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Axisymmetric perturbations of thin gaseous disks. I - Unstable convective modes and their consequences for the solar nebula

The axisymmetric perturbations of a thin, differentially rotating gas disk in which the vertical temperature stratification is superadiabatic are analyzed. The growth rate of adiabatic convective normal modes is calculated, departures from simple polytropic disk models are briefly discussed, and the detailed vertical structure of the eigenfunctions is analyzed. The stabilizing effect of radiative diffusion on convective modes is considered. It is found that rotation and compressibility tend to reduce the rate of growth of the disturbances, and that the growth rate increases without limit and is proportional to the square root of the radial wavenumber in polytropic equilibria. The maximum radial size of convective eddies scales like the square root of the degree of superadiabaticity times the size of the convective zone. There is significant convective penetration into radiatively stable layers only for the fundamental and low-order harmonic modes, whose vertical wavelength is comparable to the size of the convective layer.

Ruden, Steven P.↗

Solar rotation as determined from OSO-4 EUV spectroheliograms.

Spectroheliograms obtained in extreme ultraviolet (EUV) lines and the Lyman continuum are used to determine the rotation rate of the solar chromosphere, transition region, and corona. A cross-correlation analysis of the observations indicates the presence of differential rotation through the chromosphere and transition region. The rotation rate does not vary with height. The average sidereal rotation rate is given by omega (deg/day) = 13.46-2.99 sin squared B where B is the solar latitude. This rate agrees with spectroscopic determinations of the photospheric rotation rate, but is slower by about 1 deg/day than rates determined from the apparent motion of photospheric magnetic fields and from the brightest points of active regions observed in the EUV. The corona does not clearly show differential rotation as do the chromosphere and transition region.

Dupree, A. K.↗

Solar Cycle Fine Structure and Surface Rotation from Ca II K-Line Time Series Data

Analysis of three and a half decades of data from the NSO/AFRL/Sac Peak K-line monitoring program yields evidence for four components to the variation: (a) the solar cycle, with considerable fine structure and a quasi-periodicity of 122.4 days; (b) a stochastic process, faster than (a) and largely independent of it, (c) a quasi-periodic signal due to rotational modulation, and of course (d) observational errors (shown to be quite small). Correlation and power spectrum analyses elucidate periodic and aperiodic variation of these chromospheric parameters. Time-frequency analysis is especially useful for extracting information about differential rotation, and in particular elucidates the connection between its behavior and fine structure of the solar cycle on approximately one-year time scales. These results further suggest that similar analyses will be useful at detecting and characterizing differential rotation in stars from stellar light-curves such as those being produced at NASA's Kepler observatory.

Scargle, Jeff↗

Coronal Rotation at Solar Minimum from UV Observations

UVCS/SOHO observations have been analyzed to reconstruct intensity time series of the O VI 1032 A and H 11216 A spectral lines at different coronal heliolatitudes from 1.5 to 3.0 solar radii from Sun center. Evidence was found for coronal differential rotation that differs significantly from that of the photospheric plasma. The study of the latitudinal variation shows that the UV corona decelerates toward the photospheric rates from the equator up to the poleward boundary 2 of the midlatitude streamers, reaching a peak of 28.16+/-0.20 days around +30 from the equator at 1.5 solar radii, while a less evident peak is observed in the northern hemisphere. This result suggests a real north-south rotational asymmetry as a consequence of different activity and weak coupling between the magnetic fields of the two hemispheres. The study of the radial rotation profiles shows that the corona is rotating almost rigidly with height.

Mancuso, S.↗

Coronal mass ejections and the evolution of the large-scale corona

Coronal mass ejections (CMEs) are dynamic, large-scale events in the solar corona that expel plasma and magnetic fields into the solar wind. The structure of the large-scale corona influences CME occurrence; for example, CMEs are most frequently observed to be disruptions of coronal or helmet streamer configurations on the Sun. We have investigated the evolution of the large-scale corona in the presence of differential rotation, using time-dependent magnetohydrodynamic (MHD) simulations in two and three dimensions. An equilibrium coronal configuration is first computed by superimposing a Parker solar wind flow on an initial potential field, the equations are integrated in time until a steady-state is reached. When differential rotation is introduced, we find that the configuration does not reach a steady state; the closed field regions (helmet streamers) disrupt recurrently, ejecting plasmoids into the solar wind. Our results suggest that differential rotation may be one of the mechanisms by which mass ejections are initiated. We will describe the evolution of the polarization brightness (pB) for the resulting configurations, as well as the propagation of the ejected plasmoids in the solar wind, and we will compare the effects of differential rotation with other possible initiation mechanisms, such as the emergence of new magnetic flux.

Linker, J. A.↗

Chromospheric Variability: Analysis of 36 years of Time Series from the National Solar Observatory/Sacramento Peak Ca II K-line Monitoring Program

Analysis of more than 36 years of time series of seven parameters measured in the NSO/AFRL/Sac Peak K-line monitoring program elucidates five elucidates five components of the variation: (1) the solar cycle (period approx. 11 years), (2) quasi-periodic variations (periods approx 100 days), (3) a broad band stochastic process (wide range of periods), (4) rotational modulation, and (5) random observational errors. Correlation and power spectrum analyses elucidate periodic and aperiodic variation of the chromospheric parameters. Time-frequency analysis illuminates periodic and quasi periodic signals, details of frequency modulation due to differential rotation, and in particular elucidates the rather complex harmonic structure (1) and (2) at time scales in the range approx 0.1 - 10 years. These results using only full-disk data further suggest that similar analyses will be useful at detecting and characterizing differential rotation in stars from stellar light-curves such as those being produced by NASA's Kepler observatory. Component (3) consists of variations over a range of timescales, in the manner of a 1/f random noise process. A timedependent Wilson-Bappu effect appears to be present in the solar cycle variations (1), but not in the stochastic process (3). Component (4) characterizes differential rotation of the active regions, and (5) is of course not characteristic of solar variability, but the fact that the observational errors are quite small greatly facilitates the analysis of the other components. The recent data suggest that the current cycle is starting late and may be relatively weak. The data analyzed in this paper can be found at the National Solar Observatory web site http://nsosp.nso.edu/cak_mon/, or by file transfer protocol at ftp://ftp.nso.edu/idl/cak.parameters.

Solar physics↗

The power spectrum of the solar wind speed for periods greater than 10 days

The use of the more than 11 years of solar wind speed data obtained by Vela 2-6 and Imp 6-8 to study the power spectrum of speed variations in the range near the solar rotational frequency is discussed. The broad bands of power near periods of 27 days (corresponding to the rotational period of the sun), 13.5 days, and higher harmonics are characterized, and it is suggested that the described individual peaks in both the solar wind and the geomagnetic spectra are probably not due to differential rotation. The alternate explanation is that the multipeak nature of the power spectra are explained by a wave packet concept in which recurring highspeed streams are described as a series of pulses (separated by a constant period) that last for a varying number of solar rotations.

Fenimore, E. E.↗

The Sun as a star

Solar physics was reviewed in the context of the solar atmoshere. The understanding of the solar atmosphere is linked to stellar atmospheric research. Topics covered include: the existence of the chromosphere, the corona, and the solar wind; the interactive complex of convection, differential rotation, magnetic field generation and concentration, and the activity cycle; phenomena such as granulation, supergranulation, the 5 minute oscillation, filigree, faculae, sunspots, spicules, prominences, surges, and the spectacular flares.

Jordan, S. D.↗

Space Weather Modeling and Prediction for Intermediate Time-scales

Much of solar activity within a sunspot cycle occurs as bursts, or 'seasons' of strong activity over several months, separated by periods of much less activity. The most important space weather effects occur during these bursts. Previous modeling and forecasting efforts have focused on time-scales of hours-to-days and decades-to-centuries. The recent discovery of Rossby waves in the Sun, together with recently developed global models of solar MHD Rossby waves and their interactions with differential rotation and spot-producing magnetic fields, reveal the opportunity to simulate and predict the occurrence, strength and location of enhanced activity bursts a few weeks up to several months in advance. We now have a golden opportunity to fill in this gap in time-scales of forecasting space weather. This requires a) continuous observations of solar Rossby waves by various techniques; b) development of coupled nonlinear MHD models that simulate both global Rossby waves and the much smaller spatial scale emergence of new active regions; c) application of advanced data assimilation techniques to couple surface observations to update the model-system to integrate forward in time for creating forecasts months ahead. Then it will be possible to build operational prediction models to meet the needs of customers and stakeholders, including support of future NASA missions, regarding what kind and level of space weather to expect a few weeks to several months ahead.

SMD↗

Meridional Flow in Solar Cycle 24: The Impact on the Polar Magnetic Fields

Axisymmetric flows, Differential Rotation and Meridional Flow (MF), were measured by tracking the motion of magnetic elements on the surface of the Sun using data obtained by the Helioseismic and Magnetic Imager (HMI) on the NASA Solar Dynamics Observatory (SDO) Mission. HMI provides the highest resolution full ]disk magnetograms available to date. This dramatically reduces the noise in axisymmetric flows, particularly at high latitudes (i.e. near the poles). The MF was found to vary greatly from one Carrington Rotation to the next. Furthermore, a distinct north ]south difference was found in the MF at high latitudes: Flow in the South was persistently weaker than flow in the North. Conclusions will be drawn concerning the MF variability, north ]south differences, and the impact on the polar magnetic field strengths and the timing of their reversals.

Upton, Lisa↗

Magnetic Helicity Condensation and the Solar Cycle

Solar filaments exhibit a global chirality pattern where dextral/sinistral filaments, corresponding to negative/ positive magnetic helicity, are dominant in the northern/southern hemisphere. This pattern is opposite to the sign of magnetic helicity injected by differential rotation along east–west oriented polarity inversion lines, posing a major conundrum for solar physics. A resolution of this problem is offered by the magnetic helicity-condensation model of Antiochos. To investigate the global consequences of helicity condensation for the hemispheric chirality pattern, we apply a temporally and spatially averaged statistical approximation of helicity condensation. Realistic magnetic field configurations in both the rising and declining phases of the solar cycle are simulated. For the helicity-condensation process, we assume convective cells consisting of positive/negative vorticities in the northern/southern hemisphere that inject negative/positive helicity. The magnitude of the vorticity is varied as a free parameter, corresponding to different rates of helicity injection. To reproduce the observed percentages of dominant and minority filament chiralities, we find that a vorticity of magnitude 2.5 x 10(exp −6)/s is required. This rate, however, is insufficient to produce the observed unimodal profile of chirality with latitude. To achieve this, a vorticity of at least 5 x 10(exp −6)/s is needed. Our results place a lower limit on the small-scale helicity injection required to dominate differential rotation and reproduce the observed hemispheric pattern. Future studies should aim to establish whether the helicity injection rate due to convective flows and/or flux emergence across all latitudes of the Sun is consistent with our results.

Mackay, Duncan H.↗

Active region evolution in the chromosphere and transtition region

Images in the C IV 1548 A and the Si II 1526 S lines taken with the ultraviolet spectrometer polarimeter (UVSP) instrument on board the Solar Maximum Mission (SMM) satellite were combined into movies showing the evolution of active regions and the neighboring supergranulation over several days. The data sets generally consist of 240 by 240 arc second rasters with 3 arc second pixels taken one per orbit (about every 90 minutes). The images are projected on a latitude/longitude grid to remove the forshortening as the region rotates across the solar disk and further processed to remove jitter and gain variations. Movies were made with and without differential rotation. Although there are occasional missing orbits, these series do not suffer from the long nighttime gaps that occur in observations taken at a single groundbased observatory and are excellent for studying changes on time scales of several hours. The longest sequence processed to date runs from 20 Oct. 1980 to 25 Oct. 1980. This was taken during an SMM flare buildup study on AR 2744. Several shorter sequences taken in 1980 and 1984 will also be shown. The results will be presented on a video disk which can be interactively controlled to view the movies.

Shine, R. A.↗

Axisymmetric Flow Properties for Magnetic Elements of Differing Strength

Aspects of the structure and dynamics of the flows in the Sun's surface shear layer remain uncertain and yet are critically important for understanding the observed magnetic behavior. In our previous studies of the axisymmetric transport of magnetic elements we found systematic changes in both the differential rotation and the meridional flow over the course of Solar Cycle 23. Here we examine how those flows depend upon the strength (and presumably anchoring depth) of the magnetic elements. Line of sight magnetograms obtained by the HMI instrument aboard SDO over the course of Carrington Rotation 2097 were mapped to heliographic coordinates and averaged over 12 minutes to remove the 5-min oscillations. Data masks were constructed based on the field strength of each mapped pixel to isolate magnetic elements of differing field strength. We used Local Correlation Tracking of the unmasked data (separated in time by 1- to 8-hours) to determine the longitudinal and latitudinal motions of the magnetic elements. We then calculated average flow velocities as functions of latitude and longitude from the central meridian for approx 600 image pairs over the 27-day rotation. Variations with longitude indicate and characterize systematic errors in the flow measurements associated with changes in the signal from disk center to limb. Removing these systematic errors reveals changes in the axisymmetric flow properties that reflect changes in flow properties with depth in the surface shear layer.

Rightmire-Upton, Lisa↗

Anomalous solar rotation in the early 17th century

The character of solar rotation has been examined for two periods in the early 17th century for which detailed sunspot drawings are available: A.D. 1625 through 1626 and 1642 through 1644. The first period occurred 20 years before the start of the Maunder sunspot minimum, 1645 through 1715; the second occurred just at its commencement. Solar rotation in the earlier period was much like that of today. In the later period, the equatorial velocity of the sun was faster by 3 to 5 percent and the differential rotation was enhanced by a factor of 3. The equatorial acceleration with declining solar activity is in the same sense as that found in recent Doppler data. It seems likely that the change in rotation of the solar surface between 1625 and 1645 was associated with the onset of the Maunder Minimum.

Eddy, J. A.↗

Solar Simulation

Simulation of the surface region and interior of the Sun's convection zone. The objective is to provide understanding of the tachocline at the base of the convection zone. of the differential rotation generated by global convective motions, and of supergranules that are observed on the solar surface. Two large-scale simulation codes are used, one for the global dynamics in spherical coordinates and another for the local surface events in Cartesian geometry. We work in close collaboration with the Helioseismic and Magnetic Imager instrument developers for the Solar Dynamics Observatory satellite. NASA Program: Living with a Star - Sun-Earth Connection.

Wray, Alan↗

An anticorrelation between polar and equatorial rotation of the solar photosphere

Published spectroscopic measurements of solar rotation are analyzed to show that when the rotation velocity increases at high latitudes it tends to decrease at low latitudes, and that when the rotation velocity decreases at high latitudes it increases at low latitudes. The high-latitude velocities typically vary over only 20% of the range of those near the equator and the smallest variations of all occurred near latitude 60 deg during the rising portion of the previous solar cycle. The anticorrelation is consistent with a recent suggestion that differential rotation on the sun arises from photospheric wind systems whose strength is determined, ultimately, by oscillations within the sun.

Wolff, C. L.↗

How Large Scales Flows May Influence Solar Activity

Large scale flows within the solar convection zone are the primary drivers of the Sun's magnetic activity cycle and play important roles in shaping the Sun's magnetic field. Differential rotation amplifies the magnetic field through its shearing action and converts poloidal field into toroidal field. Poleward meridional flow near the surface carries magnetic flux that reverses the magnetic poles at about the time of solar maximum. The deeper, equatorward meridional flow can carry magnetic flux back toward the lower latitudes where it erupts through the surface to form tilted active regions that convert toroidal fields into oppositely directed poloidal fields. These axisymmetric flows are themselves driven by large scale convective motions. The effects of the Sun's rotation on convection produce velocity correlations that can maintain both the differential rotation and the meridional circulation. These convective motions can also influence solar activity directly by shaping the magnetic field pattern. While considerable theoretical advances have been made toward understanding these large scale flows, outstanding problems in matching theory to observations still remain.

Hathaway, D. H.↗

The sensitivity of various mode sets for probing differential rotation shear zones

The potential of future data sets from global oscillations network group (GONG) and solar oscillations investigation (SOI) for resolving long-lived azimuthal jets and shearing flows, is investigated. Various artificial data sets are constructed, containing noise resembling that of a one-year observation run. These are inverted using a two dimensional regularized least squares inversion. The ability of this method to form well localized averages of the rotation rate, as measured by the averaging kernels, is investigated using an extensive mode set and subsets. It is shown that it is possible to keep the noise in the solution down to a few nHz in much of the solar interior, while obtaining a reasonable resolution for a GONG-like data set. At low latitudes in the middle of the convection zone, an angular resolution of less than 10 deg and a radial resolution of about 0.04 solar radii, are obtained. The averaging kernels depend on the mode set, and a reduction in the number of modes tends to introduce small-scale near surface structures into the averaging kernels which would adversely affect the inferred rotation rate.

Christensen-Dalsgaard, Joergen↗