J. K. Lawrence

Multifractal measure of the solar magnetic field

We analyze high-resolution, digital, photoelectric images of solar photospheric magnetic fields. The line-of-sight fields are found to scale in a self-similar way with resolution and thus can be expressed in the form of a signed multifractal measure. The scaling properties of the measure are used to extrapolate field integrals, such as moments of the magnetic field, below resolvable limits. The scaling of the field moments is characteristic of highly intermittent fields. We suggest that the quiet-Sun photospheric fields are generated by local dynamo action based on random convective motions at high magnetic Reynolds number. The properties of active region images are determined by the presence of fields generated by the global, mean field dynamo

Anomalous Diffusion of Solar Magnetic Elements

The diffusion properties of photospheric bright points associated with magnetic elements (magnetic bright points) in the granulation network are analyzed. We find that the transport is subdiffusive for times less than 20 minutes but normal for times larger than 25 minutes. The subdiffusive transport is caused by the walkers being trapped at stagnation points in the intercellular pattern. We find that the distribution of waiting times at the trap sites obeys a truncated Levy type (power-law) distribution. The fractal dimension of the pattern of sites available to the random walk is less than 2 for the subdiffusive range and tends to 2 in the normal diffusion range. We show how the continuous time random walk formalism can give an analytical explanation of the observations. We simulate this random walk by using a version of a phenomenological model of renewing cells introduced originally for supergranules by Simon, Title, & Weiss. We find that the traps that cause the subdiffusive transport arise when the renewed convection cell pattern is neither fixed nor totally uncorrelated from the old pattern, as required in Leightons model, but in some intermediate state between these extremes.

Solar luminosity fluctuations during the disk transit of an active region

On presente des observations photometriques monochromatiques des fluctuations du rayonnement solaire causees par une region active durant tout son transit sur le disque entier, en aout 1982

Multi-color photometric observations of facular contrasts

We have analyzed high-resolution, digital, photometric images of solar active regions made at various center-limb positions on 21–24 July, 1983. The images were made at three continuum wavelengths: 5245 Å in the green (bandpass 1.5 Å), 6264 Å in the red (bandpass 1.5 Å), 10 000 Å in the infrared (bandpass 3 Å), and also at 8662 Å in the Caii infrared line (bandpass 3 Å). In all continuum colors, the contrasts of facular patches, as opposed to individual facular elements, appear to behave as linear functions of 1/cos θ, where θ is the heliocentric angle (μ = 0 at the limb, 1 at disk center). The relative contrasts in the different continuum colors are roughly proportional to (wavelength)-1, as expected from a Planck distributioin in the Wien approximation. The observed variation of the relative contrasts with center-limb position is compared to two simple theoretical models.

Diffusion of magnetic flux elements on a fractal geometry

Recent observations have indicated that magnetic field elements are distributed on the Sun in fractal patterns with dimension D < 2. We suggest that the transport of magnetic field elements across the solar surface should be treated as diffusion on a fractal geometry. We review a semi-analytical, theoretical treatment of fractal diffusion. Comparison with observations of small-scale motions of solar magnetic flux concentrations indicates that fractal diffusion may be taking place with dimension in the range 1.3 to 1.8. It is shown that, compared to the predictions that would be made for two-dimensional diffusion, fractal diffusion in this range would lead to an increased level of in situ flux cancellation in decaying active regions by 7% to 35%. Other work in specialities outside of solar physics may be useful in explaining solar magnetic phenomena.

The correlation of solar flare production with magnetic energy in active regions

An investigation of 531 active regions was made to determine the correlation between energy released by flares and the available energy in magnetic fields of the regions. Regions with magnetic flux greater than 1021 maxwell during the years 1967–1969, which included sunspot maximum, were selected for the investigation. A linear regression analysis of flare production on magnetic flux showed that the flare energy is correlated with magnetic energy with a coeificient of correlation of 0.78. Magnetic classification and field configuration also significantly affect the production of flares.

A Simple Model of Stratospheric Dynamics Including Solar Variability

A simple dynamic model, truncated from the stratospheric wave‐zonal flow interaction Holton and Mass model, is introduced and studied. This model consists of three ordinary differential equations controlled by two parameters: the initial amplitude of planetary waves and the vertical gradient of the zonal wind. The changes associated with seasonal variations and with the solar variability are introduced as periodic modulations of the zonal wind gradient. The major climatic response to these changes is seen through modulation of the number of cold and warm winters.

Photometric determination of facular contrasts near the solar disk center

Pairs of simultaneous digital photometric images of several solar active regions made with 3-A effective bandpasses in the CA II line at 8662 A have been analyzed. Images were obtained in 1984 with the 28-cm San Fernando Observatory solar telescope. After correction for bolometric and stray light effects, a continuum facular contrast at the disk center of 0.74 + or - 0.11 percent is found which remains roughly constant from the disk center out to r = 0.45 solar radii before increasing. These results demonstrate an increase of 10-20 percent over previous estimates of the contribution of faculae to solar luminosity fluctuations. 31 references.

Characteristic Scales of Photospheric Flows and Their Magnetic and Temperature Markers

We study the characteristic scales of quiet-Sun photospheric velocity fields along with their temperature and magnetic markers in Doppler images from the Michelson Doppler Imager aboard the SOHO satellite (SOHO/MDI) in simultaneous, Doppler, magnetic, and intensity images from the San Fernando Observatory and in full-disk magnetograms and an intensity image from National Solar Observatory (Kitt Peak). Wavelet flatness spectra show that velocity fluctuations are normally distributed (Gaussian). This is often assumed in stochastic models of turbulence but had not yet been verified observationally for the Sun. Temperature fluctuations also are Gaussian distributed, but magnetic fields are intermittent and are gathered into patterns related to flow structures. Wavelet basis functions designed to detect characteristic convection cell-flow topologies in acoustically filtered SOHO/MDI Doppler images reveal granulation scales of 0.7-2.2 Mm and supergranulation scales of 28-40 Mm. Mesogranular flows are weakly but significantly detected in the range 4-8 Mm. The systematic flows account for only 30% of the image variances at granular and supergranular scales and much less in between. The main flows for the intermediate range of 2-15 Mm are self-similar, i.e., chaotic or turbulent.

Weak magnetic fields and solar irradiance variations

NOAA active region 5643 was observed from August 17 to 21, 1989. Sets of video spectra-spectroheliograms including the Fe I line at 6302.5 A were made at least daily with the San Fernando Observatory 28 cm vacuum telescope and vacuum spectroheliograph. These give simultaneous, co-registered digital images representing monochromatic continuum intensity, line core intensity and line-of-sight magnetic field. Three different criteria are used to define the pixels representing the quiet sun and the facular portions of the images. These criteria are the magnetic field strength, the line core intensity, and the distribution of continuum intensities. Each of these definition schemes is used to estimate the irradiance change due to facular emission. The magnetic field and the continuum intensity distribution definitions give estimates which agree closely. The line core intensity definition leads to larger estimates of the facular irradiance contribution. Some model-dependent investigations of the contrasts and sizes of individual facular elements also are presented.