Simple Reflectance Model Research Articles

Evaluation of total ozone measurements from Geostationary Environmental Monitoring Spectrometer (GEMS)

Abstract. The continued interest in air pollution and stratospheric ozone variability has motivated the development of a Geostationary Environmental Monitoring Spectrometer (GEMS) for hourly ozone monitoring. This paper provides the atmospheric science community with the world's first assessment of GEMS total column ozone (TCO) retrieval performance and diurnal ozone variation. The algorithm used for GEMS is a more advanced version of its predecessor, the Total Ozone Mapping Spectrometer (TOMS) V8, that incorporates several improvements, including a new lookup table, a simple Lambertian-equivalent reflectivity model, and a spectral dependence correction. The GEMS algorithm also uses the optimal estimation method (OEM) to make error analysis more accessible and robust. The estimated retrieval errors range from 1.5 to 2 DU in September and 2 DU in December, with a constant degree of freedom of the signal (DFS) of 1 in September and a variable DFS of 1.25 to 1.4 in December throughout the day, depending on solar zenith angle (SZA). To assess the performance of the GEMS algorithm, the hourly GEMS total ozone was compared with ground-based measurements from Pandora instruments and other satellite platforms from TROPOMI (TROPOspheric Monitoring Instrument) and OMPS (Ozone Mapping and Profiler Suite Nadir Mapper). GEMS has a high correlation of 0.97 and small RMSE values compared to Pandora TCO at Busan and Seoul in South Korea. It is notable that despite exhibiting seasonal dependence in the mean bias of GEMS with Pandora, GEMS is capable of observing daily variations in ozone that are highly consistent with Pandora measurements, with a bias of approximately 1 %. The comparison of GEMS TCO data with TROPOMI and OMPS TCO data shows a high correlation of 0.99 and low RMSE compared to TROPOMI and OMPS TCO data, but the data have a negative bias of −2.38 % and −2.17 %, with standard deviations of 1.33 % and 1.57 %, respectively. Similar to OMPS, the influence of SO2 from volcanic eruptions is not properly removed in some regions, leading to GEMS overestimating TCO in those areas. The mean biases of GEMS TCO data with TROPOMI and OMPS TCO are within ±1 % at low latitudes but become negative at midlatitudes, with an increasingly negative dependence on latitude. Furthermore, this dependence becomes more prominent from summer to winter. The empirical correction applied to the GEMS irradiance data improves the dependence of the mean bias on season and latitude, but a consistent bias still remains, and a marginal positive trend was observed in December. Therefore, further investigation into correction methods is needed. The results are a meaningful scientific advance by providing the first validated, hourly UV ozone retrievals from a satellite in geostationary orbit. This experience can be used to advance research with future geostationary environmental satellite missions, including the incoming TEMPO (Tropospheric Emissions: Monitoring of Pollution) and Sentinel-4.

Modeling reflection by structured building-integrated photovoltaics

Evaluating the reflection of solar radiation by Building Integrated Photovoltaics (BIPV) with structured front-glass is challenging for two reasons. First, the resulting irregular scattering of light cannot be accounted for by simple reflection models. Second, the locations where the evaluation needs to take place cannot be predicted by simple geometric considerations, as in the case of mirror-like reflection. The detailed modelling of a BIPV module featuring a periodical, linear structure based on the scanning of its surface is described. The application of the model is demonstrated in the assessment of solar reflection by a concave array of the modules. The stochastic sampling of the BIPV modules from each location in a dense sensor grid, that is required to ensure that no local concentration of reflected solar radiation is missed, is supported by re-orienting the sensors. Rather than relying on a data-driven Bidirectional Reflectance Distribution Function (BRDF) model of limited directional resolution, the geometric structure of the front-glass is modelled by modulating the normal of a mirror-like surface. The method allows an accurate and dense simulation with moderate computational demand.

Digital fabrics for online shopping and fashion design

Improving the digital presentation of fabrics enhances the online shopping experience and, in turn, reduces textile waste. In this study, we examined how the manipulation of simple surface reflectance models can bias the perception of fabric properties simulated online in a web browser. We showed that motion and three-dimensional (3D) folds (i.e., rumple) influence the perception of sheen for different fabric types (cotton knit and satin). Also, we found complex interactions between these parameters in their effects on perceived sheen and perceived color saturation. Moreover, we showed that changing the level of specular roughness significantly influences visual perception of sheen, color and lightness, which in turn, can categorically alter perceptual judgments of material type. In contrast to visual attributes, specular roughness did not influence visually perceived tactile characteristics of digital fabrics (thickness and stretch). The knowledge gained about perceptual biases of digital fabrics from this study will inform future considerations for optimizing the fidelity of textiles depicted in digital commerce.

IRS-Assisted Multicell Multiband Systems: Practical Reflection Model and Joint Beamforming Design

Intelligent reflecting surface (IRS) has been regarded as a promising and revolutionary technology for future wireless communication systems owing to its capability of tailoring signal propagation environment in an energy/spectrum/ hardware-efficient manner. However, most existing studies on IRS optimizations are based on a simple and ideal reflection model that is impractical in hardware implementation, which thus leads to severe performance loss in realistic wideband/multi-band systems. To deal with this problem, in this paper we first propose a more practical and more tractable IRS reflection model that describes the difference of reflection responses for signals at different frequencies. Then, we investigate the joint transmit beamforming and IRS reflection beamforming design for an IRS-assisted multi-cell multi-band system. Both power minimization and sum-rate maximization problems are solved by exploiting popular second-order cone programming (SOCP), Riemannian manifold, minimization-majorization (MM), weighted minimum mean square error (WMMSE), and block coordinate descent (BCD) methods. Simulation results illustrate the significant performance improvement of our proposed joint transmit beamforming and reflection design algorithms based on the practical reflection model in terms of power saving and rate enhancement.

Effects of Arctic Wetland Dynamics on Tower-Based GNSS Reflectometry Observations

A tower-based global navigation satellite system reflectometry (GNSS-R) experiment is set up in an Arctic wetland environment for investigating the possibility of monitoring wetland inundation and freeze/thaw (FT) dynamics which are additionally impacted by snow on the ground. Effects of inundation, snow cover, and soil FT state on observed GNSS-R signal-to-noise ratios (SNRs) are analyzed for horizontal (H) and vertical (V) polarizations. A simple classification approach is suggested to detect the inundated, frozen, or thawed soil state. A simple forward reflectivity model is formulated to evaluate the influence of snow cover, overlying frozen, or thawed soil, on the reflected GNSS signals. Reflectivity time series are simulated in H- and V-polarizations using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> observations of the Arctic wetland site. The simulations are used to verify the tower-based observations, which show a significant impact of wet snow on reflectivity during melting conditions in spring. The observed SNR is strongly correlated with the Sentinel-1 backscatter coefficient. Generally, soil states detected by GNSS-R are in high agreement with ground truth soil states, especially for inundated and frozen soils. Wet snow conditions, however, complicate the correct timing estimation of soil thawing by inducing reflectivities of a similar order as thawing soil. It is recommended that GNSS-R land application models and retrieval algorithms consider snow cover effects to reduce false classification, especially in FT detection. Overall, the outcome of this study is relevant to the upcoming ESA HydroGNSS mission.

Cutting out the middleman: calibrating and validating a dynamic vegetation model (ED2-PROSPECT5) using remotely sensed surface reflectance

Abstract. Canopy radiative transfer is the primary mechanism by which models relate vegetation composition and state to the surface energy balance, which is important to light- and temperature-sensitive plant processes as well as understanding land–atmosphere feedbacks. In addition, certain parameters (e.g., specific leaf area, SLA) that have an outsized influence on vegetation model behavior can be constrained by observations of shortwave reflectance, thus reducing model predictive uncertainty. Importantly, calibrating against radiative transfer outputs allows models to directly use remote sensing reflectance products without relying on highly derived products (such as MODIS leaf area index) whose assumptions may be incompatible with the target vegetation model and whose uncertainties are usually not well quantified. Here, we created the EDR model by coupling the two-stream representation of canopy radiative transfer in the Ecosystem Demography model version 2 (ED2) with a leaf radiative transfer model (PROSPECT-5) and a simple soil reflectance model to predict full-range, high-spectral-resolution surface reflectance that is dependent on the underlying ED2 model state. We then calibrated this model against estimates of hemispherical reflectance (corrected for directional effects) from the NASA Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and survey data from 54 temperate forest plots in the northeastern United States. The calibration significantly reduced uncertainty in model parameters related to leaf biochemistry and morphology and canopy structure for five plant functional types. Using a single common set of parameters across all sites, the calibrated model was able to accurately reproduce surface reflectance for sites with highly varied forest composition and structure. However, the calibrated model's predictions of leaf area index (LAI) were less robust, capturing only 46 % of the variability in the observations. Comparing the ED2 radiative transfer model with another two-stream soil–leaf–canopy radiative transfer model commonly used in remote sensing studies (PRO4SAIL) illustrated structural errors in the ED2 representation of direct radiation backscatter that resulted in systematic underestimation of reflectance. In addition, we also highlight that, to directly compare with a two-stream radiative transfer model like EDR, we had to perform an additional processing step to convert the directional reflectance estimates of AVIRIS to hemispherical reflectance (also known as “albedo”). In future work, we recommend that vegetation models add the capability to predict directional reflectance, to allow them to more directly assimilate a wide range of airborne and satellite reflectance products. We ultimately conclude that despite these challenges, using dynamic vegetation models to predict surface reflectance is a promising avenue for model calibration and validation using remote sensing data.

Isolated AGNs NGC 5347, ESO 438‐009, MCG‐02‐04‐090, and J11366‐6002: Swift and NuSTAR joined view1

AbstractWe present the spectral analysis with the Nuclear Spectroscopic Telescope Array (NuSTAR) of four isolated galaxies with active galactic nuclei selected from the 2MIG catalogue: NGC 5347, ESO 438‐009, MCG‐02‐09‐040, and IGR J11366‐6002. We also used the Swift/Burst Alert Telescope (BAT) data up to ∼150 keV for MCG 02‐09‐040, ESO 438‐009, and IGR J11366‐6002 as well as the Swift/XRT data in 0.3–10 keV energy band for NGC 5347, ESO 438‐009, and IGR J11366‐6002. All the sources appear to have the reflected spectrum component with different reflection fractions in addition to the primary power‐law continuum. We found that power‐law indices for these sources lie between 1.6 and 1.8. The spectra of two sources, NGC 5347 and MCG‐02‐09‐040, show the Fe Kα emission line. For both of these sources, the Fe Kα lines have a significant value of EW ∼1 keV. The X‐ray spectrum of NGC 5347 is best fitted by a pure reflection model with Ecut ∼ 117 keV and without the presence of any additional primary power‐law component. We also found that the X‐ray spectrum of MCG‐02‐09‐040 shows the presence of heavy neutral obscuration of NH ∼ 1024 cm−2. However, this provides a non‐physical value of reflection in the case with fitting by a simple reflection model. A more appropriate fit is obtained with adopting the physical Monte Carlo‐based model as BNTorus. It allowed us to determine the absorption value of NH ∼ 1.04 × 1024 cm−2 and reasonable power‐law index of Γ ≈ 1.63. Results for MCG‐02‐09‐040 are presented for the first time.

A perturbed ghost model for estimating air-gun array signatures

Source designature for seismic data acquired using an air-gun array aims to remove the effects of pulse asymmetry, bubble oscillation, array directivity, and ghosting at the sea surface. For the process to be successful, we require an accurate representation of the source signature in the far field over the full data bandwidth. The well-established approach to this problem is to derive signatures from hydrophone data recorded in the near field of the source array. We perform a least-squares inversion of the near-field data, using a representation of the physics of propagation within the vicinity of the array, according to the measured geometry and incorporating bubble motion and source ghost formation. While ghost formation is typically treated using a simple linear model of propagation and reflection at the sea surface, observations suggest that this may be too simplistic. For example, ghost amplitudes are often found to be lower than expected, and features indicative of acoustically induced cavitation are observed. Hence there is interest in developing approaches that allow us to solve for the ghost directly using additional measurements made in the near field. We present an approach that builds on the standard method of inverting for notional sources and that seeks to take account of nonlinear perturbations to the downgoing wavefield, including attenuation of the ghost. Perturbation of the ghost is described using a series of virtual notional sources situated in the water column between the guns and the sea surface. This is found to provide a more accurate treatment of the ghost and does not require optimization of model parameters as is often necessary in practice with the standard approach. It is also found that the inversion is more stable than an alternative parameter-free approach that solves directly for real and mirror virtual notional sources. The improved performance and stability are demonstrated with a field data example.

The Design of Unit-Lesson Reflection Model For Senior High School English Teachers

Each of us in our professional lives as a teacher is likely to face different kind of events or incidents during teaching and learning process in the classroom. The situation in the classroom is sometimes unpredictable. The teachers are expected to be proactive and decide wisely to respons any unpredictable situations. They need to reflect on what happened, describe the events and identify the possible causes of the unexpected events. Then, teachers may analyse the findings and think of what to do to improve the unexpected events to be applied in the future actions. This study purposed to help teachers to evaluate such unexpected events occured in order to plan a new action if it is occured in the future time. So, the writer designed and provided a simple and efficient model of pedagogical practice reflection for senior high school teachers. Questionnaires and interview were contributed to gain feedback from the English teachers (as the participants in this study) related to the proposed design of unit-lesson reflection model. The library study was also conducted to generate theories in this issue.

SMAP radar receiver measures land surface freeze/thaw state through capture of forward-scattered L-band signals

Quantifying freeze/thaw status of the landscape (soils and vegetation) is important for identifying the availability of liquid water in the high latitudes to support ecosystem processes controlling carbon sequestration and release. A better understanding of the seasonal transition of high latitude landscapes between frozen and thawed states is therefore critical for predicting carbon cycle feedbacks in a warming climate. However, observations of freeze/thaw state are not at sufficient temporal and spatial resolution to observe fast (~days–weeks) transitions in highly heterogeneous regions. Here, we present new evidence that reflected Global Navigation Satellite System (GNSS) signals captured by the SMAP radar receiver have the potential to quantify changes in high-latitude soil freeze/thaw state at kilometer-scale resolution. Boreal wetland observations indicate a ~10dB seasonal difference in the signal-to-noise ratio (SNR), in agreement with simulations from a simple reflectivity model. Our analysis indicates that ground-reflected GNSS signals as a form of L-band bistatic radar could be a robust observable to quantify soil freeze/thaw state at process-relevant scales. We describe the caveats and potential limitations of this approach, and highlight areas for continuing research.

Enhanced RTI for gloss reproduction

The Digital Humanities Lab (DHLab) is a technological oriented research group within the faculty of Humanities of the University of Basel. The research profile of the DHLab integrates computer science, digital imaging, computational photography, the accessibility of digital objects and solutions for digital preservation with the aim to support scholars in the emerging field of humanities research. The project Digital Materiality, a collaboration with the Seminar of Art History, examines how new imaging and visualization methods can be applied to describe the reflection of light on surfaces of artworks. Of main interest are mosaics and early prints; both types of artworks have a strong interaction with light that can not captured adequately by standard photographic approaches. Conventional photographic processes are not able to capture the dynamic component of the light-surface interdependence that is specific for this kind of art. The technical part of the project focuses on improving the methodology that is in general described as Reflectance Transformation Imaging (RTI) techniques. RTI is an approach based on a mathematical model, that is fitted in image data derived from photographs. By modifying the mathematical model that is used to represent the light-surface interaction, the digital reproduction can be improved so that relevant attributes of artworks can be transported into the digital domain in such a way that the requirements and needs of humanities researchers to a digital representation can be fulfilled. The improvements take into account more sophisticated but still robust and simple reflection models for the realistic visualization of localized diffuse and specular surfaces within the same digital reproduction. For humanities research the most important aspect is the compatibility to web-based Virtual Research Environments (VRE). The presented approach can be integrated in such environments because the client-side visualization is implemented in WebGL. For flexibility, performance and data permanence aspects the server side will be an enhanced image server layer following the International Image Interoperability Framework (IIIF) image based environment.

Contribution of ion reflection to the energy budgets of dipolarization fronts

AbstractDipolarization fronts, earthward propagating structures in the Earth's magnetotail characterized by sharp enhancements of the northward magnetic field, are important sites of energy conversion from electromagnetic to particle energy. The large energy conversion rate observed at these fronts suggests significant particle acceleration and heating, which powers the ambient current sheet to generate plasma flows in the magnetotail plasma sheet and its boundary layer. Using a simple model of ion reflection at the dipolarization front, we estimate ion energy enhancement in the ambient plasma sheet and find it to be comparable with typical electromagnetic energy converted at the front. Validated by dipolarization front statistics from THEMIS (Time History of Events and Macroscale Interactions during Substorms) observations, this result suggests the important contribution of ion reflection to the energy budgets of dipolarization fronts during their earthward propagation.

Spectral signature of atmospheric reflection in Hercules X-1/HZ Hercules during low and short high states

We analyse RXTE/PCA X-ray spectra of the binary X-ray pulsar Her X-1/HZ Her during short high state and one binary orbit in the preceding low state, just before short high turn-on. The spectrum is well described by two continuum components (absorbed and unabsorbed). The resulting spectral parameters are modulated with orbital phase. During low state a significant component of the flux, and its spectrum, is consistent with X-ray reflection off the face of the companion star HZ Her. This component has a significantly harder X-ray spectrum than the rest of the flux from the Her X-1 system. A second component in low state is consistent with emission from the accretion disk corona. During short high a third strong component is present with a softer spectrum, which is associated with the neutron star and accretion disk. Due to this direct emission from the neutron star and accretion disk, the reflected emission is less clear, however parameters and fluxes modulations during short high state indicate its presence. In low state, the hard X-ray flux ($h \nu$ $>$ $10 keV$) peaks at orbital phase $\phi_{orb}\simeq$ 0.55, which is expected from a simple model of atmospheric reflection from the companion star. The offset indicates an asymmetry in the X-ray illumination of the companion, which could be due to shadowing of the the inner face of HZ Her by the accretion disk and/or stream.

THE COMPLEX ACCRETION GEOMETRY OF GX 339–4 AS SEEN BYNuSTARANDSWIFT

We present spectral analysis of five NuSTAR and Swift observations of GX 339-4 taken during a failed outburst in summer 2013. These observations cover Eddington luminosity fractions in the range ~0.9-6%. Throughout this outburst, GX 339-4 stayed in the hard state, and all five observations show similar X-ray spectra with a hard power-law with a photon index near 1.6 and significant contribution from reflection. Using simple reflection models we find unrealistically high iron abundances. Allowing for different photon indices for the continuum incident on the reflector relative to the underlying observed continuum results in a statistically better fit and reduced iron abundances. With a photon index around 1.3, the input power-law on the reflector is significantly harder than that which is directly observed. We study the influence of different emissivity profiles and geometries and consistently find an improvement when using separate photon indices. The inferred inner accretion disk radius is strongly model dependent, but we do not find evidence for a truncation radius larger than 100 r_g in any model. The data do not allow independent spin constraints but the results are consistent with the literature (i.e., a>0). Our best-fit models indicate an inclination angle in the range 40-60 degrees, consistent with limits on the orbital inclination but higher than reported in the literature using standard reflection models. The iron line around 6.4 keV is clearly broadened, and we detect a superimposed narrow core as well. This core originates from a fluorescence region outside the influence of the strong gravity of the black hole and we discuss possible geometries.

X-ray time delays from the Seyfert 2 galaxy IRAS 18325−5926

Using new XMM-Newton observations we detect hard X-ray time lags in the rapid variability of the Compton-thin Seyfert 2 galaxy IRAS 18325-5926. The higher-energy X-ray variations lag behind correlated lower-energy variations by up to ~3ks and the magnitude of the lag increases clearly with energy separation between the energy bands. We find that the lag-energy spectrum has a relatively simple log(E) shape. This is quite different in both shape and magnitude from the lags predicted by simple reflection models, but very similar to the hard X-ray lags often seen in black hole X-ray binaries. We apply several spectral models to the lag-energy spectrum and rule out simple reflection as an origin for the hard lags. We find that both propagating fluctuations embedded in the accretion flow and electron scattering from material embedded in or behind a cold absorbing medium offer equally good fits to the observed low-frequency hard X-ray lags and are both consistent with the time-averaged spectrum. Such models will likely look very different outside of XMM-Newton's observable bandpass, paving the way for future studies with NuSTAR.

Influence of Intake on Fan Blade Flutter

The main aim of this paper is to study the influence of upstream reflections on flutter of a fan blade. To achieve this goal, flutter analysis of a complete fan assembly with an intake duct and the downstream outlet guide vanes (OGVs) (whole low pressure (LP) domain) is undertaken using a validated computational fluid dynamics (CFD) model. The computed results show good correlation with measured data. Due to space constraints, only upstream (intake) reflections are analyzed in this paper. It will be shown that the correct prediction of flutter boundary for a fan blade requires modeling of the intake and different intakes would produce different flutter boundaries for the same fan blade. However, the “blade only” and intake damping are independent and the total damping can be obtained from the sum of the two contributions. In order to gain further insight into the physics of the problem, the pressure waves created by blade vibration are split into an upstream and a downstream traveling wave in the intake. The splitting of the pressure wave allows one to establish a relationship between the phase and amplitude of the reflected waves and flutter stability of the blade. By using this approach, a simple reflection model can be used to model the intake effects.

A Physically‐Based BSDF for Modeling the Appearance of Paper

AbstractWe present a novel appearance model for paper. Based on our appearance measurements for matte and glossy paper, we find that paper exhibits a combination of subsurface scattering, specular reflection, retroreflection, and surface sheen. Classic microfacet and simple diffuse reflection models cannot simulate the double‐sided appearance of a thin layer. Our novel BSDF model matches our measurements for paper and accounts for both reflection and transmission properties. At the core of the BSDF model is a method for converting a multi‐layer subsurface scattering model (BSSRDF) into a BSDF, which allows us to retain physically‐based absorption and scattering parameters obtained from the measurements. We also introduce a method for computing the amount of light available for subsurface scattering due to transmission through a rough dielectric surface. Our final model accounts for multiple scattering, single scattering, and surface reflection and is capable of rendering paper with varying levels of roughness and glossiness on both sides.

Emergence of the active magnetotail plasma sheet boundary from transient, localized ion acceleration

Observations of the Earth's magnetotail plasma sheet boundary layer (PSBL) have been typically accompanied by field‐aligned crescent‐shaped ion beams, thought to emanate at distant or mid‐tail semi‐permanent or impulsive acceleration sites. Typically such observations, and the theoretical and modeling efforts to explain them, have been disjoint from the adjacent plasma sheet properties near the equatorial projection of the observation. Thus the plasma sheet boundary layer has been thought of as a harbinger of remote, rather than local plasma sheet activity, exception of plasma sheet expansions during the recovery phase of substorms. Using case and statistical studies from THEMIS, obtained simultaneously at the near‐Earth PSBL and at its adjacent central plasma sheet (CPS), we study the transient and impulsive nature of PSBL beams and their inherent connection with CPS bursty bulk flows and associated dipolarization fronts. We show that PSBL beams typically commence a few minutes before CPS flow bursts, which in turn are seen tens of seconds ahead of the arrival of dipolarization fronts. These timing correlations, the crescent shapes of PSBL ion beams, the CPS ion flux enhancements in the earthward and dawnward directions, and other particle distribution characteristics can all be well reproduced by a simple model of ion reflection and acceleration at earthward‐propagating dipolarization fronts associated with CPS flow bursts. The emerging paradigm, therefore, unifies impulsive transport phenomena across latitudes in the near‐Earth magnetotail plasma sheet.

Joint spectral-timing modelling of the hard lags in GX 339−4: constraints on reflection models

The X-ray variations of hard state black hole X-ray binaries above 2 keV show 'hard lags', in that the variations at harder energies follow variations at softer energies, with a time-lag \tau depending on frequency \nu approximately as \tau \propto \nu^{-0.7}. Several models have so far been proposed to explain this time delay, including fluctuations propagating through an accretion flow, spectral variations during coronal flares, Comptonisation in the extended hot corona or a jet, or time-delays due to large-scale reflection from the accretion disc. In principle these models can be used to predict the shape of the energy spectrum as well as the frequency-dependence of the time-lags, through the construction of energy-dependent response functions which map the emission as a function of time-delay in the system. Here we use this approach to test a simple reflection model for the frequency-dependent lags seen in the hard state of GX 339-4, by simultaneously fitting the model to the frequency-dependent lags and energy spectrum measured by XMM-Newton in 2004 and 2009. Our model cannot simultaneously fit both the lag and spectral data, since the relatively large lags require an extremely flared disc which subtends a large solid angle to the continuum at large radii, in disagreement with the observed Fe K\alpha emission. Therefore, we consider it more likely that the lags > 2 keV are caused by propagation effects in the accretion flow, possibly related to the accretion disc fluctuations which have been observed previously.

Ionized X-ray reverberation mapping: testing a light-bending model for 1H0707−495

The narrow-line Seyfert 1 galaxy 1H0707−495 has shown the first clear evidence of X-ray reverberation in which the soft, disc-reflection and Fe-L-dominated 0.3–1 keV band lags behind the hard, continuum-dominated 1–4 keV band by ≈ 30 s. A simple reflection model, however, cannot explain the different amplitudes of variability between the continuum and reflection components in time-resolved spectra. Here we apply a light-bending model (LBM) to 1H0707−495 to determine whether or not it can fully account for both the time-averaged spectrum and observed X-ray variability and time lags. A point-like source is assumed to move vertically from 3.5rg to 8 rg approximately along the rotation axis of the black hole. Photon paths are integrated via a numerical method for each source position to calculate the corresponding direct and ionized reflection spectra from the accretion disc. The source is assumed to move up and down in such a way as to reproduce the 1–4 keV light curve from the XMM–Newton observations. We find that, even though the reproduced time-averaged spectrum generally agrees with the observations, this LBM cannot account for the observed time lags between the continuum and reflection spectrum. Furthermore, timing properties such as coherence are sensitive to the ionization state of the inner disc. We conclude that a more complex model of the source geometry and intrinsic variability are required, and probably one in which fluctuations propagating through the disc are directly associated with the X-ray sources. Our ionized reverberation mapping model is completely general, allowing other scenarios to be investigated in the future. Reverberation signatures are beginning to constrain the true nature of the X-ray source of not only 1H0707−495, but also other active galactic nuclei.