# Posts Tagged structure function

## Today's Postings

### OH Maser Sources in W49N: Probing Magnetic Field and Differential Anisotropic Scattering with Zeeman pairs using the VLBA

Our analysis of a VLBA 12-hour synthesis observation of the OH masers in a well-known star-forming region W49N has yielded valuable data that enables us to probe distributions of magnetic fields in both the maser columns and the intervening interstellar medium (ISM). The data consisting of detailed high angular-resolution images (with beam-width ~20 milli-arc-seconds) of several dozen OH maser sources or "spots", at 1612, 1665 and 1667 MHz, reveal anisotropic scatter broadening, with typical sizes of a few tens of milli-arc-seconds and axial ratios between 1.5 to 3. Such anisotropies have been reported earlier by Desai, Gwinn & Diamond (1994) and interpreted as induced by the local magnetic field parallel to the Galactic plane. However, we find a) the apparent angular sizes on the average a factor of ~2.5 less than those reported by Desai et al. (1994), indicating significantly less scattering than inferred earlier, and b) a significant deviation in the average orientation of the scatter-broadened images (by ~10 degrees) from that implied by the magnetic field in the Galactic plane. More intriguingly, for a few Zeeman pairs in our set, significant differences (up to 6 sigma) are apparent in the scatter broadened images for the two hands of circular polarization, even when apparent velocity separation is less than 0.1 km/s. This may possibly be the first example of a Faraday rotation contribution to the diffractive effects in the ISM. Using the Zeeman pairs, we also study the distribution of magnetic field in the W49N complex, finding no significant trend in the spatial structure function. In this paper, we present the details of our observations and analysis leading to these findings, discuss implications of our results for the intervening anisotropic magneto-ionic medium, and suggest the possible implications for the structure of magnetic fields within this star-forming region.

### Modeling Statistical Properties of Solar Active Regions through DNS of 3D-MHD Turbulence

Statistical properties of the Sun’s photospheric turbulent magnetic field, especially those of the Active Regions (ARs), have been studied using the line-of-sight data from magnetograms taken by SOHO and several other instruments (see e.g. Abramenko et al (2002, 2003),Abramenko and Yurchyshyn (2010)). This includes structure functions and their exponents, flatness curves and correlation functions. In these works, the dependence of structure function exponents ($\zeta_p$) of the order of the structure functions ($\it{p}$) was modeled using a non-intermittent K41 model. It is now well known that the ARs are highly turbulent and are associated with strong intermittent events. In this paper we compare some of the observations from Abramenko et al (2003) with the log-Poisson model (Biskamp 2003) used for modeling intermittent MHD turbulent flows. Next, we analyze the structure function data obtained from the direct numerical simulations (DNS) of homogeneous, incompressible 3D-MHD turbulence in three cases: sustained by forcing, freely decaying and a flow initially driven and later allowed to decay (case 3). The respective DNS replicate the properties seen in the plots of $\zeta_p$ against $\it{p}$ of ARs. We also reproduce the trends and changes observed in intermittency in flatness [Abramenko and Yurchyshyn (2010)] and correlation functions [Abramenko et al (2003)] of ARs. It is suggested from this analysis that an AR in the onset phase of a flare can be treated as a forced 3D-MHD turbulent system in its simplest form and that the flaring stage is representative of decaying 3D-MHD turbulence. It is also inferred that significant changes in intermittency from the initial onset phase of a flare to its final peak flaring phase, are related to the time taken by the system to reach the initial onset phase.

### A multi-epoch spectroscopic study of the BAL quasar APM 08279+5255: I. C IV absorption variability

Broad Absorption Lines indicate gas outflows with velocities from thousands km/s to about 0.2 the speed of light, which may be present in all quasars and may play a major role in the evolution of the host galaxy. The variability of absorption patterns can provide informations on changes of the density and velocity distributions of the absorbing gas and its ionization status. We collected 23 photometrical and spectro-photometrical observations at the 1.82m Telescope of the Asiago Observatory since 2003, plus other 5 spectra from the literature. We analysed the evolution in time of the equivalent width of the broad absorption feature and two narrow absorption systems, the correlation among them and with the R band magnitude. We performed a structure function analysis of the equivalent width variations. We present an unprecedented monitoring of a broad absorption line quasar based on 28 epochs in 14 years. The shape of broad absorption feature shows a relative stability, while its equivalent width slowly declines until it sharply increases during 2011. In the same time the R magnitude stays almost constant until it sharply increases during 2011. The equivalent width of the narrow absorption redwards of the systemic redshift only shows a decline. The broad absorption behaviour suggests changes of the ionisation status as the main cause of variability. We show for the first time a correlation of this variability with the R band flux. The different behaviour of the narrow absorption system might be due to recombination time delay. The structure function of the absorption variability has a slope comparable with typical optical variability of quasars. This is consistent with variations of the 200 A ionising flux originating in the inner part of the accretion disk.

### The Perils of Analytic Continuation [Cross-Listing]

A nice paper by Morrison demonstrates the recent convergence of opinion that has taken place concerning the graviton propagator on de Sitter background. We here discuss the few points which remain under dispute. First, the inevitable decay of tachyonic scalars really does result in their 2-point functions breaking de Sitter invariance. This is obscured by analytic continuation techniques which produce formal solutions to the propagator equation that are not propagators. Second, Morrison’s de Sitter invariant solution for the spin two sector of the graviton propagator involves derivatives of the scalar propagator at $M^2 = 0$, where it is not meromorphic unless de Sitter breaking is permitted. Third, de Sitter breaking does not require zero modes. Fourth, the ambiguity Morrison claims in the equation for the spin two structure function is fixed by requiring it to derive from a mode sum. Fifth, Morrison’s spin two sector is not "physically equivalent" to ours because their coincidence limits differ. Finally, it is only the noninvariant propagator that gets the time independence and scale invariance of the tensor power spectrum correctly.

### Principal Component Analysis of Spectral Line Data: Analytic Formulation

Principal component analysis is a powerful statistical system to investigate the structure and dynamics of the molecular interstellar medium, with particular emphasis on the study of turbulence, as revealed by spectroscopic imaging of molecular line emission. To-date, the method to retrieve the power law index of the velocity structure function or power spectrum has relied on an empirical calibration and testing with model turbulent velocity fields, while lacking a firm theoretical basis. In this paper, we present an analytic formulation that reveals the detailed mechanics of the method and confirms previous empirical calibrations of its recovery of the scale dependence of turbulent velocity fluctuations.

### A Study of starless dark cloud LDN 1570: Distance, Dust properties and Magnetic field geometry

We wish to map the magnetic field geometry and to study the dust properties of the starless cloud, L1570, using multi-wavelength optical polarimetry and photometry of the stars projected on the cloud. We made R-band imaging polarimetry of the stars projected on a cloud, L1570, to trace the magnetic field orientation. We also made multi-wavelength polarimetric and photometric observations to constrain the properties of dust in L1570. We estimated a distance of 394 +/- 70 pc to the cloud using 2MASS JHKs colours. Using the values of the Serkowski parameters namely $\sigma_{1}$, $\bar \epsilon$, {\lambda}max and the position of the stars on near infrared color-color diagram, we identified 13 stars that could possibly have intrinsic polarization and/or rotation in their polarization angles. One star, 2MASS J06075075+1934177, which is a B4Ve spectral type, show the presence of diffuse interstellar bands in the spectrum apart from showing H{\alpha} line in emission. There is an indication for the presence of slightly bigger dust grains towards L1570 on the basis of the dust grain size-indicators such as {\lambda}max and Rv values. The magnetic field lines are found to be parallel to the cloud structures seen in the 250{\mu}m images (also in 8{\mu}m and 12{\mu}m shadow images) of L1570. Based on the magnetic field geometry, the cloud structure and the complex velocity structure, we believe that L1570 is in the process of formation due to the converging flow material mediated by the magnetic field lines. Structure function analysis showed that in the L1570 cloud region the large scale magnetic fields are stronger when compared with the turbulent component of magnetic fields. The estimated magnetic field strengths suggest that the L1570 cloud region is sub-critical and hence could be strongly supported by the magnetic field lines.

### Complementarity of direct and indirect Dark Matter detection experiments [Cross-Listing]

We investigate the prospects for reconstructing the mass, spin-independent and spin-dependent cross-sections of Dark Matter particles with a combination of a future direct detection experiments such as XENON1T, and the IceCube neutrino telescope in the 86-string configuration including the DeepCore array. We quantify the degree of complementarity between the two experiments by adopting realistic values for their exposure, energy threshold and resolution. Starting from benchmark models arising from a supersymmetric model with 25 free parameters, we show that despite the stringent constraints set by the run with 79 strings, IceCube can help break the degeneracies in the Dark Matter cross-section parameter space, even in the unfortunate case where it fails to discover high energy neutrinos from the Sun. We also discuss how the uncertainties associated with the nuclear structure function and with astrophysical quantities such as the Dark Matter density and velocity distribution affect the reconstruction of the Dark Matter particle parameters from the combined datasets.

### Yaglom law in the expanding solar wind

We study the Yaglom law, which relates the mixed third order structure function to the average dissipation rate of turbulence, in a uniformly expanding solar wind by using the two scales expansion model of magnetohydrodynamic (MHD) turbulence. We show that due to the expansion of the solar wind two new terms appear in the Yaglom law. The first term is related to the decay of the turbulent energy by nonlinear interactions, whereas the second term is related to the non-zero cross-correlation of the Els\"asser fields. Using magnetic field and plasma data from WIND and Helios 2 spacecrafts, we show that at lower frequencies in the inertial range of MHD turbulence the new terms become comparable to Yaglom’s third order mixed moment, and therefore they cannot be neglected in the evaluation of the energy cascade rate in the solar wind.

### Simulated Faraday Rotation Measures toward High Galactic Latitudes

We study the Faraday rotation measure (RM) due to the Galactic magnetic field (GMF) toward high Galactic latitudes. The RM arises from the global, regular component as well as from the turbulent, random component of the GMF. We model the former based on observations and the latter using the data of magnetohydrodynamic turbulence simulations. For a large number of different GMF models, we produce mock RM maps around the Galactic poles and calculate various statistical quantities with the RM maps. We find that the observed medians of RMs toward the north and south Galactic poles, $\sim 0.0\pm 0.5 {\rm rad m^{-2}}$ and $\sim +6.3\pm 0.5 {\rm rad m^{-2}}$, are difficult to explain with any of our many alternate GMF models. The standard deviation of observed RMs, $\sim 9 {\rm rad m^{-2}}$, is clearly larger than that of simulated RMs. The second-order structure function of observed RMs is substantially larger than that of simulated RMs, especially at small angular scales. We discuss other possible contributions to RM toward high Galactic latitudes. Besides observational errors and the intrinsic RM of background radio sources against which RM is observed, we suggest that the RM due to the intergalactic magnetic field may account for a substantial fraction of the observed RM. Finally we note that reproducing the observed medians may require additional components or/and structures of the GMF that are not present in our models.

### A comparative study of optical/ultraviolet variability of narrow-line Seyfert 1 and broad-line Seyfert 1 active galactic nuclei

The ensemble optical/ultraviolet variability of narrow-line Seyfert 1 (NLS1) type active galactic nuclei (AGNs) is investigated, based on a sample selected from the Sloan Digital Sky Survey (SDSS) Stripe-82 region with multi-epoch photometric scanning data. As a comparison a control sample of broad-line Seyfert 1 (BLS1) type AGNs is also incorporated. To quantify properly the intrinsic variation amplitudes and their uncertainties, a novel method of parametric maximum-likelihood is introduced, that has, as we argued, certain virtues over previously used methods. The majority of NLS1-type AGNs exhibit significant variability on timescales from about ten days to a few years with, however, on average smaller amplitudes compared to BLS1-type AGNs. About 20 NLS1- type AGNs showing relatively large variations are presented, that may deserve future monitoring observations, for instance, reverberation mapping. The averaged structure functions of variability, constructed using the same maximumlikelihood method, show remarkable similarity in shape for the two types of AGNs on timescales longer than about 10 days, which can be approximated by a power-law or an exponential function. This, along with other similar properties, such as the wavelength-dependent variability, are indicative of a common dominant mechanism responsible for the long-term optical/UV variability of both NLS1- and BLS1-type AGNs. Towards the short timescales, however, there is tentative evidence that the structure function of NLS1-type AGNs continues declining, whereas that of BLS1-type AGNs flattens with some residual variability on timescales of days. If this can be confirmed, it may suggest that an alternative mechanism, such as X-ray reprocessing, starts to become dominating in BLS1-type AGNs, but not in NLS1-, on such timescales.

### Variability and the X-ray/UV ratio of active galactic nuclei. II. Analysis of a low-redshift Swift sample

Variability, both in X-ray and optical/UV, affects the well-known anti-correlation between the $\alpha_{ox}$ spectral index and the UV luminosity of active galactic nuclei, contributing part of the dispersion around the average correlation ("intra-source dispersion"), in addition to the differences among the time-average $\alpha_{ox}$ values from source to source ("inter-source dispersion"). We want to evaluate the intrinsic $\alpha_{ox}$ variations in individual objects, and their effect on the dispersion of the $\alpha_{ox}-L_{UV}$ anti-correlation. We use simultaneous UV/X-ray data from Swift observations of a low-redshift sample, to derive the epoch-dependent $\alpha_{ox}(t)$ indices. We correct for the host galaxy contribution by a spectral fit of the optical/UV data. We compute ensemble structure functions to analyse variability of multi-epoch data. We find a strong "intrinsic $\alpha_{ox}$ variability", which makes an important contribution ($\sim40%$ of the total variance) to the dispersion of the $\alpha_{ox}-L_{UV}$ anti-correlation ("intra-source dispersion"). The strong X-ray variability and weaker UV variability of this sample are comparable to other samples of low-z AGNs, and are neither due to the high fraction of strongly variable NLS1s, nor to dilution of the optical variability by the host galaxies. Dilution affects instead the slope of the anti-correlation, which steepens, once corrected, becoming similar to higher luminosity sources. The structure function of $\alpha_{ox}$ increases with the time lag up to $\sim$1 month. This indicates the important contribution of the intermediate-long timescale variations, possibly generated in the outer parts of the accretion disk.

### SgrA* emission at 7mm: variability and periodicity

We present the result of 6 years monitoring of SgrA*, radio source associated to the supermassive black hole at the centre of the Milky Way. Single dish observations were performed with the Itapetinga radio telescope at 7 mm, and the contribution of the SgrA complex that surrounds SgrA* was subtracted and used as instantaneous calibrator. The observations were alternated every 10 min with those of the HII region SrgB2, which was also used as a calibrator. The reliability of the detections was tested comparing them with simultaneous observations using interferometric techniques. During the observing period we detected a continuous increase in the SgrA* flux density starting in 2008, as well as variability in timescales of days and strong intraday fluctuations. We investigated if the continuous increase in flux density is compatible with free-free emission from the tail of the disrupted compact cloud that is falling towards SgrA* and concluded that the increase is most probably intrinsic to SgrA*. Statistical analysis of the light curve using Stellingwerf and Structure Function methods revealed the existence of two minima, 156 +/- 10 and 220 +/- 10 days. The same statistical tests applied to a simulated light curve constructed from two quadratic sinusoidal functions superimposed to random variability reproduced very well the results obtained with the real light curve, if the periods were 57 and 156 days. Moreover, when a daily sampling was used in the simulated light curve, it was possible to reproduce the 2.3 GHz structure function obtained by Falcke in 1999, which revealed the 57 days period, while the 106 periodicity found by Zhao et al in 2001 could be a resonance of this period.

### Nuclear uncertainties in the spin-dependent structure functions for direct dark matter detection [Cross-Listing]

We study the effect that uncertainties in the nuclear spin-dependent structure functions have in the determination of the dark matter (DM) parameters in a direct detection experiment. We show that different nuclear models that describe the spin-dependent structure function of specific target nuclei can lead to variations in the reconstructed values of the DM mass and scattering cross-section. We propose a parametrization of the spin structure functions that allows us to treat these uncertainties as variations of three parameters, with a central value and deviation that depend on the specific nucleus. The method is illustrated for germanium and xenon detectors with an exposure of 300 kg yr, assuming a hypothetical detection of DM and studying a series of benchmark points for the DM properties. We find that the effect of these uncertainties can be similar in amplitude to that of astrophysical uncertainties, especially in those cases where the spin-dependent contribution to the elastic scattering cross-section is sizable.

### Nuclear uncertainties in the spin-dependent structure functions for direct dark matter detection [Replacement]

We study the effect that uncertainties in the nuclear spin-dependent structure functions have in the determination of the dark matter (DM) parameters in a direct detection experiment. We show that different nuclear models that describe the spin-dependent structure function of specific target nuclei can lead to variations in the reconstructed values of the DM mass and scattering cross-section. We propose a parametrization of the spin structure functions that allows us to treat these uncertainties as variations of three parameters, with a central value and deviation that depend on the specific nucleus. The method is illustrated for germanium and xenon detectors with an exposure of 300 kg yr, assuming a hypothetical detection of DM and studying a series of benchmark points for the DM properties. We find that the effect of these uncertainties can be similar in amplitude to that of astrophysical uncertainties, especially in those cases where the spin-dependent contribution to the elastic scattering cross-section is sizable.

### Driven Multifluid MHD Molecular Cloud Turbulence

It is believed that turbulence may have a significant impact on star formation and the dynamics and evolution of the molecular clouds in which this occurs. It is also known that non-ideal magnetohydrodynamic effects influence the nature of this turbulence. We present the results of a numerical study of 4-fluid MHD turbulence in which the dynamics of electrons, ions, charged dust grains and neutrals and their interactions are followed. The parameters describing the fluid being simulated are based directly on observations of molecular clouds. We find that the velocity and magnetic field power spectra are strongly influenced by multifluid effects on length-scales at least as large as 0.05 pc. The PDFs of the various species in the system are all found to be close to log-normal, with charged species having a slightly less platykurtic (flattened) distribution than the neutrals. We find that the introduction of multifluid effects does not significantly alter the structure functions of the centroid velocity increment.

### A divergence-cleaning scheme for cosmological SPMHD simulations

In magnetohydrodynamics (MHD), the magnetic field is evolved by the induction equation and coupled to the gas dynamics by the Lorentz force. We perform numerical smoothed particle magnetohydrodynamics (Spmhd) simulations and study the influence of a numerical magnetic divergence. For instabilities arising from divergence B related errors, we find the hyperbolic/parabolic cleaning scheme suggested by Dedner et al. 2002 to give good results and prevent numerical artifacts from growing. Additionally, we demonstrate that certain current Spmhd implementations of magnetic field regularizations give rise to unphysical instabilities in long-time simulations. We also find this effect when employing Euler potentials (divergenceless by definition), which are not able to follow the winding-up process of magnetic field lines properly. Furthermore, we present cosmological simulations of galaxy cluster formation at extremely high resolution including the evolution of magnetic fields. We show synthetic Faraday rotation maps and derive structure functions to compare them with observations. Comparing all the simulations with and without divergence cleaning, we are able to confirm the results of previous simulations performed with the standard implementation of MHD in Spmhd at normal resolution. However, at extremely high resolution, a cleaning scheme is needed to prevent the growth of numerical errors at small scales.

### A seasonal cycle and an abrupt change in the variability characteristics of the intraday variable source S4~0954+65

The BLLac object S4 0954+65 is one of the main targets of the Urumqi monitoring program for IntraDay Variable (IDV) sources. Between August 2005 and December 2009, the source was included in 41 observing sessions, carried out at a frequency of 4.8 GHz. The time analysis of the collected light curves, performed through both a structure function analysis and a specifically developed wavelet-based algorithm, disclosed the existence of an annual cycle in the variability timescales, suggesting a fundamental contribution of interstellar scintillation to the IDV pattern of the source. The combined use of the two analysis methods also revealed a dramatic change in the variability characteristics of the source between February and March 2008, at the starting time of a strong outburst phase. The analysis’ results suggest that the flaring state of the source coincides with the appearance of multiple timescales in its light curves, indicating that changes in the structure of the relativistically moving emitting region may strongly influence the variability observed on IDV timescales.

### A seasonal cycle and an abrupt change in the variability characteristics of the intraday variable source S4 0954+65 [Replacement]

The BLLac object S4 0954+65 is one of the main targets of the Urumqi monitoring program targeting IntraDay Variable (IDV) sources. Between August 2005 and December 2009, the source was included in 41 observing sessions, carried out at a frequency of 4.8 GHz. The time analysis of the collected light curves, performed by applying both a structure function analysis and a specifically developed wavelet-based algorithm, discovered an annual cycle in the variability timescales, suggesting that there is a fundamental contribution by interstellar scintillation to the IDV pattern of the source. The combined use of the two analysis methods also revealed that there was a dramatic change in the variability characteristics of the source between February and March 2008, at the starting time of a strong outburst phase. The analysis’ results suggest that the flaring state of the source coincides with the appearance of multiple timescales in its light curves, indicating that changes in the structure of the relativistically moving emitting region may strongly influence the variability observed on IDV timescales.

### Magnetic Discontinuities in Magnetohydrodynamic Turbulence and in the Solar Wind

Recent measurements of solar wind turbulence report the presence of intermittent, exponentially distributed angular discontinuities in the magnetic field. In this Letter, we study whether such discontinuities can be produced by magnetohydrodynamic (MHD) turbulence. We detect the discontinuities by measuring the fluctuations of the magnetic field direction, Delta theta, across fixed spatial increments Delta x in direct numerical simulations of MHD turbulence with an imposed uniform guide field B_0. A large region of the probability density function (pdf) for Delta theta is found to follow an exponential decay, proportional to exp(-Delta theta/theta_*), with characteristic angle theta_* ~ (14 deg) (b_rms/B_0)^0.65 for a broad range of guide-field strengths. We find that discontinuities observed in the solar wind can be reproduced by MHD turbulence with reasonable ratios of b_rms/B_0. We also observe an excess of small angular discontinuities when Delta x becomes small, possibly indicating an increasing statistical significance of dissipation-scale structures. The structure of the pdf in this case closely resembles the two-population pdf seen in the solar wind. We thus propose that strong discontinuities are associated with inertial-range MHD turbulence, while weak discontinuities emerge from near-dissipation-range turbulence. In addition, we find that the structure functions of the magnetic field direction exhibit anomalous scaling exponents, which indicates the existence of intermittent structures.

### Stochastic variability in X-ray emission from the black hole binary GRS 1915+105

We examine stochastic variability in the dynamics of X-ray emission from the black hole system GRS 1915+105, a strongly variable microquasar commonly used for studying relativistic jets and the physics of black hole accretion. The analysis of sample observations for 13 different states in both soft (low) and hard (high) energy bands is performed by flicker-noise spectroscopy (FNS), a phenomenological time series analysis method operating on structure functions and power spectrum estimates. We find the values of FNS parameters, including the Hurst exponent, flicker-noise parameter, and characteristic time scales, for each observation based on multiple 2,500-second continuous data segments. We identify four modes of stochastic variability driven by dissipative processes that may be related to viscosity fluctuations in the accretion disk around the black hole: random (RN), power-law (1F), one-scale (1S), and two-scale (2S). The variability modes are generally the same in soft and hard energy bands of the same observation. We discuss the potential for future FNS studies of accreting black holes.

### Tiny scale opacity fluctuations from VLBA, MERLIN and VLA observations of HI absorption toward 3C 138

The structure function of opacity fluctuations is a useful statistical tool to study tiny scale structures of neutral hydrogen. Here we present high resolution observation of HI absorption towards 3C 138, and estimate the structure function of opacity fluctuations from the combined VLA, MERLIN and VLBA data. The angular scales probed in this work are ~ 10-200 milliarcsec (about 5-100 AU). The structure function in this range is found to be well represented by a power law S_tau(x) ~ x^{beta} with index beta ~ 0.33 +/- 0.07 corresponding to a power spectrum P_tau(U) ~ U^{-2.33}. This is slightly shallower than the earlier reported power law index of ~ 2.5-3.0 at ~ 1000 AU to few pc scales. The amplitude of the derived structure function is a factor of ~ 20-60 times higher than the extrapolated amplitude from observation of Cas A at larger scales. On the other hand, extrapolating the AU scale structure function for 3C 138 predicts the observed structure function for Cas A at the pc scale correctly. These results clearly establish that the atomic gas has significantly more structures in AU scales than expected from earlier pc scale observations. Some plausible reasons are identified and discussed here to explain these results. The observational evidence of a shallower slope and the presence of rich small scale structures may have implications for the current understanding of the interstellar turbulence.

### 12 years of X-ray variability in M31 globular clusters, including 8 black hole candidates, as seen by Chandra [Replacement]

We examined 134 Chandra observations of the population of X-ray sources associated with globular clusters (GCs) in the central region of M31. These are expected to be X-ray binary systems (XBs), consisting of a neutron star or black hole accreting material from a close companion. We created long-term lightcurves for these sources, correcting for background, interstellar absorption and instrumental effects. We tested for variability by examining the goodness of fit for the best fit constant intensity. We also created structure functions (SFs) for every object in our sample, the first time this technique has been applied to XBs. We found significant variability in 28 out of 34 GCs and GC candidates; the other 6 sources had 0.3–10 keV luminosities fainter than ~2E+36 erg/s, limiting our ability to detect similar variability. The SFs of XBs with 0.3–10 keV luminosities ~2–50 E+36 generally showed considerably more variability than the published ensemble SF of AGN. Our brightest XBs were mostly consistent with the AGN SF; however, their 2–10 keV fluxes could be matched by <1 AGN per square degree. These encouraging results suggest that examining the long term lightcurves of other X-ray sources in the field may provide an important distinction between X-ray binaries and background galaxies, as the X-ray emission spectra from these two classes of X-ray sources are similar. Additionally, we identify 3 new black hole candidates (BHCs) using additional XMM-Newton data, bringing the total number of M31 GC BHCs to 9, with 8 covered in this survey.

### Constraints on the ICM velocity power spectrum from the X-ray lines width and shift

Future X-ray observations of galaxy clusters by high spectral resolution missions will provide spatially resolved measurements of the energy and width for the brightest emission lines in the intracluster medium (ICM) spectrum. In this paper we discuss various ways of using these high resolution data to constrain velocity power spectrum in galaxy clusters. We argue that variations of these quantities with the projected distance R in cool core clusters contain important information on the velocity field length scales in the ICM. The effective length $l_{\rm eff}$ along the line of sight, which provides dominant contribution to the line flux, increases with R, allowing one to probe the amplitude of the velocity variations at different spatial scales. In particular, we show that the width of the line as a function of R is closely linked to the structure function of the 3D velocity field. Yet another easily obtainable proxy of the velocity field length scales is the ratio of the amplitude of the projected velocity field (line energy) variations to the dispersion of the velocity along the line of sight (line width). Finally the projected velocity field can be easily converted into 3D velocity field, especially for clusters like Coma with an extended flat core in the surface brightness. Under assumption of a homogeneous isotropic Gaussian 3D velocity field we derived simple expressions relating the power spectrum of the 3D velocity field (or structure function) and the observables. The uncertainties in the observables, caused by stochastic nature of the velocity field, are estimated by making multiple realizations of the random Gaussian velocity field and evaluating the scatter in observables. If large scale motions are present in the ICM these uncertainties may dominate the statistical errors of line width and shift measurements.

### Characterization of Turbulence from Submillimeter Dust Emission

In this paper we use our recent technique for estimating the turbulent component of the magnetic field to derive the structure functions of the unpolarized emission as well as that of the Stokes Q and U parameters of the polarized emission. The solutions for the structure functions to 350-um SHARP polarization data of OMC-1 allow the determination of the corresponding turbulent correlation length scales. The estimated values for these length scales are 9.4″ +/- 0.1″, 7.3″ +/- 0.1″, 12.6″ +/- 0.2″ (or 20.5 +/- 0.2, 16.0 +/- 0.2, and 27.5 +/- 0.4 mpc at 450 pc, the adopted distance for OMC-1) for the Stokes Q and U parameters, and for the unpolarized emission N, respectively. Our current results for Q and U are consistent with previous results obtained through other methods, and may indicate presence of anisotropy in magnetized turbulence. We infer a weak coupling between the dust component responsible for the unpolarized emission N and the magnetic field B from the significant difference between their turbulent correlation length scales.

### Long-term X-ray variability of Swift J1644+57

We studied the X-ray timing and spectral variability of the X-ray source Sw J1644+57, a candidate for a tidal disruption event. We have separated the long-term trend (an initial decline followed by a plateau) from the short-term dips in the Swift light-curve. Power spectra and Lomb-Scargle periodograms hint at possible periodic modulation. By using structure function analysis, we have shown that the dips were not random but occurred preferentially at time intervals ~ [2.3, 4.5, 9] x 10^5 s and their higher-order multiples. After the plateau epoch, dipping resumed at ~ [0.7, 1.4] x 10^6 s and their multiples. We have also found that the X-ray spectrum became much softer during each of the early dip, while the spectrum outside the dips became mildly harder in its long-term evolution. We propose that the jet in the system undergoes precession and nutation, which causes the collimated core of the jet briefly to go out of our line of sight. The combined effects of precession and nutation provide a natural explanation for the peculiar patterns of the dips. We interpret the slow hardening of the baseline flux as a transition from an extended, optically thin emission region to a compact, more opaque emission core at the base of the jet.

### Long-term X-ray variability of Swift J1644+57 [Replacement]

We studied the X-ray timing and spectral variability of the X-ray source Sw J1644+57, a candidate for a tidal disruption event. We have separated the long-term trend (an initial decline followed by a plateau) from the short-term dips in the Swift light-curve. Power spectra and Lomb-Scargle periodograms hint at possible periodic modulation. By using structure function analysis, we have shown that the dips were not random but occurred preferentially at time intervals ~ [2.3, 4.5, 9] x 10^5 s and their higher-order multiples. After the plateau epoch, dipping resumed at ~ [0.7, 1.4] x 10^6 s and their multiples. We have also found that the X-ray spectrum became much softer during each of the early dip, while the spectrum outside the dips became mildly harder in its long-term evolution. We propose that the jet in the system undergoes precession and nutation, which causes the collimated core of the jet briefly to go out of our line of sight. The combined effects of precession and nutation provide a natural explanation for the peculiar patterns of the dips. We interpret the slow hardening of the baseline flux as a transition from an extended, optically thin emission region to a compact, more opaque emission core at the base of the jet.

### Local Anisotropy, Higher Order Statistics, and Turbulence Spectra [Cross-Listing]

Correlation anisotropy emerges dynamically in magnetohydrodynamics (MHD), producing stronger gradients across the large-scale mean magnetic field than along it. This occurs both globally and locally, and has significant implications in space and astrophysical plasmas, including particle scattering and transport, and theories of turbulence. Properties of local correlation anisotropy are further documented here by showing through numerical experiments that the effect is intensified in more localized estimates of the mean field. The mathematical formulation of this property shows that local anisotropy mixes second-order with higher order correlations. Sensitivity of local statistical estimates to higher order correlations can be understood in connection with the stochastic coordinate system inherent in such formulations. We demonstrate this in specific cases, illustrate the connection to higher order statistics by showing the sensitivity of local anisotropy to phase randomization, and thus establish that the local structure function is not a measure of the energy spectrum. Evidently the local enhancement of correlation anisotropy is of substantial fundamental interest, and this phenomenon must be understood in terms of higher order correlations, fourth-order and above.

### Ensemble Variability of Near-Infrared-Selected Active Galactic Nuclei

We present the properties of the ensemble variability $V$ for nearly 5000 near-infrared (NIR) AGNs selected from the catalog of Quasars and Active Galactic Nuclei (13th Ed.) and the SDSS-DR7 quasar catalog. From 2MASS, DENIS, and UKIDSS/LAS point source catalogs, we extract 2MASS-DENIS and 2MASS-UKIDSS counterparts for cataloged AGNs by catalog cross-identification. We further select variable AGNs based on an optimal criterion for selecting the variable sources. The sample objects are divided into subsets according to whether NIR light originates by optical or NIR emission in the rest frame; and we examine the correlations of the ensemble variability with the rest-frame wavelength, redshift, luminosity, and rest-frame time lag. In addition, we also examine the correlations of variability amplitude with optical variability, radio intensity, and radio-to-optical flux ratio. The rest-frame optical variability of our samples shows known negative correlations with luminosity and positive correlations with rest-frame time lag (i.e., the structure function, SF). However, no well-known negative correlation exists between the rest wavelength and optical variability. This inconsistency might be due to a biased sampling of high-redshift AGNs. NIR variability in the rest frame is anticorrelated with the rest wavelength, which is consistent with previous suggestions. However, correlations of NIR variability with luminosity and rest-frame time lag are the opposite of these correlations of the optical variability; that is, the NIR variability is positively correlated with luminosity but negatively correlated with the rest-frame time lag. Because these trends are qualitatively consistent with the properties of radio-loud quasars reported by some previous studies, most of our sample objects are probably radio-loud quasars. Finally, we also discuss the negative correlations seen in the NIR SFs.

### The Coincidence Limit of the Graviton Propagator in de Donder Gauge on de Sitter Background [Cross-Listing]

We explicitly work out the de Sitter breaking contributions to the recent solution for the de Donder gauge graviton propagator on de Sitter. We also provide explicit power series expansions for the two structure functions, which are suitable for implementing dimensional regularization. And we evaluate the coincidence limit of the propagator.

### The Coincidence Limit of the Graviton Propagator in de Donder Gauge on de Sitter Background [Replacement]

We explicitly work out the de Sitter breaking contributions to the recent solution for the de Donder gauge graviton propagator on de Sitter. We also provide explicit power series expansions for the two structure functions, which are suitable for implementing dimensional regularization. And we evaluate the coincidence limit of the propagator.

### H\alpha\ Emission Variability in Active M Dwarfs

We use ~12,000 spectra of ~3,500 magnetically active M0-M9 dwarfs from the Sloan Digital Sky Survey taken at 10-15 minute intervals, together with ~300 spectra of ~60 M0-M8 stars obtained hourly with the Hydra multi-object spectrometer, to probe H\alpha\ variability on timescales of minutes to weeks. With multiple observations for every star examined, we are able to characterize fluctuations in H\alpha emission as a function of activity strength and spectral type. Stars with greater magnetic activity (as quantified by L_H\alpha/L_bol) are found to be less variable at all spectral types. We attribute this result to the stronger level of persistent emission in the high activity stars, requiring a larger heating event in order to produce measurable variability. We also construct H\alpha\ structure functions to constrain the timescale of variability. The more active objects with lower variability exhibit a characteristic timescale longer than an hour, likely due to larger, longer lasting heating events, while the less active objects with higher variability have a characteristic timescale shorter than 15 minutes.

### Statistical properties of supersonic turbulence in the Lagrangian and Eulerian frameworks [Replacement]

We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution, hydrodynamical grid simulations with Lagrangian tracer particles and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing on structure functions, their scaling exponents, and the probability density functions of the gas density and velocity increments. Compressively driven simulations show a significantly larger density contrast, a more intermittent behaviour, and larger fractal dimension of the most dissipative structures at the same root mean square Mach number. We show that the absolute values of Lagrangian and Eulerian structure functions of all orders in the integral range are only a function of the root mean square Mach number, but independent of the forcing. With the assumption of a Gaussian distribution for the probability density function of the velocity increments on large scales, we derive a model that describes this behaviour.

### Interaction of Fanaroff-Riley class II jets with a magnetised intra-cluster medium

We present 3-D MHD and synthetic numerical simulations to follow the evolution of randomly magnetized intra-cluster medium plasma under the effects of powerful, light, hypersonic and bipolar jets. We prescribe the cluster magnetic field (CMF) as a Gaussian random field with power law energy spectrum tuned to the expectation for Kolmogorov turbulence. We investigate the power of jets and the viewing angle used for the synthetic Rotation Measure (RM) observations. We find the model radio sources introduce and amplify fluctuations on the RM statistical properties; the average RM and the RM standard deviation are increased by the action of the jets. This may lead to overestimations of the CMFs’ strength up to 70%. The effect correlates with the jet power. Jets distort and amplify CMFs especially near the edges of the lobes and the jets’ heads. Thus the RM structure functions are flattened at scales comparable to the source size. Jet-produced RM enhancements depend on the orientation of the jet axis to the line of sight and are thus more apparent in quasars than in radio galaxies.

### Power Spectral Distribution of the BL Lacertae Object S5 0716+714 [Replacement]

Observational data in the BVRI bands of the variable BL Lacertae Object S5 0716+714 is discussed from the point of view of its Power Spectral Distribution (PSD). Analysis of the noise properties exhibited by the source. Assessment of the validity of a turbulent model. We fitted a model of the type $P(f) = \beta f^{-\alpha} + \gamma$ to the data for two null hypothesis and calculated the Bayesian p parameter for the fits. Different theoretical models are discussed and applied to these data and a special focus is placed on the MagnetoRotational Instability (MRI). The $P(f) = \beta f^{-\alpha}$ fit provides slopes with values ranging from 0.376 to 2.237, with medium values for each band of $\bar{\alpha}_B = 1.756$, $\bar{\alpha}_V = 1.704$, $\bar{\alpha}_R = 1.780$ and $\bar{\alpha}_I = 1.272$ respectively. An interval for the calculated effective $\alpha_{SS}$ parameter is obtained to be $[0.18,1.72]\cdot 10^{-2}$, corresponding to the order of magnitude previously inferred through both observational and numerical investigations. Structure function analysis, fractal dimension analysis and DFT analysis (all performed in other studies) plus our own analysis establish that the source is turbulent in a nontrivial way, i.e. there is “intrinsic” noise superimposed on the deterministic behavior of the source. We propose that embedding a weakly stochastic magnetic field component in the MRI (MagnetoRotational Instability) framework and taking into account stochastic reconnection of magnetic field lines might explain microvariability in AGN objects.

### Power Spectral Distribution of the BL Lacertae Object S5 0716+714

Observational data in the BVRI bands of the variable BL Lacertae Object S5 0716+714 is discussed from the point of view of its Power Spectral Distribution (PSD). Analysis of the noise properties exhibited by the source. Assessment of the validity of a turbulent model. We fitted a model of the type $P(f) = \beta f^{-\alpha} + \gamma$ to the data for two null hypothesis and calculated the Bayesian p parameter for the fits. Different theoretical models are discussed and applied to these data and a special focus is placed on the MagnetoRotational Instability (MRI). The $P(f) = \beta f^{-\alpha}$ fit provides slopes with values ranging from 0.376 to 2.237, with medium values for each band of $\bar{\alpha}_B = 1.756$, $\bar{\alpha}_V = 1.704$, $\bar{\alpha}_R = 1.780$ and $\bar{\alpha}_I = 1.272$ respectively. An interval for the calculated effective $\alpha_{SS}$ parameter is obtained to be $[0.18,1.72]\cdot 10^{-2}$, corresponding to the order of magnitude previously inferred through both observational and numerical investigations. Structure function analysis, fractal dimension analysis and DFT analysis (all performed in other studies) plus our own analysis establish that the source is turbulent in a nontrivial way, i.e. there is “intrinsic” noise superimposed on the deterministic behavior of the source. We propose that embedding a weakly stochastic magnetic field component in the MRI (MagnetoRotational Instability) framework and taking into account stochastic reconnection of magnetic field lines might explain microvariability in AGN objects.

### Ensemble X-ray variability of Active Galactic Nuclei from serendipitous source catalogues [Replacement]

The X-ray variability of the Active Galactic Nuclei (AGN) has been most often investigated with studies of individual, nearby, sources, and only a few ensemble analyses have been applied to large samples in wide ranges of luminosity and redshift. We want to determine the ensemble variability properties of two serendipitously selected AGN samples extracted from the catalogues of XMM-Newton and Swift, with redshift between ~0.2 and ~4.5, and X-ray luminosities, in the 0.5-4.5 keV band, between ~10^43 erg/s and ~10^46 erg/s. We use the structure function (SF), which operates in the time domain, and allows for an ensemble analysis even when only a few observations are available for individual sources and the power spectral density (PSD) cannot be derived. SF is also more appropriate than fractional variability and excess variance, because such parameters are biased by the duration of the monitoring time interval in the rest-frame, and thus by cosmological time dilation. We find statistically consistent results for the two samples, with the SF described by a power law of the time lag, approximately as SF \propto tau^0.1. We do not find evidence of the break in the SF, at variance with the case of lower luminosity AGNs. We confirm a strong anti-correlation of the variability with X-ray luminosity, accompanied by a change of the slope of the SF. We find evidence in support of a weak, intrinsic, average increase of X-ray variability with redshift. The change of amplitude and slope of the SF with X-ray luminosity provides new constraints on both single oscillator models and multiple subunits models of variability.

### Ensemble X-ray variability of Active Galactic Nuclei from serendipitous source catalogs

The X-ray variability of the Active Galactic Nuclei (AGN) has been most often investigated with studies of individual, nearby, sources, and only a few ensemble analyses have been applied to large samples in wide ranges of luminosity and redshift. We want to determine the ensemble variability properties of two serendipitously selected AGN samples extracted from the catalogs of XMM-Newton and Swift, with redshift between ~0.2 and ~4.5, and X-ray luminosities, in the 0.5-4.5 keV band, between ~10^43 erg/s and ~10^46 erg/s. We use the structure function (SF), which operates in the time domain, and allows for an ensemble analysis even when only a few observations are available for individual sources and the power spectral density (PSD) cannot be derived. SF is also more appropriate than fractional variability and excess variance, because such parameters are biased by the duration of the monitoring time interval in the rest-frame, and thus by cosmological time dilation. We find statistically consistent results for the two samples, with the SF described by a power law of the time lag, approximately as SF tau^0.1. We do not find evidence of the break in the SF, at variance with the case of lower luminosity AGNs. We confirm a strong anti-correlation of the variability with X-ray luminosity, accompanied by a change of the slope of the SF. We find evidence in support of a weak, intrinsic, average increase of X-ray variability with redshift. The change of amplitude and slope of the SF with X-ray luminosity provides new constraints on both single oscillator models and multiple subunits models of variability.

### Turbulent characteristics in the intensity fluctuations of a solar quiescent prominence observed by the \textit{Hinode} Solar Optical Telescope

We focus on Hinode Solar Optical Telescope (SOT) calcium II H-line observations of a solar quiescent prominence (QP) that exhibits highly variable dynamics suggestive of turbulence. These images capture a sufficient range of scales spatially ($\sim$0.1-100 arc seconds) and temporally ($\sim$16.8 s – 4.5 hrs) to allow the application of statistical methods used to quantify finite range fluid turbulence. We present the first such application of these techniques to the spatial intensity field of a long lived solar prominence. Fully evolved inertial range turbulence in an infinite medium exhibits multifractal \emph{scale invariance} in the statistics of its fluctuations, seen as power law power spectra and as scaling of the higher order moments (structure functions) of fluctuations which have non-Gaussian statistics; fluctuations $\delta I(r,L)=I(r+L)-I(r)$ on length scale $L$ along a given direction in observed spatial field $I$ have moments that scale as $\sim L^{\zeta(p)}$. For turbulence in a system that is of finite size, or that is not fully developed, one anticipates a generalized scale invariance or extended self-similarity (ESS) $\sim G(L)^{\zeta(p)}$. For these QP intensity measurements we find scaling in the power spectra and ESS. We find that the fluctuation statistics are non-Gaussian and we use ESS to obtain ratios of the scaling exponents $\zeta(p)$: these are consistent with a multifractal field and show distinct values for directions longitudinal and transverse to the bulk (driving) flow. Thus, the intensity fluctuations of the QP exhibit statistical properties consistent with an underling turbulent flow.

### Turbulent characteristics in the intensity fluctuations of a solar quiescent prominence observed by the \textit{Hinode} Solar Optical Telescope [Replacement]

We focus on Hinode Solar Optical Telescope (SOT) calcium II H-line observations of a solar quiescent prominence (QP) that exhibits highly variable dynamics suggestive of turbulence. These images capture a sufficient range of scales spatially ($\sim$0.1-100 arc seconds) and temporally ($\sim$16.8 s – 4.5 hrs) to allow the application of statistical methods used to quantify finite range fluid turbulence. We present the first such application of these techniques to the spatial intensity field of a long lived solar prominence. Fully evolved inertial range turbulence in an infinite medium exhibits multifractal \emph{scale invariance} in the statistics of its fluctuations, seen as power law power spectra and as scaling of the higher order moments (structure functions) of fluctuations which have non-Gaussian statistics; fluctuations $\delta I(r,L)=I(r+L)-I(r)$ on length scale $L$ along a given direction in observed spatial field $I$ have moments that scale as $\sim L^{\zeta(p)}$. For turbulence in a system that is of finite size, or that is not fully developed, one anticipates a generalized scale invariance or extended self-similarity (ESS) $\sim G(L)^{\zeta(p)}$. For these QP intensity measurements we find scaling in the power spectra and ESS. We find that the fluctuation statistics are non-Gaussian and we use ESS to obtain ratios of the scaling exponents $\zeta(p)$: these are consistent with a multifractal field and show distinct values for directions longitudinal and transverse to the bulk (driving) flow. Thus, the intensity fluctuations of the QP exhibit statistical properties consistent with an underling turbulent flow.

### New 6cm and 11cm observations of the supernova remnant CTA 1

(Abridged) We conducted new 6cm and 11cm observations of CTA 1 using the Urumqi 25-m and Effelsberg 100-m telescopes. Data at other wavelengths were included to investigate the spectrum and polarisation properties. We obtained new total intensity and polarisation maps at 6cm and 11cm with angular resolutions of 9.5 arcmin and 4.4 arcmin, respectively. We derived a spectral index of alpha=-0.63+/-0.05 based on the integrated flux densities at 408 MHz, 1420 MHz, 2639 MHz, and 4800 MHz. The spectral index map calculated from data at the four frequencies shows a clear steepening of the spectrum from the strong shell emission towards the north-western breakout region with weak diffuse emission. The decrease of the spectral index is up to about 0.3. The RM map derived from polarisation data at 6cm and 11cm shows a sharp transition between positive RMs in the north-eastern and negative RMs in the south-western part of the SNR. We note a corresponding RM pattern of extragalactic sources and propose the existence of a large-diameter Faraday screen in front of CTA 1, which covers the north-eastern part of the SNR. The RM of the Faraday screen is estimated to be about +45 rad/m2. A RM structure function of CTA 1 indicates a very regular magnetic field within the Faraday screen, which is larger than about 2.7 microG in case of 500 pc distance.

### New 6cm and 11cm observations of the supernova remnant CTA 1 [Replacement]

(Abridged) We conducted new 6cm and 11cm observations of CTA 1 using the Urumqi 25-m and Effelsberg 100-m telescopes. Data at other wavelengths were included to investigate the spectrum and polarisation properties. We obtained new total intensity and polarisation maps at 6cm and 11cm with angular resolutions of 9.5 arcmin and 4.4 arcmin, respectively. We derived a spectral index of alpha=-0.63+/-0.05 based on the integrated flux densities at 408 MHz, 1420 MHz, 2639 MHz, and 4800 MHz. The spectral index map calculated from data at the four frequencies shows a clear steepening of the spectrum from the strong shell emission towards the north-western breakout region with weak diffuse emission. The decrease of the spectral index is up to about 0.3. The RM map derived from polarisation data at 6cm and 11cm shows a sharp transition between positive RMs in the north-eastern and negative RMs in the south-western part of the SNR. We note a corresponding RM pattern of extragalactic sources and propose the existence of a large-diameter Faraday screen in front of CTA 1, which covers the north-eastern part of the SNR. The RM of the Faraday screen is estimated to be about +45 rad/m2. A RM structure function of CTA 1 indicates a very regular magnetic field within the Faraday screen, which is larger than about 2.7 microG in case of 500 pc distance.

### Numerical Simulations of Driven Relativistic MHD Turbulence

A wide variety of astrophysical phenomena involve the flow of turbulent magnetized gas with relativistic velocity or energy density. Examples include gamma-ray bursts, active galactic nuclei, pulsars, magnetars, micro-quasars, merging neutron stars, X-ray binaries, some supernovae, and the early universe. In order to elucidate the basic properties of the relativistic magnetohydrodynamical (RMHD) turbulence present in these systems, we present results from numerical simulations of fully developed driven turbulence in a relativistically warm, weakly magnetized and mildly compressible ideal fluid. We have evolved the RMHD equations for many dynamical times on a uniform grid with 1024^3 zones using a high order Godunov code. We observe the growth of magnetic energy from a seed field through saturation at about 1% of the total fluid energy. We compute the power spectrum of velocity and density-weighted velocity and conclude that the inertial scaling is consistent with a slope of -5/3. We compute the longitudinal and transverse velocity structure functions of order p up to 11, and discuss their possible deviation from the expected scaling for non-relativistic media. We also compute the scale-dependent distortion of coherent velocity structures with respect to the local magnetic field, finding a weaker scale dependence than is expected for incompressible non-relativistic flows with a strong mean field.

### Numerical Simulations of Driven Relativistic MHD Turbulence [Replacement]

A wide variety of astrophysical phenomena involve the flow of turbulent magnetized gas with relativistic velocity or energy density. Examples include gamma-ray bursts, active galactic nuclei, pulsars, magnetars, micro-quasars, merging neutron stars, X-ray binaries, some supernovae, and the early universe. In order to elucidate the basic properties of the relativistic magnetohydrodynamical (RMHD) turbulence present in these systems, we present results from numerical simulations of fully developed driven turbulence in a relativistically warm, weakly magnetized and mildly compressible ideal fluid. We have evolved the RMHD equations for many dynamical times on a uniform grid with 1024^3 zones using a high order Godunov code. We observe the growth of magnetic energy from a seed field through saturation at about 1% of the total fluid energy. We compute the power spectrum of velocity and density-weighted velocity and conclude that the inertial scaling is consistent with a slope of -5/3. We compute the longitudinal and transverse velocity structure functions of order p up to 11, and discuss their possible deviation from the expected scaling for non-relativistic media. We also compute the scale-dependent distortion of coherent velocity structures with respect to the local magnetic field, finding a weaker scale dependence than is expected for incompressible non-relativistic flows with a strong mean field.

### Long-term optical variability of PKS 2155-304

Aims: The optical variability of the blazar PKS 2155-304 is investigated to characterise the red noise behaviour at largely different time scales from 20 days to O(>10 yrs). Methods: The long-term optical light curve of PKS 2155-304 is assembled from archival data as well as from so-far unpublished observations mostly carried out with the ROTSE-III and the ASAS robotic telescopes. A forward folding technique is used to determine the best-fit parameters for a model of a power law with a break in the power spectral density function (PSD). The best-fit parameters are estimated using a maximum-likelihood method with simulated light curves in conjunction with the Lomb Scargle Periodogram (LSP) and the first-order Structure Function (SF). In addition, a new approach based upon the so-called Multiple Fragments Variance Function (MFVF) is introduced and compared to the other methods. Simulated light curves have been used to confirm the reliability of these methods as well as to estimate the uncertainties of the best-fit parameters. Results: The light curve is consistent with the assumed broken power-law PSD. All three methods agree within the estimated uncertainties with the MFVF providing the most accurate results. The red-noise behaviour of the PSD in frequency f follows a power law with f^-{\beta}, {\beta}=1.8 +0.1/-0.2 and a break towards f^0 at frequencies lower than f_min=(2.7 +2.2/-1.6 yrs)^-1.

### Velocity Anisotropy as a Diagnostic of the Magnetization of the Interstellar Medium and Molecular clouds

We use a set of magnetohydrodynamics (MHD) simulations of fully-developed (driven) turbulence to study the anisotropy in the velocity field that is induced by the presence of the magnetic field. In our models we study turbulence characterized by sonic Mach numbers M_s from 0.7 to 7.5, and Alfven Mach numbers M_A from 0.4 to 7.7. These are used to produce synthetic observations (centroid maps) that are analyzed. To study the effect of large scale density fluctuations and of white noise we have modified the density fields and obtained new centroid maps, which are analyzed. We show that restricting the range of scales at which the anisotropy is measured makes the method robust against such fluctuations. We show that the anisotropy in the structure function of the maps reveals the direction of the magnetic field for M_A \lesssim 1.5, regardless of the sonic Mach number. We found that the degree of anisotropy can be used to determine the degree of magnetization (i.e. M_A) for M_A \lesssim 1.5. To do this, one needs an additional measure of the sonic Mach number and an estimate of the LOS magnetic field, both feasible by other techniques, offering a new opportunity to study the magnetization state of the interstellar medium.

### Interaction of Fanaroff-Riley class II radio jets with a randomly magnetised intra-cluster medium

A combination of three-dimensional (3D) magnetohydrodynamics (MHD) and synthetic numerical simulations are presented to follow the evolution of a randomly magnetised plasma that models the intra-cluster medium (ICM), under the isolated effects of powerful, light, hypersonic and bipolar Fanaroff-Riley class II (FR II) jets. We prescribe the cluster magnetic field (CMF) as a Gaussian random field with a Kolmogorov-like energy spectrum. Both the power of the jets and the viewing angle that is used for the synthetic Rotation Measure (RM) observations are investigated. We find the model radio sources introduce and amplify fluctuations on the RM statistical properties which we analyse as a function of time as well as the viewing angle. The average RM and the RM standard deviation are increased by the action of the jets. Energetics, RM statistics and magnetic power spectral analysis consistently show that the effects also correlate with the jets’ power, and that the lightest, fastest jets produce the strongest changes in their environment. We see jets distort and amplify the CMFs especially near the edges of the lobes and the jets’ heads. This process leads to a flattening of the RM structure functions at scales comparable to the source size. The edge features we find are similar to ones observed in Hydra A. The results show that jet-produced RM enhancements are more apparent in quasars than in radio galaxies. Globally, jets tend to enhance the RM standard deviation which may lead to overestimations of the CMFs’ strength by about 70%. This study means to serve as a pathfinder for the SKA, EVLA and LOFAR to follow the evolution of cosmic magnetic fields.

### The Turbulence Spectrum of Molecular Clouds in the Galactic Ring Survey: A Density-Dependent PCA Calibration

Turbulence plays a major role in the formation and evolution of molecular clouds. The problem is that turbulent velocities are convolved with the density of an observed region. To correct for this convolution, we investigate the relation between the turbulence spectrum of model clouds, and the statistics of their synthetic observations obtained from Principal Component Analysis (PCA). We apply PCA to spectral maps generated from simulated density and velocity fields, obtained from hydrodynamic simulations of supersonic turbulence, and from fractional Brownian motion fields with varying velocity, density spectra, and density dispersion. We examine the dependence of the slope of the PCA structure function, alpha_PCA, on intermittency, on the turbulence velocity (beta_v) and density (beta_n) spectral indexes, and on density dispersion. We find that PCA is insensitive to beta_n and to the log-density dispersion sigma_s, provided sigma_s 2, alpha_PCA increases with sigma_s due to the intermittent sampling of the velocity field by the density field. The PCA calibration also depends on intermittency. We derive a PCA calibration based on fBms with sigma_s<2 and apply it to 367 CO spectral maps of molecular clouds in the Galactic Ring Survey. The average slope of the PCA structure function, =0.62\pm0.2, is consistent with the hydrodynamic simulations and leads to a turbulence velocity exponent =2.06\pm0.6 for a non-intermittent, low density dispersion flow. Accounting for intermittency and density dispersion, the coincidence between the PCA slope of the GRS clouds and the hydrodynamic simulations suggests beta_v~1.9, consistent with both Burgers and compressible intermittent turbulence.

### Structure Function and Variability Mechanism of Quasars from SDSS Stripe 82 [Replacement]

Theoretical predictions for the ensemble quasar structure function are tested using multi-epoch observations of Stripe 82 collected by the Sloan Digital Sky Survey. We reanalyze the entire available volume of the g-band imaging data using difference image photometry and build high quality light curves for 7562 spectroscopically confirmed quasars. Our structure function includes ~4.8×10^6 pairs of measurements and covers a wide range of time lags between 3 days and 6.9 years in the quasar rest frame. A broken power-law fit to this data shows the presence of two slopes alpha_1=0.33 and alpha_2=0.79 with the break at ~42 days. The structure function compiled using only flux increases is slightly lower than that for variations of the opposite sign, revealing a slight asymmetry between the leading and trailing edge of a typical flare. The reality of these features is confirmed with monte-carlo simulations. We give simple interpretation of the results in the frames of existing theoretical models.

### Structure Function and Variability Mechanism of Quasars from SDSS Stripe 82

Theoretical predictions for the ensemble quasar structure function are tested using multi-epoch observations of Stripe 82 collected by the Sloan Digital Sky Survey. We reanalyze the entire available volume of the g-band imaging data using difference image photometry and build high quality light curves for 7562 spectroscopically confirmed quasars. Our structure function includes ~4.8×10^6 pairs of measurements and covers a wide range of time lags between 3 days and 6.9 years in the quasar rest frame. A broken power-law fit to this data shows the presence of two slopes alpha_1=0.33 and alpha_2=0.79 with the break at ~42 days. The structure function compiled using only flux increases is slightly lower than that for variations of the opposite sign, revealing a slight asymmetry between the leading and trailing edge of a typical flare. The reality of these features is confirmed with monte-carlo simulations. We give simple interpretation of the results in the frames of existing theoretical models.

### Diffractive and refractive timescales at 4.8 GHz in PSR B0329+54

We present the results of flux density monitoring of PSR B0329+54 at the frequency of 4.8 GHz using the 32-meter TCfA radiotelescope. The observations were conducted between 2002 and 2005. The main goal of the project was to find interstellar scintillation (ISS) parameters for the pulsar at the frequency at which it was never studied in detail. To achieve this the 20 observing sessions consisted of 3-minute integrations which on average lasted 24 hours. Flux density time series obtained for each session were analysed using structure functions. For some of the individual sessions as well as for the general average structure function we were able to identify two distinctive timescales present, the timescales of diffractive and refractive scintillations. To the best of our knowledge, this is the first case when both scintillation timescales, t_DISS=42.7 minutes and t_RISS=305 minutes, were observed simultaneously in a uniform data set and estimated using the same method. The obtained values of the ISS parameters combined with the data found in the literature allowed us to study the frequency dependence of these parameters over a wide range of observing frequencies, which is crucial for understanding the ISM turbulence. We found that the Kolmogorov spectrum is not best suited for describing the density fluctuations of the ISM, and a power-law spectrum with beta =4 seems to fit better with our results. We were also able to estimate the transition frequency (transition from strong to weak scintillation regimes) as 10.1 GHz, much higher than was previously predicted. We were also able to estimate the strength of scattering parameter u=2.67\$ and the Fresnel scale as 6.7×10^8 meters.

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