Alfvén waves in the solar atmosphere

We examine the propagation of Alfvén waves in the solar atmosphere. The principal theoretical virtues of this work are: (i) The full wave equation is solved without recourse to the small-wavelength eikonal approximation (ii) The background solar atmosphere is realistic, consisting of an HSRA/VAL representation of the photosphere and chromosphere, a 200 km thick transition region, a model for the upper transition region below a coronal hole (provided by R. Munro), and the Munro-Jackson model of a polar coronal hole. The principal results are:

1. If the wave source is taken to be near the top of the convection zone, where n _H = 5.2 × 10¹⁶ cm^?3, and if B _⊙ = 10.5 G, then the wave Poynting flux exhibits a series of strong resonant peaks at periods downwards from 1.6 hr. The resonant frequencies are in the ratios of the zeroes of J ₀, but depend on B _⊙, and on the density and scale height at the wave source. The longest period peaks may be the most important, because they are nearest to the supergranular periods and to the observed periods near 1 AU, and because they are the broadest in frequency.
2. The Poynting flux in the resonant peaks can be large enough, i.e. P _⊙ ≈ 10⁴–10⁵ erg cm^?2s^?1, to strongly affect the solar wind.
3. ¦δv¦ and ¦δB¦ also display resonant peaks.
4. In the chromosphere and low corona, ¦δv ≈ 7–25 kms^?1 and ¦δB¦ ≈0.3–1.0 G if P _⊙≈10⁴-10⁵ erg cm^?2s^?1.
5. The dependences of ¦δv¦ and ¦δB¦ on height are reduced by finite wavelength effects, except near the wave source where they are enhanced.
6. Near the base, ¦δB¦ ≈ 350–1200 G if P _⊙ ～- 10⁴–10⁵. This means that nonlinear effects may be important, and that some density and vertical velocity fluctuations may be associated with the Alfvén waves.
7. Below the low corona most wave energy is kinetic, except near the base where it becomes mostly magnetic at the resonances.
8. ?₀ < δv ² > v _A or < δB ² > v _A/4π are not good estimators of the energy flux.
9. The Alfvén wave pressure tensor will be important in the transition region only if the magnetic field diverges rapidly. But the Alfvén wave pressure can be important in the coronal hole.

     

Orbital eccentricity study for the spherical component of our galaxy

An analysis of the data concerning high-velocity stars from Eggen's catalogue aimed at a determination of the approximate slope of the mass function for the spherical component of our Galaxy, and at estimating the local circular velocity, as well as the local rotation velocity, as by-products, has been performed. Our conclusions are that:

1. A linear dependence of the mass on the radius is very likely;
2. the value of the limiting radius is most likely equal to (40±10) kpc;
3. the two local velocities are approximately equal to each other, being both equal to (230±30) km s^?1;
4. the local escape velocity appears to be most likely equal to (520±30) km s^?1;
5. the total mass of a corona, obtained in this way, is (5±1)×10¹¹ M _⊙.

     

Study of physical properties of spectroscopic binary stars

The main results of a study of a catalogue of physical parameters of 1041 spectroscopic binaries are presented. The distribution of spectroscopic binaries over all main parametersM ₁, a, e, M₁/M₂, P, and certain dependencies between some of them have been found.

1. It appears that among bright (m _v?3 ^m –5 ^m ) stars withM?1M _⊙, about 40% are apparently spectroscopic binaries with comparable masses of components.
2. The majority of spectroscopic binaries with the ratio of the large semiaxis of the orbit to the radius of the primarya/R ₁?20, have eccentricities close to zero. This is probably a consequence of the tidal circularization of orbits of close binaries by viscous friction.
3. The discovery of duplicity of double-line spectroscopic binaries is possible only if the semiamplitude of radial velocityK ₁ is almost 10 times higher than the semiamplitude of the radial velocity of a single-line spectroscopic binary of the same mass.
4. Double-line spectroscopic binaries witha/R _⊙?6(M ₁/M _⊙)^1/3,M ₁≈M ₂?1.5M _⊙ are almost almost absent, and the number of stars witha/R _⊙?6(M ₁/M _⊙)^1/3,M ₁≈1.5M _⊙ is relatively low.
5. The distribution of unevolved SB stars over the large semiaxis may be described by the expression d(N _d/N_t)≈0.2 d loga for 6(M ₁/M _⊙)^1/3?a/R _⊙?100.
6. The intial mass-function for primaries of spectroscopic binaries is the same Salpeter function dN _d≈M ₁ ^?2.35 dM ₁ for 1?M ₁/M _⊙?30.
7. It is possible to explain the observed ratio of the number of single-line spectroscopic binaries to the number of double-line binaries if one assumes that the average initial mass ratio is close to 1 and that the mass of the postmass-exchange remnant of the primary exceeds the theoretical one and/or that half of the angular momentum of the system is lost during mass-exchange.
8. The above-mentioned distributions ofM ₁ anda and assumptions on the mass of remnant and/or momentum loss also allow us to explain the observed shapes of dN/dM, dN/dq, and dN/da distributions after some selection effects are taken into account.

     

On the spin distributions of ΛCDM haloes

We used merger trees realizations, predicted by the extended Press-Schechter theory, in order to study the growth of angular momentum of dark matter haloes. Our results showed that:

1. The spin parameter λ′ resulting from the above method, is an increasing function of the present day mass of the halo. The mean value of λ′ varies from 0.0343 to 0.0484 for haloes with present day masses in the range of 10⁹h^?1 M _⊙ to 10¹⁴h^?1 M _⊙.
2. The distribution of λ′ is close to a log-normal, but, as it is already found in the results of N-body simulations, the match is not satisfactory at the tails of the distribution. A new analytical formula that approximates the results much more satisfactorily is presented.
3. The distribution of the values of λ′ depends only weakly on the redshift.
4. The spin parameter of an halo depends on the number of recent major mergers. Specifically the spin parameter is an increasing function of this number.

     

On the Hβ, [OIII] lines and continuum variability character in the nucleus of Seyfert galaxy NGC 1275

The radiation fluxes of the NGC 1275 galaxy central region are being observed on the 1.25-m telescope, using a scanning spectrophotometer with the entrance aperture 10″ in three Δλ=80 Å spectral regions: Hβ, 4959+5007 Å [OIII] and continuum. There were 35 nights of observations during 1982–1987. With the time resolution of half an hour 379 measurements were obtained in each spectral region. The analysis of these results shows:

1. The standard deviations of measurements in each spectral region 2–3 times exceed the errors of observations.
2. The radiation flux distribution resembles to normal one only for Hβ line.
3. Two-humps forms of continuum flux distribution curve is like that of radio emission in 8 mm and 2.6 cm wavelengths.
4. Various forms of fluxes distribution curves of Hβ and [OIII] lines permit us to suppose that the location of these lines emission regions near the sources of excitation are different.

     

A concentric ellipse multiple-arch system in the solar corona

A typical concentric ellipse multiple-arch system was observed in the solar corona during the February 4, 1962 eclipse in New Guinea. The following results have been obtained from analysis of a white-light photograph taken by N. Owaki (see Owaki and Saito, 1967a).

1. The arches are composed of four equidistant components, elliptical in shape, and almost concentric with a prominence at the common center of the ellipses.
2. The prominence and arch system appears to be the lower region of a helmet-shaped streamer.
3. The widths of the arches are observed to increase with height.
4. Analysis was made in the light of three models for the coronal structures that could lead to the observed arches: (a) rod-like concentrations of electrons; (b) tunnel-shaped elliptical shells of electrons; and (c) dome-like ellipsoidal shells of electrons. Electron densities are derived for the models, and the dome-like model is excluded as a possibility for arch systems exhibiting a coronal cavity.
5. The scale height in the arch-streamer region is found to be almost the same as that of the K-corona, suggesting equal temperatures, density distributions, etc. in each region.
6. There is a dark space (a coronal cavity) between the innermost arch and the prominence. The brightness of this cavity is 1/5 that of the adjacent arch. It is 3% brighter than the background corona of the arch-streamer system.
7. A comparison is made between the deficiency of electrons in the coronal cavity and the excess of electrons in the prominence. It is found that the ratio of the excess to the deficiency lies between 0.9 and 40.
8. A comparison between the electron efflux from the ‘leaky magnetic bottle’ possibly formed by rod-shaped coronal arches and the electron influx into those arches from the chromosphere leads us to the conclusion that the rod model is probably valid and that spicules appear to be an adequate supply for the electrons observed in the arches. The tunnel model may be valid, but in that case spicules are probably not the sources of the electrons observed in coronal arches.

     

Spectral analysis of four quiescent prominences observed at the Peruvian eclipse

Two-dimensional distributions of kinetic temperature, density and turbulent velocity are obtained for four quiescent prominences observed at the Peruvian eclipse of 12 November, 1966.

1. The kinetic temperature derived from line widths is around 6000–7000 K in the central part of prominences and rises to 12000K in both edges and possibly in the top of prominences.
2. The turbulent velocity shows a similar tendency, being 7–9 km/sec in the central part and ≈ 20 km/sec in the outer part. The turbulent velocity also increases slowly towards higher heights in the prominence.
3. The electron density derived both from the Stark effect and the intensity ratio of the continuous spectra turns out to be about 10^10.2–10^10.6 cm^?3 in the central portion of two prominences.
4. From the width and the intensity, neutral helium lines are shown to originate in the same region as hydrogen and metallic lines where the kinetic temperature goes down to 6000 K. This indicates that neutral helium is emitted after the ionization due to UV radiation from the corona and the transition region.

     

Radial pulsation of less-massive yellow supergiants

Linear and nonlinear pulsation computations for the modelsM=0.8M _⊙,L=10000 and 20000L _⊙ were carried out in order to understand FG Sge's pulsation. The results may be summarized as follows:

1. In the modelsL=10000L _⊙, the fundamental blue edge is nearT _e =5700 K. The models show that instability of the third overtone extends to 7400 K and still has large positive growth rates. A nonlinear model of 7000 K shows a small amplitude ΔV=10 km s^?1, ΔM _bol=0.03 with a period of around 18 days, nearly equal to that of the third overtone.
2. In the linear models ofL=20000L _⊙, the fundamental blue edge is shifted to 7000 K but the damping of this mode is so small that it is marginally stable to 7700 K. The third overtone has large positive growth rates of this region. The nonlinear model at 7700 K, however, shows no indication of third overtone pulsation.

We also examine the possibility, suggested by Whitney (1978), that the mass of FG Sge is 0.4M _⊙.     

A statistical study of the spiral spots on the solar disc

After adding the data observed in the years from 1979 to 1982 to those obtained earlier (Ding et al., 1981), we re-examine the previous results and conclude:

1. The longitudinal distribution of spiral spots on the solar disc is generally the same as that of sunspot groups with areas of S _p ≥ 400, but their active longitudes seem to be more concentrated.
2. The distribution of spiral patterns in the southern and northern hemispheres shows that the differential rotation may be a fundamental solar dynamo for the formation of the spiral spots.
3. The statistical directions of the emerging twisted magnetic vectors in the active regions in the southern and northern hemispheres are synchronously inverse with a period of about two years. This period seems to be detected in other solar observations.

     

Structure and evolution of single WR stars

New computations of massive stars follow the evolution up to advanced stages and include:

-A large and flexible nuclear network consisting of 174 nuclear species that are linked by 1742 nuclear reactions.

-Semiconvection, overshooting and mass loss.

-Modern rates for both strong and weak interaction processes as well as the latest rates for the neutrino processes.

-Improved grid distribution and a large number of grid points.

The nuclear network and the diffusion equation are solved for each time step during the whole evolution. In this way the accuracy of nuclear yields and chemical abundances are mainly limited by uncertainties in the diffusion coefficient found from the convection theories. Several instability mechanisms may affect the mass loss rates of massive stars and thereby the structure and abundances of WR stars. Due to heavy mass loss at the LBV and WR stages, the masses at the pre-SN stage may be less than 5M _⊙. Yields and abundances throughout the stars are discussed together with the amount of all elements expelled.     

Delta spots and great flares

Using eighteen years of observations at Big Bear, we summarize the development of δ spots and the great flares they produce. We find δ groups to develop in three ways: eruption of a single complex active region formed below the surface, eruption of large satellite spots near (particularly in front of) a large older spot, or collision of spots of opposite polarity from different dipoles. Our sample of twenty-one δ spots shows that once they lock together, they never separate, although rarely an umbra is ejected. The δ spots are already disposed to their final form when they emerge. The driving force for the shear is spot motion, either flux emergence or the forward motion of p spots in an inverted magnetic configuration. We observe the following phenomena preceding great flares:

1. δ spots, preferentially Types 1 and 2.
2. Umbrae obscured by Hα emission.
3. Bright Hα emission marking flux emergence and reconnection.
4. Greatly sheared magnetic configurations, marked by penumbral and Hα fibrils parallel to the inversion line.

We assert that with adequate spatial resolution one may predict the occurrence of great flares with these indicators.     

Coronal Diagnostics from Narrowband Images Around 30.4 nm

Images taken in the band centered at 30.4 nm are routinely used to map the radiance of the He?ii Ly?α line on the solar disk. That line is one of the strongest, if not the strongest, line in the EUV observed in the solar spectrum, and one of the few lines in that wavelength range providing information on the upper chromosphere or lower transition region. However, when observing the off-limb corona, the contribution from the nearby Si?xi 30.3 nm line can become significant. In this work we aim at estimating the relative contribution of those two lines in the solar corona around the minimum of solar activity. We combine measurements from CDS taken in August 2008 with temperature and density profiles from semiempirical models of the corona to compute the radiances of the two lines, and of other representative coronal lines (e.g. Mg?x 62.5 nm, Si?xii 52.1 nm). Considering both diagnosed quantities from line ratios (temperatures and densities) and line radiances in absolute units, we obtain a good overall match between observations and models. We find that the Si?xi line dominates the He?ii line from just above the limb up to ≈?2?R _⊙ in streamers, while its contribution to narrowband imaging in the 30.4 nm band is expected to become smaller, even negligible in the corona beyond ≈?2?–?3?R _⊙, the precise value being strongly dependent on the coronal temperature profile.     

Keynote address: Outstanding problems in solar physics

Celebrating the diamond jubilee of the Physics Research Laboratory (PRL) in Ahmedabad, India, we look back over the last six decades in solar physics and contemplate on the ten outstanding problems (or research foci) in solar physics:

1. The solar neutrino problem
2. Structure of the solar interior (helioseismology)
3. The solar magnetic field (dynamo, solar cycle, corona)
4. Hydrodynamics of coronal loops
5. MHD oscillations and waves (coronal seismology)
6. The coronal heating problem
7. Self-organized criticality (from nanoflares to giant flares)
8. Magnetic reconnection processes
9. Particle acceleration processes
10. Coronal mass ejections and coronal dimming

The first two problems have been largely solved recently, while the other eight selected problems are still pending a final solution, and thus remain persistent Challenges for Solar Cycle 24, the theme of this jubilee conference.     

Inhibition of conductive heat flow by magnetic constriction in the corona and transition region: Dependence on the shape of the constriction

The magnetic field that fills the corona is rooted in a small fraction of the solar surface. The consequent constriction of the field lines inhibits the conduction of heat down from the corona, thereby strongly affecting the energy balance in the corona and transition region. In this paper, we clarify how the shape of the constriction acts together with the amount of constriction to inhibit the heat flow. We analyze the heat flow in model tapered flux tubes in which the plasma properties are constant on cross sections, the plasma is static, and the only energy transfer is by thermal conduction. We find:

1. From the general solution to the model, only two particular solutions are readily applied to the solar atmosphere. One is the steady-state case, appropriate for quiet regions and active regions which are not flaring; the other is the time-dependent case in which no heat enters the hot end, appropriate for conductive cooling of flare loops.
2. In the steady-state case, the inhibition factor Φ/Φ _P (the ratio of the heat flow through a constricted flux tube to the heat flow through the otherwise equivalent unconstricted tube) is simply the ratio of the harmonic mean area of the constricted tube to the area of the unconstricted tube. The inhibition of heat flow thus results from the amount and shape of the constriction.
3. For any given shape and amount of monotonic tube taper, the inhibition factor in the steady-state case is a good estimate of that in the time-dependent case (within a factor of 2).
4. The amount of constriction Γ (the ratio of the flux tube's hot end area to its cold end area) limits the range of possible values of the inhibition factor; the value of the inhibition factor within this range is set by the shape of the constriction. For the steady-state case, Γ ^?1 ≤ Φ/Φ _P ≤ 1. Therefore, the shape of the constriction is as important as the amount of constriction in determining the amount of inhibition.
5. For the linear taper of a cone-shaped tube, the inhibition factor is an especially simple function of the amount of constriction: Φ/Φ _P = Γ ^?1/2. This inhibition-constriction relation for the cone correctly estimates the inhibition to order of magnitude for any tube in which the constriction occurs gradually all along the tube. If the constriction is more concentrated to the hot (cold) end of the tube than in a cone, then the inhibition is greater (less) than in a cone.
6. Because most flux tubes that pass from the corona down through the transition region should not differ greatly from a cone in shape of constriction, the simple inhibition-constriction relation for the cone should correctly estimate the magnitude of the inhibition in quiet regions, active regions, and flare loops. The only observational input needed for this estimate is the amount of magnetic constriction through the transition region.

     

Analysis of EUV limb-brightening observations from ATM

Limb-brightening curves for EUV resonance lines of O vi and Mg x have been constructed from spectroheliograms (5″ resolution) of quiet limb regions observed with the Harvard experiment on Skylab. The observations are interpreted with a simple model for the transition layer and the corona. A comparison of theoretical and observed limb-brightening curves indicates that the lower boundary of the corona, where T _e= 10⁶K, is at a height of about 8000 km in typical quiet areas. For 1.01 R _⊙?r1.25 R _⊙, the corona can be represented by a homogeneous model in hydrostatic equilibrium with a temperature of 10₆K for 1.01 R _⊙?r<1.1 R _⊙ and 1.1 × 10₆K for r?1.1 R _⊙. The model for the transition layer is inhomogeneous, with the temperature gradient a factor of 3 shallower in the network than in the intranetwork regions. It appears that spicules should be included in the model in order to account for the penetration into the corona of cool (T _e<10⁶K) EUV-emitting material to heights up to 20000 km above the limb.     

Transmission of light by slit designed for astronomical spectrograph

The paper discusses an investigation of linear polarization produced by the transmission of light through an astronomical spectrograph slit. An experimental apparatus was designed and set up to carry out this work. The parallel beam of plane polarized light was rotated in the measuring system, by optically active of half-wave plate. The intensity of normally incident of polarized light of wavelength 0.436 μm transmitted by various slit was measured as a function of slit width. The results indicate:

1. That the degree of polarization increased as thedepth of the narrow slit was increased.
2. That the degree of polarization increased as thewidth of the narrow slit was decreased.
3. That when the width of slit was widened the degree of polarization tended to approach a constant value asymptotically.
4. That the theoretical calculation of Slater (1942) predicts the measured experimental values more accurately than Thiessen (1947) and Jones and Richards (1954).

It is shown that the existence and order of magnitude of all these effects may be predicted from the propagation losses of the electromagnetic theory of light in metallic wave guide. The paper brings out the salient points related to the degree of polarization of light by a dielectric slit of finite depth. The polarization effects from one such slit have been investigated and the results were compared with those for metallic slits.     

Radio spectrum of two active regions

The results of the total solar eclipse of November 12, 1966, observed at 8 different wave-lengths between 3 and 21 cm, are studied and the spectrum of two active regions present on the disk is deduced. It is shown that the observed increase of the flux of the most intense source in the range 3–10 cm is due to geometrical effects. Neglecting the influence of the magnetic field, the following quantities are deduced.

1. the mean and central temperature of the coronal condensation.
2. the ∫ _corona N ²dh (N = electron density).

Both these quantities are in good agreement with optical observations.     

Electron-Temperature Maps of the Low Solar Corona: ISCORE Results from the Total Solar Eclipse of 29 March 2006 in Libya

We conducted an experiment in conjunction with the total solar eclipse of 29 March 2006 in Libya that measured the coronal intensity through two filters centered at 3850 Å and 4100 Å with bandwidths of ≈?40 Å. The purpose of these measurements was to obtain the intensity ratio through these two filters to determine the electron temperature. The instrument, Imaging Spectrograph of Coronal Electrons (ISCORE), consisted of an eight inch, f/10 Schmidt Cassegrain telescope with a thermoelectrically-cooled CCD camera at the focal plane. Results show electron temperatures of 10⁵ K close to the limb to 3×10⁶ K at 1.3R _⊙. We describe this novel technique, and we compare our results to other relevant measurements. This technique could be easily implemented on a space-based platform using a coronagraph to produce global maps of the electron temperature of the solar corona.     

On the nature of some active regions in the microwave range

The radio emission of a selected number of solar active regions has been investigated with high angular resolution at two frequencies: 10 and 17 GHz. By comparing the results of the two observations the following conclusions can be drawn:

1. The brightness temperature distribution of an active region is often composed of very bright cores of small dimension (angular extent θ?20″) imbedded in extended halos of lower brightness.
2. The radio emission of such structures as well as the degree of polarization can be explained with a thermal process. The halos can originate by pure thermal bremsstrahlung while in the case of the very bright cores found at 10 GHz (brightness temperature T _b?1–9 × 10⁶K) the emission at the harmonics of the gyrofrequency is needed.

     

Models of the open solar atmosphere

McWhirter et al. (1975) have presented a standard model for the transition region and inner corona that matches with the Harvard Smithsonian Reference Atmosphere. They assume an open field line configuration and solve numerically the equations of energy and hydrostatic equilibrum. The purpose of the present paper is to generalise their model for the temperature and density as functions of height in several ways and, in particular, to determine the temperature maxium and its location. The effect of varying the following characteristics of the model is determined:

1. Boundary conditions on temperature and density;
2. magnitude of the heating;
3. form of the heating term;
4. divergence of the field lines;
5. presence of subsonic flows, either upward or downward.

If the heating is localised at great altitudes, it tends to produce a narrower and larger temperature maximum at a greater altitude than a uniform heating and even more so than a heating proportional to density. For fixed base conditions, an increase in heating or field line divergence or downflow decreases the coronal temperature and reduces the height of the temperature maximum, while a steady upflow has the opposite effects. A maximum possible upflow was found, beyond which a catastrophe occurs so that no steady hot solution exists.