References• Cohen, L., Proc. IEEE, 77, 72, 1989; • Shkelev, E.I., Kislyakov, A.G., Lupov, S, Yu., Radiophys.& Quant.Electronics, 45, 433, 2002.• Wigner, E.P., Phys. Rev., 40, 749, 1932. • Ville, J., Cables Transm., 2A, 61, 1948; • Blanc, M., et al., Space Sci. Rev., 104, 253, 2002• Gurnett, D. A., et al., Space Sci. Rev., 114, 395, 2002

ABSTRACT

The analysis of the long period modulations of the Saturn Kilometric Radiation (SKR) and near-Saturn solar wind parameters based on “sliding window” Fourier and nonlinear Wigner-Ville methods is presented. For this investigation the data collected by Cassini-RPWS (SKR radio emission measurements) and Cassini-MAG (magnetic field measurements) experiments have been used. The SKR data have been analysed in the time interval from Jan 1, 2004 until Dec 31, 2004. Existence of strong impulsive ~11 hour modulations of the SKR connected to the Saturn rotation has been confirmed. This ~11 hour impulses appear in the form of almost regular, periodic storms with a periodicity of about 9 days. Additionally, signatures of 13 days modulation of the SKR as well as several modulation lines of the magnetic filed are well seen. The nature of these long periodic modulations is discussed in the terms of possible influences of the Saturn’s moons on the SKR generation, global structure of the Saturn’s magnetosphere, variations of the solar wind parameters as well as some instrumental or observational effects.

1. THE ALGORITHM FOR DATA ANALYSIS. Wigner-Ville and Fourier transforms.

The classical Fourier transform allows to perform the analysis of the studied signal in terms of separate frequency components, and to study the relative distribution of energy between these components. However such energetic spectrum does not provide the information on the appearance time of particular spectral components. One possible improvement of this is “sliding window” Fourier (SWF) transform method.

Recently one more spectral analysis method has been applied in astrophysics. This method is based on the Wigner-Ville (WV) transform

where z(t) = s(t) + jsG(t) is an analytic signal made of s(t) – the real signal sample to be investigated, and sG(t) its Gilbert conjugate. Function P(f,t) gives the distribution of the signal energy over the frequency and time. This function can be also interpreted as Fourier image (relative the shifted time) of the local autocorrelation function of the analyzed signal.

WV method allows to analyze by means of the dynamical spectra the temporal and frequency distribution of the energy of the low-frequency pulsations, modulating the analyzed signal. WV method appears the most efficient for the analysis of cases with the quasi-harmonic modulating signals with a changing frequency. It allows also high resolution analysis of frequency-time structures of the modulating signals. At the same time, the non-linearity of the WV method results in the appearance of artificial intermodulation spectral components (artefacts) at the combination frequencies (see Fig. 1). Our data analysis algorithm takes into account all these features of the WV transform.

The combination of the “sliding window” Fourier (SWF) and Wigner-Ville (WV) transforms enable to detailed studies of the dynamical spectra of the low frequency signal.

Analysis of long-periodic modulations of SKR and solar wind parameters

M. Panchenko 1, M. L. Khodachenko 1, A.G. Kislyakov 2,3, H. O. Rucker 1

1 Space Research Institute, Austrian Academy of Sciences, Schmiedlstr.6, A-8042 Graz, Austria2 Institute of Applied Physics, Russian Academy of Sciences, Ulyanov str. 46, 603950, Nizhny Novgorod, Russia

3 Lobachevsky State University Nizhny Novgorod, Gagarin av. 23, 603950, Nizhny Novgorod, Russia

► Advantages of the SWF-WV algorithm:

- High sensitivity: detection of the modulating LF signals appear- ed below the noise level

- High spectral and temporal resolution

- Ability to detect complex multi-signal modulations

► Technical requirements:

- The length of the analyzed time series should include at least several periods of the LF modulating component;

- Sampling cadence of analyzed time series is 104 equidistant points per realization;

detztztfP fj2*

22,

Fig.1: WV spectrum for the test digital signal with the frequency discretization fD. The test signal consists of three frequency-modulated components si(t) (I =1,2,3) with constant amplitudes. The signals s1(t)

and s2(t) have the linear frequency modulation:

f 1(t) = fmax t, f2(t) = fmin + t ,

where fmin = 0.05 fD ,fmax = 0.2 fD and = 0.0001. Modulation of the third signal s3(t) differs from the modulation of s2(t) by the presence of the additional phase modulation:

f3(t) = f2(t) - with ,

where the temporal shift of phase is ts = (fmax - fmin)/6 and k=0.01. 1,2,3 - the spectral lines of the test signal. They represent the power distribution of the signal over the time and frequency. 4,5,6 - Intermodulation components (artifacts) at combination freq. f12(t) = (f1(t) + f2(t))/2, f23(t) = (f2(t) + f3(t))/2, and f13(t) = (f1(t) + f3(t))/2

t th k t t ts 0 04, d t

dt

2. DATA ANALYSISThe data collected by Cassini-RPWS (Saturn Kilometric Radiation measurements) and Cassini-MAG (magnetic field) instruments during time period from 1 Jan., 2004 to 31 Dec 2004 have been selected. For the analysis of the long-periodic modulations the combination of the “sliding window” Fourier (SWF) and Wigner-Ville (WV) methods have been applied. We expect that the analysis of the LF spectra will allow to judge about conditions of SKR generation, global structure of the Saturn’s magnetosphere and variations of the solar wind parameters.

Acknowledgements: This work was supported by the Austrian Academy of Sciences, Space Research Institute AAS and Austrian “Fonds zur Förderung der wissenschaftlichen Forschung” (Project P16919-N08).

Analysis of long-periodic modulations in the Magnetic field data

Impulsive modulation activity storms Modulation burst on 51-th day Duration: ~ 4.7 days

Modulation burst on 168-th day Duration: ~ 5.5 days

Modulation burst on 337-th day Duration: ~ 4.9 days

Data averaged over 50 samples (1000 min); W=256 ~ 8.0 microHz

(1.4 days)

~ 7.5 microHz (1.5 days)

- 8.0 microHz line - during the strong emission periods- 7.5 microHz line - when the emission is weaker- Both may be caused by same process (changing velocity of rotation)

Analysis of long-periodic modulations in the Saturn Kilometric Radiation (SKR) data

Comparison of the MF and SKR 10.7 h lines amplitude (intensity)

Comon features: - Similar periodicity and morphology; - Similar number of wavelets ( ~23)

Correlation of minima in the MF and SKR 10.7 h lines amplitude (intensity)

Line equation: Y = 0.95 X + 0.38- Delay of SKR reative MF (for the 10.7 h modulation) - Shift between MF and SKR: ~12.8 days ( ! )

SKR intensity

integrated over 20-1000 kHz frequency range

FFT transform Wigner-Ville transform

Modulation lines: Data averaged over 10 samples (200 min); W=256

Interrupted modulation

at ~ 0.9 microHz (12.8 days)

Data averaged over 50 samples (1000 min). “Normalized” signal (divided by module curve) removing pulses, visibility of sin-type processes

~ 0.9 microHz

(12.8 days) ~ 1.28 microHz

(9 days)

~10.7 h (0.026 mHz) modulation periodExact period: 10.75 h (± 0.02 h)

~9 days (1.28 microHz) and ~ 12.8 days (0.9 microHz) modulation periods

~1.4 days (8.0 microHz) and ~ 1.5 days (7.5 microHz) modulation periods

Modulation activity storms

Cassini inside

Saturnian magnetosphere

Results and conclusions:

• SKR intensity is modulated in a form of quasi-periodic modulation activity storms or modulation bursts. 43 stormsmay be distinguished during 2004.

• Modulation activity storms (modulation bursts) repeat almost periodically

(~ 9 days)

• Series of periodic pulses: ~10.75 h (0.02585 mHz) (correlated with Saturn rotation) with changing amplitude produce the modulation activity storms

• Amplitude of 10.75 h pulses has complex modulation with well pronounced 1.4-1.5 days and 12.8 days components.

• 9 days modulation may be due to propagating periodic compressions in solar wind; 12.8 days may be related to Titan (?), 1.4 days – to Enceladus (?)

• Magnetic field modulations show presence of 10.7 h, 12.8 days; 20 days and other components

• 10.7 h modulations of SKR and MF seem to be connected

Current work and future planes:Further identification of modulation lines to distinguish between solar and planetary effects requires similar analysis of 2005 records, extrapolation of SW data from other space missions.

Current work consist in long-periodic analysis of the Solar Wind parameters (SW density and velocity) measured by Ulysses spacecraft and propagated to the Cassini orbit using MHD model of the SW propagation (see Fig.4).

FFT with 2048 window size

Days, 2004

SW velocity

measured by Ulysses

SW velocity

measured by Ulysses

and propagated to the

Saturn orbitTime delay

~ 10 days

SKR intensity profile

Fig. 4

Fig. 2

Fig. 3

Filtered 10.7 h line intensity

Correlation with SKR pulse activity : (digital filter: f0 =0.0258 mHz , Δf = 0.001 mHz)

~0.026 mHz (~10.7 h)