A Study on the Periodicity of Hardness Ratio of the X-ray Binary Cyg X-1 as a Black Hole Candidate

Using the All-Sky Monitor (ASM, 1.5∼12 keV) data of Rossi X-ray Timing Explorer (RXTE) from January 1996 to October 2011, we have analyzed in detail the power spectrum of the hardness ratio (HR) (5∼12 keV/3∼5 keV) of the X-ray binary Cyg X-1 as a black hole candidate. The results show that the HR exhibits the following periodical variations: (1) During MJD = 50087∼55841, the HR presented the the periods T ≈ 5.6 d, T ≈ 40.0 d, T ≈ 78.4 d, T ≈ 173.8 d, and T ≈ 400/800 d; (2) When Cyg X-1 was in the hard state, the HR exhibited the periods T ≈ 5.6 d, T ≈ 33.7/67.6 d, T ≈ 45.3 d, and T ≈ 165.3 d; (3) When Cyg X-1 was in the soft state, the HR exhibited the periods T ≈ 38.5 d, T ≈ d, and T ≈ 128.3 d. Moreover, using the viscosity theory and Zdziarski accretion disk model, we have made a discussion on the physical mechanism of this kind of periodicity.     

Study of X-ray and γ-ray flare from Mkn-421 during February 2010 using Swift and Fermi observations

In this work, we report on the intense flaring activity from Mkn-421 in X-ray and γ-ray regimes simultaneously observed by Swift-XRT/BAT and Fermi-LAT satellite telescopes in February 2010. With the aim of understanding the underlying physics of the flaring state in Mkn-421, we have performed a detailed spectral analysis of Swift/XRT and Fermi/LAT observations of Mkn-421 during February 12–25, 2010 (MJD 55239–55252). Over this period, we study the daily light curves and spectral variability of the source in 1–10 keV, 0.1–1 GeV and 1–100 GeV energy bands. We have performed the spectral analysis of Swift-XRT and Fermi/LAT observations to study the spectral evolution in the X-ray and gamma-ray energy domains respectively. We also compute the fractional variability amplitude in both the energy bands during the above period. We study trends between spectral parameters and physical insights provided by the parameter responsible for X-ray and γ-ray emission from the source. We search for energetic features phenomenologically linked to the single zone SSC model for blazar emission. We also produce the broad band SED with a leptonic single zone SSC model for the source.     

An Observational Study of the Strong Single Pulses of PSR J0034-0721

Using the 25m radio telescope of the Urumqi Observatory, the strong single pulses of the pulsar PSR J0034-0721 were observed at 1.54 GHz on 6th Aug. 2007. With the technique of single-pulse detection, 116 single pulses with the signal-to-noise ratios of R_SN≥5 were detected from the observed data of 1 h. At 1.54 GHz, the signal-to-noise ratios of the detected single pulses are in the range from 5 to 10.5, and the peak flux densities of these pulses are approximately 14∼29 times that of the average pulse (AP), much less than the ratios between the intensities of typical giant pulses and the intensity of AP. The cumulative distribution of the intensities of these pulses is basically a powerlaw distribution with the spectral index α = −4.3 ± 0.4. The detection rates for the pulses of R_SN≥5 and R_SN≥10 are 3% and 0.08%, respectively. For these pulses, the half-peak width W₅₀ ranges from 1.6 ms to 8 ms, 3.9 ms in average. The phases of the vast majority of the strong single pulses are concentrated around the peak position of AP, but 2 strong pulses of R_SN≥8.5 are detected at the phases about 33 ms earlier than the phase of the AP peak. This implies that there probably exist two emission regions of strong pulses, and this is consistent with the previously observed results at 40 MHz and 111 MHz, except that at 1.54 GHz the profile of AP exhibits only one component.     

Light yield in DarkSide-10: A prototype two-phase argon TPC for dark matter searches

As part of the DarkSide program of direct dark matter searches using two-phase argon TPCs, a prototype detector with an active volume containing 10 kg of liquid argon, DarkSide-10, was built and operated underground in the Gran Sasso National Laboratory in Italy. A critically important parameter for such devices is the scintillation light yield, as photon statistics limits the rejection of electron-recoil backgrounds by pulse shape discrimination. We have measured the light yield of DarkSide-10 using the readily-identifiable full-absorption peaks from gamma ray sources combined with single-photoelectron calibrations using low-occupancy laser pulses. For gamma lines of energies in the range 122–1275 keV, we get light yields averaging 8.887±0.003(stat)±0.444(sys) p.e./keV_ee. With additional purification, the light yield measured at 511 keV increased to 9.142±0.006(stat) p.e./keV_ee.     

Under the shadow of the Magellanic Bridge: A measurement of the extragalactic background at ∼ 0.7 keV

We measured the extragalactic 0.7 keV X-ray background by observing the X-ray shadow of a neutral gas cloud in the Magellanic Bridge region. Two ROSAT PSPC observations of total 104 ks were complemented by a detailed H I mapping of the cloud with both the Parkes 64 m telescope and the Australia Telescope Compact Array. From the detected anti-correlation between the observed background intensity and the H I column density of the cloud, we derived the unabsorbed extragalactic background intensity as ∼ 28 keV s⁻¹ cm⁻² keV⁻¹ sr⁻¹ at ∼ 0.7 keV. The 95% confidence lower limit 18 keV s⁻¹ cm⁻² keV⁻¹ sr⁻¹ is greater than the expected point-like source contribution ? 14 keV s⁻¹ cm⁻² keV⁻¹ sr⁻¹, constrained by the mean source spectrum together with the total background intensity in the 1-2 keV band. A significant fraction of the 0.7 keV background likely arises in a diffuse hot intergalactic medium of a few million degrees, as has been predicted in hydrodynamic simulations of cosmological structure formation.Richard McCray     

Broadband spectrum of the total X-ray emission from the galaxy M31

We present the results of measurements of the total X-ray flux from the Andromeda galaxy (M31) in the 3-100 keV band based on data from the RXTE/PCA, INTEGRAL/ISGRI, and SWIFT/BAT space experiments. We show that the total emission from the galaxy has a multicomponent spectrum whose main characteristics are specified by binaries emitting in the optically thick and optically thin regimes. The galaxy’s luminosity at energies 20–100 keV gives about 6% of its total luminosity in the 3–100 keV band. The emissivity of the stellar population in M31 is L _{2–20 keV} ～ 1.1 × 10²⁹ erg s^?1 M _⊙ ^?1 in the 2–20 keV band and L _{20–100 keV} ～ 8 × 10²⁷ erg s^?1 M _⊙ ^?1 in the 20–100 keV band. Since low-mass X-ray binaries at high luminosities pass into a soft state with a small fraction of hard X-ray emission, the detection of individual hard X-ray sources in M31 requires a sensitivity that is tens of times better (up to 10^?13 erg s^?1 cm^?2) than is needed to detect the total hard X-ray emission from the entire galaxy. Allowance for the contribution from the hard spectral component of the galaxy changes the galaxy’s effective Compton temperature approximately by a factor of 2, from ～1.1 to ～2.1 keV.     

A Study of the γ-ray and X-ray Radiations of BL Lac Objects

The X-ray and γ-ray flux densities of 18 γ-loud BL Lac objects as well as their average spectral indices of X-ray wave band (1 keV) and γ-ray wave band (>100 MeV) are collected, and the correlations among the various quantities are examined. The results indicate: (1) The X-ray flux density and the γ-ray flux density exhibit rather strong correlations in all the states, high, low or mediate. (2) Between the mean spectral indices in X-ray and γ-ray wave bands there is a comparatively intense anti-correlation. (3) Between the average spectral indices and the X-ray and γ- flux densities there is no evident correlation either in the high or the mediate state. (4) Between the average spectral index of γ-ray wave band and the flux density of X-rays in low state there is a rather strong anticorrelation. Between the mean spectral index of X-ray wave band and the γ-flux density in low state there also exists a weak correlation. The results of our analysis support the viewpoint that both the X-ray and γ-ray emissions of BL Lac objects come from the synchrotron radiation and synchrotron self Compton (SSC) radiation with one and the same distribution of relativistic electrons.     

Comparison and Analysis of the Light Variations of 3C 273, 3C 279 and 3C 345

The blazar 3C 345 is quite similar to the γ-ray blazar 3C 279 in respect of redshift, spectral energy distribution from the radio to the X-ray wave band, and so on. However, it was not detected by EGRET. We compared the differences and similarities between 3C 345 and the γ-ray sources 3C 279 and 3C 273 in respect of variation amplitudes (in the 8 GHz, 22 GHz, 37 GHz and B band), the smallest variation time scales in the optical and the time lags between different bands to search possible reason for the lack of the γ-ray radiation in 3C 345. From our analyses it is found that the variation amplitudes in the radio band for 3C 345 and 3C 279 are quite similar; the variation amplitudes in the optical wave band gradually decrease in the order 3C 279, 3C 345 and 3C 273, and variations on the order of days are found in these three sources. It is also found that the time lag in 3C 345 is much longer than that in 3C 279 and is approximately the same as that in 3C 273. Based on the similarity of other observational properties between 3C 345 and 3C 273, such as the presence of the big blue bump and their comparable infrared luminosities, it is proposed that the spectral energy distribution and the luminosity in the γ-ray band for 3C 345 are similar to those for 3C 273. It is indicated by our simple calculations that if 3C 273 has a similar redshift to that of 3C 345, then even at the burst state, EGRET could not detect any radiations from 3C 273. This might be the reason why 3C 345 had never been detected by EGRET.     

The Unusual Absorption Line Spectrum of Quasar SDSS J2220+0109

We report the Balmer broad absorption lines (BALs) in the quasar SDSS J2220 + 0109 discovered from the SDSS data, and present a detailed analysis of the peculiar absorption line spectrum, including the He I* multiplet at λλ3189, 3889 arising from the metastable 2³s-state helium and the Balmer Hα and Hβ lines from the excited hydrogen H I of n = 2 level, which are rarely seen in quasar spectra, as well as many absorption lines arising from the excited Fe II* of the levels 7 955 cm⁻¹, 13 474 cm⁻¹ and 13 673 cm⁻¹ in the wavelength range 3100∼3300 Å. Ca II H, K absorption line doublets also clearly appear in the SDSS spectrum. All absorption lines show a similar blueshifted velocity structure of Δv ≈ − 1500 ∼ 0 km·s⁻¹ relative to the quasar's systematic redshift determined from the emission lines. Detailed analysis suggests that the Balmer absorption lines should arise from the partially ionized region with a column density of N_HI ≈ 10²¹ cm⁻² for an electron density of ne ∼ 10⁶ cm⁻³; and that the hydrogen n = 2 level may be populated via collisional excitation with Lyα pumping.     

A Study of the [OII]λ3727/Hα Flux Ratio of Emission Line Galaxies

With the sample of 10⁵ emission line galaxies selected from the Sloan Digital Sky Survey Data Release 4 (SDSS DR4), we have investigated the relations of the [O_II]λ3727/H_α flux ratio with the dust extinction, the ionization state of interstellar gas and the metal abundance of galaxies. It is found that the dust extinction correction has a significant effect on the [O_II]λ3727/H_α flux ratio. Before and after the dust distinction correction is made, the mean [O_II]λ3727/H_α flux ratios are 0.48 and 0.89, respectively. After the dust extinction is corrected, the dispersion of the distribution of F([O_II]λ3727) as a function of F(H_α) is obviously reduced. The [O_II]λ3727/H_α flux ratio of metal-poor galaxies decreases with the increasing ionization degree of interstellar gas, but this relation does not exist in metal-rich galaxies. Besides, it is found that the [O_II]λ3727/H_α flux ratio is correlated with the metal abundance. When 12 + lg(O/H) > 8.5, the [O_II]λ3727/H_α flux ratio decreases with the increasing metal abundance; for the galaxies of 12 + lg(O/H) > 8.5, the spectral flux ratio correlates positively with the metal abundance. Finally, by using the parameters of gas ionization degree and metal abundances of galaxies, the formulae for calculating the [O_II]λ3727/H_α flux ratios of different types of galaxies are given. With the [O_II]λ3727/H_α flux ratio given by these formulae, the star formation rate can be derived by using the [O_II]λ3727-line flux, for the galaxies of the redshift z > 0.4, such as the large number of galaxies to be observed by the LAMOST telescope.     

The impulsive X-ray burst of October 10, 1970

An impulsive burst of 100–400 keV solar X-rays associated with a small solar flare was observed on October 10, 1970 with a large area scintillator aboard a balloon floating at an altitude of 4.2 g cm^-2 above the Earth's surface. The X-ray burst was also observed simultaneously in 10–80 keV range by the OGO-5 satellite and in 8–20 Å range by the SOLRAD-9 satellite. The impulsive X-ray emission reached its maximum at 1643 UT at which time the differential photon spectrum in 20–80 keV range was of the form 2.3 × 10⁴ E ^-3.2 photons cm^-2 s^-1 keV^-1 at 1 AU. The event is attributed to a H-subflare located approximately at S13, E88 on the solar disc. The spectral characteristics of this event are examined in the light of the earlier X-ray observations of small solar flares.     

Deep Impact, Stardust-NExT and the behavior of Comet 9P/Tempel 1 from 1997 to 2010

We present observational data for Comet 9P/Tempel 1 taken from 1997 through 2010 in an international collaboration in support of the Deep Impact and Stardust-NExT missions. The data were obtained to characterize the nucleus prior to the Deep Impact 2005 encounter, and to enable us to understand the rotation state in order to make a time of arrival adjustment in February 2010 that would allow us to image at least 25% of the nucleus seen by the Deep Impact spacecraft to better than 80 m/pixel, and to image the crater made during the encounter, if possible. In total, ∼500 whole or partial nights were allocated to this project at 14 observatories worldwide, utilizing 25 telescopes. Seventy percent of these nights yielded useful data. The data were used to determine the linear phase coefficient for the comet in the R-band to be 0.045 ± 0.001 mag deg⁻¹ from 1° to 16°. Cometary activity was observed to begin inbound near r ∼ 4.0 AU and the activity ended near r ∼ 4.6 AU as seen from the heliocentric secular light curves, water-sublimation models and from dust dynamical modeling. The light curve exhibits a significant pre- and post-perihelion brightness and activity asymmetry. There was a secular decrease in activity between the 2000 and 2005 perihelion passages of ∼20%. The post-perihelion light curve cannot be easily explained by a simple decrease in solar insolation or observing geometry. CN emission was detected in the comet at 2.43 AU pre-perihelion, and by r = 2.24 AU emission from C₂ and C₃ were evident. In December 2004 the production rate of CN increased from 1.8 × 10²³ mol s⁻¹ to Q_CN = 2.75 × 10²³ mol s⁻¹ in early January 2005 and 9.3 × 10²⁴ mol s⁻¹ on June 6, 2005 at r = 1.53 AU.     

Analyses of the Light Variations of OJ 287, 0716+714 and BL Lacertae

OJ 287 is a BL Lac object which exhibits intense activities of low peak-frequencies. Its energy spectrum in low frequency band is quite similar with those of two other TeV BL Lac objects (i.e., 0716+714 and BL Lacertae). However, the Cerenkov telescope did not detect its TeV rays. By using the observational data of these three heavenly bodies and comparing the discrepan- cies of their minimal periods of light variations and delays at 22 GHz, 37 GHz and B-waveband, we have further investigated the possible reason why the TeV gamma-rays of OJ 287 have not been observed. The results of analyses are as fol- lows. (1) For the minimal periods of light variations, the periods of OJ 287 at 37 GHZ and B-waveband are short. At 22 GHz the results of OJ 287 and 0716+714 are comparable, but the period of OJ 287 is much shorter in comparison with that of BL Lacertae, and this shows that its activity is more intense. However, the TeV gamma-rays of OJ 287 have not been detected, which implies that the radiation of OJ 287 in TeV waveband may have no connection with the minimal periods of light variations in these three low-energy wavebands. (2) In respect of delays, the delay of OJ 287 in the B waveband with respect to 37 GHz is longer than that of 0716+714, but shorter than that of BL Lacertae. Its delay at 37 GHz in respect to 22 GHz is shorter than that of 0716+714. Meanwhile, the delay of BL Lacertae at 37 GHz in respect to 22 GHz is negative, which implies that 22 GHz precedes 37 GHz. Via the comparison and analysis of delays, no obvious differences between OJ 287 and 0716+714 as well as BL Lacertae have been found. On the side of energy spectra, it is quite possible that due to the steep energy spectrum of OJ 287 in TeV waveband, the Cerenkov telescope has not detected the gamma radiation of OJ 287. However, nowadays it is still not clear whether the steep energy spectrum in TeV energy range has some influence on the light variations in low energy realm.     

An investigation of the SO2 content of the venusian mesosphere using SPICAV-UV in nadir mode

Using the SPICAV-UV spectrometer aboard Venus Express in nadir mode, we were able to derive spectral radiance factors in the middle atmosphere of Venus in the 170-320 nm range at a spectral resolution of R ? 200 during 2006 and 2007 in the northern hemisphere. By comparison with a radiative transfer model of the upper atmosphere of Venus, we could derive column abundance above the visible cloud top for SO₂ using its spectral absorption bands near 280 and 220 nm. SO₂ column densities show large temporal and spatial variations on a horizontal scale of a few hundred kilometers. Typical SO₂ column densities at low latitudes (up to 50°N) were found between 5 and 50 μm-atm, whereas in the northern polar region SO₂ content was usually below 5 μm-atm. The observed latitudinal variations follow closely the cloud top altitude derived by SPICAV-IR and are thought to be of dynamical origin. Also, a sudden increase of SO₂ column density in the whole northern hemisphere has been observed in early 2007, possibly related to a convective episode advecting some deep SO₂ into the upper atmosphere.     

Warming the early earth—CO2 reconsidered

Despite a fainter Sun, the surface of the early Earth was mostly ice-free. Proposed solutions to this so-called “faint young Sun problem” have usually involved higher amounts of greenhouse gases than present in the modern-day atmosphere. However, geological evidence seemed to indicate that the atmospheric CO₂ concentrations during the Archaean and Proterozoic were far too low to keep the surface from freezing. With a radiative-convective model including new, updated thermal absorption coefficients, we found that the amount of CO₂ necessary to obtain 273 K at the surface is reduced up to an order of magnitude compared to previous studies. For the late Archaean and early Proterozoic period of the Earth, we calculate that CO₂ partial pressures of only about 2.9 mb are required to keep its surface from freezing which is compatible with the amount inferred from sediment studies. This conclusion was not significantly changed when we varied model parameters such as relative humidity or surface albedo, obtaining CO₂ partial pressures for the late Archaean between 1.5 and 5.5 mb. Thus, the contradiction between sediment data and model results disappears for the late Archaean and early proterozoic.     

Photometric observations and orbital period variations of HS 0705 + 6700 and NY Vir

We present photometric observations of two post-common-envelope stars, NY Vir (=PG 1336-018) and HS 0705 + 6700. The V band CCD observation of NY Vir was performed by a 40 cm telescope at Ege University Observatory and the R band observations of HS 0705 + 6700 were performed by 100 cm telescope at TÜB?TAK National Observatory. The new light curves were analyzed by the WD code and the physical parameters of stars were determined. We obtained new mid-eclipse timings for HS 0705 + 6700 and combined them with those previously published data. The analysis of the O-C residuals yields a period of about 8.06 ± 0.28 yr and an amplitude of 98.5 s for the system HS 0705 + 6700, which is attributed to the third star physically bounded to the evolved eclipsing pair. A mass function of 1.2 × 10⁻⁴ M_⊙ for the third star is obtained. The existence of a third star is also confirmed by the light curve analysis, indicating light contribution of about 0.043 at phase 0.25 in R-bandpass of the eclipsing pair. Using mass-luminosity relationship of the low mass stars we estimate a mass of 0.12 M_⊙ with an orbital inclination of about 20°. The O-C residuals obtained for the system NY Vir were represented by a downward parabola which indicates orbital period decrease in the system. Using the coefficient of quadratic term we calculate a rate of orbital period decrease of about dP/dt = −4.09 × 10⁻⁸days yr⁻¹. The period decrease we have measured in NY Vir may be explained by angular momentum loss from the binary system.     

Ten Years of Monitoring 3C 273 with XMM–Newton

We present ten years optical/UV/X-ray observations of 3C 273 performed using XMM–Newton between 2000 and 2009. The short-time scale variability behaviour of the soft and hard X-ray light curves may suggest different origins of the soft/hard X-ray emissions. We fit well the 0.2–10 keV X-ray spectrum with a hard power-law component plus a soft Comptonization component. The lack of Γ???F correlation of the hard power-law component and the weakness of iron K _α lines may support dominance of the jet component. The soft X-ray excess correlates much better with ultraviolet than with the hard power-law component, strongly suggesting that soft excess emission originates from inverse Comptonization of UV photons.     

Spectral measurements of galactic and extragalactic sources in the hard X-ray region of 20-200 keV using balloon borne telescope

The spectral and temporal measurements in the hard X-ray region between 20-200 keV not only determines the extended behaviour of thermal X-ray spectrum below 10 keV but also provide a unique insight into the non-thermal processes in relativistic astrophysical plasma. From our present understanding of the X-ray sources, a significant fluxin the 20-200 keV band is expected from a variety of astrophysical phenomena, however, the available spectral data on the galactic and extragalactic X-ray source is very limited. This is mainly due to the fact that sensitivity of the detector systems used for earlier measurements was relatively poor. Since 1997, we have been carrying out a programme of hard X-ray observations galactic and extragalactic sources, in the 20-200 keV energy band using a highly sensitive balloon borne experiment. The X-ray telescope consists of three modules of large area scintillation counters specially configured in the back-to-back geometry and have a combined sensitivity of ∼ 10^-6 ph cm^-2 s^-1 keV^-1 for an on-source observations of 3 hrs. A total of 30 hours of ceiling data above an altitude of 3 mbar has been collected in 4 successful balloon flights from Hyderabad, India. Almost a dozen galactic and extragalactic X-ray sources were targeted and tracked during these observations. A positive detection was made in each case and in some cases the observed spectra extended right up to 150 keV. A brief account of the observed spectral and temporal features on some of the sources along with accurate measurement of diffuse background spectrum and a weak gamma ray burst will be presented in the paper. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dust extinction and X-ray emission from the starburst galaxy NGC 1482

We present the results based on multiwavelength imaging observations of the prominent dust lane starburst galaxy NGC 1482 aimed to investigate the extinction properties of dust existing in the extreme environment. (B-V) colour-index map derived for the starburst galaxy NGC 1482 confirms two prominent dust lanes running along its optical major axis and are found to extend up to ∼11 kpc. In addition to the main lanes, several filamentary structures of dust originating from the central starburst are also evident. Though, the dust is surrounded by exotic environment, the average extinction curve derived for this target galaxy is compatible with the Galactic curve, with R_V = 3.05, and imply that the dust grains responsible for the optical extinction in the target galaxy are not really different than the canonical grains in the Milky Way. Our estimate of total dust content of NGC 1482 assuming screening effect of dust is ∼2.7 × 10⁵ M_⊙, and provide lower limit due to the fact that our method is not sensitive to the intermix component of dust. Comparison of the observed dust in the galaxy with that supplied by the SNe to the ISM, imply that this supply is not sufficient to account for the observed dust and hence point towards the origin of dust in this galaxy through a merger like event.Our multiband imaging analysis reveals a qualitative physical correspondence between the morphologies of the dust and Hα emission lines as well as diffuse X-ray emission in this galaxy. Spatially resolved spectral analysis of the hot gas along outflows exhibit a gradient in the temperature. Similar gradient was also noticed in the measured values of metallicity, indicating that the gas in the halo is not yet enriched. High resolution, 2-8 keV Chandra image reveals a pair of point sources in the nuclear region with their luminosities equal to 2.27 × 10³⁹ erg s⁻¹ and 9.34 × 10³⁹ erg s⁻¹, and are in excess of the Eddington-limit of 1.5 M_⊙ accreting source. Spectral analysis of these sources exhibit an absorbed-power law with the hydrogen column density higher than that derived from the optical measurements.     

Observations of solar gamma ray continuum between 360 keV and 7 MeV on August 4, 1972

Measurements were made of the time-averaged gamma ray energy loss spectrum in the energy range 360 keV to 7 MeV by the gamma ray detector on the OSO-7 satellite during the 3B flare on August 4, 1972. The differential photon spectrum unfolded from this spectrum after subtracting the background spectrum and contributions from gamma ray lines is best described by a power law with spectral index of 3.4±0.3 between 360–700 keV and by an exponential law of the form exp (-E/E ₀) with E ₀ = 1.0±0.1 MeV above 700 keV. It is suggested that this spectrum is due to nonthermal electron bremsstrahlung from a population of electrons, with a strong break in the spectrum at 2 MeV. Since the observational data indicates that the matter number density must be n _H ? 5 × 10¹⁰ cm^-3 in the production region, the number of electrons above 100 keV required to explain the results is ?2 × 10³⁴.