On the directional dependence of the emission of acoustic noise by convective turbulence in a gravitational atmosphere

The directional dependence of the emission of sound waves in the solar atmosphere is studied. It is shown that quadrupole acoustic radiation generated in convective turbulence is strongly enhanced in the direction of the mean convective flow. The intensity in a direction with the convective velocity is proportional to (1 – M _c cos)^–17/2, where M _c is the Mach number of the convective motion. The influence of the atmospheric cut off frequency on the transmitted acoustic spectrum is taken into account. It is suggested that low frequency atmospheric oscillations may modulate the flux of high frequency sound waves.     

The Evolution of the Sun's Open Magnetic Flux – I. A Single Bipole

In this paper the origin and evolution of the Sun's open magnetic flux are considered for single magnetic bipoles as they are transported across the Sun. The effects of magnetic flux transport on the radial field at the surface of the Sun are modeled numerically by developing earlier work by Wang, Sheeley, and Lean (2000). The paper considers how the initial tilt of the bipole axis () and its latitude of emergence affect the variation and magnitude of the surface and open magnetic flux. The amount of open magnetic flux is estimated by constructing potential coronal fields. It is found that the open flux may evolve independently from the surface field for certain ranges of the tilt angle. For a given tilt angle, the lower the latitude of emergence, the higher the magnitude of the surface and open flux at the end of the simulation. In addition, three types of behavior are found for the open flux depending on the initial tilt angle of the bipole axis. When the tilt is such that ge2° the open flux is independent of the surface flux and initially increases before decaying away. In contrast, for tilt angles in the range –16°<<2° the open flux follows the surface flux and continually decays. Finally, for le–16° the open flux first decays and then increases in magnitude towards a second maximum before decaying away. This behavior of the open flux can be explained in terms of two competing effects produced by differential rotation. Firstly, differential rotation may increase or decrease the open flux by rotating the centers of each polarity of the bipole at different rates when the axis has tilt. Secondly, it decreases the open flux by increasing the length of the polarity inversion line where flux cancellation occurs. The results suggest that, in order to reproduce a realistic model of the Sun's open magnetic flux over a solar cycle, it is important to have accurate input data on the latitude of emergence of bipoles along with the variation of their tilt angles as the cycle progresses.     

EVOLUTION OF A DELTA GROUP IN THE PHOTOSPHERE AND CORONA

We present a study of the evolution of NOAA AR 7205 in the photosphere and corona, including an analysis of sunspot motions, and show the evolutionary aspects of flare activity using full-disc white-light observations from Debrecen, vector magnetograms from Mees Observatory, Hawaii, and Yohkoh soft X-ray observations. NOAA AR 7205 was born on the disc on 18 June, 1992. During the first 3 days it consisted of intermittent minor spots. A vigorous evolution started on 21 June when, through the emergence and merging (v 100–150 m s^-1) of several bipoles, a major bipolar sunspot group was formed. Transverse magnetic fields and currents indicated the presence of shear (clockwise twist) already on 21 June (with 0.015 Mm^-1). On 23 June, new flux emerged in the trailing part of the region with the new negative polarity spot situated very close to the big positive polarity trailing spot of the main bipole. The secondary bipole seemed to emerge with high non-potentality (currents). From that time the AR became the site of recurrent flare activity. We find that all 14 flares observed with the Yohkoh satellite occurred between the highly sheared new bipole and the double-headed principal bipole. Currents observed in the active region became stronger and more extended with time. We propose that the currents have been (i) induced by sunspot motions and (ii) increased by non-potential flux emergence leading to the occurrence of energetic flares (X1.8 and X3.9). This observation underlines the importance of flare analysis in the context of active region evolution.     

Implications of a strongly peaked polar magnetic field

Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed _m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin ^p cos ^q which peaks near the equator (q p) will correspond to a cos ⁿ magnetic field at high latitudes only if p = 1 and _m = n /R. Recent measurements of n 8 and 600 km² s^–1 would then give _m 7 m s^–1.     

Meridional flow of small photospheric magnetic features

We study the meridional flow of small magnetic features, using high-resolution magnetograms taken from 1978 to 1990 with the NSO Vacuum Telescope on Kitt Peak. Latitudinal motions are determined by a two-dimensional crosscorrelation analysis of 514 pairs of consecutive daily observations from which active regions are excluded. We find a meridional flow of the order of 10 m s^–1, which is poleward in each hemisphere, increases in amplitude from 0 at the equator, reaches a maximum at mid-latitude, and slowly decreases poleward. The average observed meridional flow is fit adequately by an expansion of the formM () = 12.9(±0.6) sin(2) + 1.4(±0.6) sin(4), in m s^–1 where is the latitude and which reaches a maximum of 13.2 m s^–1 at 39°. We also find a solar-cycle dependence of the meridional flow. The flow remains poleward during the cycle, but the amplitude changes from smaller-than-average during cycle maximum to larger-than-average during cycle minimum for latitudes between about 15° and 45°. The difference in amplitude between the flows at cycle minimum and maximum depends on latitude and is about 25% of the grand average value. The change of the flow amplitude from cycle maximum to minimum occurs rapidly, in about one year, for the 15–45° latitude range. At the highest latitude range analyzed, centered at 52.5°, the flow is more poleward-than-average during minimumand maximum, and less at other times. These data show no equatorward migration of the meridional flow pattern during the solar cycle and no significant hemispheric asymmetry. Our results agree with the meridional flow and its temporal variation derived from Doppler data. They also agree on average with the meridional flow derived from the poleward migration of the weak large-scale magnetic field patterns but differ in the solar-cycle dependence. Our results, however, disagree with the meridional flow derived from sunspots or plages.Operated by the Association of Universities for Research in Astronomy, Inc. under cooperative agreement with the National Science Foundation.     

The effect of luminosity-redshift correlation on the analysis of the angular size-redshift relation for radio galaxies

The variation of radio luminosity with redshift and its effect on the analysis of the angular size-redshift ( –z) relation for a bright radio source sample (s ₁₇₈ 10Jy) has been investigated. By assuming a power law dependence of luminosity on redshift of the formP (1 +z), it was found that 4.4 (with correlation coefficientr 0.99) for at leastz 0.3. Correction for such a strongP – (1 +z) correlation when considering the –z data for the sample led to a steeper –z slope. This could be explained by assuming linear size evolution of the formD (1 +z)^–n withn = 2.8 – 3.3 consistent with both theoretical results and those obtained for more homogeneous source samples.     

On the influence of gradients in the angular velocity on the solar meridional motions

If fluctuations in the density are neglected, the large-scale, axisymmetric azimuthal momentum equation for the solar convection zone (SCZ) contains only the velocity correlations and where u are the turbulent convective velocities and the brackets denote a large-scale average. The angular velocity, , and meridional motions are expanded in Legendre polynomials and in these expansions only the two leading terms are retained (for example, where is the polar angle). Per hemisphere, the meridional circulation is, in consequence, the superposition of two flows, characterized by one, and two cells in latitude respectively. Two equations can be derived from the azimuthal momentum equation. The first one expresses the conservation of angular momentum and essentially determines the stream function of the one-cell flow in terms of : the convective motions feed angular momentum to the inner regions of the SCZ and in the steady state a meridional flow must be present to remove this angular momentum. The second equation contains also the integral indicative of a transport of angular momentum towards the equator.With the help of a formalism developed earlier we evaluate, for solid body rotation, the velocity correlations and for several values of an arbitrary parameter, D, left unspecified by the theory. The most striking result of these calculations is the increase of with D. Next we calculate the turbulent viscosity coefficients defined by whereC _ro ⁰ and C _o ⁰ are the velocity correlations for solid body rotation. In these calculations it was assumed that ₂ was a linear function of r. The arbitrary parameter D was chosen so that the meridional flow vanishes at the surface for the rotation laws specified below. The coefficients v _ro ⁱ and v _0o ⁱ that allow for the calculation of C _ro and C _0o for any specified rotation law (with the proviso that ₂ be linear) are the turbulent viscosity coefficients. These coefficients comply well with intuitive expectations: v _ro ¹ and –v _0o ³ are the largest in each group, and v _0o ³ is negative.The equations for the meridional flow were first solved with ₀ and ₂ two linear functions of r ( ₀ ¹ = – 2 × 10 ^–12 cm ^–1) and ( ₂ ¹ = – 6 × 10 ¹² cm ^–1). The corresponding angular velocity increases slightly inwards at the poles and decreases at the equator in broad agreement with heliosismic observations. The computed meridional motions are far too large ( 150m s^–1). Reasonable values for the meridional motions can only be obtained if _o (and in consequence ), increase sharply with depth below the surface. The calculated meridional motion at the surface consists of a weak equatorward flow for gq < 29° and of a stronger poleward flow for > 29°.In the Sun, the Taylor-Proudman balance (the Coriolis force is balanced by the pressure gradient), must be altered to include the buoyancy force. The consequences of this modification are far reaching: is not required, now, to be constant along cylinders. Instead, the latitudinal dependence of the superadiabatic gradient is determined by the rotation law. For the above rotation laws, the corresponding latitudinal variations of the convective flux are of the order of 7% in the lower SCZ.     

Very Large Array-RATAN 600 observations of a solar active region

The Very Large Array (VLA) and the RATAN 600 were used to observe a solar active region on two consecutive days around the time of a partial solar eclipse in July 1990. VLA synthesis maps at 2.0, 3.5, and 6.2 cm wavelength reveal bright (T _b = 0.2 – 2.2 × 10⁶ K), compact ( = 10–40) sources above the penumbra of the leading sunspot while maps at 20 cm wavelength reveal an extended ( 4.5) looplike structure (T _b 10⁶ K) between the dominant spots. Total flux and brightness temperature spectra of both components were obtained by the RATAN at nine wavelengths between 1.7 and 21 cm. The relatively-flat spectrum of the extended emission is attributed to the optically thin thermal brems Strahlung of electrons trapped in a magnetic loop at coronal temperatures. Step-spectrum sunspot-associated emission is attributed to thermal gyroresonance radiation at different heights along the leg of a loop joining regions of opposite magnetic polarity. Comparisons with predicted distributions of gyroresonance radiation indicate that the compact sunspot-associated sources lie at heights of h = 2500–17500 km above the photosphere. Although potential fields of sufficient strength appear to exist at coronal heights, differences n the observed and predicted brightness distributions suggest some role for non-potential fields or for an inhomogeneous distribution of electron density or temperature above the sunspot.     

Gyro-synchrotron emission in a magnetic dipole field for the application to the center-to-limb variation of microwave impulsive bursts

In order to interpret the observed center to limb variations of spectrum and polarization of microwave impulsive bursts, gyro-synchrotron emission from nonthermal electrons trapped in a magnetic dipole field is computed. The theoretical spectrum and polarization are consistent with observed ones if we put an outer boundary of the radio source at a layer of 100-60 G or (7–9) × 10⁴ km in height. Rather small observed center-limb variations in intensity and polarization are attributed to the distribution of , an angle between the magnetic field and the direction of observer, in the radio source emitting the burst, though the intensity and polarization depend strongly on especially at small values of .     

Latitudinal Distribution of Polar Faculae

The distribution of polar faculae with respect to latitude is investigated, using data obtained at the Ussuriysk Observatory during the years 1963–1994. To correct the data for the effect of visibility, a visibility function of polar faculae is derived. Corrected surface density of polar faculae is calculated as a function of latitude and time. During most part of each solar cycle, polar faculae exhibit pronounced concentrations at high latitudes with maxima of the surface density located near the poles. Such concentrations of polar faculae (below referred to as `polar condensations') are formed after a lapse of 1–2 years from the polar magnetic field reversals, and then they persist for 7–9 years, until the high-latitude magnetic fields again start to reverse. During several years after the sunspot minima, the polar condensations co-exist with the new latitudinal belts of polar faculae which appear at middle latitudes and then migrate toward the poles. To describe the evolution of the polar condensations quantitatively, the polar faculae density n at latitudes above 60° has been approximated by means of the power law nn ₀ cos^m where is polar angle. The parameters n ₀ and m both are found to vary during the course of the solar cycle, reaching maximum values near or shortly after the minimum of sunspot activity. At the minimum phase of the solar cycle, on average, the surface density of polar faculae varies as cos¹⁴. In addition to the 11-yr variation, the latitude–time distribution of polar faculae exhibits short-term variations occurring on the time scale of 2–3 years.     

Non-inductive current driven by Alfvén waves in solar coronal loops

It has been shown that Alfvén waves can drive non-inductive current in solar coronal loops via collisional or collisionless damping. Assuming that all the coronal-loop density of dissipated wave power (W= 10–3 erg cm^–3 s^–1), which is necessary to keep the plasma hot, is due to Alfvén wave electron heating, we have estimated the axial current density driven by Alfvén waves to be jz 10³–10⁵ statA cm^–2. This current can indeed support the quasi-stationary equilibrium and stability of coronal loops and create the poloidal magnetic field up to B 1–5 G.     

The creation of magnetic monopoles in outer gaps of pulsars

The production of magnetic monopoles-antimonopoles pairs is expected in the interactions of highly energetic particles in the outer gaps of a pulsar. We estimate upper limit for production of monopoles withm _g 10⁴ GeV _c ^–2 ine ⁺ e ^– interactions of the order _ee 10^–32 cm^–2.     

High-Latitude Solar Rotation Traced by Magnetic Elements

Sequential observations at Huairou Solar Observation Station, China, and Kitt Peak, U.S.A., show that polar magnetic elements can live from several to more than 58 hours. This enables measurement of the solar rotation rate near the polar region by tracing magnetic element motions. With observations carried out on 8–15 July 1997, we identify and trace more than 1300 elements at north heliographic latitudes between 55°–85° using two methods, and fit the mean sidereal rotation rate as =14.0±0.54–(2.24±1.22)sin²–(1.78±0.79)sin⁴ deg per day.     

Iras observations of solar-like stars

IRAS has detected 70% of the 66 F, G, K nearby dwarf stars investigated here. The sample included chromospherically active as well as non-active dwarfs. The detected stars show emission at 12 and 25 m. Their 12 m luminosity is in the range 1–13×10³⁰ erg s^–1 and it is strongly correlated to the star's total luminosity (L _bol).There are indications that some of the stars possess IR emission in excess of that expected from a stellar photosphere.Paper presented at the 11th European Regional Astronomical Meeting of the IAU on New Windows to the Universe, held 3–8 July, 1989, Tenerife, Canary Islands, Spain.     

Study of the nonradial directional property of the rays of the streamer belt and chains in the solar corona

Based on analyzing corona images taken by the LASCO C1, C2, and C3 instruments, a study is made of the behavior of the streamer belt spanning one half of the 1996–2001 cycle of solar activity, from minimum to maximum activity, in the absence of coronal mass ejections. It is shown that: (1) The position of the streamer belt relative to the solar equator is generally characterized by two angles: _o and _E, where _o is the latitudinal position (near the solar surface) of the middle of the base of the helmet, the top of which gradually transforms to a ray of the streamer belt with a further distance from the Sun, and _E is the latitude of this ray for R>5–6 R from the Sun's center where the ray becomes radial. (2) Only rays lying at some of the selected latitudes _o retain their radial orientation (_oE) throughout their extent. Namely: _o0° (equator), _o±90° (north and south poles), and the angle _o lying in the range ±(65°–75°) in the N- and S-hemispheres. (3) A deviation of rays from their radial orientation in the direction normal to the surface of the streamer belt occurs: for latitudes _o<|65°–75°| toward the equator (>0°) reaching a maximum in the N and S hemispheres, respectively, when _OM40°, and _OM–42° for latitudes _o>|65°–75°| toward the pole (<0°). The regularities obtained here are a numerical test which can be used to assess of the validity of the theory for describing the behavior of the Sun's quasi-stationary corona over a cycle of solar activity.     

Velocity Field of a Complex Sunspot with Light Bridges

For the leading part of sunspot group NOAA 8323, which rapidly changed its complex structure, a time series of the line-of-sight (LOS) component of the velocity field was obtained. With a two-dimensional Fabry–Pérot spectrometer, the magnetically insensitive line Fei 557.6 nm was scanned. The inclination of the LOS (heliographic angle) to the vertical was =28.5°. The umbra of the observed spot was divided by a system of light bridges into several parts. The spatial and temporal velocity field also exhibits a considerable complexity: in one extended umbral area there is a downward flow of 1 km s^–1 relative to other dark sub-umbrae. At the center-side penumbra, with a line-of-sight Evershed outflow of 1.5 km s^–1, a persistent patch, somewhat darker than the average penumbra, has a LOS velocity of 1.3 km s^–1 in opposite direction, probably a downflow. At the limb-side penumbra, a photosphere-like area is interspersed, interrupting the Evershed flow which resumes with typical strength beyond this feature towards the outer penumbral boundary. Most interesting is the behavior of the light bridges, which have a slight blue shift, interrupted by short events of strong blue or red shifts which – within the time resolution of 35 s – instantly affect a considerable part of a light bridge.     

Latitude and Magnetic Flux Dependence of the Tilt Angle of Bipolar Regions

Magnetogram data of 517 bipolar active regions are analyzed to study latitude, magnetic flux, polarity separation dependence of tilt angle of the active regions with well-defined bipolar magnetic configurations. The data were obtained at Huairou Solar Observing Station in Beijing during 1988 to October 2001. By statistical analysis, it is found: (1) The tilt angle () is a function of the latitude (). Our observed result, sin=0.5 sin, is in good agreement with that obtained by Wang and Sheeley (1991). (2) The tilt angle is a function of the magnetic flux. The tilt angle increases (decreases) with flux increasing when the flux is smaller (larger) than 5×10²¹ Mx. (3) The tilt angle is a function of the magnetic polarity separation. The tilt angle increases (decreases) with the separation increasing when the separation is smaller (larger) than 8×10⁹ cm. (4) The magnetic flux ( in 10²⁰ Mx) is correlated to the magnetic polarity separation (d in Mm), following ₂₀d ^1.15. The result is close to the observed result of Wang and Sheeley (1989), ₂₀d ^1.3. (5) The tilt fluctuations are independent of the latitude, but depend slightly on the separation, which is similar to the result obtained by Fisher, Fan, and Howard (1995). (6) The distribution function of the ratio of net magnetic flux to total magnetic flux is almost centered around zero net flux. The imbalance of magnetic flux is lower than 10% for 47% of our samples; 31% of active regions are in imbalance of the magnetic flux between 10% and 20%.     

Numerical simulations of pulsationally unstable accretion disks around supermassive black holes

The innermost region of slim accretion disks with standard viscosity is unstable against axisymmetric radial inertial acoustic perturbations under certain conditions. Numerical simulations are performed in order to demonstrate behaviors of such unstable disks. It is shown that oscillations with the period of 10^–3 (M _BH/M ) s can be excited near the inner edge of the disks, whereM _BH is the mass of the central object. This kind of unstable disks is a possible origin of the periodic X-ray time variabilities with period of 10⁴s observed in a Seyfert galaxy NGC 6814.     

Seven-digit tables of Lane-Emden functions

In Table I we present seven digit numerical solutions of the Lane-Emden equation for the plane-parallel, cylindrical, and spherical case for polytropic indices ofn=–10, –5, –4, –3, –2, –1.5, –1.01, –0.9, –0.5, 0, 0.5, 1, 1.5, 2, 3, 4, 5, 6, 10, 20, ±, supplemented byn=2.5, 3.5, 4.5, and 4.99 for the spherical case.In Table II some finite boundary values of polytropic slabs, cylinders, and spheres are summarized. For polytropic spheres (N=3) we have also quoted boundary values near the minimum of the dimensionless mass -² ₁₁ occurring atn4.823 (Seidov and Kuzakhmedov, 1978).     

Continuum photometry of solar white-light faculae

We have determined absolute continuum intensities and brightness temperatures of individual facular grains at a spatial resolution limited by the =50 cm aperture of the SVST on La Palma. A facular region at 57° was observed simultaneously in three narrow continuum windows at 450.5, 658.7, and 863.5 nm. We corrected for image degradation by the Earth's atmosphere using the speckle masking method. The brightness temperatures do not exactly follow the Planck law. The differences of T _blue–T _red=220 K and T _ir–T _red=–42 K reflect the wavelength dependence of the continuum formation depth. The (red) temperatures of 250 facular grains show excesses between 250 and 450 K above their undisturbed neighborhood. The wavelength dependence of the relative intensity ratios C= [I ^fac/I ^phot] show a large scatter around mean values of C _blue/C _red=1.075 and C _ir/C _red=0.98. We determined the center-to-limb variation of the 863.5 nm continuum contrast for 0.17>cos>0.39 by measuring 270 grains in reconstructed facular images. The upper envelope of the data points increases linearly to 1.5 at cos=0.17. Application of the mean color dependence yields green contrasts up to C ₅₅₀=1.7, which is far higher than previously observed values. The behaviour for cos>0.17 is estimated from (unreconstructed) frame-selected best images taken over a time interval of 7 hours. Six distinct facular regions clearly discernible during the whole time interval indicate a slight contrast decrease towards the extreme limb. The observed quantities are useful for an adjustment of model calculations and for a discrimination of competing models.