WR 140 (=V1687 Cyg): Infrared photometry, 2001–2010

We present the results of our infrared observations of WR 140 (=V1687 Cyg) in 2001–2010. Analysis of the observations has shown that the J brightness at maximum increased near the periastron by about 0 ^m .3; the M brightness increased by ∼2 ^m in less than 50 days. The minimum J brightness and the minimum L and M brightnesses were observed 550–600 and 1300–1400 days after the maximum, respectively. The JHKLM brightness minimum was observed in the range of orbital phases 0.7–0.9. The parameters of the primary O5 component of the binary have been estimated to be the following: R(O5) ≈ 24.7R _⊙, L(O5) ≈ 8 × 10⁵ L _⊙, and M _bol(O5) ≈ −10 ^m . At the infrared brightness minimum, T _g ∼ 820–880 K, R _g ≈ 2.6 × 10⁵ R _⊙, the optical depth of the shell at 3.5 μm is ∼5.3 × 10⁻⁶, and its mass is ≈1.4 × 10⁻⁸ M _⊙. At the maximum, the corresponding parameters are ∼1300 K, 8.6 × 10⁴ R _⊙, ∼2 × 10⁻⁴, and ∼6 × 10⁻⁸ M _⊙; the mean rate of dust inflow (condensation) into the dust structure is ∼3.3 × 10⁻⁸ M _⊙ yr⁻¹. The mean escape velocity of the shell from the heating source is ∼10³ km s⁻¹ and the mean dispersal rate of the shell is ∼1.1 × 10⁻⁸ M _⊙ yr⁻¹.     

Production of dust by massive stars at high redshift

The large amounts of dust detected in sub-millimeter galaxies and quasars at high redshift pose a challenge to galaxy formation models and theories of cosmic dust formation. At z>6 only stars of relatively high mass (>3 M_⊙) are sufficiently short-lived to be potential stellar sources of dust. This review is devoted to identifying and quantifying the most important stellar channels of rapid dust formation. We ascertain the dust production efficiency of stars in the mass range 3–40 M_⊙ using both observed and theoretical dust yields of evolved massive stars and supernovae (SNe) and provide analytical expressions for the dust production efficiencies in various scenarios. We also address the strong sensitivity of the total dust productivity to the initial mass function. From simple considerations, we find that, in the early Universe, high-mass (>3 M_⊙) asymptotic giant branch stars can only be dominant dust producers if SNe generate ≲3×10⁻³ M_⊙ of dust whereas SNe prevail if they are more efficient. We address the challenges in inferring dust masses and star-formation rates from observations of high-redshift galaxies. We conclude that significant SN dust production at high redshift is likely required to reproduce current dust mass estimates, possibly coupled with rapid dust grain growth in the interstellar medium.     

Search for ultrahigh-energy cosmic gamma-ray bursts on the Baksan underground scintillation telescope

Based on data from the Baksan underground scintillation telescope (BUST) for the period 2001–2004, we searched for cosmic gamma-ray bursts (GRBs) at primary photon energies of 0.5 TeV or higher. We obtained constraints on the rate of bursts with durations of 1–10 s for fluences within the range 4.6 × 10⁻³-1.8 × 10⁻² erg cm⁻² in the declination band 30° ≤ δ ≤ 80°. We searched for ultrahigh-energy gamma rays from GRBs detected on spacecraft during and within ±2 h of the burst. No statistically significant excesses above the background of random coincidences were found. The derived constraints on the ultrahigh-energy gamma-ray fluence during GRBs lie within the range 4.6 × 10⁻³-3.7 × 10⁻² erg cm⁻².     

Upper limits on neutrino fluxes from point-like sources with AMANDA-II

The AMANDA-II telescope, operated by the IceCube collaboration, is currently the world’s most sensitive telescope to fluxes of neutrinos from individual sources. A data sample of 4282 neutrino induced events collected in 1001 days of detector livetime during the years 2000–2004 have now been analyzed looking for a neutrino signal from point-like sources. A sensitivity to fluxes of of d Φ/dE=1.0×10⁻¹⁰(E/TeV)⁻² TeV⁻¹ cm⁻²s⁻¹ was reached in the energy range between 1.7 TeV and 2.4 PeV. So far no statistically significant localized excess of events over the background of atmospheric neutrinos has been found, which would be ascribed to a neutrino source. However, the flux upper limits derived from the non-observation of a signal are comparable to observed fluxes of high energy gamma rays from blazars and within the range of current models for neutrino emission from selected sources. Possible constraints on these models are discussed.      

A massive, dusty toroid with large grains in the pre-planetary nebula IRAS22036+5306

Using the Submillimeter Array (SMA), we have obtained high angular-resolution (∼1″) interferometric maps of the submillimeter (0.88 mm) continuum and CO J=3–2 line from IRAS 22036+5306 (I 22036), a bipolar pre-planetary nebula (PPN) with knotty jets discovered in our HST SNAPshot survey of young PPNe. In addition, we have obtained supporting lower-resolution (∼10″) 2.6 mm continuum and CO, ¹³CO J=1–0 observations with the Owens Valley Radio Observatory (OVRO) interferometer. We find an unresolved source of submillimeter (and millimeter-wave) continuum emission in I 22036, implying a very substantial mass (0.02–0.04M _⊙) of large (i.e., radius ≳1 mm), cold (≲50 K) dust grains associated with I 22036’s toroidal waist. The CO J=3–2 observations show the presence of a very fast (∼220 km s⁻¹), highly collimated, massive (0.03M _⊙) bipolar outflow with a very large scalar momentum (about 10³⁹ g cm s⁻¹), and the characteristic spatio-kinematic structure of bow-shocks at the tips of this outflow. The fast outflow in I 22036, as in most PPNe, cannot be driven by radiation pressure. The large mass of the torus suggests that it has most likely resulted from common-envelope evolution in a binary, however it remains to be seen whether or not the time-scales required for the growth of grains to millimeter sizes in the torus are commensurate with such a formation scenario. The presence of the torus should facilitate the formation of the accretion disk needed to launch the jet. We also find that the ¹³C/¹²C ratio in I 22036 is very high (0.16), close to the maximum value achieved in equilibrium CNO-nucleosynthesis (0.33). The combination of the high circumstellar mass (i.e., in the torus and an extended dust shell inferred from ISO far-infrared spectra) and the high ¹³C/¹²C ratio in I 22036 provides strong support for this object having evolved from a massive (≳4M _⊙) progenitor in which hot-bottom-burning has occurred.     

The moon’s permanent magnetic field: a cratered-shell model

As part of our study of the larger-scale remanent magnetic field of the Moon, we have examined the effects of cratering in an otherwise spherically symmetrical shell magnetized by a concentric dipolar magnetic fieldH _o to an intensity of magnetizationc H _o, wherec is a constant. In our initial model, we assume that the material excavated from the craters is distributed with random orientation and thus does not contribute to the remanent dipole momentM _g . We further assume that the mare fill does not contribute significantly toM _g . We choose the magnetizing dipole momentM _o and the constantc such that the magnitude of the productcH _o ≃ 3 × 10⁻⁴Г at the outer surface of the shell in the equatorial plane of the dipole. This value of the intensity of remanent magnetization was chosen to be within the range 10⁻⁷−10⁻³Г’; the intensities of thermo-remanent magnetization exhibited by Apollo samples. Finally, we use the locations and diameters of the 10 largest craters on the Moon and the depth-to-diameter ratios of Pike’s formulation to model approximately the excavation of the magnetized shell. The remanent dipole momentM _g was calculated for each of three orthogonal orientations of the magnetizing dipoleM _o. The three magnitudes ofM _g fall in the range 4 × 10¹⁸−1 × 10¹⁹Г cm³ which is close to the upper limit of 10¹⁹Г cm³ estimated forM _g from the field measurements obtained with the Apollo subsatellites. Further, the distribution of the craters is such as to produce a significant transverse component ofM _g with acute angles between the spin axis andM _g in the range 51°–77°.     

Stability criterion for a light binary attracted by a heavy body

Dynamical behaviour of a small binary with equal components, each of mass m, is considered under attraction of a heavy body of mass M. Differential equations of the general three-body problem are integrated numerically using the code by S. J. Aarseth (Aarseth, Zare 1974) for mass ratios m/M within 10⁻¹¹–10⁻⁴ range. The direct and retrograde orbits of light bodies about each other are considered which lie either in the plane of moving their center of mass or in the plane perpendicular to it. It is shown numerically that the critical separation between the binary components which leads to disruption of binary is proportional to (m/M)^1/3. The criterion can be used for studying (in the first approximation) the motion of double stars and binary asteroids or computing the parameters of magnetic monopol and antimonopol pairs.     

Complex of Meteoroid Orbits with Eccentricities Near 1 and Higher

In our work, the method that can help to predict the existence of distant objects in the Solar system is demonstrated. This method is connected with statistical properties of a heliocentric orbital complex of meteoroids with high eccentricities. Heliocentric meteoroid orbits with high eccentricities are escape routes for dust material from distant parental objects with near-circular orbits to Earth-crossing orbits. Ground-based meteor observations yield trajectory information from which we can derive their place of possible origin: comets, asteroids, and other objects (e.g. Kuiper Objects) in the Solar system or even interstellar space. Statistical distributions of radius vectors of nodes, and other parameters of orbits of meteoroids contain key information about position of greater bodies. We analyze meteor orbits with high eccentricities that were registered in 1975–1976 in Kharkiv (Ukraine). The orbital data of the Kharkiv electronic catalogue are received from observations of radiometeors with masses 10⁻⁶−10⁻³ g.     

A dynamical model of type I supernova atmosphere with the velocity gradient

A compact structure of a low-mass Type I presupernovae is assumed to be an essential feature of the hydrodynamical problem dealing with the supernova Type I (SNI) envelope outbursts. This structure is characterized by a degenerate carbon-oxygen core, which suffers a thermonuclear explosion of carbon fuel (M ₀≃1.40M _⊙), and by a compact lowmass envelope (M _e ≲0.1M _⊙) with external radiusR _e≃10⁹ cm. The parameters, of this hydrostatic envelope are specified and then, for a relatively small explosion energy, ofW ₀≃(2–10)×10⁴⁹ erg, hydrodynamic problem of the envelope ejection is solved numerically. This energy comes from neutrino-induced detonative carbon burning. The resulting structure of the SNI atmosphere expanding with the velocity gradient can be employed for an interpretation of the observed SNI spectra. In accordance with our previous papers, the SNI light curves are considered to occur due to an additional slow (with time-scale 10⁶–10⁷ s) release of the bulk of the SNI energy,W≃10⁵¹, erg. The slow energy release does not, however, affect the structure of the outermost expanding layers of the envelope which are responsible for the SNI spectra. A short (Δt≃10⁻² s) burst of soft (2–10 keV) X-rays with total radiated energy of about 10⁴⁰ erg is found to appear 10–20 days before the SNI optical maximum.     

Observations of Powerful Type III Bursts in the Frequency Range 10 – 30 MHz

The properties of powerful (flux >10⁻¹⁹ W m⁻² Hz⁻¹) type III bursts observed in July – August 2002 by the radio telescope UTR-2 at frequencies 10 – 30 MHz are analyzed. Most bursts have been registered when the active regions associated to these bursts were located near the central meridian or at 40° – 60° to the East or West from it. All powerful type III bursts drift from high to low frequencies with frequency drift rates 1 – 2.5 MHz s⁻¹. It is important to emphasize that according to our observations the drift rate is linearly increasing with frequency. The duration of the bursts changes mainly from 6 s at frequency 30 MHz up to 12 s at 10 MHz. The instantaneous frequency bandwidth does not depend on the day of observations, i.e. on the disk location of the source active region, and is increasing with frequency.     

Solving Kepler’s Equation using Bézier curves

This paper presents a non-iterative approach to solve Kepler’s Equation, M = E − e sin E, based on non-rational cubic and rational quadratic Bézier curves. Optimal control point coordinates are first shown to be linear with respect to orbit eccentricity for any eccentric anomaly range. This property yields the development of a piecewise (e.g., 3, 4) solving technique providing accuracies better than 10⁻¹³ degree for orbit eccentricity e ≤ 0.99. The proposed method does not require large pre-computed discretization data, but instead solves a cubic/quadratic algebraic equation and uses a single final Halley iteration in only a few lines of code. The method still provides accuracies better than 10⁻⁵ degree for the near parabolic worst case (e = 0.9999) with very small mean anomalies (M < 0.0517 deg). The complexity of the proposed algorithm is constant, independent of the parameters e and M. This makes the method suitable for extensive orbit propagations. Presented at the 7th Dynamics and Control of Systems and Structures in Space Conference, July 18–22, 2006, Greenwich, England.     

The morphological and spectral investigation of the galaxies Kaz 5, Kaz 92, and Kaz 390

The results of morphological and spectral study of the galaxies Kaz 5, Kaz 92, and Kaz 390 are presented. The observations were made on the 2.6-m telescope at the Byurakan Observatory with the VAGR microlenses spectrograph. Isophotes of the images of the galaxies are constructed in the Hα, [NII] λλ6584 , 6548, and [SII] λλ6731, 6717 emission lines and in the continuum. The masses of Kaz 5 and Kaz 92 are determined to be 8.6 × 10⁸ M_⊙ and 6.1 × 10⁹ M_⊙ , respectively. The mass of the gaseous component in the centers of regions I and IV of Kaz 390, which encompass a 1 pixel area, are also determined. The morphological structure of the central region of Kaz 5 in the observed spectral range, λλ6400–6800?, differs completely from the structure of the same part of the galaxy observed with the 6-m and 2.5-m telescopes. It is shown that these differences in the structure in images of Kaz 5 are mostly explained by the comparatively low resolution of the telescope in combination with the VAGR spectrograph. Absorbing matter also contributes to this effect. It is also shown that a “deficit” of nitrogen has been observed in the region of Kaz 390 studied here (a circle of diameter 40″). Translated from Astrofizika, Vol. 52, No. 1, pp. 63–74 (February 2009).     

Stability of strange dwarfs II. Computational results

The stability of strange dwarfs for quark cores with M _0core /M _⨀ = 10⁻⁴, has been studied by calculating, in each individual case, a series of strange dwarfs with configurations in which 5 ⋅ 10⁻⁴, 10⁻³, 5 ⋅ 10⁻³, 10⁻², 1.31 ⋅ 10⁻², 1.6 ⋅ 10⁻², 1.7 ⋅ 10⁻², 2 ⋅ 10⁻², ranges from the values in white dwarfs to ρ _drip = 4.3 ⋅ 10¹¹ g/cm³, at which free neutrons are produced in the crust. For the series with M _0core /M _⨀ < 0.0131, stability is lost when ρ _tr < ρ _drip . For the series with M _0core /M _⨀ > 0.0131, the equality ρ _tr = ρ _drip is reached before the strange dwarf attains its maximum mass. Although the frequency of the radial pulsations in the fundamental mode obeys ω₀² > 0 for these configurations, they are unstable with respect to transitions into a strange star state with the same total number of baryons and a radius on the order of that of neutron stars. An energy on the order of the energy in a supernova explosion is released during these transitions. It is shown that the gravitational red shift of white and strange dwarfs are substantially different for low and limiting (high) masses.     

InFOCμS Hard X-ray Imaging Telescope

InFOCμS is a new generation balloon-borne hard X-ray telescope with focusing optics and spectroscopy. We had a successful 22.5-hour flight from Fort Sumner, NM on September 16,17, 2004. In this paper, we present the performance of the hard X-ray telescope, which consists of a depth-graded platinum/carbon multilayer mirror and a CdZnTe detector. The telescope has an effective area of 49 cm² at 30 keV, an angular resolution of 2.4 arcmin (HPD), and a field of view of 11 arcmin (FWHM) depending on energies. The CdZnTe detector is configured with a 12 × 12 segmented array of detector pixels. The pixels are 2 mm square, and are placed on 2.1 mm centers. An averaged energy resolution is 4.4 keV at 60 keV and its standard deviation is 0.36 keV over 128 pixels. The detector is surrounded by a 3-cm thick CsI anti coincidence shield to reduce background from particles and photons not incident along the mirror focal direction. The inflight background is 2.9 × 10⁻⁴ cts cm⁻² sec⁻¹ keV⁻¹ in the 20–50 keV band.     

The fresnel interferometric imager

The Fresnel Interferometric Imager has been proposed to the European Space Agency (ESA) Cosmic Vision plan as a class L mission. This mission addresses several themes of the CV Plan: Exoplanet study, Matter in extreme conditions, and The Universe taking shape. This paper is an abridged version of the original ESA proposal. We have removed most of the technical and financial issues, to concentrate on the instrumental design and astrophysical missions. The instrument proposed is an ultra-lightweight telescope, featuring a novel optical concept based on diffraction focussing. It yields high dynamic range images, while releasing constraints on positioning and manufacturing of the main optical elements. This concept should open the way to very large apertures in space. In this two spacecraft formation-flying instrument, one spacecraft holds the focussing element: the Fresnel interferometric array; the other spacecraft holds the field optics, focal instrumentation, and detectors. The Fresnel array proposed here is a 3.6 ×3.6 m square opaque foil punched with 10⁵ to 10⁶ void “subapertures”. Focusing is achieved with no other optical element: the shape and positioning of the subapertures (holes in the foil) is responsible for beam combining by diffraction, and 5% to 10% of the total incident light ends up into a sharp focus. The consequence of this high number of subapertures is high dynamic range images. In addition, as it uses only a combination of vacuum and opaque material, this focussing method is potentially efficient over a very broad wavelength domain. The focal length of such diffractive focussing devices is wavelength dependent. However, this can be corrected. We have tested optically the efficiency of the chromatism correction on artificial sources (500 < λ < 750 nm): the images are diffraction limited, and the dynamic range measured on an artificial double source reaches 6.2 10^− 6. We have also validated numerical simulation algorithms for larger Fresnel interferometric arrays. These simulations yield a dynamic range (rejection factor) close to 10^− 8 for arrays such as the 3.6 m one we propose. A dynamic range of 10^− 8 allows detection of objects at contrasts as high as than 10^− 9 in most of the field. The astrophysical applications cover many objects in the IR, visible an UV domains. Examples are presented, taking advantage of the high angular resolution and dynamic range capabilities of this concept.     

INTEGRAL serendipitous detection of the gamma-ray microquasar LS 5039

LS 5039 is the only X-ray binary persistently detected at TeV energies by the Cherenkov HESS telescope. It is moreover a γ-ray emitter in the GeV and possibly MeV energy ranges. To understand important aspects of jet physics, like the magnetic field content or particle acceleration, and emission processes, such as synchrotron and inverse Compton (IC), a complete modeling of the multiwavelength data is necessary. LS 5039 has been detected along almost all the electromagnetic spectrum thanks to several radio, infrared, optical and soft X-ray detections. However, hard X-ray detections above 20 keV have been so far elusive and/or doubtful, partly due to source confusion for the poor spatial resolution of hard X-ray instruments. We report here on deep (∼300 ks) serendipitous INTEGRAL hard X-ray observations of LS 5039, coupled with simultaneous VLA radio observations. We obtain a 20–40 keV flux of 1.1±0.3 mCrab (5.9 (±1.6) ×10⁻¹² erg cm⁻² s⁻¹), a 40–100 keV upper limit of 1.5 mCrab (9.5×10⁻¹² erg cm⁻² s⁻¹), and typical radio flux densities of ∼25 mJy at 5 GHz. These hard X-ray fluxes are significantly lower than previous estimates obtained with BATSE in the same energy range but, in the lower interval, agree with extrapolation of previous RXTE measurements. The INTEGRAL observations also hint to a break in the spectral behavior at hard X-rays. A more sensitive characterization of the hard X-ray spectrum of LS 5039 from 20 to 100 keV could therefore constrain key aspects of the jet physics, like the relativistic particle spectrum and the magnetic field strength. Future multiwavelength observations would allow to establish whether such hard X-ray synchrotron emission is produced by the same population of relativistic electrons as those presumably producing TeV emission through IC.     

Identification of SrF molecular lines in the spectrum of sunspot umbra

A high resolution spectrum of a sunspot umbra is used for identification of rotational lines due to (0, 0) band of the A ²Π–X ²Σ⁺ system and (0, 0), (1, 1), and (2, 2) bands of the B ²Σ⁺–X ²Σ⁺ system of the molecule SrF. The published sunspot umbral spectrum obtained with Fourier Transform Spectrometer and solar telescope of National Solar Observatory/National Optical Astronomy Observatory at Kitt Peak was used for the study. The new identification of more than 200 SrF lines in the umbral spectrum confirms that this molecule accounts for the majority of lines in the spectral range 15050 to 15360 cm⁻¹ and 17240 to 17300 cm⁻¹. Equivalent widths have been measured for well-resolved lines of these bands and the effective rotational temperatures have been estimated for which the presence is confirmed.     

Orbital period analysis of eclipsing dwarf novae: U Geminorum

A new orbital period analysis for U Geminorum is made by means of the standard O–C technique based on 187 times of light minima including the three newest CCD data from our observation. Although there are large scatter near 70,000 cycles in its O–C diagram, there is strong evidence (>99.9% confidence level) to show the secular increase of orbital period with a rate  s⁻¹. Using the physical parameters recently derived by Echevarría et al. (Astron. J. 134:262, 2007), the range of mass transfer rate for U Geminorum is estimated as from −3.5(5)×10⁻⁹ M _⊙ yr⁻¹ to −1.30(6)×10⁻⁸ M _⊙ yr⁻¹. Moreover, the data before 60,000 cycles shows the obvious quasi-period variations. The least square estimation of a ∼17.4 yr quasi-periodic variation superimposed on secular orbital period increase is derived. Considering the possibility that solar-type magnetic activity cycles in the secondary star of U Geminorum may produce the quasi-period variations of the orbital period, Applegate’s mechanism is discussed and the results indicate such mechanism has difficulty explaining the quasi-period variation for U Geminorum. Hence, we attempted to apply the light-travel time effect to interpret the quasi-period variation and found the perturbation of ∼17.4 yr quasi-period may result from a brown dwarf. If the orbital inclination is assumed as i∼15°, corresponding to the upper limit of mass of a brown dwarf, then its orbital radii is ∼7.7 AU.     

Exploring morphological correlations among H2CO, 12CO, MSX and continuum mappings

There are relatively few H₂CO mappings of large-area giant molecular cloud (GMCs). H₂CO absorption lines are good tracers for low-temperature molecular clouds towards star formation regions. Thus, the aim of the study was to identify H₂CO distributions in ambient molecular clouds. We investigated morphologic relations among 6-cm continuum brightness temperature (CBT) data and H₂CO (1₁₁−1₁₀; Nanshan 25-m radio telescope), ¹²CO (1–0; 1.2-m CfA telescope) and midcourse space experiment (MSX) data, and considered the impact of background components on foreground clouds. We report simultaneous 6-cm H₂CO absorption lines and H110α radio recombination line observations and give several large-area mappings at 4.8 GHz toward W49 (50′×50′), W3 (70′×90′), DR21/W75 (60′×90′) and NGC2024/NGC2023 (50′×100′) GMCs. By superimposing H₂CO and ¹²CO contours onto the MSX color map, we can compare correlations. The resolution for H₂CO, ¹²CO and MSX data was ∼10′, ∼8′ and ∼18.3″, respectively. Comparison of H₂CO and ¹²CO contours, 8.28-μm MSX colorscale and CBT data revealed great morphological correlation in the large area, although there are some discrepancies between ¹²CO and H₂CO peaks in small areas. The NGC2024/NGC2023 GMC is a large area of HII regions with a high CBT, but a H₂CO cloud to the north is possible against the cosmic microwave background. A statistical diagram shows that 85.21% of H₂CO absorption lines are distributed in the intensity range from −1.0 to 0 Jy and the ΔV range from 1.206 to 5 km s⁻¹.     

Acoustic Events in the Solar Atmosphere from <Emphasis Type="Italic">Hinode</Emphasis>/SOT NFI Observations

We investigate the properties of acoustic events (AEs), defined as spatially concentrated and short duration energy flux, in the quiet Sun, using observations of a 2D field of view (FOV) with high spatial and temporal resolution provided by the Solar Optical Telescope (SOT) onboard Hinode. Line profiles of Fe i 557.6 nm were recorded by the Narrow-band Filter Imager (NFI) on a 82″×82″ FOV during 75 min with a time step of 28.75 s and 0.08″ pixel size. Vertical velocities were computed at three atmospheric levels (80, 130, and 180 km) using the bisector technique, allowing the determination of energy flux to be made in the range 3 – 10 mHz using two complementary methods (Hilbert transform and Fourier power spectrum). Horizontal velocities were computed using local correlation tracking (LCT) of continuum intensities providing divergences. We found that the net energy flux is upward. In the range 3 – 10 mHz, a full FOV space and time averaged flux of 2700 W m⁻² (lower layer 80 – 130 km) and 2000 W m⁻² (upper layer 130 – 180 km) is concentrated in less than 1 % of the solar surface in the form of narrow (0.3″) AE. Their total duration (including rise and decay) is of the order of 10³ s. Inside each AE, the mean flux is 1.6×10⁵ W m⁻² (lower layer) and 1.2×10⁵ W m⁻² (upper). Each event carries an average energy (flux integrated over space and time) of 2.5×10¹⁹ J (lower layer) to 1.9×10¹⁹ J (upper). More than 10⁶ events could exist permanently on the Sun, with a birth and decay rate of 3500 s⁻¹. Most events occur in intergranular lanes, downward velocity regions, and areas of converging motions.