Метод периодических главных компонент динамического спектра радиопульсаров и фарадеевское вращение девяти составляющих импульса PSR B0329+54

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Abstract

Развит метод периодических главных компонент для сигналов с квазипериодическим динамическим спектром, свойственным радиопульсарам. Метод основан на анализе собственных векторов и значений матрицы частотно-временных корреляций сигнала, усредненной по многим периодам обращения пульсара. На примере наблюдений PSR В0329+54 радиотелескопом ПРАО АКЦ ФИАН вблизи частоты 111 МГц в полосе 2.5 МГц показано, что даже для коротких интервалов данных (несколько минут) развитый метод позволяет выделить до девяти составляющих импульса излучения пульсара, оценить степень корреляции между ними и для каждой составляющей найти период модуляции фарадеевского типа, а также ее относительную фазу и скорость частотно-временного чирпа, т.е. позволяет судить о структуре источника излучения.

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В. В. Кочаровский

Институт прикладной физики им. А.В. Гапонова-Грехова РАН

Author for correspondence.
Email: kochar@ipfran.ru
Russian Federation, Нижний Новгород

В. В. Вдовин

Институт прикладной физики им. А.В. Гапонова-Грехова РАН

Email: kochar@ipfran.ru
Russian Federation, Нижний Новгород

A. С. Гаврилов

Институт прикладной физики им. А.В. Гапонова-Грехова РАН

Email: kochar@ipfran.ru
Russian Federation, Нижний Новгород

Е. Р. Кочаровская

Институт прикладной физики им. А.В. Гапонова-Грехова РАН

Email: kochar@ipfran.ru
Russian Federation, Нижний Новгород

С. В. Логвиненко

Пущинская радиоастрономическая обсерватория Астрокосмического центра Физического института им. П.Н. Лебедева РАН

Email: kochar@ipfran.ru
Russian Federation, Москва

E. M. Лоскутов

Пущинская радиоастрономическая обсерватория Астрокосмического центра Физического института им. П.Н. Лебедева РАН

Email: kochar@ipfran.ru
Russian Federation, Москва

В. М. Малофеев

Институт прикладной физики им. А.В. Гапонова-Грехова РАН

Email: kochar@ipfran.ru
Russian Federation, Нижний Новгород

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Supplementary files

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2. Fig. 1. A sweep with a step of 10δτ ≈ 2.0496 ms, corresponding to a pulsar rotation of ≈ 1°, of the intensity profile of the PSR B0329+54 emission (arbitrary units), received in the range of 109.6–112 MHz, for a series of consecutive frames N = 1, ..., 450 of the pulsar pulse after compensation for the dispersion delay using the found dispersion measure = 26.76 pc/cm³.

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3. Fig. 2. The first, most significant QFEOF in the decomposition of the dynamic spectrum of PSR B0329+54 by the periodic principal component method: (a) — the relative contribution Y₁ (τN) to the sequence of frames (pulsar revolutions) N = 1, ..., 450; (b) — the frequency-time form with signs of Faraday-type modulation.

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4. Fig. 3. The third FTE in the decomposition of the dynamic spectrum of PSR B0329+54: (a) — the relative contribution of Y₃ (τN) (triangles, black broken line) in comparison with the contribution of Y₁ (τN) of the first FTE (circles, gray broken line) on the sequence of frames N = 1, ..., 450; (b) — the frequency-time form with signs of Faraday-type modulation, including mainly the “upper” component of the pulse V at times of about 26 ms and partly the “lower” components I and VI at times of about –33 ms and –10 ms, as well as traces of the “central” component III at t ≈ 0.

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5. Fig. 4. Approximation of the PSR B0329+54 pulse intensity (arbitrary units), summed over 500 channels in a band of almost 2.5 MHz at a carrier frequency of 111 MHz, for the N-th time window (frame) of 50 ms duration with a step of δτ ≈ 2.0496 ms, corresponding to a pulsar rotation of ≈ 1°: (a) — initial data ⟨∑jS(vj,tk)⟩ (after primary processing according to Section 3, but without transition to the logarithm s = ln(S + C) ); (c) — pulse profile ⟨∑jS(vj,tk)⟩ averaged over the frequency and all observation series; (b)–(e) — modification of this profile by additional inclusion of a number of the first CHVEOFs with the largest weights — one, two, three, and fourteen, respectively.

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6. Fig. 5. The second (a) a₂, fourth (b) a₄ and fifth (c) a₅ of the QVEOF in the decomposition of the dynamic spectrum of PSR B0329+54, demonstrating the asymmetry and weak correlation of the main components of the pulse: the “central” III at t ≈ 0 (with its fine structure) and the “remote” V-th and I-th (corresponding to times t of about 26 ms and –33 ms, respectively), differing in the depth of the “Faraday” modulation.

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7. Fig. 6. The eleventh (a) a₁₁ and twelfth (b) a₁₂ of the QVEOF in the decomposition of the dynamic spectrum of PSR B0329+54, confirming the asymmetry of the time profile or jitter of the pulse sequence along with a weak cross-correlation of the most “remote” components of the pulse - the V-th and I-th (corresponding to times of about 26 ms and -33 ms, respectively), both with similar signs of Faraday-type modulation.

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8. Fig. 7. The tenth a10 QVEOF in the decomposition of the dynamic spectrum of PSR B0329+54: (a) — frequency-time shape in the region of the IX-th component of the pulse, concentrated at times t of about 5 ms (below, a row of dark spots corresponds to the IV-th component at t ≈ 2.5 ms); (b) — approximation of the “Faraday” modulation (conventional units) for one of the frames of the dynamic spectrum with a well-defined IX-th component at the level of tIX = 5 ms by a harmonic oscillation with a frequency period of tIX = 0.38 MHz, equal to the width of almost 78 spectral channels of the receiver, each with a band of 4.88 kHz.

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9. Fig. 8. Distribution of the frequency period of the “Faraday” modulation vm for nine components of the pulse (number m is given on the ordinate axis). Each point is the result of measuring the period for one frame of three series of observations containing about 1350 frames, from which those with the maximum dynamic spectrum for a given component at t = tm, significantly exceeding the noise level, were selected. The triangle and the thin line passing through it correspond to the position of the median and the quartile from 25% to 75%; the rhombus and thick line correspond to the mean value and standard deviation, respectively.

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10. Fig. 9. Histograms of the frequency period of the “Faraday” modulation vm for four components of the pulse m (indicated in the corner of the graphs (a)–(g)) according to the corresponding distributions of Fig. 8. The frequency on the abscissa axis is given in units of the number of frequency channels of the receiver, each with a band of 4.88 kHz.

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11. Fig. 10. Histograms of the relative phase of the “Faraday” modulation for four components of the pulse m (indicated in the corner of the graphs (a)–(d)), ∆ϕm = ϕIII - ϕm, calculated by subtracting the third component III from the Faraday rotation phase and reducing it to the interval [0, 2π] by adding the appropriate number of values ​​of ±2π.

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12. Fig. 11. Histograms of the frequency chirp of the “Faraday” modulation for four components of the pulse m (indicated in the corner of the graphs (a)–(g)), calculated using the formula g = ∆ϕmνm / (2π | tm |) and approximately equal to the local velocity of the shift of the maximum or minimum of the signal on the frequency–time plane (ν,t). In the histogram (b), two possible chirp distributions are shown in gray and black shades, in the calculation of which for each frame two physically justified values ​​of the phase difference – ∆ϕV, differing by 2 π, were used.

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