Radiophysics and Quantum Electronics, Vol. 57, No. 2, July, 2014 (Russian Original Vol. 57, No. 2, February, 2014)
MULTI-POINT DETECTION OF THE ELF TRANSIENT CAUSED BY THE GAMMA FLARE OF DECEMBER 27, 2004 A. P. Nickolaenko,1 A. Yu. Schekotov,2 ∗ M. Hayakawa,3,4 Y. Hobara,4 G. S´ atori,5 J. Bor,5 and M. Neska6
UDC 550.388.22+521.37
We present the experimental records of the radio pulse related to the gamma burst that took place on December 27, 2004. The records, which are synchronized by GPS time marks, were obtained in the observatories at Moshiri and Onagawa (Japan), Esrange (Sweden), Karimshino (Kamchatka, Russia), Nagycenk (Hungary), and Hornsund (Polish Polar Station Spitzbergen). The data demonstrate exceptional similarity and contain characteristic pulses that correspond to the time of gamma-ray arrival. Processing of the signals shows that along with the time match, the following modeling predictions are confirmed: radio pulses contain a signal at the main frequency of the Schumann resonance, the field source has positive polarity (the current is directed from the ionosphere towards the Earth), the polarization of the horizontal magnetic field of the radio wave is almost linear, and the directions towards the source indicate the epicenter of the gamma-quanta flux collision with the ionosphere. These properties correspond to the concept of the parametric electromagnetic pulse that is produced due to a significant change in the current in the global electric circuit, which is caused by a cosmic gamma-ray flare.
1.
INTRODUCTION
The gamma-ray flare of the SGR 1806–20 magnetar [1–7] recorded on December 27, 2004 turned to have the highest intensity in the entire history of observations of cosmic gamma rays: the recorded density of the energy flux exceeded the corresponding value in the strongest solar X-ray flares by three orders of magnitude. Gamma quanta changed radically the altitude profile of electron density in the lower ionosphere, which resulted in an abrupt variation in the amplitude and phase in trans-Pacific records of the signals emitted by superlong-wave transmitters [8] (superlong or very-low-frequency (VLF) waves occupy the band from 3 kHz to 30 kHz). Before the modification of artificial radio signals, an increase in the natural VLF noise was observed. The epicenter of the region illuminated by gamma rays was located geographically at 20.4◦ S and 146.2◦ W, only 450 km from the subsolar point, and nearly coincided with the center of the diurnal hemisphere. The beginning of a giant gamma-ray flare was recorded at 21:30:26.35 UT by the GEOTAIL satellite (see, e.g., [5]). Using the known position of the satellite, one can calculate the time of arrival of the gamma rays to the Earth’s center [9] equal to 21:30:26.65 UT. The time delay between the arrival of the flare ∗
[email protected] 1 O. Ya. Usikov
Institute for Radio-Physics and Electronics, National Academy of Sciences of Ukraine, Kharkov, Ukraine; 2 O. Yu. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia; 3 Hayakawa Institute of Seismo Electromagnetics, University of Electro-Communications, Tokyo, Japan; 4 University of Electro-Communications, Tokyo, Japan; 5 Research Centre for Astronomy and Earth Sciences, Hungarian Academy of Sciences, Sopron, Hungary; 6 Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 57, No. 2, pp. 137–153, February 2014. Original article submitted August 1, 2013; accepted December 9, 2013. c 2014 Springer Science+Business Media New York 0033-8443/14/5702-0125 125
radiation to the epicenter of the perturbation on the Earth’s surface and to the planet center is equal to 21 ms. Earlier publications [9–12] described the electromagnetic pulse found in the records made at different points of observation of the Schumann resonance which was time-related to the beginning of the gamma-ray flare. Herein, we gathered all experimental records, which are known to us and were obtained in six observatories of the world. The observation points were located as follows: the Japanese observatories Moshiri and Onagawa (44.37◦ N, 142.24◦ E and 38.43◦ N, 141.48◦ E), respectively, the observatories at Esrange in Sweden (67.83◦ N, and 21.1◦ E), Karymshino in Russia ((52.83◦ N, 158.13◦ E), Nagycenk in Hungary (47.6◦ N, 16.7◦ 16.7◦ E), and at the Polish polar station in Hornsund on Spitzbergen (77.0◦ N, 15.5◦ E). Two orthogonal horizontal components of the magnetic field were recorded in Esrange, Onagawa, and Karymshino, and the facilities in Moshiri, Nagycenk, and Hornsund recorded two horizontal magnetic components and the vertical electric field. The latter allows one to determine the polarity of the source and eliminate ambiguity of its bearing. Unfortunately, no observatory could provide simultaneous high-precision records of all three field components. The records were synchronized by means of GPS time marks, so that the maximum deviation of individual time markings did not exceed several milliseconds. The magnetic antennas of all observatories were oriented with respect to geographic cardinal directions, excluding that in Karymshino, where it was directed along the geomagnetic coordinates. Exclusively good similarity of the records obtained worldwide is demonstrated. Specifically, they contain a pair of characteristic ELF bursts recorded in the direct time vicinity of the arrival of the cosmic gamma-ray flare. The electromagnetic pulses were expected to appear as a result of pulsed modification in the current of the global electric circuit over the basin of the Pacific ocean [13–16]. Model calculations simplified the search for parametric ELF bursts indicating their following expected properties. 1) Appearance of the ELF burst is time-tagged to the moment of arrival of gamma-ray quanta. 2) The signal spectrum contains only the lowest mode of the Schumann resonance. 3) The polarity of the source should be positive (the current is directed from the ionosphere to the Earth). This means that the beginning of the pulse in the vertical component of the electric field should be negative (directed downwards). 4) The pulsed magnetic field should be linearly polarized on condition that the changes in the leak current of the global electric circuit are symmetric in space relative to the perturbation center. 5) Radio waves should arrive approximately from the perturbation center with the coordinates 20.4◦ S, ◦ 146.2 W. 6) The pulse amplitude should exceed the background signal of the Schumann resonance. In what follows, we briefly describe the receiving equipment, present the experimental records, make a note of the main features of signal processing, and compare the observation data with model predictions for the characteristic observation points and determined field components. 2.
EXPERIMENTAL DATA AND THEIR PROCESSING
The orthogonal components of the horizontal magnetic field were recorded in all observatories by means of induction magnetometers. The equipment used in each observatory was different, since it was designed and manufactured by the experimentalists independently. The detailed description of the receiving equipment can be found in [17–25]. The sensors have much in common, since all of them are designed for the purposes of studying the global electromagnetic (Schumann) resonance. Different sampling rates are used at the observation points: 4000 Hz in Moshiri, 400 Hz in Onagawa and Esrange, 150 Hz in Karymshino, about 514 Hz in Nagycenk, and 100 Hz in Hornsund. Figure 1 presents the records made simultaneously in six widely spaced observatories. Part of the data were published in [9, 11], while the others are published for the first time. The universal time (with respect to GMT) is plotted along the horizontal axis in the interval ±1.5 s at about 21:30:26.5 UT. The top plot shows variations in the vertical electric field E recorded in the observatory in Nagycenk. The rest of
126
the plots in the figure reflect pair records of the orthogonal magnetic-field components HWE = HX and HSN = HY made in other observatories. The values of the field strength are given in relative units. We had to change the sign of the HWE component measured in Moshiri, since the sign bias was found in earlier works, when the records of atmospherics from known sources were analyzed [19, 23, 24]. Before constructing the plots in Fig. 1, we applied singular spectral analysis based on the “Caterpillar” algorithm [26, 27]. This allowed us to eliminate the high-frequency noise and the remnants of the interference at a frequency of 50 Hz. Figure 1 demonstrates outstanding similarity of the records made under conditions of the global spread of observation points, though the plots do have some deviations. They are explained by different propagation conditions and the influence of local interference. Surely, the differences in the frequency characteristics of the receiving equipment in the observatories manifest themselves as well. However, we decided to use these records as they were.
Fig. 1. Records of the Schumann resonance data made by the global networks of observatories: NCK is for Nagycenk, KRM for Karymshino, MSR for Moshiri, ONW for Onagawa, HOR for Hornsund, and ESR for Esrange. The universal (Greenwich) time near the moment of the gamma-ray flare is plotted along the horizontal axis.
Each of the three horizontal black stripes above the time axis in Fig. 1 denotes an interval that contains a characteristic fragment of the pulse signal: 26.3–26.4 s, 26.5–26.6 s, and 26.7–26.95 s. In these intervals, the direction of the wave arrival, i.e., the azimuth AZ of the source was determined basing on the data about the horizontal magnetic field. The azimuth AZ is the angle between the northward direction (the Y axis of the local system of coordinates) and the minor axis of the wave polarization ellipse. The azimuth is counted, as by the compass, from the northward direction clockwise. The polarization characteristics of the magnetic field were calculated with respect to the elements PY Y , PXX , and PXY of the coherence matrix PXX PXY . PY X PY Y The latter values are found from the spectra of the orthogonal magnetic-field components (see in what follows). We applied the special wavelet transform method for finding the bearing (azimuth) of the source [19, 23, 24]. Unlike the Fourier transform, the wavelet transform uses the expansion of the field with respect to complex Gaussian wavelets of the third order. The auxiliary angle θ between the X axis, which is directed from East to West, and the major axis of the ellipse is found by means of the equation tan(2θ) =
2 Re PY X , PXY − PXX
(1)
where the elements of the coherence matrix are expressed as the second statistical momenta of the spec∗ , P tral density of the orthogonal components of the horizontal magnetic field, PXX = HWE HWE YY = ∗ ∗ HSN HSN and PY X = HSN HWE , and the asterisk denotes complex conjugation [28]. The angle θ lies within the interval from −π/2 to π/2 under the condition of allowance for the signs of the enumerator and denominator in Eq. (1). If the components H and D of the geomagnetic field are 127
used, the azimuth of the source is found as AZ = (90◦ − θ − G) ± 90◦ ,
(2)
where G denotes the geomagnetic declination of an observatory. When geographic coordinates are used, G = 0 is substituted to Eq. (2). For each time moment, the wavelet transform of each field component was used. In this manner, a set of azimuths was obtained with respect to the frequency (wavelet time scale). The average azimuth of the source was estimated by averaging over the wavelet frequency band, 3–20 Hz. Simultaneously, the standard azimuth deviation was determined [19, 23, 24]. Average arrival angles were used in constructing the azimuthal histogram with a resolution of 10◦ . The data of each observatory were represented as angular diagrams superimposed on a global map. Additionally, we found the ellipticity el of the signal, which is related to the ratio of the minor and major axes of the polarization ellipse:
where
el = tan β,
(3a)
1 2 Im PY X β = − arcsin . 2 (PY Y − PXX )2 + 4 |PY X |2
(3b)
The sign of the angle β determines the polarization type of a radio wave. The positive values of β correspond to the left-hand polarization, and the negative values, to the right-hand one. Polarization becomes linear when β = 0. The average ellipticity and its standard deviation were found similarly to the source azimuth: for each time moment, averaging over the wavelet frequency range from 3 to 20 Hz. 3.
RESULTS OF DATA PROCESSING
Figure 2 shows the evolution of the recorded magnetic field in the vicinity of ±0.5 s starting at the moment of the gamma-ray flare arrival. The topmost row of graphs contains pulses for the horizontal magnetic field recorded in different observatories. The components HSN and HWE are shown on the graphs in the black and gray color, respectively. The lower rows of the graphs (top to bottom) show the Lissajous figures of recorded signals, bearing of the source, ellipticity of the field, and wavelet spectra of the total magnetic-field amplitude. The topmost row of graphs allows one to perceive the connection between the dynamic characteristics and specific fragments of the records. The vertical dashed lines mark the moment t = 0 or 21:30:26.5 UT. Lissajous figures (i.e., field hodographs) illustrate the typical problem: pulses, as a rule, have an elliptical polarization, rather than linear ones. Therefore, sometimes determining of the source azimuth becomes a rather complicated problem, whereas for the linear polarization, the arrival angle is found fairly easily. This is well seen on an example of the first of the two pulses. Its Lissajous figure is drawn as a bold black line, unlike the rest of the interval shown as a thinner gray dashed line. The third row of graphs represents the statistics of the source azimuth. Here, bold lines show the average azimuth. The horizontal dashed straight line corresponds to the geometrical direction from the observatory to the center of the region illuminated by the gamma rays, i.e., to the epicenter of the perturbation. The darkened region around the mean azimuth indicates the zone a standard deviation wide. One can see that despite the complicated Lissajous figures, the experimental data still allow one to detect the intervals with a stable source bearing, which are related to specific pulse elements. It is seen that it is not always possible to derive such information by using the usual Lissajous figures. The fourth line of plots from top in Fig. 2 shows variations in the field ellipticity. The average value is also represented by a bold black line, and the standard deviation is shown by the darkened region around this line. In the bottommost row of graphs, the wavelet spectra of the total magnetic field are shown in relative units in the frequency band from 2 to 20 Hz (time scales from 0.05 to 0.5 s). 128
Fig. 2. Results of signal processing in the interval ±0.5 s relative to the moment of the gamma-ray flare. The moment t = 0 corresponds to 21:30:26.5 UT. The top panels show the shape of the signal components in relative units in the time domain for each observation point. The HSN component is shown in black, and the HWE component, in gray. The next lower row shows the Lissajous figures for the magnetic field. The black lines in the middle horizontal row shows the frequency-averaged azimuths of the signal sources, the gray background shows their standard deviation, and the horizontal dashed lines show the true azimuth of the source. The two bottom rows in the panels show the signal polarization ellipticity and signal spectra observed at different points. In all horizontal axes, excluding the second row, the identical time is plotted. Figure 2 illustrates the fact that the Lissajous figures do not always guarantee determining of the source bearing, whereas the wavelet transform with statistical postprocessing allows one to single out the time intervals when the azimuth is stable and indicates the center of the atmospheric modification. In the intervals of the stable signal arrival angle, the horizontal magnetic field turns to be linearly polarized, as a rule. The horizontal components of the magnetic field contain two discernible pulses that arrive within the time intervals of the stable azimuth. The dynamic spectra show that the energy of both pulses is maximum at the frequencies near the first Schumann resonance. All the above-specified features of the signal correspond to model predictions for a parametric ELF burst. The source location can be determined basing on the known bearings of the globally spread observatories. In Fig. 3, we compare the results of source triangulation with the coordinates of the gamma-ray flare for three time intervals: t = −(0.2–0.1) s (a), t = 0.0–0.1 s (b), and t = 0.2–0.45 s (c). The circular diagrams in Fig. 3 represent the triangulation in the spherical projection. The length of the lobes of the angular histograms and blackening of the lobes is proportional to the number of cases where the source bearing fits in a specific sector. The observation points are marked with black diamonds, and the star marks the center of the region illuminated with a gamma-ray flare. As before, the abbreviations ESR, KRM, MSR, HON, and ONW denote the observatories in Esrange, Karymshino, Moshiri, Hornsund, and Onagawa, respectively. One can see in Fig. 3 that the bearings point at the perturbation center for the first and second time intervals, as a rule. They correspond to the arrival of the forward and antipodal 129
Fig. 3. Histograms of the source bearing distribution, which show source triangulation on the global map for three intervals of the time t: t = −(0.2–0.1) s (a), t = 0.0–0.1 s (b), and t = 0.2–0.45 s (c). Observation points are marked with diamonds, and the source epicenter, with a star. waves of the first pulse. In the third time interval, a significant spread in the bearings is observed. The spread in the source coordinates is easily explained by a relatively low signal-to-noise ratio, which is equal to 5 approximately. The deviations of the bearings from the direction towards the perturbation center can be also explained by the asymmetry of the spatial distribution of the currents in the global electric circuit. The observations in individual observatories correspond to expectations. The directions to the source cross in the diurnal hemisphere, and their spread indicates indirectly that the currents of the parametric source created by the gamma rays is spatially asymmetric. This asymmetry looks natural if one allows for the fact that the charging currents in the global electric circuit are concentrated mainly over thunderstorm cells, which are most active in the afternoon (local time). At the same time, the leakage currents in the global circuit are connected with the fair-weather regions. Moreover, modifications of these currents should depend on the terrain. Thus, one can hardly expect that the spatial distribution of the loss current will be uniform. Finally, it should be noted that the “early” pulse, which is observed in the first time interval, i.e., before the detection of the main gamma-ray burst, can be related to the increase in radio interference at very long waves which was mentioned in [8]. This increase can be easily explained by a preliminary modification of the global electric circuit. Specifically, the charging and leak currents can be modulated before the main flux of the gamma-ray quanta arrives due to a variation in the air conductivity over the active storm cells and such Pacific structures as archipelagoes. Such fast preliminary variations can produce random pulsed radiation in the ELF band, which is perceived as “discrete noise.” Due to the extremely long wavelength, at the frequencies of the global resonance such sources merge to form one structured source. The main gamma-ray flux, which arrives later, is the reason for fast changes in the ionosphere and the corresponding Trimpi effect in the records of the VLF transmitters [8, 29]. It also modulates the structure of the Schumann resonance spectra, which was observed in [12–15] and produces the second parametric pulse [9, 11]. This burst will be connected with a different spatial distribution of the parametric current. 4.
COMPARISON OF THE MODEL AND OBSERVATION DATA
In the modeling, we considered the simplest variation of the parametric current, which was caused by ionizing radiation distributed uniformly in space [16]. The cosmic gamma rays increase air conductivity between the Earth and the ionosphere, and the leak current increases suddenly. An event starts when the ionizing radiation reaches the layer, where the main part of air resistance is concentrated, i.e., the top layers of the troposphere (see, e.g., [30]). Using the time of the gamma-ray flare detection, one can estimate the starting time of the variations as 21:30:26.67 UT [9]. The conductivity modification lags behind due to the 130
Earth’s curvature as the distance from this point grows. At the point located at the angular distance α from the epicenter, the time delay will amount to τ = a cos(α)/c, where a is the Earth’s radius, and c is the speed of light. In what follows, we assume that the cosmic radiation doubles the leak current abruptly from its regular density of 1 pA/m2 to 2 pA/m2 . The modification lasts for 1/60 of a second, and then the current density returns to its normal value. The elementary current moment of this type has a constant spectral density in the Schumann resonance frequency band. According to the ELF observations in the Antarctic [8], the gamma rays illuminated no less than a sector with an angular halfwidth of 60◦ from the epicenter. We assume that the variations occupy a sector of the same size. The elementary current moment, which is related to an air column with a cross-sectional area of 1 m2 , is equal to the product of the ionosphere altitude (60 km) by the additional current density (1 pA/m2 ). Such a source produces an elementary field, whereas the total field is produced by the sum of such fields. In the calculations, the frequency spectra of the elementary fields are used allowing for the delays caused by the Earth’s curvature within the model of the Earth—ionosphere cavity, which is uniform with respect to the angular coordinates. The components of the electromagnetic field produced by a source with the unit current moment MT (ω) = 1 are found from Eqs. [13, 31]: 1 iν (ν + 1) Pν [cos(π − θH )] , 4ha2 ε0 ω sin πν hX (ω, θH ) = hϕ (ω, θH ) cos AZ ,
er (ω, θH ) =
hY (ω, θH ) = hϕ (ω, θH ) sin AZ , hϕ (ω, θH ) = −
Pν1 [cos(π
− θH )] . 4πa sin πν
(4) (5) (6) (7)
Here, er and hϕ are the vertical electric and the horizontal magnetic fields, repectively, ε0 is the dielectric permittivity of vacuum, and Pν (x) and Pν1 (x) are the Legendre function and the associated Legendre function, respectively, ν is the complex propagation constant in the Earth—ionosphere cavity, θH is the angular distance between the source and the receiver, and AZ is the azimuth of the source. We use the geographical system of coordinates with the Y axis directed from the South to the North along the meridian and the X axis directed from the West to the East. The azimuth is counted clockwise from the direction towards the North Pole. In the calculations, we use the heuristic linear dependence of the propagation constant [31, 32]: ν=
f [Hz] f [Hz] − 2 −i . 6 100
(8)
The estimations were performed with the function ν(f ) corresponding to the so-called “knee model” [13–15, 32–34]. It turned out that the shape of the function ν(f ) plays a small part and its influence on the shape of the pulse signal is weak. The reason for that is that the frequency band occupied by the spectrum of the parametric pulse is too narrow to let one notice the differences in the models for calculations of the propagation constant. The field produced by spatially distributed currents is a convolution of spectra (4)–(7) with spatial distribution of the source current moment MT (β, ψ): π
2π dβ β
Er = 0
π 0
(9)
dψ hϕ (cos γ)MT (β, ψ) cos AZ ,
(10)
0
2π dβ β
HX =
dψ er (cos γ)MT (β, ψ),
0
131
TABLE 1. Parameters of the propagation paths. Observatory Nagycenk (NCK) Hornsund (HOR) Esrange (ESR) Karymshino (KRM) Moshiri (MSR) Onagawa (ONW)
Distance, mm 16.61 13.63 14.66 9.74 10.20 9.96
π HY =
2π dβ β
0
Bearing of the source epicenter AZ −32.9◦ −20.5◦ −16.1◦ 129.2◦ 117.2◦ 116.8◦
dψ hϕ (cos γ)MT (β, ψ) sin AZ .
(11)
0
Here, the angles β and ψ denote, respectively, the colatitude and longitude of the current element relative to the flare epicenter, γ(β, ψ) is the angular distance between the observatory and the current element, and AZ (β, ψ) is the bearing of the current element from the observation point. The convolution operation has a clear physical meaning. The parametric source consists of small elements, each of which makes its contribution to the resulting field. The fields of elementary emitters reach the observer having their own amplitudes and phases. Summing them up with allowance for all the aforesaid factors, we obtain the resulting spectrum of the selected field component. This is the operation of convolution of the field with elementary sources. When introducing “minor” elements of the source, we should remember that the wavelength under consideration is comparable with the length of the equator, being 40 Mm. Therefore, the dimensions of the elementary source can remain great in the common meaning of the word. We used elementary cells with dimensions 5.8◦ in the angle β and 24◦ in the angle ψ. It is evident in advance that the parametric source, whose dimensions are comparable with the hemisphere, is capable of exciting only the first (main) mode of the Schumann resonance. The matter is that the waves coming from remote intervals of a big source extinguish each other at high frequencies [13–16]. The capability to excite oscillations of the lowest-frequency mode allows one to discern parametric pulses from the usual ones. Geometric parameters of the propagation paths are listed in Table 1, where the observatories are categorized in two groups. There are three observatories in the Far East (Moshiri, Onagawa, and Karymshino), which are located at a distance of about 10 Mm from the flare epicenter. The azimuths of the parametric source for these observatories are equal to approximately 120◦ , i.e., the pulse comes to them from the SouthEast. The second group is formed by the observation points in Europe (Esrange, Nagycenk, and Hornsund), which are located at a distance of more than 15 Mm from the flare epicenter. The source bearing from these observatories is close to −20◦ , since the wave arrives there from the North-West. Complex signal spectra in all six observatories were calculated for the region with an angular halfwidth of 60◦ with respect to the epicenter of the perturbation. The temporal shapes of the pulses shown in Fig. 4 were obtained by means of fast Fourier transform. Model plots are arranged in two columns, the left column with the data from the observatories in the Far East, and the right column with the data of the observations in Europe. Magnetic (top plots) and electric (the vertical component of the field) temporal shapes of the pulse in relative units were constructed for each observatory. The time within an interval from 0 to 1 s is plotted along the horizontal axis. The lines with dots relate to the HSN component and the lines without dots, to the HWE field. In the Far East observatories, calculated pulses of the magnetic field contain well-pronounced decaying oscillations at the frequency of the first Schumann resonance. The same property was observed in the experiment illustrated in Fig. 2. In the vertical electric field, the second mode of the Schumann resonance is dominant, which is explained by the distance between the observer and the flare epicenter, which is equal 132
Fig. 4. Wave shapes of the parametric ELF burst calculated in relative units for all observatories. Lines with dots correspond to the data related to the HSN component of the magnetic field, and lines without dots to the HWE component. to approximately 10 Mm. Therefore, the spectra of time variations of the magnetic and electric fields in the records of the Far East observatory should differ noticeably. Unfortunately, the inoperable electric channel of the observatory in Moshiri did not allow us to check this characteristic property. Calculations demonstrated also that the large size of the source levels the amplitudes of the magneticfield components. For example, the amplitudes HSN and HWE turn to be close to each other, whereas the flare epicenter is located at an azimuth of about 130◦ , for which the amplitude ratio should equal to 2 : 1 in the case of a point source. Sharp stepwise variations in some of the calculated amplitude spectra are also due to the large size of the source. In the process of modeling, we allowed for the typical transmission coefficient of the electric antenna [35] iωRC0 C0 + C1 . (12) GE = 1 + iωR (C0 + C1 ) C0 Here, C0 = 25 pF is the intrinsic capacity of the active antenna electrode (sphere with a diameter of about 55 cm), C1 = 50 pF is the input capacity of the antenna amplifier, and R = 109 Ω is the input resistance of the amplifier. Electric antennas are insensitive to low frequencies, therefore, the observed video pulse is slightly deformed due to the suppression of ultra-low-frequency components. The negative half-wave at the leading edge of the electric pulse indicates the positive polarity of the field source unambiguously. This polarity follows from the calculation as well, since a decrease in the atmosphere resistance increases the leak current from the ionosphere to the Earth, whose direction 133
corresponds to the motion of positive charges. The negative first half-wave is also typical of the majority of usual ELF bursts, since they are excited mainly by positive thunderstorm breakdowns. Unfortunately, there were no perfectly reliable data from any observatory, which would contain all three components of the electromagnetic pulse simultaneously. Therefore, the possibility to determine the direction to the source basing on the Umov-Poynting vector P(t) = [E(t), H(t)] was absolutely impossible. To demonstrate that the source of the parametric pulses was located over the Pacific Ocean indeed, we will use its positive polarity. Due to the invariable polarity of the ELF burst in the vertical electric field over the entire globe, we can determine the quadrant of the source for each observatory. For that purpose, it is necessary to use the sign of the first half-wave of the pulse in the components of the “mutual Umov—Poynting vector,” which are determined by the equalities PW E (t) = −E(t)HSN (t) and PSN (t) = E(t)HWE (t). The difference of the mutual vector is in that the record of the electric field in it is taken from the Nagycenk observatory data, whereas the magnetic-field components are taken from each of the other observation points. The position of the source depending on the polarity of the first half-wave for the horizontal magnetic components is shown in Table 2. The first five columns in this table list all variants TABLE 2. Position of the source depending on the of the signs of the first half-wave at the leading edge of polarity of the first half-wave at the leading edge the magnetic pulse for the constant negative half-wave of the pulses in the HWE and HN S components. + of the field. The last column of the table shows the source quadrant in the local system of coordinates, which Leading edge Source is found uniquely based on this or that sign combination. polarity quadrant E HX HY PX PY By applying Table 2 to the observations, one can − + − − − I easily find the direction to the source. These data are − + + + − II presented in Table 3. The first column shows the names of − − − + + III the observation points, the two following columns contain the sign of the first half-wave at the leading edge of the − − + − + IV pulse for the HWE and HSN components. The next-to-last column gives the source quadrant found by means of Table 2, and the last one, the geographical azimuth of the perturbation epicenter. The comparison of the data in the two last columns of Table 3 shows that the source is situated in the Pacific Ocean unambiguously. To estimate the arrival direction, one can use time variations of the mutual Umov—Poynting vector. For this purpose, though, the records had to be transformed for the equal sampling rate. Surely, this vector is a non-rigorous characteristic, but the resulting Lissajous figures prove to be rather informative (see Fig. 5). The left-hand column of graphs in Fig. 5 shows the components of the mutual Umov—Poynting vector as time functions. The West-to-East component PW E (t) = −E(t)HSN (t) and the South-to-North component PSN (t) = E(t)HWE (t) are shown by the curves with and without dots, respectively. We selected time interval No. 1, when the first, “preliminary” pulse was registered. To the right of the time functions, the corresponding Lissajous figures are shown. A greater part of the plots that fits within the interval 26.3–26.5 s is shown with thin lines, whereas the bold lines with dots correspond to the range 26.3 to 26.36 within the aforesaid interval. This time range is marked with a bold horizontal line on the time axis in the graphs on the left. One can see that the forward wave arrived to the observation point at this time. The arrows in the diagrams to the right indicate the direction from the observatory to the epicenter of the perturbation. It is evident that the Lissajous figure of the mutual Umov—Pointing vector is elongated in the direction perpendicular to the direction of the arrows in all the cases with no exception, which was expected for the Pacific source. The shapes of the observed and modeled pulses are compared thoroughly in Fig. 6. We chose the data from Nagycenk (field E), Esrange (the HWE field component), and Karymshino (the D field component). The time is plotted along the X axis and is measured from 21:30:26.2 to 21:30:27.4 UT. The signal amplitude is plotted along the Y axis. The vertical component of the electric field is specified in mV/m, and the magnetic component, in μA/m. The latter units are used widely in radio engineering, since the product 134
TABLE 3. Quadrant of the source of the first-pulse as seen from individual observatories. Observatory
Nagycenk (NCK) Hornsund (HOR) Esrange (ESR) Karymshino (KRM) Moshiri (MSR)
Polarity at the leading edge of the pulse HWE HN S + + + + − + ? − − −
Source quadrant II II III ? III
Geographical azimuth of the epicenter −16◦ −33◦ 129◦ 117◦ 117◦
Fig. 5. Time dependence in relative units (left) and the corresponding Lissajous figures (right) of the mutual Umov—Poynting vector found on the basis of the records from all the observatories. Bold loops with dots in the Lissajous figures illustrate the hodograph of the mutual Umov—Poynting vector in the time interval 26.3–26.36 s, which is marked with the horizontal stripe on the time axis of the left graphs. The arrows show the direction from the observation points towards the flare epicenter. of the magnetic field expressed in μA/m by the wave resistance of vacuum, 120π Ω, yields the electric field expressed in μV/m. To convert the results to pT, one should use the equality 1 μA/m = 0.4π pT = 1.256 pT. The experimental data are shown in Fig. 6 as bold black lines, and the results of the modeling, as the curves with dots. If one shifts the calculated pulse in time, then the coefficient of mutual correlation of the modeled and observed data will be changing. This allows one to estimate the arrival time at each point from the maximum absolute value of the mutual-correlation coefficient. The corresponding times are shown in Fig. 4. One can see that they agree well for all the observatories. The initial half-wave of the first of the two ELF bursts is noticeably shorter at all observation points. To obtain a short pulse, one has to reduce the angular size of the region where the current of the global electric circuit is modified to 5◦ . At the same time, it is necessary to increase the current density variation by an order of magnitude, up to 30 pA/m2 , since otherwise it will be impossible to obtain a pulse with an appropriate amplitude. The wave shape of the second pulse was calculated for the case of the angular half-width of the conductivity modification region and the additional leak current equal to 60◦ and 1 pA/m2 , respectively. The first pulse arrived before the moment of detection of the main gamma-ray burst, and the arrival time of the second pulse nearly coincided with the moment of sharp variations in the ELF signals propagating along the Pacific paths. The correspondence between the model and observations is evident both for the 135
TABLE 4. Times of the pulse arrival to the observatories and the coefficients of mutual correlation of the modeled and observed data.
Observatory
Nagycenk (NCK) Hornsund (HOR) Esrange (ESR) Karymshino (KRM) Moshiri (MSR) Onagawa (ONW)
Time of arrival of the first pulse relative to 21:30:00 UT 27.12.2004, s 26.25 26.27 26.28 26.29 26.31 26.31
Time of arrival of the second pulse relative to 21:30:00 UT 27.12.2004, s 26.65 26.69 26.71 26.60 26.61 26.60
Coefficient of mutual correlation for the first pulse 0.60 0.35 0.37 0.28 0.28 0.10
Coefficient of mutual correlation for the second pulse 0.78 0.72 0.67 0.46 0.59 0.40
European and Asian data. The arrival times and the corresponding mutual-correlation coefficients are shown in the graphs for each pair of the pulses. The data deviations in Fig. 6 can be attributed to the natural background noise. 5.
DISCUSSION AND CONCLUSIONS
The closeness of the pulse arrival times to the moment of detection of the gamma-ray burst, the single-mode composition of the Schumann resonance spectra, azimuth of the wave arrival and its linear polarization suggest that the observed radiation appeared due to a sharp short-term variation in the leak current of the global electric circuit under the action of cosmic gamma-ray quanta. All available records of the Schumann resonance contain ELF bursts occurring at the time moments, which are close to the arrival time of the gamma-ray burst. In this case, the records contain two pulses, rather than one. Summing up the independent observations in globally distributed observatories, we point out the following. 1) ELF bursts are detected at the same time globally at the time moment close to the time of detection of the cosmic gamma-ray radiation. 2) The spectral density of pulsed radio signals is concentrated near the first mode of the resonance oscillations of the Earth—ionosphere cavity. 3) The amplitude of the pulse exceeds the natural background by 4–6 times. 4) The source of the parametric pulse has the positive polarity, i.e., the pulsed positive current was directed towards the Earth. 5) The polarization of the parametric radio wave was nearly linear. 6) Global triangulation indicates the epicenter of the perturbation for the first pulse, whereas the bearings are biased for the second pulse and characterized by a significant spread. The first ELF burst had all expected characteristics of the parametric signal excluding the earlier arrival time. This event was detected 0.3–0.4 s before the onset of conductivity variations which were observed in the records of the signals from ELF radio transmitters. The simplest explanation is a random coincidence of dissimilar events [9]. One can assume that the earlier pulse is due to a usual positive lightning breakdown, which coincidentally happened before the arrival of gamma rays. One should not reject such a coincidence, certainly, but we regard it as rather doubtful, since such an interpretation requires that the following hard questions should be answered. 1) Why did the above-noted positive thunderstorm breakdown occur in the middle of the Pacific Ocean, whereas this region is known to have the lowest storm activity on the Earth? 2) Why did the positive-polarity thunderstorm breakdown occur at local noon? The maximum of worldwide storms fall on the afternoon time. Additionally, positive breakdowns are prevalent in the final 136
Fig. 6. Comparison of the observed (bold lines) and modeled (lines with dots) pulses in the vertical electric field and the horizontal magnetic field in different observatories. The left-hand parts correspond to the angular width of the perturbation being equal to 5◦ , while the right-hand parts correspond to 60◦ . The values of t shown in the graphs correspond to the arrival times of the first and second pulses relative to 21:30:00 UT on December 27, 2004, and the values of R are the coefficients of correlation of the modeled and observed data. phase (“death”) of a thunderstorm, which corresponds usually to 18–22 h, local time. Why did the random event under consideration occur during “off-hours” and was that much ahead of the typical time of occurrence of positive breakdowns? 3) In order to obtain the correct shape of the first pulse, we had to use a distributed source, whose coherent currents occupy a region with an angular half-width of about 5◦ , rather than a point source. This 137
model has little in common with vertical lightning discharges. Why do the shapes of pulses from a storm source, which are calculated for different observatories, not correspond to the observation data? 4) A thunderstorm in the middle of the Pacific Ocean that occurred at noon and generated a positive breakdown seems rather odd. Why was it located in the epicenter of the approaching gamma rays and occur just before the arrival of the flare? 5) The hypothesis of a random lightning discharge does not provide any explanation for the special spectral composition of the recorded pulse. The spectrum of an ELF burst generated by a positive breakdown even with a duration of 1/60 s, which is located at the epicenter of the perturbation, should still contain the second and third resonance modes with noticeable amplitudes at all receiving points, whereas they are absent in the observation data. Why is that so? Trying to find answers to these questions, we came to the conclusion that the both pulses own their origin to the galactic gamma-ray flare, most probably. The first of them can be explained by a certain “preliminary” activity before the arrival of the main flux. The rest of its parameters correspond to the model expectations. Excluding the source bearing, all characteristics of the second pulse coincide with the expectations perfectly. The pulse wave arrived at the proper time, it had the due spectral composition, its amplitude corresponded to the calculations, the source had the positive polarity, and the wave polarization was nearly linear. However, the triangulation yields a wide spread of the source positions relative to the epicenter of the perturbation. The reason for that may the spatially nonuniform modifications of the leak current in the global electric circuit. Thus, we have two candidates for the role of the parametric pulse. Each of them has five (of the six) characteristics that coincide with the expectations, and each one has deviations in one of the characteristics. To put it differently, if it is necessary to choose one pulse of the two, one will have to accept either the earlier arrival, or significant deviations in the source coordinates. It stands to reason that both pulses are related to the galactic flare. The first of them was caused by a certain preliminary activity which remained “unnoticed” by the orbital gamma-ray telescopes. At the same time, this activity was observed as an increase in the level of the natural VLF noise before the arrival of the gamma-ray flare detected in the signals of the VLF transmitters [8]. If one refers to the record made by the RHESSI satellite, which is shown in Figs. 2 and 3 in [8], then one can observe a certain activity that precedes the arrival of the main flare. It started at 21:30:26.3 UT, approximately. In the region of the global-resonance frequencies, where the enormous wavelength combines with slow time processes, such an activity could form a pulse precursor. The step in the record of VLF radio signals, which is related to the arrival of the main flux of gamma-ray quanta, occurs at 21:30:26.6 UT. The time of the second ELF burst coincides with these changes, but is characterized by a greater spread of source bearings. There is no doubt that the predicted parametric pulsed radio emission was detected by the worldwide network of radio observatories successfully. A distinctive feature of the observation data is that two closetimed pulses were received, rather than one. The first pulse satisfies all the requirements, but arrived earlier than the modification of the lower ionosphere, which was detected in the Antarctic measurements of the trans-Pacific signals of VLF radio stations. It is possible that an unknown agent caused the first parametric ELF burst at the same time with an increase in the VLF radio noise due to a variation in the leak resistance of the global electric current. In this case, the ionosphere altitude stayed constant, the signals from the VLF transmitters were stable, and only insignificant variations in the gamma-ray background were detected by the orbital gamma-ray telescopes. To conclude the paper, we outline the main results obtained. All available records of the Schumann resonance made by the worldwide station network contain the characteristic pulses that correspond to the arrival of the cosmic gamma-ray burst of December 27, 2004. Parametric pulses are found in the mutually orthogonal horizontal components of the magnetic field and in the vertical component of the electric field. The negative polarity at the leading edge of the pulse in the vertical component of the electric field 138
indicates the positive polarity of the source. Therefore, the signal appeared due to the increase in the leak current in the global electric circuit by 2–10 times. The observed and modeled pulses are similar, and the coefficients of their mutual correlation turned to be high. The records contain two pulses, rather than one pulse. One of them outstrips the time of arrival of the main gamma-ray flux, whereas the second pulse coincides with the maximum of this flux. Global triangulation showed that the first pulse arrived from the epicenter of the atmospheric modification caused by the gamma-ray burst, whereas the source of the second pulse is characterized by a wide spread of bearings relative to the azimuth of the epicenter. Both pulses are probably related to the gamma-ray burst. However, it is difficult to make final conclusions, since the event was unique, and the ratio of the pulse amplitude and the natural background did not exceed 4–6. The studies of the Hungarian group were supported by the European Social Fund (project TAMOP4.2.2.C-11/1/KONV-2012-0015 (system Earth). The authors are grateful to the anonymous Reviewer for his valuable comments, proposals, and corrections which improved the article beyond any doubt. REFERENCES
1. C. Thompson and R. C. Duncan, Mon. Not. R. Astron. Soc., 275, 255 (1995). 2. C. Thompson and R. C. Duncan, Astrophys. J., 473, 322 (1996). 3. K. Hurley, S. E. Boggs, D. M. Smith, et al., Nature, 434, 1098 (2005). 4. D. M. Palmer, S. Barthelmy, N. Gehrels, et al., Nature, 434, 1107 (2005). 5. T. Terasawa, Y. T. Tanaka, Y. Takei, et al., Nature, 434, 1110 (2005). 6. S. Mereghetti, D. G¨otz, A. von Kienlin, et al., Astrophys. J. Lett., 624, L105 (2005) 7. D. D. Frederiks, S. V. Golenetskii, V. D. Palshin, et al., Astron. Lett., 33, 1 (2007). 8. U. S. Inan, N. G. Lehtinen, R. C. Moore, et al., Geophys. Res. Lett., 34, L08103 (2007). 9. Y. T. Tanaka, M. Hayakawa, Y. Hobara, et al., Geophys. Res. Lett., 38, L08805 (2011). 10. R. L. Dowden, N. R. Thomson, C. J. Roger, and M. Hayakawa, in: URSI General Assembly, Toronto. Section G2, p. 2 (1999). 11. A. P. Nickolaenko and A. Yu. Schekotov, Radiophys. Quantum Electron., 54, No. 1, 15 (2011). 12. A. P. Nickolaenko, I. G. Kudintseva, O. Pechony, et al., Ann. Geophys., 30, 1321 (2012). 13. A. P. Nickolaenko and M. Hayakawa, J. Atmos. Electr., 30, No. 1, 1 (2010). 14. A. P. Nickolaenko, I. G. Kudintseva, O. B. Pechonaya, et al., Radiophys. Quantum Electron., 53, Nos. 9– 10, 542 (2010). 15. M. Hayakawa, A. P. Nickolaenko, A. V. Shvets, and Y. Hobara, in: M. D. Wood, ed., Lightning: Properties, Formation and Types, Nova Sci. Pub., Ch. 3, p. 39 (2011). 16. A. P. Nickolaenko, J. Atmos. Electr., 31, No. 2, 95 (2011). 17. Y. Ando, M. Hayakawa, A. Shvets, et al., J. Atmos. Electr., 25, 29 (2005). 18. Y. Hobara, N. Iwasaki, T. Hayashida, et al., J. Atmos. Electr., 20, 99 (2000). 19. A. Yu. Schekotov, V. Pilipenko, K. Shiokawa, and E. Fedorov, Earth Planets Space, 63, No. 2, 119 (2011). 20. M. Sato and H. Fukunishi, Geophys. Res. Lett., 30, No. 16, 1859 (2003). 139
21. G. S´ atori, J. Szendr¨ oi, and J. Ver¨ o, J. Atmos. Terr. Phys., 58, No. 13, 1475 (1996). 22. G. S´ atori, M. Neska, E. Williams, and J. Szendroi, Radio Sci., 42, RS2S10 (2007). 23. A. Yu. Schekotov, O. A. Molchanov, M. Hayakawa, et al., Radio Sci., 42, RA6S90 (2007). 24. A. Yu. Schekotov, O. A. Molchanov, M. Hayakawa, et al., Nat. Hazards Earth Syst. Sci., 8, 1237 (2008). 25. M. Neska and G. S´ atori, Przegl. Geofiz. (Engl. Transl.), Nos. 3–4, 189 (2006). 26. D. L. Danilov and A. A. Zhiglyavskiy, Main Components of Time Series: the “Caterpillar” Method [in Russian], St. Petersburg Univ. Press (1997). 27. V. Troyan and M. Hayakawa, Inverse Geophysical Problems, Terrapub, Tokyo (2002). 28. R. A. Fowler, B. J. Kotick, and R. D. Elliot, J. Geophys. Res., 72, 2871 (1967). 29. Y. T. Tanaka, T. Terasawa, M. Yoshida, et al., J. Geophys. Res., 113, A07307 (2008). 30. M. J. Rycroft, R. G. Harrison, K. A. Nicoll, and E. A. Mareev, Space Sci. Rev., 137, 83 (2008). 31. A. P. Nickolaenko and M. Hayakawa, Resonances in the Earth—Ionosphere Cavity, Kluwer Acad. Publ. (2002). 32. A. P. Nickolaenko and M. Hayakawa, J. Atmos. Electr., 29, No. 1, 19 (2009). 33. V. C. Mushtak and E. R. Williams, J. Atmos. Solar-Terr. Phys., 64, 1989 (2002). 34. O. Pechony and C. Price, Radio Sci., 39, RS5007 (2004). 35. T. Ogawa, Y. Tanaka, T. Miura, and M. Yasuhara, J. Geomagn. Geoelectr., 18, 443 (1966).
140
