Theoretical Signature of Solar Meridional Flow in Global Seismic Data

Approximate expressions are derived for the perturbations in solar p- and f-mode oscillation eigenfunctions, due to large-scale, meridional flows which are symmetric about the equator. The essential signature of the perturbed eigenfunctions in global helioseismic data is derived and the prospects for detecting meridional flow using global seismic techniques are discussed.     

Solar-Cycle-Related Variations in the Solar Differential Rotation and Meridional Flow: A Comparison

We have analysed a large set of sunspot group data (1874 – 2004) and find that the meridional flow strongly varies with the phase of the solar cycle, and the variation is quite different in the northern and the southern hemispheres. We also find the existence of considerable cycle-to-cycle variation in the meridional velocity, and about a 11-year difference between the phases of the corresponding variations in the northern and the southern hemispheres. In addition, our analysis also indicates the following: (i) the existence of a considerable difference (about 180^°) between the phases of the solar-cycle variations in the latitude-gradient terms of the northern and the southern hemispheres’ rotations; (ii) the existence of correlation (good in the northern hemisphere and weak in the southern hemisphere) between the mean solar-cycle variations of meridional flow and the latitude-gradient term of solar rotation; (iii) in the northern hemisphere, the cycle-to-cycle variation of the mean meridional velocity leads that of the equatorial rotation rate by about 11 years, and the corresponding variations have approximately the same phase in the southern hemisphere; and (iv) the directions of the mean meridional velocity is largely toward the pole in the longer sunspot cycles and largely toward the equator in the shorter cycles.     

Meridional Circulation and Global Solar Oscillations

We investigate the influence of large-scale meridional circulation on solar p modes by quasi-degenerate perturbation theory, as proposed by Lavely and Ritzwoller (Roy. Soc. Lond. Phil. Trans. Ser. A 339, 431, 1992). As an input flow we use various models of stationary meridional circulation obeying the continuity equation. This flow perturbs the eigenmodes of an equilibrium model of the Sun. We derive the signatures of the meridional circulation in the frequency multiplets of solar p modes. In most cases the meridional circulation leads to negative average frequency shifts of the multiplets. Further possibly observable effects are briefly discussed.     

Subsurface Meridional Flow from HMI Using the Ring-Diagram Pipeline

We have determined the meridional flows in subsurface layers for 18 Carrington rotations (CR 2097 to 2114) analyzing high-resolution Dopplergrams obtained with the Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO). We are especially interested in flows at high latitudes up to 75^° in order to address the question whether the meridional flow remains poleward or reverses direction (so-called counter cells). The flows have been determined in depth from near-surface layers to about 16 Mm using the HMI ring-diagram pipeline. The measured meridional flows show systematic effects, such as a variation with the B ₀-angle and a variation with central meridian distance (CMD). These variations have been taken into account to lead to more reliable flow estimates at high latitudes. The corrected average meridional flow is poleward at most depths and latitudes with a maximum amplitude of about $20~\mathrm{m\,s}^{-1}$ near 37.5^° latitude. The flows are more poleward on the equatorward side of the mean latitude of magnetic activity at 22^° and less poleward on the poleward side, which can be interpreted as convergent flows near the mean latitude of activity. The corrected meridional flow is poleward at all depths within ±?67.5^° latitude. The corrected flow is equatorward only at 75^° latitude in the southern hemisphere at depths between about 4 and 8 Mm and at 75^° latitude in the northern hemisphere only when the B ₀ angle is barely large enough to measure flows at this latitude. These counter cells are most likely the remains of an insufficiently corrected B ₀-angle variation and not of solar origin. Flow measurements and B ₀-angle corrections are difficult at the highest latitude because these flows are only determined during limited periods when the B ₀ angle is sufficiently large.     

Solar Extreme Ultraviolet Irradiance Measurements During Solar Cycle 22

The solar extreme ultraviolet (EUV) irradiance, the dominant global energy source for Earth's atmosphere above 100 km, is not known accurately enough for many studies of the upper atmosphere. During the absence of direct solar EUV irradiance measurements from satellites, the solar EUV irradiance is often estimated at the 30–50% uncertainty level using both proxies of the solar irradiance and earlier solar EUV irradiance measurements, primarily from the Air Force Geophysics Laboratory (now Phillips Laboratory) rockets and Atmospheric Explorer (AE) instruments. Our sounding rocket measurements during solar cycle 22 include solar EUV irradiances below 120 nm with 0.2 nm spectral resolution, far ultraviolet (FUV) airglow spectra below 160 nm, and solar soft X-ray (XUV) images at 17.5 nm. Compared to the earlier observations, these rocket experiments provide a more accurate absolute measurement of the solar EUV irradiance, because these instruments are calibrated at the National Institute of Standards and Technology (NIST) with a radiometric uncertainty of about 8%. These more accurate sounding-rocket measurements suggest revisions of the previous reference AE–E spectra by as much as a factor of 2 at some wavelengths. Our sounding-rocket flights during the past several years (1988–1994) also provide information about solar EUV variability during solar cycle 22.     

Subsurface Zonal and Meridional Flow During Cycles 23 and 24

We study the solar-cycle variation of subsurface flows from the surface to a depth of 16 Mm. We have used ring-diagram analysis to analyze Dopplergrams obtained with the Michelson Doppler Imager (MDI) Dynamics Program, the Global Oscillation Network Group (GONG), and the Helioseismic and Magnetic Imager (HMI) instrument. We combined the zonal and meridional flows from the three data sources and scaled the flows derived from MDI and GONG to match those from HMI observations. In this way, we derived their temporal variation in a consistent manner for Solar Cycles 23 and 24. We have corrected the measured flows for systematic effects that vary with disk positions. Using time-depth slices of the corrected subsurface flows, we derived the amplitudes and times of the extrema of the fast and slow zonal and meridional flows during Cycles 23 and 24 at every depth and latitude. We find an average difference between maximum and minimum amplitudes of \(8.6 \pm0.4~\mbox{m}\,\mbox{s}^{-1}\) for the zonal flows and \(7.9 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the meridional flows associated with Cycle 24 averaged over a depth range from 2 to 12 Mm. The corresponding values derived from GONG data alone are \(10.5 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the zonal and \(10.8 \pm0.3~\mbox{m}\,\mbox{s}^{-1}\) for the meridional flow. For Cycle 24, the flow patterns are precursors of the magnetic activity. The timing difference between the occurrence of the flow pattern and the magnetic one increases almost linearly with increasing latitude. For example, the fast zonal and meridional flow appear \(2.1 \pm 0.6\) years and \(2.5\pm 0.6\) years, respectively, before the magnetic pattern at \(30^{\circ}\) latitude in the northern hemisphere, while in the southern hemisphere, the differences are \(3.2 \pm 1.2\) years and \(2.6 \pm 0.6\) years. The flow patterns of Cycle 25 are present and have reached \(30^{\circ}\) latitude. The amplitude differences of Cycle 25 are about 22% smaller than those of Cycle 24, but are comparable to those of Cycle 23. Moreover, polynomial fits of meridional flows suggest that equatorward meridional flows (counter-cells) might exist at about \(80^{\circ}\) latitude except during the declining phase of the solar cycle.     

Solar Variability Induced in a Dynamo Code by Realistic Meridional Circulation Variations

In this work we use an already-published method to infer a variation profile for the solar meridional circulation over the last 250 years. We feed this variation profile into a numerical dynamo code, and we reconstruct a sunspot time series that acts as a proxy for solar cycle activity. We perform three simulations with slightly different parameters, and the results are compared with the observational data. The medium and large correlation coefficients between reconstructed and observational time series seem to indicate that variations in meridional circulation play an important role in the modulation of solar activity.     

Observation and Modeling of the Solar-Cycle Variation of the Meridional Flow

We present independent observations of the solar-cycle variation of flows near the solar surface and at a depth of about 60 Mm, in the latitude range ±?45°. We show that the time-varying components of the meridional flow at these two depths have opposite sign, whereas the time-varying components of the zonal flow are in phase. This is in agreement with previous results. We then investigate whether the observations are consistent with a theoretical model of solar-cycle-dependent meridional circulation based on a flux-transport dynamo combined with a geostrophic flow caused by increased radiative loss in the active region belt (the only existing quantitative model). We find that the model and the data are in qualitative agreement, although the amplitude of the solar-cycle variation of the meridional flow at 60 Mm is underestimated by the model.     

Solar Coronal Plasma in Doppler Measurements

Doppler tracking of an interplanetary spacecraft near solar conjunction is strongly affected by the plasma in the solar corona, the main competitive contribution in measurements of the gravitational deflection of light rays. With the simultaneous availability of carriers in X band and K_a band for interplanetary communications, the plasma contribution to the corona can be accurately eliminated and measured. If, as in the Cassini mission, three different observables are available, this can be done in two ways: one deals with the total plasma content in the electric approximation, even in the ionosphere and interplanetary space; another is limited to the corona, but has access to subtler effects, like the magnetic correction to the refractive index. This technique will allow important progress in the radio investigation of the solar corona.     

Seeing-Induced Errors in Solar Doppler Velocity Measurements

Imaging systems based on a narrow-band tunable filter are used to obtain Doppler velocity maps of solar features. These velocity maps are created by taking the difference between the blue- and red-wing intensity images of a chosen spectral line. This method has the inherent assumption that these two images are obtained under identical conditions. With the dynamical nature of the solar features as well as the Earth’s atmosphere, systematic errors can be introduced in such measurements. In this paper, a quantitative estimate of the errors introduced due to variable seeing conditions for ground-based observations is simulated and compared with real observational data for identifying their reliability. It is shown, under such conditions, that there is a strong cross-talk from the total intensity to the velocity estimates. These spurious velocities are larger in magnitude for the umbral regions compared to the penumbra or quiet-Sun regions surrounding the sunspots. The variable seeing can induce spurious velocities up to about 1 km s⁻¹. It is also shown that adaptive optics, in general, helps in minimising this effect.     

ICME Identification from Solar Wind Ion Measurements

Interplanetary coronal mass ejections (ICMEs), the interplanetary counterpart of coronal mass ejections (CMEs), are most commonly identified by their enhanced magnetic field strengths and rotating magnetic field orientation. However, there are other frequent signatures in the plasma. We use a pair of these signatures, a linearly decreasing plasma bulk velocity and a cool (< 20 km s⁻¹) ion thermal speed, to identify candidate ICMEs. Many ICMEs, identified through their magnetic signatures, are also found by their ion signatures alone. However, many are not. These missed ICMEs appear not to be expanding, even when they are accompanied by leading shocks. The ICMEs with both the magnetic and ion signatures appear to be expanding as judged from either set of observations. The most clearly defined ICMEs have transit times from the Sun and growth times to the observed size that are equal. These ropes fit the paradigm of compact magnetic structures arising low in the corona and expanding uniformly in time, as they travel at constant center of mass speed toward 1 AU.     

On Short-Term Periodicity of the Solar Radius Measurements

The aim of the present study is to investigate the short-term periodicity in the solar radius measurements and to compare with the short periods in sunspot numbers, sunspot areas and flare index data. The spectral analysis of data sets covering a time interval from 26 February 2000 to 26 October 2007 during Solar Cycle 23 were made by using the Date Compensated Discrete Fourier Transform (DCDFT). The power spectrum of solar radius data corrected for the seeing effect gives an evident peak at 25.7 days with the amplitude of 0.034 arcsec, which is slightly different from the peaks of 26.2 and 26.7 days produced by sunspot numbers and sunspot areas data, respectively. Besides, the main peak of 25.7 days detected in the power spectrum of solar radius data is in agreement with the period of 25.5 days, suggested to be the fundamental period of the Sun by Bai and Sturrock (in Nature 350, 141, 1991).     

SUMER - Solar Ultraviolet Measurements of Emitted Radiation

The instrument SUMER - Solar Ultraviolet Measurements of Emitted Radiation is designed to investigate structures and associated dynamical processes occurring in the solar atmosphere, from the chromosphere through the transition region to the inner corona, over a temperature range from 10⁴ to 2 × 10⁶ K and above. These observations will permit detailed spectroscopic diagnostics of plasma densities and temperatures in many solar features, and will support penetrating studies of underlying physical processes, including plasma flows, turbulence and wave motions, diffusion transport processes, events associated with solar magnetic activity, atmospheric heating, and solar wind acceleration in the inner corona. Specifically, SUMER will measure profiles and intensities of EUV lines; determine Doppler shifts and line broadenings with high accuracy; provide stigmatic images of the Sun in the EUV with high spatial, spectral, and temporal resolution; and obtain monochromatic maps of the full Sun and the inner corona or selected areas thereof. SUMER will be flown on the Solar and Heliospheric Observatory (SOHO), scheduled for launch in November, 1995. This paper has been written to familiarize solar physicists with SUMER and to demonstrate some command procedures for achieving certain scientific observations.     

Long Term Evolution of Solar Meridional Circulation and Phase Synchronization Viewed Through a Symmetrical Kuramoto Model

The solar-cycle oscillations of the toroidal and poloidal components of the solar magnetic field in the northern solar hemisphere have a persistent phase difference of about \(\pi \). We propose a symmetrical Kuramoto model with three coupled oscillators as a simple way to understand this anti-synchronization. We solve an inverse problem and reconstruct natural frequencies of the top and bottom oscillators under the conditions of a constant coupling strength and a non-delayed coupling. These natural frequencies are associated with angular velocities of the meridional flow circulation near the solar surface and in the deep layer of the solar convection zone. A relationship between our reconstructions of the shallow and the deep meridional flow speed during recent Solar Cycles 21?–?23 is in agreement with estimates obtained in helioseismology and flux-transport dynamo modeling. The reconstructed top oscillator speed presents significant solar-cycle like variations that agree with recent helioseismical reconstructions. The evolution of reconstructed natural frequencies strongly depends on the coupling strength. We find two stable regimes in the case of strong coupling with a change of regime during anomalous solar cycles. We see the onset of a new transition in Solar Cycle 24. We estimate the admitted range of coupling values and find evidence of cross-equatorial coupling between solar hemispheres not accounted for by the model.     

Pioneer Venus Orbiter Measurements of Solar EUV Flux During Solar Cycles 21 and 22

The Pioneer Venus Orbiter (PVO) had on board the electron temperature probe experiment which measured temperature and concentration of electrons in the ionosphere of Venus. When the probe was outside the Venus ionosphere and was in the solar wind, the probe current was entirely due to solar photons striking the probe surface. This probe thus measured integrated solar EUV flux (Ipe) over a 13-year period from January 1979 to December 1991, thereby covering the declining phase of solar cycle 21 and the rising phase of solar cycle 22. In this paper, we examine the behavior of Ipe translated to the solar longitude of Earth (to be called EIpe) during the two solar cycles. We find that total EUV flux changed by about 60% during solar cycle 21 and by about 100% in solar cycle 22. We also compare this flux with other solar activity indicators such as F_10.7 , Lα, and the solar magnetic field. We find that while the daily values of EIpe are highly correlated with F_10.7 (correlation coefficient 0.87), there is a large scatter in EIpe for any value of this Earth-based index. A comparison of EIpe with SME and UARS SOLSTICE Lα measurements taken during the same period shows that EIpe tracks Lα quite faithfully with a correlation coefficient of 0.94. Similar comparison with the solar magnetic field (Bs) shows that EIpe correlates better with Bs than with F_10.7 . We also compare EIpe with total solar irradiance measured during the same period.     

Solar Wind Electron Parameters from Ulysses/URAP Quasi-Thermal Noise Measurements at Solar Maximum

We present the solar wind plasma parameters obtained from the Ulysses spacecraft during its second pole-to-pole fast latitude scan near the 2001 solar maximum. We study the solar wind properties from the electron density and core temperature measurements made by the radio receiver on Ulysses using the method of quasi-thermal noise spectroscopy. We analyze these parameters as functions of heliographic latitude and distance. We present their histograms normalized to 1 AU and find a bimodal distribution for the electron core temperature. The cooler population can be associated with the fast wind flow emanating from coronal holes present at various latitudes. We discuss a slight north/south asymmetry found for the electron density. Finally, we compare the present results to those obtained during the 1996 solar minimum and 1991 solar maximum.     

Measurements of Frequencies of Solar Oscillations from the Mdi Medium-l Program

Inversions of solar internal structure employ both the frequencies and the associated uncertainties of the solar oscillation modes as input parameters. In this paper we investigate how systematic errors in these input parameters may affect the resulting inferences of the sun's internal structure. Such systematic errors are likely to arise from inaccuracies in the theoretical models which are used to represent the spectral lines in the observational power spectra, from line blending, from asymmetries in the profiles of these lines, and from other factors. In order to study such systematic effects we have employed two different duration observing runs (one of 60 days and the second of 144 days) obtained with the Medium-l Program of the Michelson Doppler Imager experiment onboard the SOHO spacecraft. This observing program provides continuous observations of solar oscillation modes having angular degrees, l, ranging from 0 to ∼ 300. For this study intermediate- and high-degree p-mode oscillations having degrees less than 251 were employed. In the first of our tests we employed two different methods of estimating the modal frequencies and their associated uncertainties from the 144-day observational power spectra. In our second test we also repeated both methods of frequency estimation on the 60-day time series in order to assess the influence of the duration of the observed time series on the computed frequencies and uncertainties. In a third test we investigated the sensitivity of the computed frequencies to the choice of initial-guess, or ‘seed’ frequencies that are used in the frequency estimation codes. In a fourth test we attempted to investigate the possible systematic frequency errors which are introduced when the observational asymmetry in the p-mode peaks is ignored. We carried out this particular test by fitting simple models of asymmetric line profiles to the peaks in the observational power spectra. We were then able to compute the differences between those frequencies and our previous frequencies which had been obtained using the assumption that all of the observational peaks were symmetric in shape. In order to study the possible influence of the two different frequency estimation methods upon the radial profile of the internal sound speed, we carried out four parallel structural inversions using the different sets and subsets of frequency estimates and uncertainties as computed from the 144-day observing run as inputs. The results of these four inversions confirm the previous finding by the GONG project (Gough et al., 1996) and by the MDI Medium-l Program (Kosovichev et al., 1997) that, in a thin layer just beneath the convection zone, helium appears to be less abundant than predicted by theory. However, differences in our four inverted radial sound speed profiles demonstrate that the currently-available techniques for determining the frequencies of the Medium-l oscillation peaks introduce systematic errors which are large enough to affect the results of the structural inversions. Moreover, based upon the differences in these four inverted sound speed profiles, it appears that the choice of which subset of modes is included in a particular inversion and which modes are not included may also be introducing systematic errors into our current understanding of solar internal structure. Hence, it appears to be very important that consistent sets of modal selection criteria be employed. Finally, at least one of the two frequency estimation codes which we used was not sensitive to changes in the input ‘seed’ frequencies which were employed as initial guesses for that code. This result allays fears that the difference in the helium abundance between the sun and the reference solar model in the thin layer beneath the convection zone which was mentioned above might have been due to the particular seed frequencies which were employed in the earlier inversions. Since this thin layer may likely be the place where the solar dynamo operates, it will be extremely important to observe any possible evolution of this transition layer throughout the upcoming 11-year activity cycle. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1004963425123     

Comparative Analyses of Brookhaven National Laboratory Nuclear Decay Measurements and Super-Kamiokande Solar Neutrino Measurements: Neutrinos and Neutrino-Induced Beta-Decays as Probes of the Deep Solar Interior

An experiment carried out at the Brookhaven National Laboratory over a period of almost 8 years acquired 364 measurements of the beta-decay rates of a sample of \({}^{32}\mbox{Si}\) and, for comparison, of a sample of \({}^{36}\mbox{Cl}\). The experimenters reported finding “small periodic annual deviations of the data points from an exponential decay?…?of uncertain origin”. We find that power-spectrum and spectrogram analyses of these datasets show evidence not only of the annual oscillations, but also of transient oscillations with frequencies near 11 year^?1 and 12.5 year^?1. Similar analyses of 358 measurements of the solar neutrino flux acquired by the Super-Kamiokande neutrino observatory over a period of about 5 years yield evidence of an oscillation near 12.5 year^?1 and another near 9.5 year^?1. An oscillation near 12.5 year^?1 is compatible with the influence of rotation of the radiative zone. We suggest that an oscillation near 9.5 year^?1 may be indicative of rotation of the solar core, and that an oscillation near 11 year^?1 may have its origin in a tachocline between the core and the radiative zone. Modulation of the solar neutrino flux may be attributed to an influence of the Sun’s internal magnetic field by the Resonant Spin Flavor Precession (RSFP) mechanism, suggesting that neutrinos and neutrino-induced beta decays can provide information about the deep solar interior.