ВАК 1.3.4 Радиофизика
ВАК 1.6.9 Геофизика
УДК 523-1/-8 Свойства, процессы и т.п.
УДК 52-423 Гравитационные взаимодействия
УДК 52 Астрономия. Геодезия
УДК 53 Физика
УДК 520 Инструменты, приборы и методы астрономических наблюдений, измерений и анализа
УДК 521 Теоретическая астрономия. Небесная механика. Фундаментальная астрономия. Теория динамической и позиционной астрономии
УДК 523 Солнечная система
УДК 524 Звезды и звездные системы. Вселенная Солнце и Солнечная система
УДК 52-1 Метод изучения
УДК 52-6 Излучение и связанные с ним процессы
ГРНТИ 37.00 ГЕОФИЗИКА
ГРНТИ 41.19 Солнечная система
ГРНТИ 41.00 АСТРОНОМИЯ
ГРНТИ 29.35 Радиофизика. Физические основы электроники
ГРНТИ 29.31 Оптика
ГРНТИ 29.33 Лазерная физика
ГРНТИ 29.27 Физика плазмы
ГРНТИ 29.05 Физика элементарных частиц. Теория полей. Физика высоких энергий
ОКСО 03.03.03 Радиофизика
ОКСО 03.05.01 Астрономия
ОКСО 03.06.01 Физика и астрономия
ББК 223 Физика
ББК 2 ЕСТЕСТВЕННЫЕ НАУКИ
ТБК 6144 Солнечная система
ТБК 614 Астрономия
ТБК 6135 Оптика
BISAC SCI004000 Astronomy
BISAC SCI033000 Gravity
BISAC SCI032000 Physics / Geophysics
BISAC SCI005000 Physics / Astrophysics
Using an eigenvector and signal component analyzer (eigenoscope), the problem of identifying the impact of gravitational waves of relativistic binary star systems (RBSS) with large and small eccentricity on the vertical component of the electric field strength ($E_\text{z}$) in the Earth's atmospheric surface layer in the infra-low frequency (ILF) range at high harmonics of the EDS circulation frequencies has been solved. The results were obtained using monitoring data at four spatially separated $E_\text{z}$ observation stations. A model is proposed to explain the effect of the gravitational wave influence of relativistic binary star systems on the vertical component of the Earth's electric field strength in the surface layer of the atmosphere, previously discovered by the authors. The model considers as the mechanism the disturbance of the Earth's orbit by gravitational waves from relativistic binary star systems, leading to small displacements of the Earth relative to the free space charge in the troposphere. The estimates of the amplitude of the $E_\text{z}$ components, spectrally localized at the frequencies of gravitational waves of relativistic binary star systems, obtained on the basis of the presented model do not contradict the experimental results.
gravitation; gravitational waves; Earth; (stars:) binaries: general; relativistic processes; atmospheric effects; methods: statistical
Susceptibility of electromagnetic fields in the Solar System to gravitational wave effects from relativistic binary star systems
L. Grunskaya1 , V. Isakevich2 , and D. Isakevich2
1
2
Vladimir State University, Vladimir, 600000, Russia
Eigenvector LLC, 50 Gorkogo St, Vladimir 600005, Russia
Abstract. Using an analyzer of eigenvectors and signal components (eigenoscope), the problem of identifying the impact of gravitational waves of relativistic binary star
systems (RDSS) with high and low eccentricity on the vertical component of the electric field strength (Ez ) in the ground layer of the Earth’s atmosphere in the infra-low
frequency (ILF) range is solved high harmonics of the EDS circulation frequencies. The results were obtained using monitoring data at four spatially separated Ez observation stations. A model is proposed to explain the effect of the gravitational wave influence of relativistic binary star systems on the vertical component of the Earth’s electric field strength in the surface layer of the atmosphere, previously discovered by the authors. The model considers as a mechanism the disturbance of the Earth’s orbit by gravitational waves from relativistic binary star systems, leading to small displacements of the Earth relative to the free space charge in the troposphere. The estimates of the amplitude of the Ez components, spectrally localized at the frequencies of gravitational waves of relativistic binary star systems, obtained on the basis of the presented model do not contradict the experimental results.
Keywords: relativistic binary star systems; Earth’s atmosphere; eigenvectors
DOI: 10.26119/VAK2024-ZZZZ
SAO RAS, Nizhny Arkhyz, Russia 2024
https://vak2024.ru/1
Introduction
Using an analyzer of eigenvectors and signal components (eigenoscope), the problem of identifying the impact of gravitational waves of relativistic binary star systems
(RDSS) with high and low eccentricity on the vertical component of the electric field strength (Ez ) in the ground layer of the Earth’s atmosphere in the infra-low
frequency (ILF) range is solved high harmonics of the EDS circulation frequencies.
2
Observation
The results were obtained using monitoring data at four spatially separated Ez observation stations (three Rosgidromet stations at Voeikovo, Verkhnee Dubrovo, Dusheti
and the Vladimir state university General and Applied Physics Dept. experimental base). All these time series have the same sampling time equal to 3600 sec; some
data about the series is presented in Table 1.
Table 1. The used time series of Ez observations
No. Observation station
1
2
3
4
Total sample count Duration, Duration, Duration,
days
months years
Voeikovo
170000
7083
236
20
Dusheti
120000
5000
167
14
Verkhnee Dubrovo
120000
5000
167
14
VlSU experimental base 36000
1500
50
4
Six RBSS from the Johnston’s list (see second column of the Table 2) which have high eccentricity (0.58–0.89) have been selected while forming sample of the eigenvectors which are spectrally localized at the gravitational waves frequencies according to (6).
Table 2. The selected high-eccentricity relativistic binaries (e is eccentricity, n are the orders of multiples).
No.
RB
T , days
e
n Frequency range, μHz
1 J0514-4002A 18.785
0.889 1–90 0.6161338 . . . 55.452045
2 J1811-1736 18.77917 0.82802 1–90 0.6163251 . . . 55.46926
3 J1823-1115 357.7620 0.79461 20–70 0.6470265 . . . 2.2645926
4
J1750-37
17.3
0.71
1–36 0.6690216 . . . 24.084778
5 J2305+4707 12.3395445 0.65837 1–25 0.9379661 . . . 23.449152
6 J1740-3052 231.02965 0.578872 10–16 0.5009779 ∗ . . . 0.8015646Susceptibility of electromagnetic fields
3
Forty three RBSS which have low eccentricity have been selected from the John-
ston’s list. Theirs’ doubled orbital frequences have been calculated.
3Analysis
3.1Theoretical premises
The classical work Zeldovitch et al. (1975) shows that energy irradiated by the RBSS
gravitational waves at the multiplied orbital frequency energy is proportional to
g(n, e) =
n4
[g1 (n, e) + g2 (n, e) + g3 (n, e)],
32
(1)
where
g1 (n, e) = [Jn−2 (ne) − 2eJn−1 (ne) +
2
Jn (ne)+
n
+ 2eJn+1 (ne) − Jn+2 (ne)]2 , (2)
g2 (n, e) =
= (1 − e2 )[Jn−2 (ne) − 2Jn (ne) + Jn+2 (ne)]2 , (3)
4
[Jn (ne)]2 ,
(4)
2
3n
n is order of the multiplied frequency; e is the eccentricity; Jn (x) is Bessel function.
Use of (1) allows to compute the ratio
g3 (n, e) =
GR.2 (n, e) =
g(n, e)
,
g(2, e)
(5)
which may be used for prospective RBSS selection which have GW irradiation at the
multiple frequencies higher than of second order. The Johnston’s list contains much
high-eccentricity RBSS. Those of them which have the ratio (5) higher than 1 and
the multiple frequencies corresponding to condition
5T < (nk,j Fj )−1 < MT , j = 1 : Q,
(6)
where T is a sampling time (equals to 3600 sec in our work); nk,j is the allowable
order of the multiplied (of order k) orbital frequency of j-th RBSS; Fj , j = 1 : Q are
the RBSS orbital frequencies; Q is the high-eccentricity RBSS count (6 in our work);4
Grunskaya et al.
MT is analysis span of the eigenoscope (1000 hours in the current work), has been
selected.
Ratio (5) obviously corresponds to a condition
g(n, e)
=0
e→0,n6=2 g(2, e)
lim
(7)
therefore the small-eccentricity RBSS irradiate GW at the doubled orbital frequency
only.
The ranges of GW irradiation frequencies for high-eccentricity RBSS indices are
shown in Table 2, column 5.
3.2
Analyzer construction
A satisfying analyzer design (called eigenoscope (Isakevich et al. 2011, 2017)) does
use representation of the observation time series at the finite analysis span and
decompose observations to non-correlated components. It allows spectrally localized
components identification and analysis of individual behavior of the non-correlated
components. It uses simple, sensible and widely known component identification and
decision making criteria.
Eigenoscope is an analyzer which use signal representation at the covariance
matrix eigenvectors orthonormal basis; the covariance matrix is computed for an
ensemble consisting of the signal pieces (duration of each piece is 1000 hours). The
signal analysis take place in the basis which is not given apriori but adapted for the
specific covariance matrix. Eigenoscope decomposes signal to non-correlated compo-
nents which have the same shape since the covariance matrix eigenvectors and the
eigennumbers are equal to a mean component capacity in the ensemble. Therefore in-
dividual properties of the signal non-correlated components at a finite analysis span
are freely exposed while we analyze the signal using eigenoscopy.
The ensemble for the current task is formed as a trajectory matrix which consists
of all the signal pieces of the predefined length.
Eigenpairs has been computed for each covariance matrix. Each eigenpair con-
sists of an eigenvector and a corresponding eigennumber. An amplitude spectrum
has been computed for each of the eigenvectors; this spectrum has been normalized
to its maximal value in order to estimate the eigenvector spectral localization band.
The frequency band of spectral localization
is estimated as a band in which the
√
normed amplitude spectrum exceeds 1/ 2. We suppose that an eigenvector is spec-
trally localized at some frequency if this frequency lays in the eigenvector’s spectral
localization band.Susceptibility of electromagnetic fields
5
Indices of the eigenvectors which are spectrally localized near the RBSS irradia-
tion frequencies are listed separately. A coherence ratio which is a ratio of the maxi-
mum amplitude value to the mean amplitude in the eigenvector amplitude spectrum
has been used to estimate spectral localization of each eigenvector.
Set of coherence ratios of the eigenvectors which are spectrally localized near the
gravitational waves frequencies and sample of eigennumbers (which are the mean
square values of the non-correlated components) which correspond to these eigen-
vectors are formed. Test sets of the coherence ratios and of the eigennumbers are
formed for further comparison. A statistical decision is made concerning abnormal
behavior of non-correlated components of Ez which are spectrally localized at the
RBSS gravitational waves frequencies.
Decision for the components which are localized at the GW frequencies of low-
eccentricity RBSS is made using the Bernoulli test scheme. Smirnov-Kolmogorov
criterion is used for the high-eccentricity GW irradiation frequencies.
4
Estimations of influence
Probability of the case that the samples belong to random variables having the same
distribution law is estimated using Smirnov-Kolmogorov criterion. Probability esti-
mation for coherence ratios for each of the time series is less than 10−7 ; estimation for
the normed eigennumbers is less than 7 · 10−8 for each time series. The difference be-
tween the sets of eigenpairs is significant and is extremely unlikely to be occasional.
It means that at all the observation stations the coherence ratios and eigenvalues
have different distribution laws for the eigenvectors spectrally localized at gravita-
tional waves frequencies and for the eigenvectors spectrally localized at test samples
frequencies. So, until proven otherwise it must be assumed that the differences are
due to factors that distinguish the compared samples, i.e to the gravitational-wave
impact of RBSS on Ez Grunskaya et al. (2023,?).
Median value have been estimated for all the eigennumbers and all coherence
ratios for each of the time series. The estimations are exceeded by the eigennumbers
and coherence ratios for the eigenvectors which are spectrally localized at each of
the forty three RBSS doubled rotation frequencies. Estimations of the Bernoulli test
false alarm probability are less than 10−9 Grunskaya et al. (2014).
5
Summary
Using eigenoscopy (analysis of a time series in the basis of eigenvectors of their covari-
ance matrix at a finite analysis span) made it possible to reveal the non-correlated6
Grunskaya et al.
components spectrally localized at the gravitational irradiation frequencies of the
known relativistic binary star systems; these components have been revealed in the
Earth electric field vertical projection at the infra-low frequency range. Coherence
ratios of these components differ from those of the components spectrally localized
at the other frequencies; the difference is statistically significant. The same effect is
observed for the components amplitudes. The revealed components are not observ-
able using classic spectral analysis; they are mixed with the other components in the
analysis channel and are perceived as a noise.
A model is proposed to explain the effect of the gravitational wave influence of
relativistic binary star systems on the vertical component of the Earth’s electric field
strength in the surface layer of the atmosphere, previously discovered by the authors.
The model considers as a mechanism the disturbance of the Earth’s orbit by gravita-
tional waves from relativistic binary star systems, leading to small displacements of
the Earth relative to the free space charge in the troposphere. The estimates of the
amplitude of the Ez components, spectrally localized at the frequencies of gravita-
tional waves of relativistic binary star systems, obtained on the basis of the presented
model do not contradict the experimental results.
Acknowledgements. The results of this work are based on the observation data
of the Earth electric field donated by Y. M. Schwartz (Voeikovo, Verkhnee Dubrovo,
Dusheti stations); on the data recorded at the experimental ground of Department of
General and Applied Physics of Vladimir State University (lead by L. V. Grunskaya);
on the RBSS list published by Johnston at his site and on the innovative processing
methods (called eigenoscopy).
Funding
This work is not supported by any grants.
References
Y. B. Zel’dovitch and I. D. Novikov, 1975 The structure and evolution of Universe.
V. V. Isakevich, D. V. Isakevich, L. V. Grunskaya, 2011 The signal eigenvectors’ and components’
analyser (Utility model RU116242U1).
V. V. Isakevich, D. V.Isakevich, 2017 Signal eigenvectors’ and components’ spectrum analyzer (Util-
ity model RU178399U1).
L. V. Grunskaya, V. V. Isakevich, D. V. Isakevich, 2023 Grav. Cosmol., No. 3, p. 54.
L. V. Grunskaya, V. V. Isakevich, D. V. Isakevich, L. T. Sushkova, 2014 Space, Time and Funda-
mental Interactions, v. 2, p. 54.
L. V. Grunskaya, V. V. Isakevich, D. V. Isakevich, L. T. Sushkova, 2013 Space, Time and Funda-
mental Interactions, v. 3–4, p. 117.
1. Grunskaya L., Isakevich V., Isakevich D., 2023, Gravitation and Cosmology, 29, 3, p. 283
2. Grunskaya L., Isakevich V., Isakevich D., et al., 2014, Space, Time and Fundamental Interactions, 2, p. 54
3. Grunskaya L., Isakevich V., Isakevich D., et al., 2013, Space, Time and Fundamental Interactions, 3-4, p. 117
4. Isakevich V., Isakevich D., Grunskaya L., 2011, The signal eigenvectors' and components' analyser, RU116242U1, 20.05.2012
5. Isakevich V. and Isakevich D., 2017, Signal eigenvectors' and components' spectrum analyzer, RU178399U1, 03.04.2018
6. Zel'dovich Y. and Novikov I., 1975, The Structure and Evolution of the Universe, Moscow, Nauka
