Measurement of turbulent kinetic energy dissipation rates in the mesosphere by a 3 MHz Doppler radar

A new narrow beam Doppler radar operating at 3.17 MHz has been installed close to the Andøya Rocket Range in Andenes, Norway in summer 2002 in order to improve the ground based capabilities for measurements of turbulence in the mesosphere. The main feature of the radar is a Mills Cross transmitting/receiving antenna consisting of 29 crossed half-wave dipoles. In combination with the modular transceiver system this provides high flexibility in beam forming and pointing. In general, vertical and oblique beams with a minimum one way half-power full-beam width (HPFW) of 6.6° are used. The observations are usually performed with a height resolution of 1 km and with off-zenith beams at 7.3° directed towards NW, NE, SE, and SW. Turbulence intensities have been estimated from the width of the observed signal spectra using an computationally intensive correction method which requires precise knowledge of the antenna radiation pattern. The program uses real-time measurements of the wind field in all determinations. Turbulent kinetic energy dissipation rates based on radar observations are presented and compared with corresponding climatological summer and winter profiles from rocket measurements, as well as with single profiles from model runs for selected periods from September 2003 to Summer 2004. The mean turbulent kinetic energy dissipation rates based on these radar measurements are about 5 mW/kg at 60 km altitude and about 20 mW/kg at 80 km, in reasonable agreement with mean turbulence intensities obtained from previous rocket soundings at Andenes.     

The hard X-ray emission from the Vela pulsar wind nebula

We present the results of a preliminary spectral analysis performed on the BeppoSAX and XMM observations of the Vela plerion. The broad energy range covered by the instruments on board the two observatories allows an evaluation of the spectral parameters of the high energy emission model and provides an indication on the morphology of the source emission above 10 keV. We confirm the softening of the PWN spectrum (3–10 keV band) at distances greater than 4′ from the pulsar and estimate the diameter of the high energy (>10 keV) emission region to be on the order of 25′–30′.     

Excitation of flare-induced waves in coronal loops and the effects of radiative cooling

EUV imaging observations from several space missions (SOHO/EIT, TRACE, and SDO/AIA) have revealed a presence of propagating intensity disturbances in solar coronal loops. These disturbances are typically interpreted as slow magnetoacoustic waves. However, recent spectroscopic observations with Hinode/EIS of active region loops revealed that the propagating intensity disturbances are associated with intermittent plasma upflows (or jets) at the footpoints which are presumably generated by magnetic reconnection. For this reason, whether these disturbances are waves or periodic flows is still being studied. This study is aimed at understanding the physical properties of observed disturbances by investigating the excitation of waves by hot plasma injections from below and the evolution of flows and wave propagation along the loop. We expand our previous studies based on isothermal 3D MHD models of an active region to a more realistic model that includes full energy equation accounting for the effects of radiative losses. Computations are initialized with an equilibrium state of a model active region using potential (dipole) magnetic field, gravitationally stratified density and temperature obtained from the polytropic equation of state. We model an impulsive injection of hot plasma into the steady plasma outflow along the loops of different temperatures, warm (～1 MK) and hot (～6 MK). The simulations show that hot jets launched at the coronal base excite slow magnetoacoustic waves that propagate to high altitudes along the loops, while the injected hot flows decelerate rapidly with heights. Our results support that propagating disturbances observed in EUV are mainly the wave features. We also find that the effect of radiative cooling on the damping of slow-mode waves in 1–6 MK coronal loops is small, in agreement with the previous conclusion based on 1D MHD models.     

Mathematical description of the NaK model for MASTER-2005

The release of NaK droplets has been modeled for the new version of the European Meteoroid and Space Debris Terrestrial Environment Reference model MASTER-2005. Previously published versions of the model have been revised. The parameters of the model are introduced and discussed. NaK droplets consist of eutectic sodium–potassium alloy and have been released during RORSAT reactor core ejections. They contributed to the space debris environment in the centimeter and millimeter size regime. Sixteen nuclear powered RORSATs launched between 1980 and 1988 activated a reactor core ejection system in Sufficiently High Orbits (SHO), mostly between 900 and 950 km altitude. The core ejection caused an opening of the primary coolant circuit. The liquid coolant has been released into space during these core ejections. The outflow is considered as a discrete event for each of the sixteen core ejections in total. The NaK coolant has been forming droplets up to a diameter of 5.5 cm. NaK releases are restricted to a very narrow region near 65° inclination. This paper gives the parameters of the NaK release model as it is implemented in MASTER-2005. The quantitative values of all model parameters including characteristic diameter and uniformity parameter are presented. The ratio of the characteristic droplet size to the orifice diameter is discussed. It is estimated that altogether 128 kg of NaK-78 (8 kg per RORSAT) was released on orbit. Simulation runs show that there are still 45,000 droplets with a total mass of 97 kg in orbit at the reference epoch 1 May 2005, whereas the smallest droplet has a diameter of 5 mm. Results of orbit propagation simulation runs are presented in terms of spatial density.     

The lower ionosphere response to its disturbances by powerful radio waves

The paper presents data from some campaigns at Sura heating facility in 2011–1016. The experiments on probing of the artificial disturbed region of the lower ionosphere were carried out at two observation sites. One of them was located near Vasil’sursk 1 km from Sura facility (56.1°N; 46.1°E) and the other site was located at the Observatory (55.85°N; 48.8°E) of Kazan State University, 170 km to the East. Investigation of the features of the disturbed region of the lower ionosphere based on its diagnostics by the methods of the vertical sounding and oblique backscattering is the main goal of this paper. Ionosphere disturbance was fulfilled by the effect of the powerful radio wave of the ordinary or extraordinary polarization emitted by transmitters of the Sura facility with effective radiated power ERP = 50–120 MW at the frequency of 4.3, 4.7 and 5.6 MHz. Pumping waves were emitted with period from 30 s to 15 min. The disturbed region of the ionosphere in Vasil’sursk was probed by the vertical sounding technique using the partial reflexion radar at the frequency of 2.95 and 4.7 MHz. For the oblique sounding of the disturbed region the modified ionosonde Cyclon-M, operating at ten frequencies from 2.01 to 6.51 MHz was used at the Observatory site. On many heating sessions simultaneous variations of the probing partial reflection signals in Vasil’sursk and backscattered signals in Observatory were observed at the height at 40–100 km below the reflection height of the pumping wave. These observations were correlated with the pumping periods of the Sura facility. Possible mechanisms of the appearance of the disturbance in the lower ionosphere and its effect on the probing radio waves are discussed.     

An analysis of solar radio burst events on December 1, 2004

We present the analysis of the radio observations of December 1, 2004 from 07:00 UT to 07:40 UT in the 1.100–1.340 GHz band by Solar Broadband Radio Dynamic Spectrometer (SBRS) in Huairou Station. There are three groups of radio fine structures during the impulsive phase of this flare denoted by N1, Z2, and Z3. N1 has several emission lines with mixed fast and slow frequency drift rate which may reflect the conditions of flare loop and fast flows out from reconnection site; Z2 and Z3 are zebra patterns. The radio observations combined with hard X-ray and other observations show that the fine structures are connected with energetic particles. The information about magnetic field and energetic particle during the burst are also estimated based on our model.     

Comparison of vertical E × B drift velocities and ground-based magnetometer observations of DELTA H in the low latitude under geomagnetically disturbed conditions

In the present work, we analyzed the daytime vertical E × B drift velocities obtained from Jicamarca Unattended Long-term Ionosphere Atmosphere (JULIA) radar and ΔH component of geomagnetic field measured as the difference between the magnitudes of the horizontal (H) components between two magnetometers deployed at two different locations Jicamarca, and Piura in Peru for 22 geomagnetically disturbed events in which either SC has occurred or Dst_max < ?50 nT during the period 2006–2011. The ΔH component of geomagnetic field is measured as the differences in the magnitudes of horizontal H component between magnetometer placed directly on the magnetic equator and one displaced 6–9° away. It will provide a direct measure of the daytime electrojet current, due to the eastward electric field. This will in turn gives the magnitude of vertical E × B drift velocity in the F region. A positive correlation exists between peak values of daytime vertical E × B drift velocity and peak value of ΔH for the three consecutive days of the events. It was observed that 45% of the events have daytime vertical E × B drift velocity peak in the magnitude range 10–20 m/s and 20–30 m/s and 20% have peak ΔH in the magnitude range 50–60 nT and 80–90 nT. It was observed that the time of occurrence of the peak value of both the vertical E × B drift velocity and the ΔH have a maximum (40%) probability in the same time range 11:00–13:00 LT. We also investigated the correlation between E × B drift velocity and D_st index and the correlation between delta H and D_st index. A strong positive correlation is found between E × B drift and D_st index as well as between delta H and D_st Index. Three different techniques of data analysis – linear, polynomial (order 2), and polynomial (order 3) regression analysis were considered. The regression parameters in all the three cases were calculated using the Least Square Method (LSM), using the daytime vertical E × B drift velocity and ΔH. A formula was developed which indicates the relationship between daytime vertical E × B drift velocity and ΔH, for the disturbed periods. The E × B drift velocity was then evaluated using the formulae thus found for the three regression analysis and validated for the ‘disturbed periods’ of 3 selected events. The E × B drift velocities estimated by the three regression analysis have a fairly good agreement with JULIA radar observed values under different seasons and solar activity conditions. Root Mean Square (RMS) errors calculated for each case suggest that polynomial (order 3) regression analysis provides a better agreement with the observations from among the three.     

The 16-day waves in the mesosphere and lower thermosphere over Wuhan (30.6°N, 114.5°E) and Adelaide (35°S, 138°E)

Winds from a meteor radar at Wuhan (30.6°N, 114.5°E) and a MF radar at Adelaide (35°S, 138°E) are used to study the 16-day waves in the mesosphere and lower thermosphere (MLT). The height range is 78–98 km at Wuhan and 70–98 km at Adelaide. By comparison, it is found that the zonal components at both sites are generally larger than the meridional ones, and eastward motion of the zonal background winds is favorable for the 16-day waves penetration to the MLT region. The zonal maximum amplitude appears in the autumn (September–October) around 86–98 km at Wuhan and in the winter months and early spring (July–October) around 72–82 km at Adelaide. Differences are found in wave amplitudes and time of appearance between the two years of 2002 and 2003. In 2003, the intensity of the wave amplitudes is relatively smaller than that for 2002 at both sites. The summer 16-day waves are comparatively weaker at Adelaide in both years, but stronger in 2002 at Wuhan near the mesopause and the lower thermosphere (86–98 km). The strong summer waves at Wuhan may come from the winter southern hemisphere.     

GNSS global real-time augmentation positioning: Real-time precise satellite clock estimation,prototype system construction and performance analysis

Lots of ambiguities in un-differenced (UD) model lead to lower calculation efficiency, which isn’t appropriate for the high-frequency real-time GNSS clock estimation, like 1 Hz. Mixed differenced model fusing UD pseudo-range and epoch-differenced (ED) phase observations has been introduced into real-time clock estimation. In this contribution, we extend the mixed differenced model for realizing multi-GNSS real-time clock high-frequency updating and a rigorous comparison and analysis on same conditions are performed to achieve the best real-time clock estimation performance taking the efficiency, accuracy, consistency and reliability into consideration. Based on the multi-GNSS real-time data streams provided by multi-GNSS Experiment (MGEX) and Wuhan University, GPS + BeiDou + Galileo global real-time augmentation positioning prototype system is designed and constructed, including real-time precise orbit determination, real-time precise clock estimation, real-time Precise Point Positioning (RT-PPP) and real-time Standard Point Positioning (RT-SPP). The statistical analysis of the 6 h-predicted real-time orbits shows that the root mean square (RMS) in radial direction is about 1–5 cm for GPS, Beidou MEO and Galileo satellites and about 10 cm for Beidou GEO and IGSO satellites. Using the mixed differenced estimation model, the prototype system can realize high-efficient real-time satellite absolute clock estimation with no constant clock-bias and can be used for high-frequency augmentation message updating (such as 1 Hz). The real-time augmentation message signal-in-space ranging error (SISRE), a comprehensive accuracy of orbit and clock and effecting the users’ actual positioning performance, is introduced to evaluate and analyze the performance of GPS + BeiDou + Galileo global real-time augmentation positioning system. The statistical analysis of real-time augmentation message SISRE is about 4–7 cm for GPS, whlile 10 cm for Beidou IGSO/MEO, Galileo and about 30 cm for BeiDou GEO satellites. The real-time positioning results prove that the GPS + BeiDou + Galileo RT-PPP comparing to GPS-only can effectively accelerate convergence time by about 60%, improve the positioning accuracy by about 30% and obtain averaged RMS 4 cm in horizontal and 6 cm in vertical; additionally RT-SPP accuracy in the prototype system can realize positioning accuracy with about averaged RMS 1 m in horizontal and 1.5–2 m in vertical, which are improved by 60% and 70% to SPP based on broadcast ephemeris, respectively.     

Hard X-ray footpoint motions in solar flares: Comparing magnetic reconnection models with observations

Hard X-ray observations from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) of the October 29, 2003 GOES X10 two-ribbon flare are used together with magnetic field observations from the Michelson Doppler Imager (MDI) onboard SoHO to compare footpoint motions with predictions from magnetic reconnection models. The temporal variations of the velocity v of the hard X-ray footpoint motions and the photospheric magnetic field strength B in footpoints are investigated. The underlying photospheric magnetic field strength is generally higher (B ∼ 700–1200 G) in the slower moving (v ∼ 20–50 km s⁻¹) western footpoint than in the faster (v ∼ 20–100 km s⁻¹) moving eastern source (∼100–600 G). Furthermore, a rough temporal correlation between the HXR flux and the product vB² is observed.     

Statistical parameters of nonisothermal lower ionospheric plasma in the electrically active mesosphere

The large V/m electric fields inherent in the lower mesosphere play an essential role in lower ionospheric electrodynamics. They must be the cause of large variations in the electron temperature and the electron collision frequency and consequently of the transition of the ionospheric plasma in the lower part of the D region into a nonisothermal state. This study is based on the datasets on large mesospheric electric fields collected with the 2.2-MHz radar of the Institute of Space and Atmospheric Studies, University of Saskatchewan, Canada (52°N geographic latitude, 60.4°N geomagnetic latitude), and with the 2.3-MHz radar of the Kharkiv V. Karazin National University, Ukraine (49.6°N geographic latitude, 45.6°N geomagnetic latitude). The statistical analysis of these data is presented by [Meek, C.E., Manson, A.H., Martynenko, S.I., Rozumenko, V.T., Tyrnov, O.F. Remote sensing of mesospheric electric fields using MF radars. J. Atmos. Solar-Terr. Phys. 66, 881–890, 2004. 10.1016/j.jastp.2004.02.002]. The large mesospheric electric fields in the 60–67-km altitude range are experimentally established to follow a Rayleigh distribution in the 0 < E < 2.5 V/m interval. These data have permitted the resulting differential distributions of relative disturbances in the electron temperature, θ, and the effective electron collision frequency, η, to be determined. The most probable θ and η values are found to be in the 1.4–2.2 interval, and hence the nonstationary state of the lower part of the D region needs to be accounted for in studying processes coupling the electrically active mesosphere and the lower ionospheric plasma.     

Global MGS TES data and Mars-GRAM validation

Mars Global Reference Atmospheric Model (Mars-GRAM 2001) is an engineering-level Mars atmosphere model widely used for many Mars mission applications. From 0 to 80 km, it is based on NASA Ames Mars General Circulation Model (MGCM), while above 80 km it is based on University of Michigan Mars Thermospheric General Circulation Model. Mars-GRAM 2001 and MGCM use surface topography from Mars Global Surveyor Mars Orbiter Laser Altimeter (MOLA). Validation studies are described comparing Mars-GRAM with a global summary data set of Mars Global Surveyor Thermal Emission Spectrometer (TES) data. TES averages and standard deviations were assembled from binned TES data which covered surface to ∼40 km, over more than a full Mars year (February 1999–June 2001, just before start of a Mars global dust storm). TES data were binned in 10° × 10° latitude–longitude bins (36 longitude bins, centered at 5°–355°, by 18 latitude bins, centered at −85° to +85°), and 12 seasonal bins (based on 30° increments of L_s angle). Bin averages and standard deviations were assembled at 23 data levels (temperature at 21 pressure levels, plus surface temperature and surface pressure). Two time-of-day bins were used: local time near 2 or 14 h. Two dust optical depth bins were used: infrared optical depth, either less than or greater than 0.25 (which corresponds to visible optical depth less than or greater than about 0.5). For interests in aerocapture and precision entry and landing, comparisons focused on atmospheric density. TES densities versus height were computed from TES temperature versus pressure, using assumptions of perfect gas law and hydrostatics. Mars-GRAM validation studies used density ratio (TES/Mars-GRAM) evaluated at data bin center points in space and time. Observed average TES/Mars-GRAM density ratios were generally 1 ± 0.05, except at high altitudes (15–30 km, depending on season) and high latitudes (>45°N), or at most altitudes in the southern hemisphere at L_s ∼ 90° and 180°. Compared to TES averages for a given latitude and season, TES data had average density standard deviation about the mean of ∼2.5% for all data, or ∼1–4%, depending on time of day and dust optical depth. Average standard deviation of TES/Mars-GRAM density ratio was 8.9% for local time 2 h and 7.1% for local time 14 h. Thus standard deviation of observed TES/Mars-GRAM density ratio, evaluated at matching positions and times, is about three times the standard deviation of TES data about the TES mean value at a given position and season.     

Estimates of mesospheric gravity wave activity over convection from a global model

A new convective gravity wave source spectrum parameterization has been implemented in the Whole Atmosphere Community Climate Model version 2 (WACCM2). This parameterization specifies the momentum flux phase speed spectrum of gravity waves in the Tropics based on the properties of underlying convection; Hence, this parameterization provides realistic global estimates of gravity wave activity. In this paper, we show the estimated gravity wave phase speed spectra in the Tropics from a WACCM2 simulation, at the source level and at 85 km. Spatial distribution of gravity wave activity at 85 km is also presented. Subsequently, we discuss the factors that are primarily responsible for the estimated differences in gravity wave distribution across phase speeds with latitude and asymmetries in direction of gravity wave propagation in the mesosphere. We also examine which of the model assumptions can lead to uncertainties in our estimates of mesospheric gravity wave activity and we discuss how these assumptions provide challenges for comparison with observations of gravity waves in the mesosphere.     

Brazilian Decimetre Array (Phase-1): Initial solar observations

An East–West one-dimensional radio interferometer array consisting of 5 parabolic dish antennas has been set-up at Cachoeira Paulista, Brazil (Longitude: 45°0′20″W, Latitude: 22°41′19″S) for observations of Sun and some of the strong sidereal sources by the Instituto Nacional de Pesquisas Espaciais (INPE), Brazil. This is Phase-1 of the proposed Brazilian Decimetre Array (BDA) and can be operated at any frequency in the range 1.2–1.7 GHz. The instrument is functional since November 2004 onwards at 1.6 GHz. The angular and temporal resolution at the above frequency range are ∼3′ and 100 ms, respectively. We present here the initial solar observations carried out with this array.     

Modeling of effect of polarization on UV sky radiance during twilight

The spatial distribution of the vector of the Stokes parameters characterizing the radiance intensity and the radiance polarization describes the radiation field in the atmosphere. A simplified treatment of light as the scalar has only restricted application. A few studies compared previously results of the vector and scalar radiative transfer models and showed that scalar models are in error by up to 10% for many cases. Though several observational conditions were exploited, an effect of polarization on modeling of UV radiance has not been investigated yet for twilight. The paper presents a preliminary study of modeled UV radiance during twilight taking into account polarization. The intensity and the degree of linear polarization of the scattered UV radiance for two cases of the ground-based observations are discussed. In the first case, radiation incoming from the zenith for the solar zenith angles (SZA) from 90° to 98° is under investigation. Radiation in the solar principal plane for the beginning of twilight (SZA = 90.1°) was calculated in the second case. The study showed that the UV radiation field in the twilight atmosphere can be handled correctly only using the vector theory. The errors of scalar radiative transfer strongly depend on wavelength, line of an observation and solar position. The revealed distortion of the zenith radiance caused by using of the scalar approximation reaches maximum of 15% at 340 nm for the solar zenith angle (SZA) equal to 98°. The shorter wavelengths have the smaller errors, about 5% at 305 nm for SZA = 98°, due to the larger part of the single scattered radiance. The error of the scalar modeling may be as large as −17% for radiance incoming from the horizon for SZA = 90.1°. Scalar radiative transfer models underestimate the integral intensity in the principal plane up to 3–4% ± 0.5% at SZA = 90.1° for wavelengths from 320 to 340 nm. This should be taken into account in problems of radiative budget estimation and remote sensing of the atmosphere exploiting the twilight period.     

Evaluation of solar proton spectra using balloon cosmic ray observations and Monte Carlo simulation results

We have developed a method to evaluate the spectrum of solar energetic protons at the top of the Earth’s atmosphere from the measurements of our balloon cosmic ray experiment. By using the Monte Carlo PLANETOCOSMICS code based on Geant4 we compute the interaction of solar protons [10 MeV–10 GeV] with the Earth’s atmosphere. We obtain the angular and energy distributions of secondary particles (p, e⁻, e⁺, photons, muons) at different atmospheric levels as a function of primary proton spectra. By comparing the calculated depth dependence of the particle flux with the data obtained by our balloon experiment we can deduce the parameters of the solar proton spectrum that best fit the observations. In this paper we discuss our solar proton spectrum estimation method, and present results of its application to selected solar proton events from 2001 to 2005.     

Observations of “zebra” pattern in cm-range with spatial resolution

We present the results of the first observations of the solar microwave burst with fine spectral structure of zebra type at the frequency about 5.7 GHz. The burst has been detected simultaneously by the Siberian Solar Radio Telescope and by the spectropolarimeter of the National Astronomical Observatory of China. Zebra pattern consisted of three parallel stripes with complex frequency drift. The degree of circular polarization of emission reached 100%, the polarization sense corresponded to the extraordinary wave (X-mode). We have determined the plasma parameters in the emission source: plasma density about 10¹¹ cm⁻³, magnetic field strength 60–80 G. We argue that in the given event the most probable mechanism of the zebra pattern generation is non-linear coupling of harmonics of Bernstein modes.     

The contribution of radar interferometry to the assessment of landslide hazards

Interferometric analysis of repeat pass radar images (InSAR) enables the mapping of slope movements with high accuracy, being of great relevance for the assessment of landslide risk. The InSAR method is briefly explained, with emphasis on data processing for landslide motion mapping. Constraints of the method are discussed, mainly resulting from temporal decorrelation of the radar signal in vegetated areas. Application examples for InSAR mapping of very slow slope movements, using SAR data of the European Earth Observation Satellite ERS, are shown for a mass waste above an alpine traffic route and for slope deformation in a mountain village. The comparison with GPS measurements of surface motion shows RMSE = 3.7 mm a⁻¹ between the InSAR and GPS retrieved motion, where part of this difference is attributed to the different observation periods. The investigations demonstrate the good capability of InSAR for detecting and monitoring surface deformation on mountain slopes, thus providing valuable support for landslide inventories and risk assessment.     

Hard X-ray component in Sco X-1 spectrum: Synchrotron emission from a nano quasar

Sco X-1 is a low mass X-ray binary system and with the recent observations of a resolved radio jet, the source has been included in the list of galactic microquasars. The observed spectral data in the 2–20 keV energy band fits a thermal emission. Above 20 keV, a hard tail has been reported on occasions. During our continuing balloon borne X-ray survey in the 20–200 keV region using high sensitivity Large Area Scintillation counter Experiment, Sco X-1 was observed on two different occasions. Even though the total X-ray luminosity of the source was different, the spectral nature of the source did not show any variation. The presence of hard X-ray flux is unmistakable. We present the spectral and temporal data in the hard X-ray band and discuss the results in terms of geometrical characteristics of X-ray source and its observed temporal properties. We note that the jet activity is similar to the microquasars, however, the absence of the large magnitude abrupt changes in X-ray light curve compared to GRS1915 + 105 suggest that the quasar-like behaviour is at a nano scale.     

Supernova remnant 1987A: The latest report from the Chandra X-ray Observatory

We continue monitoring supernova remnant (SNR) 1987A with the Chandra X-ray Observatory. As of 2004 January, bright X-ray spots in the northwest and the southwest are now evident in addition to the bright eastern ring. The overall X-ray spectrum, since 2002 December, can be described by a planar shock with an electron temperature of ∼2.1 keV. The soft X-ray flux is now 8 × 10⁻¹³ ergs cm⁻² s⁻¹, which is about five times higher than four years ago. This flux increase rate is consistent with our prediction based on an exponential density distribution along the radius of the SNR between the HII region and the inner ring. We still have no direct evidence of a central point source, and place an upper limit of L_X = 1.3 × 10³⁴ ergs s⁻¹ on the 3–10 keV band X-ray luminosity.