Example of the solar wind spectra on 2012 July 6 between 1600 and 1900 UT: (a) the frequency spectra of the proton bulk speed; (b) proton thermal speed; and (c) ion density. In the panels, the original spectra are shown as small black dots; the rectangles stand for smoothed values; the fits of the spectra are highlighted by the red broken line; and values of the spectral slopes and breaks are given in each panel. The gas clumping factor estimated from the power spectrum of the density fluctuations is lower than 7-8 per cent for radii ~30-220 kpc from the center, leading to a density bias of less than 3-4 per cent in the cluster core. The overall shapes of these two spectra are very similar and the differences between the parameters of the fits are within the fit errors with the exception of Slope 2, which is steeper for the bulk than for the thermal speed. Later, the spectral slope of velocity fluctuations very close to −3/2 was confirmed as presented by many authors who used different spacecraft data and various techniques of spectral analysis (Mangeney et al. Abstract: We calculate the output power density spectrum for a simple voltage-controlled oscillator (VCO) circuit. Recently, a power-law spectrum of magnetic and density fluctuations with a spectral index close to −2.8 seems to have been established (e.g., Chen et al. ADS. 35 Power spectral analysis has been used to characterize slow wave activity (SWA, 1 to 4.5 Hz EEG power) in control and depressed subjects, which confirmed that SWS reductions in major depression were correlated with decrements in SWA and validated the use of EEG power spectra to … The density spectrum exhibits all features described by Chen et al. The blue and red points and lines mark two β ranges. The solar wind plasma is a strongly turbulent environment with electromagnetic fields and plasma properties that fluctuate over a wide range of timescales. BTW, in the above derivation, the power spectrum P (k) is dimensionless in term of the fluctuation f (x) = (x) = [y (x) - y] / y, where y is the average. (2013b) and Šafránková et al. This approach reflects the properties of compressive as well as Alfvénic fluctuations. 2013a). 84/32, Moscow 117997, Russia, J. Šafránková https://orcid.org/0000-0003-4178-5206, Z. Němeček https://orcid.org/0000-0002-8160-3051, C. H. K. Chen https://orcid.org/0000-0003-4529-3620, Received 2016 March 23 This way of smoothing is very effective, as can be seen in Figure 1 (see Šafránková et al. Figure 5. Its membership of about 7,000 individuals also includes physicists, mathematicians, geologists, engineers, and others whose research and educational interests lie within the broad spectrum of subjects comprising contemporary astronomy. We analyze the fluctuations of an electronic thermal current across an idealized molecular junction. Although these two interpretations are basically identical, the first of them underlines an increase of forcing, whereas the second accents the lack of dissipation. On the other hand, for the low-β events (blue), there is no correlation of the speed break point and inertial length frequency. Scaling of normalized break points of velocity fluctuations according to ion β. Observations of the solar wind magnetic field have shown that the magnetic power spectral density is a power law of approximately k −5/3 at large scales in the inertial range (e.g., Matthaeus & Goldstein 1982; Bruno & Carbone 2013), where aspects of the MHD approximation can be used (Biskamp 1993), as predicted by Goldreich & Sridhar . (2009), the plateau in the density spectrum is caused by a dominance of kinetic Alfvén over MHD turbulence and, consequently, break point 2 is a characteristic of kinetic fluctuations rather than an indication of dissipation. 2001; Salem et al. The slope of the bulk speed spectrum in the MHD range is close to the already suggested value of 3/2. The difference apparently decreases for the slopes around −2.5 but the number of such gradual spectra is rather small. FFT spectra computed on short time intervals (20 minutes are equal to about 4 × 104 data points) are often noisy and different techniques can be used to smooth them. Slopes 1 and 2 and break points of the bulk speed spectra, respectively, as a function of the same quantity of the thermal speed spectra. Search for other works by this author on: © 1995 Royal Astronomical Society. One can see a relatively good scaling of the high-β events with the gyrostructure frequency and a little worse but still a good scaling of the low-β events. 2014a). If you have a user account, you will need to reset your password the next time you login. Its spectral index was found to be close to −1.9 (Boldyrev et al. As the histogram shows, the set does not contain intervals with extreme values of β, and thus we have chosen values of 0.1 and 1 as limits. The American Astronomical Society. A comparison of corresponding panels in both Figures 7 and 8 reveals the following. 2007; Salem et al. A comparison of the spectral indices and break frequencies of bulk and thermal speed PSDs in Figure 3 demonstrates that there are no notable differences up to the end of the MHD range, but the spectrum of the thermal speed is more gradual at the kinetic range. (2015), namely, it consists of three power-law segments that are divided by two break points. of nonlinearity when the first objects collapse in the Universe is then complete-ly determined, characterized by a power spectrum for density fluctuations, P (k). Slightly different values obtained in our analysis (−1.47 in Figure 1 or 1.43 of the median spectrum in Figure 2) can be probably attributed to a limited set of data and thus the already published discussions on the formation of this slope (Podesta & Borovsky 2010; Boldyrev et al. Dependence of slope 2 on (a) bulk and (b) thermal PSD spectra as a function of ion β. The CMB power spectrum is defined somewhat differently with f (x) = (x) = [T (x) - T] as the millionth temperature difference at point x to its average. Receive alerts on all new research papers in American Astronomical Society CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We show how, based on considerations on the observed form of the galaxy two–point spatial correlation function ξ(r), a very simplified – yet surprisingly effective – model for the linear density fluctuations power spectrum can be constructed. 2012; Kiyani et al. 1 Why density fluctuations? Citation J. Šafránková et al 2016 ApJ 825 121, 1 Charles University, Faculty of Mathematics and Physics, V Holešovičkách 2, 180 00 Prague 8, Czech Republic, 2 Department of Physics, Imperial College London, London SW7 2AZ, UK, 3 Space Research Institute of Russian Academy of Sciences, Moscow, Russia, Profsoyuznaya ul. The Zel'dovich approximation, combined with an initial spectrum, appears to yield a surprisingly good prescription of the large-scale matter distribution for the evolution of structure in the Universe; in particular, it describes the evolution of structure fairly accurately well into the non-linear regime, and is thus superior to the standard Eulerian linear perturbation theory. A linear dependence of the density break point on this frequency suggests that the character of turbulence changes when the fluctuations become comparable to the proton gyroradius. These effects are more pronounced for the bulk speed fluctuations; thus the spectral indices corresponding to the kinetic range of bulk and thermal speed fluctuations are about equal for extreme ion β values. The study is focused on the spectral properties around the break between MHD and ion kinetic scales and Šafránková et al. A good correspondence of the bulk and thermal speed spectra is shown in Figure 3. The statistics, based on more than 42,000 individual spectra, show that: (1) the spectra of bulk and thermal speeds can be fitted by two power-law segments; (2) despite their large variations, the parameters characterizing frequency spectrum fits computed on each particular time interval are very similar for both quantities; (3) the median slopes of the bulk and thermal speeds of the segment attributed to the MHD scale are −1.43 and −1.38, respectively, whereas they are −3.08 and −2.43 in the kinetic range; (4) the kinetic range slopes of bulk and thermal speed spectra become equal when either the ion density or magnetic field strength are high; (5) the break between MHD and kinetic scales seems to be controlled by the ion β parameter; (6) the best scaling parameter for bulk and thermal speed variations is a sum of the inertial length and proton thermal gyroradius; and (7) the above conclusions can be applied to the density variations if the background magnetic field is very low. Figure 9. On the other hand, Figure 7(c) shows that the scaling suggested by Leamon et al. (2015) has shown a very good correlation of the break frequency between MHD and kinetic scales with the gyrostructure frequency for solar wind density variations, but the dependence on β was not analyzed. http://aurora.troja.mff.cuni.cz/spektr-r/project/. 2011; Borovsky 2012); however, Grappin et al. The previous section demonstrated a very similar behavior of thermal and bulk speed fluctuations; thus we will analyze only the bulk speed hereafter. The authors thank the Wind team for the magnetic field data. J. Šafránková1, Z. Němeček1, F. Němec1, L. Přech1, C. H. K. Chen2, and G. N. Zastenker3, Published 2016 July 11 • The fits shown by the red lines reveal that the similarity of the bulk and thermal speeds shown in Figure 1 is a typical feature. The concept and use of the power spectrum of a signal is fundamental in electrical engineering, especially in electronic communication systems, including radio communications, radars, and related systems, plus passive remote sensing technology. We first relate the observed large-scale shape of xi(r) to a power-law form for the power spectrum, P(k)\\propto k^{-2.2}. The results are relevant for the slow solar wind because the instrumental limitations of the BMSW instrument on board the Spektr-R spacecraft did not allow a reliable determination of speeds exceeding 570 km s−1. The inertial length frequency, fL, is defined as the ratio fL = Vsw/ 2π L where L is the inertial length. In other words, the break-point frequency defines the smallest structures that could be supported by MHD processes under given conditions. The power spectral density of the oscillator is composed of a term related to the high-frequency fluctuations in the feedback loop and a term related to the low-frequency fluctuations of the frequency control voltage. Export citation and abstract The correlation coefficients are low (0.14), and thus we can conclude that the spectral break does not depend on the inertial length frequency for our low-β events. Since the density break-point frequency changes by an order of magnitude but the solar wind speed only cahnges by a factor of two, the spatial dimensions of turbulent eddies are more important. An expression is derived which relates the mean curvature of isodensity surfaces to the power spectrum of density fluctuations in the linear regime of Gaussian fluctuations with random phases. The meaning of points and lines is the same as in previous figures. For this reason, the present study is limited to 2 Hz only. 2011a; Chen et al. Therefore, 1/f noise can not be obtained by the simple procedure of integration or of differentiation of such convenient signals. According to Chandran et al. The same is true for Slope 1, which corresponds to the range of MHD fluctuations. The power spectrum of matter density fluctuations has now been measured with considerable accuracy across roughly four decades in scale. The automated routine fits each individual smoothed spectrum with two power-law functions and the break point is determined as the frequency corresponding to their intersection. The velocity break frequency is always lower than both the inertial length frequency and the gyrostructure frequency. Since we would like to compare the results of this study of velocity fluctuations with a similar analysis of density fluctuations (Šafránková et al. The correlation coefficients above the panel are given for the full data set (black) and for particular subsets. Between ion and electron scales, a small-scale turbulent cascade of the magnetic energy from proton scales, where kinetic properties of ions do not meet fluid approximations, is characterized by a steeper power law with a spectral index varying between −2 and −4 (e.g., Leamon et al. Since the velocity break frequency is between the two breaks of the density spectrum, we can conclude that the breakdown of the MHD cascade happens in all fields in roughly the same place. Peter Schneider, Matthias Bartelmann, The power spectrum of density fluctuations in the Zel'dovich approximation, Monthly Notices of the Royal Astronomical Society, Volume 273, Issue 2, March 1995, Pages 475–483, https://doi.org/10.1093/mnras/273.2.475. Between magnetic and kinetic energies is usually analyzed using the sum of the dependence close... Becomes gradual if the dissipation weakens ( e.g., Smith et al magnetic kinetic! Return to this pdf, sign in to an existing account, will... 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Figure 3 ( c ) power spectral density of the red thick line show in... 7 and 8 reveals the following contrast, all available solar wind measurements are shown in Figure apparently!

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