Modelling X-ray RMS spectra II: the ultrafast outflow of PDS 456

ABSTRACT We present an improved model for excess variance spectra describing ultrafast outflows and successfully apply it to the luminous ($L_{\rm bol}\sim 10^{47}\mathrm{erg}\, \mathrm{s}^{-1}$) low-redshift (z = 0.184) quasar Pico del Dias Survey (PDS) 456. The model is able to account well for the broadening of the spike-like features of these outflows in the excess variance spectrum of PDS 456, by considering two effects: a correlation between the outflow velocity and the logarithmic X-ray flux and intrinsic Doppler broadening with $v_\mathrm{int} = 10^4\, \mathrm{km}\, \mathrm{s}^{-1}$. The models were generated by calculating the fractional excess variance of count spectra from a Monte Carlo simulation. We find evidence that the outflow in PDS 456 is structured, i.e. there exist two or more layers with outflow velocities $0.27\!-\!0.30\, c$, $0.41\!-\!0.49\, c$, and $0.15\!-\!0.20\, c$ for a possible third layer, which agrees well with the literature. We discuss the prospects of generally applicable models for excess variance spectra for detecting ultrafast outflows and investigating their structure. We provide an estimate for the strength of the correlation between the outflow velocity and the logarithmic X-ray flux and investigate its validity.

The structure and characteristic scales of molecular clouds

The structure of molecular clouds holds important clues regarding the physical processes that lead to their formation and subsequent dynamical evolution. While it is well established that turbulence imprints a self-similar structure onto the clouds, other processes, such as gravity and stellar feedback, can break their scale-free nature. The break of self-similarity can manifest itself in the existence of characteristic scales that stand out from the underlying structure generated by turbulent motions. In this work, we investigate the structure of the Cygnus-X North and Polaris Flare molecular clouds, which represent two extremes in terms of their star formation activity. We characterize the structure of the clouds using the delta-variance (Δ-variance) spectrum. In the Polaris Flare, the structure of the cloud is self-similar over more than one order of magnitude in spatial scales. In contrast, the Δ-variance spectrum of Cygnus-X North exhibits an excess and a plateau on physical scales of ≈0.5−1.2 pc. In order to explain the observations for Cygnus-X North, we use synthetic maps where we overlay populations of discrete structures on top of a fractal Brownian motion (fBm) image. The properties of these structures, such as their major axis sizes, aspect ratios, and column density contrasts with the fBm image, are randomly drawn from parameterized distribution functions. We are able to show that, under plausible assumptions, it is possible to reproduce a Δ-variance spectrum that resembles that of the Cygnus-X North region. We also use a “reverse engineering” approach in which we extract the compact structures in the Cygnus-X North cloud and reinject them onto an fBm map. Using this approach, the calculated Δ-variance spectrum deviates from the observations and is an indication that the range of characteristic scales (≈0.5−1.2 pc) observed in Cygnus-X North is not only due to the existence of compact sources, but is a signature of the whole population of structures that exist in the cloud, including more extended and elongated structures.

A Method for Identifying Kolmogorov’s Inertial Subrange in the Velocity Variance Spectrum

Kolmogorov’s inertial subrange is one of the most recognized concepts in fluid turbulence. However, the practical application of this theory to turbulent flows requires identifying subrange bandwidth. In the atmospheric boundary layer, decades of investigation support Kolmogorov’s theory, but the techniques used to identify the subrange vary and no systematic approach has emerged. The algorithm for robust identification of the inertial subrange (ARIIS) has been developed to facilitate empirical studies of the turbulence cascade. ARIIS systematically and robustly identifies the most probable subrange bandwidth in a given velocity variance spectrum. The algorithm is a novel approach in that it directly uses the expected 3/4 ratio between streamwise and transverse velocity components to locate the onset and extent of the inertial subrange within a single energy density spectrum. Furthermore, ARIIS does not assume a −5/3 power law but instead uses a robust, iterative statistical fitting technique to derive the slope over the identified range. This algorithm was tested using a comprehensive micrometeorological dataset obtained from the Floating Instrument Platform (FLIP). The analysis revealed substantial variation in the inertial subrange bandwidth and spectral slope, which may be driven, in part, by mechanical wind–wave interactions. Although demonstrated using marine atmospheric data, ARIIS is a general approach that can be used to study the energy cascade in other turbulent flows.

Modelling X-ray RMS spectra I: intrinsically variable AGNs

ABSTRACT We present simple xspec models for fitting excess variance spectra of active galactic nuclei. Using a simple Monte Carlo approach, we simulate a range of spectra corresponding to physical parameters varying, then calculate the resulting variance spectra. Starting from a variable power law, we build up a set of models corresponding to the different physical processes that can affect the final excess variance spectrum. We show that the complex excess variance spectrum of IRAS 13224−3809 can be well described by such an intrinsic variability model, where the power-law variability is damped by relativistic reflection and enhanced by an ultra-fast outflow. The reflection flux is correlated with that of the power law, but not perfectly. We argue that this correlation is stronger at high frequencies, where reverberation lags are detected, while excess variance spectra are typically dominated by low-frequency variability.

A simple method for retrieving significant wave height from Dopplerized X-band radar

Retrieving spectral wave parameters such as the peak wave direction and wave period from marine radar backscatter intensity is very well developed. However, the retrieval of significant wave height is difficult because the radar image spectrum (a backscatter intensity variance spectrum) has to be transferred to a wave spectrum (a surface elevation variance spectrum) using a modulation transfer function (MTF) which requires extensive calibration for each individual radar setup. In contrast to the backscatter intensity, the Doppler velocity measured by a coherent radar is induced by the radial velocity (or line-of-sight velocity) of the surface scattering and its periodic component is mainly the contribution of surface waves. Therefore, the variance of the Doppler velocity can be utilized to retrieve the significant wave height. Analyzing approximately 100 days of Doppler velocity measurements of a coherent-on-receive radar operating at X-band with vertical polarization in transmit and receive, a simple relation was derived and validated to retrieve significant wave heights. Comparison to wave measurements of a wave rider buoy as well as an acoustic wave and current profiler resulted in a root mean square error of 0.24 m with a bias of 0.08 m. Furthermore, the different sources of error are discussed and investigated.

Spatial and Temporal Network Sampling Effects on the Correlation and Variance Structures of Rain Observations

Network observations are affected by the length of the temporal interval over which measurements are combined as well as by the size of the network. When the observation interval is small, only network size matters. Networks then act as high-pass filters that distort both the spatial correlation function ρr and, consequently, the variance spectrum. For an exponentially decreasing ρr, a method is presented for returning the observed spatial correlation to its original, intrinsic value. This can be accomplished for other forms of ρr. When the observation interval becomes large, however, advection enhances the contributions from longer wavelengths, leading to a distortion of ρr and the associated variance spectrum. However, there is no known way to correct for this effect, which means that the observation interval should be kept as small as possible in order to measure the spatial correlation correctly. Finally, it is shown that, in contrast to network measurements, remote sensing instruments act as low-pass filters, thus complicating comparisons between the two sets of observations. It is shown that when the network-observed spatial correlation function can be corrected to become a good estimate of the intrinsic spatial correlation function, the Fourier transform of this function (variance spectrum) can then be spatially low-pass filtered in a manner appropriate for the remote sensor. If desired, this filtered field can then be Fourier transformed to yield the spatial correlation function relevant to the remote sensor. The network and simulations of the remote sensor observations can then be compared to better understand the physics of differences between the two set of observations.

A Simple Method for Retrieving Significant Wave Height from Dopplerized X-Band Radar

Retrieving spectral wave parameters such as the peak wave direction and wave period from marine radar backscatter intensity is very well developed. However, the retrieval of significant wave height is difficult because the radar image spectrum (a backscatter intensity variance spectrum) has to be transferred to a wave spectrum (a surface elevation variance spectrum) using a modulation transfer function (MTF) which requires extensive calibration for each individual radar setup. In contrast to the backscatter intensity, the Doppler velocity measured by a coherent radar is induced by the radial velocity of the surface scattering and its periodic component is mainly the contribution of surface waves. Therefore, the variance of the Doppler velocity can be utilized to retrieve the significant wave height. Analysing approximately 100 days of Doppler velocity measurements of a coherent on receive radar operating at X-band with vertical polarization in transmit and receive, a simple relation was derived and validated to retrieve significant wave heights. Comparison to wave measurements of a wave rider buoy as well as an acoustic wave and current profiler resulted in a root mean square error of 0.24 m with a bias of 0.08 m. Furthermore, the different sources of error are discussed and investigated.

Temperature dynamics in decaying isotropic turbulence with Joule heat production

This paper presents an extension of existing works dealing with the dynamics of a passive scalar in freely decaying isotropic turbulence, by accounting for a production mechanism of the passive scalar itself. The physically relevant case of the temperature dynamics in the presence of Joule heating via the dissipation of the turbulent kinetic energy is selected and analysed by theoretical and numerical means. In particular, the sensitivity of the temperature decay to the non-dimensional parameters Prandtl number ($\mathit{Pr}$) and Eckert number ($\mathit{Ec}$), the latter measuring the intensity of the internal energy production mechanism, is investigated. The time behaviour of the global quantities such as the temperature variance $ \overline{{\theta }^{2} } (t)$ and its destruction rate ${\varepsilon }_{\theta } (t)$ is analysed, and a detailed analysis of the temperature variance spectrum ${E}_{\theta } (k)$ is provided. In the case of a very strong heating mechanism, some important modifications of the temperature dynamics are observed. The time-decay-law exponents of the global physical quantities assume new values, which are governed only by features of the kinetic energy spectrum, while they depend on the shape of ${E}_{\theta } (k)$ in the classical free-decay case. The temperature variance spectrum ${E}_{\theta } (k)$ exhibits two new spectral ranges. One is a convective–production range such that ${E}_{\theta } (k)\propto {k}^{1/ 3} $ is observed for a finite time at all values of $\mathit{Pr}$. In the case of very diffusive fluids with $\mathit{Pr}\ll 1$, a convective–diffusive–production range with ${E}_{\theta } (k)\propto {k}^{- 7/ 3} $ is also detected.