The photospheric magnetic flux budget

The ensemble of bipolar regions and the magnetic network both contain a substantial and strongly variable part of the photospheric magnetic flux at any phase in the solar cycle. The time-dependent distribution of the magnetic flux over and within these components reflects the action of the dynamo operating in the solar interior. We perform a quantitative comparison of the flux emerging in the ensemble of magnetic bipoles with the observed flux content of the solar photosphere. We discuss the photospheric flux budget in terms of flux appearance and disappearance, and argue that a nonlinear dependence exists between the flux present in the photosphere and the rate of flux appearance and disappearance. In this context, we discuss the problem of making quantitative statements about dynamos in cool stars other than the Sun. This paper evolved out of a more comprehensive version which appeared in Harvey (1993).     

Percolation theory and the geometry of photospheric magnetic flux concentrations

The magnetic field in solar active regions forms a highly structured pattern without an apparent length scale. We study this pattern in detail for a plage and its surroundings observed with the Swedish Solar Observatory on La Palma. The magnetogram has a resolution of about 1/3, after image optimisation. We analysed the geometric properties of isolated patches of magnetic flux. Patches with a linear size up to 3 appear to be statistically self-similar, with a fractal dimension ofD _f = 1.54 ± 0.05 for the relation between area and linear size. This value agrees very well with the dimensionD _f = 1.56 which is found in percolation theory for clusters of tracers placed randomly on a lattice with a tracer density below a critical threshold. The distribution of observed cluster areas also agrees with that of clusters on such a random lattice. The correspondence between properties of observations and of clusters on randomly filled lattices suggests that- well after emergence - the magnetic flux on the Sun is randomly distributed at least up to sizes of about 3 and possibly larger.     

Magnetic flux separation in photospheric convection

Three-dimensional non-linear magnetoconvection in a strongly stratified compressible layer exhibits different patterns as the strength of the imposed magnetic field is reduced. There is a transition from a magnetically dominated regime, with small-scale convection in slender hexagonal cells, to a convectively dominated regime, with clusters of broad rising plumes that confine the magnetic flux to narrow lanes where fields are locally intense. Both patterns can coexist for intermediate field strengths, giving rise to flux separation: clumps of vigorously convecting plumes, from which magnetic flux has been excluded, are segregated from regions with strong fields and small-scale convection. A systematic numerical investigation of these different states shows that flux separation can occur over a significant parameter range and that there is also hysteresis. The results are related to the fine structure of magnetic fields in sunspots and in the quiet Sun.     

Dynamical effects in solar photospheric flux tubes

The interaction of an intense flux tube, extending vertically through the photosphere, with p-modes in the ambient medium is modelled by solving the time dependent MHD equations in the thin flux tube approximation. It is found that a resonant interaction can occur, which leads to the excitation of flux tube oscillations with large amplitudes. The resonance is not as sharp as in the case of an unstratified atmosphere, but is broadened by a factor proportional toH ^–2, whereH is the local pressure scale height. In addition, the inclusion of radiative transport leads to a decrease in the amplitude of the oscillations, but does not qualitatively change the nature of the interaction.     

The cyclical variation of energy flux and photospheric magnetic field strength from coronal holes

We measured the average soft X-ray emission from coronal holes observed on images obtained during AS & E rocket flights from 1974 to 1981. The variation of this emission over the solar cycle was then compared with photospheric magnetic flux measurements within coronal holes over the same period. We found that coronal hole soft X-ray emission could be detected and that this emission appeared to increase with the rise of the sunspot cycle from activity minimum to maximum. Our quantitative results confirmed previous suggestions that the coronal brightness contrast between holes and large-scale structure decreased during this period of the cycle. Gas pressures at the hole base were estimated for assumed temperatures and found to vary from about 0.03 dyne cm^–2 in 1974 to 0.35 dyne cm^–2 in 1981. The increase in coronal hole X-ray emission was accompanied by a similar trend in the surface magnetic flux of near-equatorial holes between 1975 and 1980 (Harvey et al., 1982).     

Observational evidence of magnetic reconnection in a coronal bright point

Magnetic reconnection is considered to be the fundamental process by which magnetic energy is converted into plasma or particle kinetic energy. Magnetic reconnection is a widely applied physics model to explain the solar eruption events, such as coronal bright points(CBPs). Meanwhile, it is an usual way of the solar physics research to look for the observational evidences of magnetic reconnection in the solar eruption events in order to support the model. In this paper, we have explored the evidences of magnetic reconnection in a CBP observed by the Atmospheric Imaging Assembly(AIA) onboard the Solar Dynamics Observatory(SDO) at NOAA No. 11163 on 2011 March 5. Our observations show that this event is a small-scale loop system in active regions that have similar size as a traditional CBP and it might shed light on the physics of a traditional CBP. This CBP is bright in all nine AIA wavelengths and displays a flaring development with three bursts intermittently. Each burst exhibits a pair of bi-directional jets almost along a line. They originate from the same position(CBP core), then move in the opposite directions. Our findings are well consistent with the magnetic reconnection process by which the bi-directional plasma outflows are produced and radiate the bi-directional jets detected by SDO/AIA. These facts further support the conclusion that the CBP is produced by the magnetic reconnection process.     

Semi-regularities in the photospheric magnetic fields

Using Stanford large-scale magnetic field synoptic charts of rotation 1676 to 1739 and by delineating LLUMR, i.e., long-lived unipolar magnetic regions of both polarities surviving at least for four solar rotations, the semi-regular nature of their photospheric magnetic field pattern and their rotational properties have been examined. The investigation demonstrates the existence of regularities in the background field patterns as shown from the regular patterns of LLUMR rows and streams. This confirms the results of Bumba and Howard concerning regularities in large-scale photospheric magnetic field patterns. LLUMR streams seem to be arranged in a wave pattern of alternating polarities. Coronal holes and associated sections of photospheric field patterns suffer differential rotation. The rotation rates of the background field patterns which are not associated with the coronal holes are different from those which are.     

Torsional oscillation patterns in photospheric magnetic features

We analyzed 689 high-resolution magnetograms taken daily with the NSO Vacuum Telescope on Kitt Peak from 1975 to 1991. Motions in longitude on the solar surface are determined by a one-dimensional crosscorrelation analysis of consecutive day pairs. The main sidereal rotation rate of small magnetic features is best fit by = 2.913(±0.004) – 0.405(±0.027) sin² – 0.422(±0.030) sin⁴ , in µrad s^–1, where is the latitude. Small features and the large-scale field pattern show the same general cycle dependence; both show a torsional oscillation pattern. Alternating bands of faster and slower rotation travel from higher latitudes toward the equator during the solar cycle in such a way that the faster bands reach the equator at cycle minimum. For the magnetic field pattern, the slower bands coincide with larger widths of the crosscorrelations (corresponding to larger features) and also with zones of enhanced magnetic flux. Active regions thus rotate slower than small magnetic features. This magnetic torsional oscillation resembles the pattern derived from Doppler measurements, but its velocities are larger by a factor of more than 1.5, it lies closer to the equator, and it leads the Doppler pattern by about two years. These differences could be due to different depths at which the different torsional oscillation indicators are rooted.Operated by the Association of Universities for Research in Astronomy Inc. under cooperative agreement with the National Science Foundation.     

Implications of rapid footpoint motions of photospheric flux tubes for coronal heating

Some recent observations at Pic-du-Midi (Mulleret al., 1992a) suggest that the photospheric footpoints of coronal magnetic field lines occasionally move rapidly with typical velocities of the order 3 km s^–1 for about 3 or 4 min. We argue that such occasional rapid footpoint motions could have a profound impact on the heating of the quiet corona. Qualitative estimates indicate that these occasional rapid motions can account for the entire energy flux needed to heat the quiet corona. We therefore carry out a mathematical analysis to study in detail the response of a vertical thin flux tube to photospheric footpoint motions in terms of a superposition of linear kink modes for an isothermal atmosphere. We find the resulting total energy that is asymptotically injected into an isothermal atmosphere (i.e., an atmosphere without any back reflection). By using typical parameter values for fast and slow footpoint motions, we show that, even if the footpoints spend only 2.5% of the time undergoing rapid motions, still these rapid motions could be more efficient in transporting energy to the corona than the slow motions that take place most of the time.     

On possible correlations in the photospheric magnetic field

We have searched for correlations between photospheric magnetic field changes in the north and south hemispheres of the Sun. Both active region logs and analysis of Mount Wilson magnetograms were employed. No correlations were found, and we infer that local convective turbulence is more important than dynamo processes with regard to the appearance of individual active regions.     

The generation of magnetic fields in photospheric layers

Recent observations concerning the growth and decay of photospheric magnetic flux present a challenge to the conventional picture of the photosphere as a passive medium through which flux tubes emerge inertly. Rather, they suggest the possibility that interactions between the magnetic flux and the photospheric velocity fields may give rise to changes in the observed surface flux.In this paper the physics of flux changes are reviewed and the various terms in the hydromagnetic equation which give rise to the growth and decay of magnetic flux are examined. Several kinematic models for field changes are examined and it is shown that new flux loops may be generated by suitable oscillatory velocity fields near the boundaries of existing magnetic structures, thus increasing the gross flux through the photosphere. It is suggested that this mechanism may account for the appearance of moving magnetic features (knots of opposite polarities) at the boundaries of decaying sunspots.Other models are discussed and a tentative explanation of the apparently unbalanced growth of opposite polarities is given in terms of a current-sheet model.     

Flare positions relative to photospheric magnetic fields

Of 21 flares of importance 1 or greater, observed on 15 days, all were found to lie adjacent to a neutral line in the longitudinal component of photospheric magnetic fields. In most of these cases, the flare consisted of two or more segments separated by the neutral line and located in areas of strong field and high-longitudinal field gradient. In some cases, the flare segments extended into areas of weak-magnetic field and low-field gradient, but maintained an orientation adjacent to a neutral line.Optical and magnetic field records of higher resolution were obtained on 6 July 1965. These observations reveal an excellent correlation between the size, shape, and intensity of the H fine structures and the longitudinal component of the photospheric magnetic fields, except in the vicinity of the neutral line. Sections of the neutral line are marked by long fibrils lying perpendicular to the neutral line or by small filaments lying along the neutral line.The development of a flare of importance 1 in this region appeared to be more precisely related to the neutral line than was found for the flares and magnetic fields observed with lower resolution. The two major segments of this flare lengthened in directions approximately parallel to the neutral line, while simultaneously drifting perpendicularly away from the neutral line. The initial rate of drift systematically varied from 1 to 12 km/sec at a series of positions approximately parallel to the neutral line and corresponding to increasing distance from strong fields. The rate of drift was also observed to decelerate throughout the life of the flare.     

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.     

Differential rotation of the photospheric magnetic field

The differential rotation of the large-scale photospheric magnetic field has been investigated with an autocorrelation technique using synoptic charts of the photospheric field during the interval 1959–66. Near the equator the rotation period of the field is nearly the same as the rotation rate of long-lived sunspots studied by Newton and Nunn. Away from the equatorial zone the field has a significantly shorter rotation period than the spots. Over the entire range of latitudes investigated the average rotation period of the photospheric magnetic field was about 1 1/4 days less than the average rotation period of the material observed with Doppler shifts by Livingston and by Howard and Harvey. Near the equator the photospheric field results agree with the results obtained from recurrent sunspots, while above 15° the photospheric field rotation rates agree with the rotation rates of the K corona and the filaments.     

East-west inclination of large-scale photospheric magnetic fields

Sixteen years of WSO magnetogram data have been studied to determine the solar cycle variation and latitude dependence of the east-west inclination of photospheric magnetic field lines. East-west inclination is here defined as the angle between a field line and its local radial vector, as projected onto the plane of the latitude and line of sight. Inclination is determined by a least-squares fit of observed magnetic fields to a simple projection model, and is found to depend on polarity and to change with the solar cycle. Leading and following polarities are tipped towards each by about 9° and have an overall net tilt in the direction of rotation (to the west) of 0.6°. New cycles are seen to begin at high latitudes and to grow through the lower latitudes over approximately 5 years, providing evidence for an extended cycle length of 16–18 years.     

Noise storms and particular photospheric magnetic structures

A comparison of flux and polarization of solar radio noise storms with photospheric source position and magnetic field configuration for six year observations is reported. Three independent results pointing to a predominance of plus magnetic structures as regards noise-storm generation are outlined. A rather strong proof towards a cause-effect connection of photospheric magnetic structure development and noise-storm evolution is stressed.     

A note on the magnetic network of photospheric magnetic fields

It is suggested that the magnetic network in the unipolar region of the photosphere can be interpreted as the field of loop currents along the boundary of the supergranulation cells. The currents are generated by the dynamo process associated with the supergranulation.     

Radio and soft X-ray evidence for dense non-potential magnetic flux tubes in the solar corona

The source positions of solar radio bursts of spectral types I, III(U) and III(J) and V observed by the Culgoora radioheliograph are found to lie almost radially above soft X-ray loops on pictures taken by the S-056 telescope aboard Skylab. The radio source positions and the X-ray loops occur near magnetic loops on computed potential field maps. However, the magnetic induction required to explain the radio observations is much greater than the computed potential field value at that height. Dense current-carrying magnetic flux tubes emanating from active regions on the Sun and extending to 1.5R above the photosphere provide a satisfactory model for the radio bursts.     

Observational evidence for stellar mass black holes

I review the evidence for stellar mass black holes in the Galaxy. The unique properties of the soft X-ray transient (SXTs) have provided the first opportunity for detailed studies of the mass-losing star in low-mass X-ray binaries. The large mass functions of these systems imply that the compact object has a mass greater than the maximum mass of a neutron star, strengthening the case that they contain black holes. The results and techniques used are discussed. I also review the recent study of a comparison of the luminosities of black hole and neutron star systems which has yielded compelling evidence for the existence of event horizons.