# Posts Tagged structure function

## Recent Postings from structure function

### The QCD analysis of the combined set for the F_3 structure function data based on the analytic approach

We apply analytic perturbation theory to the QCD analysis of the xF_3(x,Q^2) structure function considering a combined set of deep inelastic scattering data presented by several collaborations, and extract values of the scale parameter Lambda_{QCD}, the parameters of the form of the xF_3 structure function, and the x-shape of the higher twist contribution. We study the difference between the results obtained within the standard perturbative and analytic approaches in comparison with the experimental errors and state that the greatest difference occurs for large x.

### The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity

We calculate the massive flavor non-singlet Wilson coefficient for the heavy flavor contributions to the structure function $F_2(x,Q^2)$ in the asymptotic region $Q^2 \gg m^2$ and the associated operator matrix element $A_{qq,Q}^{(3), \rm NS}(N)$ to 3-loop order in Quantum Chromodynamics at general values of the Mellin variable $N$. This matrix element is associated to the vector current and axial vector current for the even and the odd moments $N$, respectively. We also calculate the corresponding operator matrix elements for transversity, compute the contributions to the 3-loop anomalous dimensions to $O(N_F)$ and compare to results in the literature. The 3-loop matching of the flavor non-singlet distribution in the variable flavor number scheme is derived. All results can be expressed in terms of nested harmonic sums in $N$ space and harmonic polylogarithms in $x$-space. Numerical results are presented for the non-singlet charm quark contribution to $F_2(x,Q^2)$.

### The ratio of the beauty structure functions $R^b = F^b_L/F^b_2$ at low x

We study the structure functions $F_{k}^{b}(x,Q^{2})$ ($k=2, L$) and the reduced cross section $\sigma_{r}^{b}(x,Q^{2})$ for small values of Bjorken$^{,}$s $x$ variable with respect to the hard (Lipatov) pomeron for the gluon distribution and provide a compact formula for the ratio $R^{b}$ that is useful to extract the beauty structure function from the beauty reduced cross section, in particular at DESY HERA. Also we show that the effects of the nonlinear corrections to the gluon distribution tame the behavior of the beauty structure function and the beauty reduced cross section at low $x$.

### Long-term optical and radio variability of BL Lacertae

Well-sampled optical and radio light curves of BL Lacertae in B, V, R, I bands and 4.8, 8.0, 14.5 GHz from 1968 to 2014 were presented in this paper. A possible $1.26 \pm 0.05$ yr period in optical bands and a $7.50 \pm 0.15$ yr period in radio bands were detected based on discrete correlation function, structure function as well as Jurkevich method. Correlations among different bands were also analyzed and no reliable time delay was found between optical bands. Very weak correlations were detected between V band and radio bands. However, in radio bands the variation at low frequency lagged that at high frequency obviously. The spectrum of BL Lacertae turned mildly bluer when the object turned brighter, and stronger bluer-when-brighter trends were found for short flares. A scenario including a precessing helical jet and periodic shocks was put forward to interpret the variation characteristics of BL Lacertae.

### The structure function of Galactic \HI opacity fluctuations on AU scales based on MERLIN, VLA and VLBA data

We use MERLIN, VLA and VLBA observations of Galactic \HI absorption towards 3C~138 to estimate the structure function of the \HI opacity fluctuations at AU scales. Using Monte Carlo simulations, we show that there is likely to be a significant bias in the estimated structure function at signal-to-noise ratios characteristic of our observations, if the structure function is constructed in the manner most commonly used in the literature. We develop a new estimator that is free from this bias and use it to estimate the true underlying structure function slope on length scales ranging $5$ to $40$~AU. From a power law fit to the structure function, we derive a slope of $0.81^{+0.14}_{-0.13}$, i.e. similar to the value observed at parsec scales. The estimated upper limit for the amplitude of the structure function is also consistent with the measurements carried out at parsec scales. Our measurements are hence consistent with the \HI opacity fluctuation in the Galaxy being characterized by a power law structure function over length scales that span six orders of magnitude. This result implies that the dissipation scale has to be smaller than a few AU if the fluctuations are produced by turbulence. This inferred smaller dissipation scale implies that the dissipation occurs either in (i) regions with densities $\gtrsim 10^3$cm$^-3$ (i.e. similar to that inferred for "tiny scale" atomic clouds or (ii) regions with a mix of ionized and atomic gas (i.e. the observed structure in the atomic gas has a magneto-hydrodynamic origin).

### Dynamical behavior connection of the gluon distribution and the proton structure function at small $x$

We make a critical study of the relationship between the singlet structure function $F_{2}^{S}$ and the gluon distribution $G(x,Q^{2})$ proposed in the past two decades, which is frequently used to extract the gluon distribution from the proton structure function. We show that a simple relation is not generally valid in the simplest state. We complete this relation by using a Laplace transform method and hard-pomeron behavior at LO and NLO at small $x$. Our study shows that this relation is dependent on the splitting functions and initial conditions at $Q^{2} = Q^{2}_{0}$ and running coupling constant at NLO. The resulting analytic expression allows us to predict the proton structure function with respect to the gluon distributions and to compare the results with H1 data and a QCD analysis fit. Comparisons with other results are made and predictions for the proposed best approach are also provided.

### Photon structure function revisited

The flux of papers from electron positron colliders containing data on the photon structure function ended naturally around 2005. It is thus timely to review the theoretical basis and confront the predictions with a summary of the experimental results. The discussion will focus on the increase of the structure function with x (for x away from the boundaries) and its rise with log Q**2, both characteristics beeing dramatically different from hadronic structure functions. Comparing the data with a specific QCD prediction a new determination of the QCD coupling coupling constant is presented. The agreement of the experimental observations with the theoretical calculations of the real and virtual photon structure is a striking success of QCD.

### A lower bound on the Longitudinal Structure Function at small x from a self-similarity based model of Proton

Self-similarity based model of proton structure function at small \textit{x} was reported in the literature sometime back. The phenomenological validity of the model is in the kinematical region $6.2\, \times \, 10^{-7} \leq x \leq 10^{-2}$ and $0.045 \leq Q^{2} \leq 120 \, \mathrm{GeV^{2}}$. We use momentum sum rule to pin down the corresponding self-similarity based gluon distribution function valid in the same kinematical region. The model is then used to compute bound on the longitudinal structure function $F_{L}\left(x,Q^{2} \right)$ for Altarelli-Martinelli equation in QCD and is compared with the recent HERA data.

### Color dipole cross section and inelastic structure function

Instead of starting from a theoretically motivated form of the color dipole cross section in the dipole picture of deep inelastic scattering, we start with a parametrization of the deep inelastic structure function for electromagnetic scattering with protons, and then extract the color dipole cross section. Using the Donnachie-Landshoff parametrization of $F_2(x,Q^2)$, we find the dipole cross section from an approximate form of the presumed dipole cross section convoluted with the perturbative photon wave function for virtual photon splitting into a color dipole with massless quarks. The color dipole cross section determined this way works quite well in the massive case, reproducing the original Donnachie-Landshoff structure function for $0.1$ GeV$^2\leq Q^2\leq 10$ GeV$^2$. We discuss the large and small form of the dipole cross section and compare with other parameterizations.

### Q2-evolution of parton densities at small x values. Effective scale for combined H1 and ZEUS F2 data

We use the Bessel-inspired behavior of the structure function F2 at small x, obtained for a flat initial condition in the DGLAP evolution equations. We fix the scale of the coupling constant, which eliminates the singular part of anomalous dimesnions at the next-to-leading order of approximation. The approach together with the "frozen" and analytic modifications of the strong coupling constant is used to study the precise combined H1 and ZEUS data for the structure function F2 published recently.

### The effect on PDFs and $\alpha_S(M_Z^2)$ due to changes in flavour scheme and higher twist contributions

I consider the effect on MSTW partons distribution functions (PDFs) due to changes in the choices of theoretical procedure used in the fit. I first consider using the 3-flavour fixed flavour number scheme instead of the standard general mass variable flavour number scheme used in the MSTW analysis. This results in the light quarks increasing at all relatively small $x$ values, the gluon distribution becoming smaller at high values of $x$ and larger at small $x$, the preferred value of the coupling constant $\alpha_S(M_Z^2)$ falling, particularly at NNLO, and the fit quality deteriorates. I also consider lowering the kinematic cut on $W^2$ for DIS data and simultaneously introducing higher twist terms which are fit to data. This results in much smaller effects on both PDFs and $\alpha_S(M_Z^2)$ than the scheme change, except for quarks at very high $x$. I show that the structure function one obtains from a fixed input set of PDFs using the fixed flavour scheme and variable flavour scheme differ significantly for $x \sim 0.01$ at high $Q^2$, and that this is due to the fact that in the fixed flavour scheme there is a slow convergence of large logarithmic terms of the form $(\alpha_S\ln(Q^2/m_c^2))^n$ relevant for this regime. I conclude that some of the most significant differences in PDF sets are largely due to the choice of flavour scheme used.

### Nonlinear correction to the longitudinal structure function at small x

We computed the longitudinal proton structure function $F_{L}$, using the nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-parisi (NLDGLAP) evolution equation approach at small $x$. For the gluon distribution, the nonlinear effects are related to the longitudinal structure function. As, the very small $x$ behavior of the gluon distribution is obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu (GLR-MQ) evolution equation with the nonlinear shadowing term incorporated. We show, the strong rise that is corresponding to the linear QCD evolution equations, can be tamed by screening effects. Consequently, the obtained longitudinal structure function shows a tamed growth at small $x$. We computed the predictions for all detail of the nonlinear longitudinal structure function in the kinematic range where it has been measured by $H1$ collaboration and compared with computation Moch, Vermaseren and Vogt at the second order with input data from MRST QCD fit.

### The approximation method for calculation of the exponent of the gluon distribution-$\lambda_{g}$ and the structure function-$\lambda_{S}$ at low $x$

We present a set of formulae using the solution of the QCD Dokshitzer-Gribov-Lipatov-Altarelli-parisi (DGLAP) evolution equation to the extract of the exponent $\lambda_g$ gluon distribution and $\lambda_S$ structure function from the Regge- like behavior at low $x$. The exponents are found to be independent of $x$ and to increase linearly with ln$Q^{2}$ and compared with the most data from H1 Collaboration. We also calculated the structure function $F_{2}(x,Q^{2})$ and the gluon distribution $G(x,Q^{2})$ at low $x$ assuming the Regge- like behavior of the gluon distribution function at this limit and compared with NLO QCD fit to the H$1$ data, two Pomeron fit, multipole Pomeron exchange fit and MRST (A.D.Martin, R.G.Roberts, W.J.Stirling and R.S.Thorne), DL(A.Donnachie and P.V.Landshoff), NLO-GRV(M.Gluk, E.Reya and A.Vogt) fit results, respectively.

### The approximation method for calculation of the exponent of the gluon distribution-$\lambda_{g}$ and the structure function-$\lambda_{S}$ at low $x$ [Replacement]

We present a set of formulae using the solution of the QCD Dokshitzer-Gribov-Lipatov-Altarelli-parisi (DGLAP) evolution equation to the extract of the exponent $\lambda_g$ gluon distribution and $\lambda_S$ structure function from the Regge- like behavior at low $x$. The exponents are found to be independent of $x$ and to increase linearly with ln$Q^{2}$ and compared with the most data from H1 Collaboration. We also calculated the structure function $F_{2}(x,Q^{2})$ and the gluon distribution $G(x,Q^{2})$ at low $x$ assuming the Regge- like behavior of the gluon distribution function at this limit and compared with NLO QCD fit to the H$1$ data, two Pomeron fit, multipole Pomeron exchange fit and MRST (A.D.Martin, R.G.Roberts, W.J.Stirling and R.S.Thorne), DL(A.Donnachie and P.V.Landshoff), NLO-GRV(M.Gluk, E.Reya and A.Vogt) fit results, respectively.

### Hard- Pomeron behavior of the Longitudinal Structure Function $F_{L}$ in the Next- to- Leading- Order at low $x$

We present an analytic formula to extract the longitudinal structure function in the next- to -leading order of the perturbation theory at low $x$, from the Regge- like behavior of the gluon distribution and the structure function at this limit. In this approach, the longitudinal structure function has the hard- Pomeron behavior. The determined values are compared with the $H1$ data and MRST model. All results can consistently be described within the framework of perturbative QCD which essentially show increases as $x$ decreases.

### Analytical approach for the approximate solution of the longitudinal structure function with respect to the GLR-MQ equation at small x

We show that the nonlinear corrections to the longitudinal structure function can be tamed the singularity behavior at low x values, with respect to GLR-MQ equations. This approach can determined the shadowing longitudinal structure function based on the shadowing corrections to the gluon and singlet quark structure functions. Comparing our results with HERA data show that at very low x this behavior completely tamed by these corrections.

### Analytical approach for the approximate solution of the longitudinal structure function with respect to the GLR-MQ equation at small x [Replacement]

We show that the nonlinear corrections to the longitudinal structure function can be tamed the singularity behavior at low x values, with respect to GLR-MQ equations. This approach can determined the shadowing longitudinal structure function based on the shadowing corrections to the gluon and singlet quark structure functions. Comparing our results with HERA data show that at very low x this behavior completely tamed by these corrections.

### Evolution of the longitudinal structure function at small x

We derive an approximation approach to evolution of the longitudinal structure function, by using a Laplace-transform method. We solve the master equation and derive the longitudinal structure function as a function of the initial condition $F_{L}(x,Q^{2}_{0})$ at small x. Our results are independent of the longitudinal coefficient functions and extend from the leading order (LO) up to next-to-next-to-leading order (NNLO). The comparisons with H1 data and other parameterizations are made and results show that they are in agreement with H1 data and some phenomenological models.

### Analysis of the logarithmic slope of $F_{2}$ from the Regge gluon density behavior at small $x$

We study of the accuracy of the Regge behavior of the gluon distribution function for obtain an approximation relation, which is frequently used to extract the logarithmic slopes of the structure function from the gluon distribution at small $x$. We show that the Regge behavior analysis results are comparable with HERA data and also are better than other methods that expand of the gluon density at distinct points of expansion. Also we show that for $Q^{2}=22.4 GeV^{2}$, the $x$ dependence of the data is well described by gluon shadowing corrections to GLR-MQ equation. The resulting analytic expression allow us to predict the logarithmic derivative $\frac{{\partial}F_{2}(x,Q^{2})}{{\partial}lnQ^{2}}$ and to compare the results with H1 data and a QCD analysis fit with MRST parametrization input.

### Analytical solution of the longitudinal structure function $F_{L}$ in the leading and next-to-leading-order analysis at low x with respect to Laguerre polynomials method

The aim of the present paper is to apply the Laguerre polynomials method for the analytical solution of the Altarelli- Martinelli equation. We use this method of the low $x$ gluon distribution to the longitudinal structure function using MRST partons as input. Having checked that this model gives a good description of the data to predict of the longitudinal structure function at leading and next to leading order analysis at low $x$

### The Ratio of the Charm Structure Functions $F^{c}_{k}(k = 2, L)$ at Low x in Deep Inelastic Scattering with Respect to the Expansion Method

We study the expansion method for the gluon distribution function at low x values and calculate the charm structure functions in the LO and NLO analysis. Our results provide a compact formula for the ratio $R^{c} =F^{c}_{L}/F^{c}_{2}$, which is approximately independent of x and the details of the parton distribution function at low x values. This ratio could be a good probe of the charm structure function $F^{c}_{2}$ in the proton deduced from the reduced charm cross sections at DESY HERA. These results show that the charm structure functions obtained are in agreement with HERA experimental data and other theoretical models.

### The predictions of the charm structure function exponents behaviour at low x in deep inelastic scattering

We use the hard (Lipatov) pomeron for the low-x gluon distribution and provide a compact formula for the ratio $R^{c} =F_{L}^{c}/F_{2}^{c}$ that is useful to extract the charm structure function from the reduced charm cross-section, in particular at DESY HERA. Our results show that this ratio is independent of x and independent of the DGLAP evolution of the gluon PDF. As a result, we show that the charm structure function and the reduced charm cross-section exponents do not have the same behaviour at very low x. This difference is independent of the input gluon distribution functions and predicts the non-linear effects and some evidence for shadowing and antishadowing at HERA and RHIC.

### Longitudinal Structure Function $F_{L}$ from Charm Structure Function $F^{c}_{2}$

We predict the effect of the charm structure function on the longitudinal structure function at small x. In NLO analysis we find that the hard Pomeron behavior gives a good description of $F_{L}$ and $F^{c}_{k}$ (k = 2,L) at small x values. We conclude that a direct relation between $F_{L}/F^{c}_{2}$ would provide useful information on how to measure longitudinal structure function at high $Q^{2}$ values. Having checked that this model gives a good description of the data, when compared with other models.

### Analysis of the proton longitudinal structure function from the gluon distribution function

We make a critical, next-to-leading order, study of the relationship between the longitudinal structure function FL and the gluon distribution proposed in Cooper- Sarkar et al. (Z. Phys. C 39:281, 1988; Acta Phys. Pol. B 34:2911 2003), which is frequently used to extract the gluon distribution from the proton longitudinal structure function at small x. The gluon density is obtained by expanding at particular choices of the point of expansion and compared with the hard Pomeron behavior for the gluon density. Comparisons with H1 data are made and predictions for the proposed best approach are also provided.

### 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 [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.

### 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.

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