is either insufficiently decoupled from tidal forces or a deficiency in the tidal correction system, or both. (In the context of this paper, the term tide and tidal forces generally refer to solid Earth tides.) And although this solar/lunar related pattern in the detection dataset can simply be dismissed as coincidental and anecdotal, they can no longer be dismissed once a link can be made between the Sun and/or Moon and properties of the detected signals. One such link will be established in the following section.

Copyright 2017 R. D. Scott

Evidence for a Likely Lunar Role in LIGO Gravitational-Wave Detections

2017-09-04

Two more patterns can be seen in Table 1. Detections GW2 and GW3 are almost exactly one year and nine days apart. This will be further discussed in the appendix. The value of the seconds reported in the detection times are all within ±8 seconds of 51 seconds. This pattern has not been examined more closely simply because without access to detailed LIGO system information, which is not readily available to the general public, there is not enough information to begin to analyze and comprehend this pattern. (It may be hypothesized, without any justification, this pattern may be related to the times when the feedforward tidal correction is applied to the interferometer arms5.)

Analysis There are four details that distinguish the signals of LIGO reported GW detections: time of detections; time duration of the signals; observatory order (for example, Hanford then Livingston detected the signal), and; the time delay of detection between the two observatories. As of this writing, only the time duration of the signal can be linked to either the Sun or the Moon orbits. Any further correlation between the detected signals and the Sun and the Moon remains elusive. Table II shows the longitude and latitude of the Hanford Washington and Livingston Louisiana observatories along with the longitude and latitude of a phantom observatory centrally located between the two physical observatories. Table II: Latitude and longitude of Hanford and Livingston observatory interferometer corners and the phantom point midway between the two observatories.

Livingston, Louisiana 30°33’46.42”N 90°46’27.27”W

Central Between Observatories 38°30’32.47”N 105°05’27.42”W

Hanford, Washington 46°27’18.52”N 119°24’27.56”W

We can find the sub-lunar points at the time of detections8. The sub-lunar point is the longitude and latitude of a point on the surface of the Earth where the moon is directly overhead (local zenith) at any particular time. The sub-lunar points are listed for all four detections in Table III. Table III: Latitude and longitude of the sub-lunar point at the time of reported detections. Times listed are UTC.

GW150914 9:50:45 1°10’S 42°31’E

LVT151012 9:54:43 3°55’S 22°26’E

GW151226 03:39:53 18°04’N 45°40W

GW170104 10:11:59 3°09’S 100°23’E

Finally, the time duration of the detected signals can be estimated from the graphic prepared by LIGO comparing the four signals (see figure 3). The values determined this graph are shown in Table IV. Table IV: Time duration of the detected signals scaled off the LIGO graph comparing all four events.

GW1 200 milliseconds

Copyright 2017 R. D. Scott

LVT1 520 milliseconds

GW2 1680 milliseconds

GW3 340 milliseconds

Evidence for a Likely Lunar Role in LIGO Gravitational-Wave Detections

2017-09-04

For each detection, we use the sub-lunar point and the phantom observatory central point and calculate cos(∅𝑆𝐿𝑃 − ∅𝐶𝑃 ) 𝑥 cos(𝜆𝑆𝐿𝑃 − 𝜆𝐶𝑃 ) = cos(∆∅) cos(∆𝜆) = 𝑥, where φ is latitude, λ is longitude, SLP is the sub-lunar point and CP is the center point (latitude and longitude) of the two LIGO observatories. We use this calculation to find the lunar gravity vector that is acting geocentrically on the central point of the observatories. We then plot the detected signal’s time duration versus the x value calculated above. We then find the best linear fit: 𝑡𝑠𝑖𝑔𝑛𝑎𝑙 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 = 1256.2 cos(∆∅) cos(∆𝜆) + 1083.4 [milliseconds]. Figure 1 shows a linear relationship between detected signal time duration and the moon’s sub-lunar point. The Sun is not included in this model and the lunar contribution provides a good fit to the data without a solar contribution. The clustering of the signal time duration into long and short durations is intriguing. As a follow up, we model the Moon with a random longitude and with a latitude constrained to ±23.5°. An ensemble of 10,000 random lunar positions is determined and the cos(Δφ)cos(Δλ) term (converted to duration times) calculated for each one. In figure 2 we can see a histogram of the signal duration times for one of the ensembles which clearly shows a bimodal spectrum with peaks that correspond to the signal duration times of reported detections for all ensembles. This is strong evidence that the signal time durations of detections made so far are also the most statistically probable based upon the relationship of the Moon to the observatories. 1800 y = 1256.2x + 1083.4 R² = 0.9939

Signal duration [milliseconds]

1600 1400 1200 1000 800 600 400 200 0

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

cos(Δφ)cos(Δλ) Figure 1: The phantom central point between observatories and the center point of the Earth defines a reference line. The two cosines of latitude and longitude deltas projects the lunar gravity vector onto the reference line and this in turn shows a good linear fit between this and the detected signal duration times. This seems to indicate a maximum signal duration time of about 2.35 seconds for this type of event. Finally, we see another pattern where signals are partitioned into long events (>1.5 seconds) and short events (