Solar flares,microflares, nanoflares,and coronal heating

Solar flare occurrence follows a power-law distribution against total flare energy W: dN/dW W ^– with an index 1.8 as determined by several studies. This implies (a) that microflares must have a different, steeper distribution if they are energetically significant, and (b) there must be a high-energy cutoff of the observed distribution. We identify the distinct soft distribution needed for coronal heating, if such a distribution exists, with Parker's nanoflares.This paper considers a microflare to be a member of the normal X-ray burst population, with comparable physical parameters except for a smaller total energy.     

The equivalent width of the Hβ emission line and the evolution of the Hii regions

The synthetic equivalent width (W _H) of the line H in emission is obtained for Hii regions opaque to the Lyman photon flux, with embedded OB associations with different initial chemical compositions and initial mass functions. The variation ofW _H as a function of the evolution of the ionizing stars is analysed. The observations ofW _H for M33, M101, and M51 by Searle (1971) are discussed.     

On the problem of detection of the circumstellar clouds from 2800 MgII observations

A new method for the detection of the circumstellar clouds around the hot stars of O-B classes is developed. The method is based on the fact, connected with the large dispersion in the observed equivalent widths,W _*(2800 MgII) of non-stellar origin, for a selected group of stars withE(B-V)=0. The separation of observed magnitudes ofW(2800) in two components interstellarW _i, and circumstellarW _c is realised. It is shown that the circumstellar clouds really existed around 90% of hot stars analysed in the present paper (total number of stars 46, Table II). In 30% cases of hot stars circumstellar clouds are very powerful (the radii are less than 1pc, the masses less than 1 solar mass). The usual model for interstellar medium seems to be unacceptable for the system hot star+circumstellar cloud.     

Properties of the solar chromosphere Hα spicules as observed spectrally

Time succession of 25 H spicules has been studied. The spectra are obtained at a height of 6 arc sec during 21 min (38 pictures) with the 53 cm Lyot coronagraph. Total intensities W, widths and radial velocities V _r are determined (about 650 H line profiles). For 14 spicules the sign of V _r varies, for the rest the sign variation is absent or it is doubtful. Characterized period of V _r variation is 3–7 min with a mean amplitude of ± 4km s^–1. W and also vary with a similar period and mean amplitudes equal to 50% and 30% respectively. dependence of W (Figure 1) points to the existence of two spicules groups: group I (70%) characterized by relatively small W and (mean values are 0.08 Å and 1.3 Å respectively); group II comprising brighter (W 0.13 Å) spicules with wider profiles ( 1.6 Å). Group II may consist of the unresolved, superimposed group I spicules. We believe, that H spicules involve formations consisting of separate elements having the temperature of 6000 K and non-thermal velocities of 25 km s^–1.     

Interstellar extinction and diffuse absorption features

The equivalent width of the 2175 Å band,W ₂₁₇₅, well known as the big bump in the interstellar extinction curves, has been found to be closely correlated with the colour excessE _B-V as well as with the extinction differencesE _8–6 andE _9–7 defined to characterize quantitatively the steep slopes of the extinction curves in the far ultraviolet.The equivalent widths of the 5780 and 5797 Å diffuse lines show good correlation withE _B-V. The correlations ofW ₅₇₈₀ andW ₅₇₉₇ withE _8–6 resp.E _9–7 are, however, rather weak. Correlations betweenW ₂₁₇₅ andW ₅₇₈₀ and betweenW ₂₁₇₅ andW ₅₇₉₇ are indicated.The results have been qualitatively interpreted in favour of the dust model consisting of a mixture of small silicate grains and larger silicate grains coated by molecular mantles.Paper presented at the Symposium on Solid State Astrophysics, held at the University College, Cardiff, Wales, between 9–12 July 1974.     

Brightness of the Coronal Green Line and Prediction for Activity Cycles 23 and 24

Cyclic variations of the mean semi-annual intensities I of the coronal green line 530.3 nm are compared with the mean semi-annual variations of the Wolf numbers W during the period of 1943–1999 (activity cycles 18–23). The values of I in the equatorial zone proved to correlate much better with the Wolf numbers in a following cycle than in a given one (the correlation coefficient r is 0.86 and 0.755, respectively). Such increase of the correlation coefficient with a shift by one cycle differs in different phases of the cycle, being the largest at the ascending branch. The regularities revealed make it possible to predict the behaviour of W in the following cycle on the basis of intensities of the coronal green line in the preceding cycle. We predict the maximum semi-annual W in cycle 23 to be 110–122 and the epoch of minimum between cycles 23 and 24 to take place at 2006–2007. A slow increase of I in the current cycle 23 permits us to forecast a low-Wolf-number cycle 24 with the maximum W50 at 2010–2011. A scheme is proposed on the permanent transformation of the coronal magnetic fields of different scales explaining the found phenomenon.     

Determination of mass-loss rates from the first order momentW 1 of unsaturated P Cygni line profiles

The escape probability method introduced by Sobolev to treat the transfer of line photons is used in order to derive the expressions of thenth order momentW _n (E()/E _c –1)(–₁₂) ⁿ ·d of a P Cygni profile formed in rapidly expanding envelopes around a central point-like source under various physical and geometrical conditions.With the only assumption that there is mass-conservation of the species in the flow, we state for the case of optically thin lines that the relation between the first order momentW ₁ and the quantityM _n (level), first established by Castoret al. (1981) under more restrictive conditions, is in fact independent of the type of velocity fieldv(r) and a fortiori of the distribution adopted for the radial opacity ₁₂ ^r (X). These results also remain unchanged when including collisions (0) and/or an additional rotational velocity fieldv (r) in the expanding atmosphere. We investigate the presence of an underlying photospheric absorption line and conclude that for realistic cases, neglecting this boundary condition to the radiative transfer leads to an underestimate of the mass-loss rate by a factor of about 20%. By means of a three-level atom model, we demonstrate that all results derived for a single line transition equally apply for an unresolved doublet profile providedW ₁ andM _n (level) are calculated with the weighted wavelength _D and total oscillator strengthf _D of the doublet.Considering the occultation and inclination effects caused by the finite size of the central core, we refine the value of the multiplicative constant fixing the ratio ofW ₁ toM _n (level). We show that this relation allows a determination of the mass-loss rate with an uncertainly less than 30%, irrespective of the sizeL _max of the atmosphere and of the limb-darkening affecting the stellar core. Reviewing all possible sources of error, we finally conclude that this method of deriving a mass-loss rate from the analysis of an unsaturated P Cygni profile is very powerful. The total uncertainty affecting the determination ofM _n (level) from the measurement ofW ₁ should be smaller than 60%.     

A generalized method for deriving mass-loss rates: The first order moment of unsaturated P Cygni line profiles

For the case of optically thin lines, we show that the relation existing between the first order momentW ₁ (E()/E _c –1)(–₁₂)d of a P Cygni profile and the quantityMn(level), whereM is the mass-loss rate of the central star andn(level) the fractional abundance of the ion under study, is in fact independent of any Sobolev-type approximations used for the transfer of line radiation, contrary to what has been assumed in some previous works (Castoret al., 1981; Surdej, 1982). Consequently, all results established in the context of very rapidly expanding atmospheres and mainly referring to the non-dependence ofW ₁ vs various physical (underlying photospheric absorption line, limb darkening, etc.) and geometrical (velocity fieldv(r), etc.) effects remain unchanged for arbitrary (e.g non-Sobolev type) outward-accelerating velocity laws.Whenever applied with caution, Equation (50) thus provides a very powerful means of deriving mass-loss rates—with a total uncertainty less than 60 percent—from the measurementW ₁ of unsaturated P Cygni profiles observed in the spectrum of early—as well as late—type stars, quasars, etc.     

The solar abundance of tungsten

Recent measurements of Wi oscillator strengths (Obbarius and Kock, 1982) lead to a solar photospheric abundance of tungsten, log _W = 1.06 ± 0.15 on the scale log _H = 12. The solar W/Si abundance ratio, 0.32 W atoms/10⁶ Si, coincides with that found in carbonaceous chrondrites. Implications for solar-system r-processes abundances are pointed out.     

Hydromagnetic stability of some non-dissipative flows subject to non-axisymmetric disturbances

We study the linear stability of nondissipative flow of an electrically conducting fluid subject to non-axisymmetric disturbances in the following cases: (i) the radial flow of an incompressible fluid between two concentric porous circular cylinders in the presence of a radial magnetic field and (ii) axial flow of a compressible fluid between two concentric circular cylinders permeated by a helical magnetic field (0,B ₀(r),B _0z) in a cylindrical coordinate system. It is shown that in case (i), the flow is stable if the Alfvén velocity based on the undisturbed radial magnetic field exceeds the radial velocity due to suction or injection at the cylinder surfaces. In case (ii), it is found that under certain conditions the complex wave speed for an unstable mode lies within a circle of diameterW _max-W _min, whereW _max andW _min are the maximum and minimum values of the axial velocity in the flow region. In the presence of a purely axial magnetic field, however, the complex wave speed for an unstable mode always lies within the above circle.     

Singposts of shock waves in the metagalactic medium

Explosions of quasars and young galaxies at large redshifts must cause propagation of blast waves in the metagalactic medium. The shock waves formed can, during the radiative cooling stage, produce dense cold spherical shells around the epicentres of explosions. But, even before that, at the stage of adiabatic expansion, each spherical shock-wave front, if it lies on one line-of-sight with a more distant quasar, can imprint into the quasar spectrum a specific absorption doublet with a distance between the components (in the rest frame) ₀ 3 Å. The L doublet components have a small but the same equivalent widthW ₀ 0.3 Å, the ratioW ₀/₀ weakly depending onW ₀ ifW ₀ is small. We demonstrate here that such absorption L doublets are really present among the L forest in the absorption spectra of distant quasars which are, according to Sargentet al. (1980), of mostly intervening (and not intrinsic) origin. Further accumulation of data on absorption doublets, which can serve as direct indicators of metagalactic shock-waves, may provide valuable information about the physical conditions in the metagalactic gas at large redshifts.     

Width of emission cores of the line K Ca ii in sunspots

Emission core widths of K Ca ii line in the umbra and penumbra of 9 sunspots and in their vicinity are measured. All sunspots are located near the solar disc center. Data on variation of widths W _K along the mean sunspot radius are obtained. Values W _K in the umbra and penumbra centers are equal or somewhat less than on stars of the same luminosity.     

The abundance of chlorine in the Sun

The Cli line 8375.943 (4s ⁴P_5/2 – 4p ⁴D7/2) is identified in the solar spectrum. This is the first identification of a chlorine line in solar spectrum. The measured equivalent width (W = 0.8 mÅ) corresponds to an abundance log N(Cl) = 5.65 on the scale log N(H) = 12.00.     

The latitude of filament bands at the sunspot minimum and the activity level in the two following 11-year solar cycles

The zonal structure of the distribution of filaments is considered. The mean latitudes of two filament bands are calculated in each solar hemisphere at the minima of the sunspot cycle in the period 1924–1986: middle latitude _{2, m} and low latitude _{1, m} . It is shown that the mean latitude of the filament band _{2, m} at the minimum -m of the cycle correlates, with = 0.94, with the maximum - M sunspot area S(M) and maximum Wolf number W(M) in the succeeding solar cycle M. It is shown that the mean latitude of the low-latitude filament band _{1, m} is linearly dependent on the mean latitude filament band _{2, m + 1} at the succeeding minimum. We found a correlation of the latitude of the low-latitude filament band _{1, m} with the maximum sunspot area in the M + 1 cycle. This enables us to predict the power of two succeeding 11-year solar cycles on the basis of the latitude of filament bands at the minimum of activity, 1985–1986: W(22) - 205 ± 10, W(23) - 210 ± 10. The importance of the relationships found for theory and applied aspects is emphasized. An attempt is made to interpret the relationships physically.     

An exact differential form to check analytical theories

As a result of a Von Zeipel's elimination of periodic arguments, the linear differential form W _i dv _i , where theW _i 's are the constant actions and thev _i 's the mean motions of the averaged angles, is exact, because, as we prove here, it is the differential of the principal function averaged over the new angles. We propose to use this exact form to check the analytical expressions developed from an elimination of periodic arguments, and we take as an example the main problem of artificial satellites.     

Circumstellar clouds derived from the 2800 Mgii data

As a result of the analysis of the observed interstellar 2800 Mgii absorption line data, an empirical relationship — a positive correlation — between the equivalent widthW(2800) and the effective temperature of the starT was discovered (Figure 1). However, in the case when this doublet is of stellar (photospheric) origin, only a negative correlation betweenW(2800) andT exists. Hence, the existence itself of such a positive correlation betweenW(2800) andT may be viewed as incomprehensible for the present influence of the star on the strength of the absorption line 2800 Mgii of nonstellar origin.On the other hand, we have evidence that the ionizing radiation of hot stars cannot provide for the observed very high degree of ionization of the interstellar magnesium. In particular, the observations give for interstellar magnesium the ratioN ⁺/N ₁ 1000, while in the case of ionization under the action of stellar radiation only we haveN ⁺/N ₁ 10.The assumption that circumstellar clouds surround hot stars can naturally explain these and other similar facts. A method for the determination of the general parameters-size, concentration, mass etc. — of the circumstellar clouds is developed. The main results of the application of this method to the relation of more than 20 hot stars are:(1) The circumstellar clouds surround almost (70%) all hot giants and subgiants. In the remaining (30%) cases, the absence of circumstellar envelopes requires additional evidence. (2) The linear sizes of circumstellar clouds vary within wide ranges — from 0.002 pc up to 1 pc. Most frequent are clouds with size of 0.1 pc. (3) The main concentration of hydrogen atoms (electrons) in circumstellar clouds is of the order of 100 cm^–3; the minimum value is 20–30 cm^–3, the maximum 10⁴ cm^–3. In one case (Deneb) the electron concentration rises up to 10⁵ cm^–3 for the size of the cloud 0.001 pc=3×10¹⁵ cm. (4) Stars of the same spectral and luminosity classes may possess circumstellar clouds characterized by quite different parameters. (5) Hydrogen in circumstellar clouds is completely ionized; for these clouds the optical depth _c 1; on the average,T _c 0.005. (6) The integrated brightness of circumstellar clouds is substantially fainter (by 8–10^m) than that of the central star. This is the reason why these clouds cannot be detected by ground-based observations. (7) The masses of individual circumstellar clouds vary from 1 down to 10^–4 . This gives for the mass ejection rate from 10^–10 to 10^–6 per year in case if these clouds are formed by the braking and accumulation of the ejected mass.The method of 2800 Mgii seems very convenient, fruitful and promising for the detection and study of circumstellar envelopes. Also, this method is very sensitive for a determination of the general parameters of such clouds, and concerns practically all their geometric, physical, kinematic and other properties.     

Uniform displacement mode for spherical systems

We study a time-independent displacement mode which is an exact solution of Vlasov-Poisson equation for spherical stellar systems and we show that it corresponds to an aspherical mode. Using Bartholomew formalism, we write it explicitly to the second order and we give its generating functionG _m. For this marginal mode we show that the second variation of energy W vanishes.     

Rate of change of vorticity covariance of MHD turbulence in a rotating system

In this paper we are concerned with incompressible MHD turbulence in a rotating system and have derived an equation for the rate of change of vorticity covariance of MHD turbulent flow. The result derived shows that the defining scalars (r,t), (r,t), and (r,t) for the rate of change of vorticity covariance solely depend on the defining scalars of the tensorsW _ij, P_ik,j, F_kj,i, T_ik,j, andR _kj,ialready defined in the text.     

Alfvén turbulence and the time dependence of non-thermal line broadening in flares

Alfvén wave turbulence is considered as the source of the non-thermal line broadenings observed in soft X-rays in solar flares. The waves are assumed to lose energy to particle acceleration and the temporal development for the case of Fermi acceleration,W(k)k ^–2, is investigated. The decay of the wave energy density is compared to that of the non-thermal velocity for the event of 1980 June 29. The wave energy densities required to explain the degree of non-thermal broadening and its temporal characteristics are consistent with those typically inferred from-ray observations. A relationship between the degree of non-thermal broadening and-ray fluxes is predicted. In general, the larger the-ray flux the shorter the time scales for the decay of the wave energy.