Large-scale horizontal flows in the solar photosphere II: Long-term behaviour and magnetic activity response

Recently, we have developed a method useful for mapping large-scale horizontal velocity fields in the solar photosphere. The method was developed, tuned and calibrated using the synthetic data. Now, we applied the method to the series of Michelson Doppler Imager (MDI) dopplergrams covering almost one solar cycle in order to get the information about the long-term behaviour of surface flows. We have found that our method clearly reproduces the widely accepted properties of mean flow field components, such as torsional oscillations and a pattern of meridional circulation. We also performed a periodic analysis, however due to the data series length and large gaps we did not detect any significant periods. The relation between the magnetic activity influencing the mean zonal motion is studied. We found an evidence that the emergence of compact magnetic regions locally accelerates the rotation of supergranular pattern in their vicinity and that the presence of magnetic fields generally decelerates the rotation in the equatorial region. Our results show that active regions in the equatorial region emerge exhibiting a constant velocity (faster by 60 +/- 9 m/s than Carrington rate) suggesting that they emerge from the base of the surface radial shear at 0.95 R_sun, disconnect from their magnetic roots, and slow down during their evolution.Comment: 9 pages, 8 figures, accepted for publication in Astronomy & Astrophysic

Fundamental Physics and General Relativity with the LARES and LAGEOS satellites

Current observations of the universe have strengthened the interest to further test General Relativity and other theories of fundamental physics. After an introduction to the phenomenon of frame-dragging predicted by Einstein's theory of General Relativity, with fundamental astrophysical applications to rotating black holes, we describe the past measurements of frame-dragging obtained by the LAGEOS satellites and by the dedicated Gravity Probe B space mission. We also discuss a test of String Theories of Chern-Simons type that has been carried out using the results of the LAGEOS satellites. We then describe the LARES space experiment. LARES was successfully launched in February 2012 to improve the accuracy of the tests of frame-dragging, it can also improve the test of String Theories. We present the results of the first few months of observations of LARES, its orbital analyses show that it has the best agreement of any other satellite with the test-particle motion predicted by General Relativity. We finally briefly report the accurate studies and the extensive simulations of the LARES space experiment, confirming an accuracy of a few percent in the forthcoming measurement of frame-dragging.Comment: To be publihed in Nuclear Physics. arXiv admin note: substantial text overlap with arXiv:1306.1826, arXiv:1211.137

Comparison of the sidereal angular velocity of subphotospheric layers and small bright coronal structures during the declining phase of solar cycle 23

Context. We compare solar differential rotation of subphotospheric layers derived from local helioseismology analysis of GONG++ dopplergrams and the one derived from tracing small bright coronal structures (SBCS) using EIT/SOHO images for the period August 2001 - December 2006, which correspond to the declining phase of solar cycle 23. Aims. The study aims to find a relationship between the rotation of the SBCS and the subphotospheric angular velocity. The northsouth asymmetries of both rotation velocity measurements are also investigated. Methods. Subphotospheric differential rotation was derived using ring-diagram analysis of GONG++ full-disk dopplergrams of 1 min cadence. The coronal rotation was derived by using an automatic method to identify and track the small bright coronal structures in EIT full-disk images of 6 hours cadence. Results. We find that the SBCS rotate faster than the considered upper subphotospheric layer (3Mm) by about 0.5 deg/day at the equator. This result joins the results of several other magnetic features (sunspots, plages, faculae, etc.) with a higher rotation than the solar plasma. The rotation rate latitudinal gradients of the SBCS and the subphotospheric layers are very similar. The SBCS motion shows an acceleration of about 0.005 deg/day/month during the declining phase of solar cycle 23, whereas the angular velocity of subsurface layers does not display any evident variation with time, except for the well known torsional oscillation pattern. Finally, both subphotospheric and coronal rotations of the southern hemisphere are predominantly larger than those of the northern hemisphere. At latitudes where the north-south asymmetry of the angular velocity increases (decreases) with activity for the SBCS, it decreases (increases) for subphotospheric layers.Comment: 6pages, 8 figures, Accepted for publication in Astronomy and Astrophysic

Partial-reflection studies of D-region winter variability

D-region electron densities were measured from December, 1972, to July, 1973, at Urbana, Illinois (latitude 40.2N) using the partial-reflection technique. During the winter, electron densities at altitudes of 72, 76.5, and 81 km show cyclical changes with a period of about 5 days that are highly correlated between these altitudes, suggesting that the mechanism responsible for the winter anomaly in D-region ionization applies throughout this height region. From January 13 to February 3, a pronounced wave-like variation occurred in the partial-reflection measurements, apparently associated with a major stratospheric warming that developed in that period. During the same time period, a traveling periodic variation is observed in the 10-mb height; it is highly correlated with the partial-reflection measurements. Electron density enhancements occur approximately at the same time as increases in the 10-mb height. Comparison of AL and A3 absorption measurements with electron density measurements below 82 km indicates that the winter anomaly in D-region ionization is divided into two types. Type 1, above about 82 km, extends horizontally for about 200 km while type 2, below about 82 km, extends for a horizontal scale of at least 1000 km

Approximation by non-symmetric networks for cross-domain learning

For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks, radial basis function networks, and a variety of kernel based methods. Motivated by applications such as invariant learning, transfer learning, and synthetic aperture radar imaging, we initiate in this paper a general approach to study the approximation capabilities of kernel based networks using non-symmetric kernels. While singular value decomposition is a natural instinct to study such kernels, we consider a more general approach to include the use of a family of kernels, such as generalized translation networks (which include neural networks and translation invariant kernels as special cases) and rotated zonal function kernels. Naturally, unlike traditional kernel based approximation, we cannot require the kernels to be positive definite. In particular, we obtain estimates on the accuracy of uniform approximation of functions in a ($L^2$)-Sobolev class by ReLU$^r$ networks when $r$ is not necessarily an integer. Our general results apply to the approximation of functions with small smoothness compared to the dimension of the input space

Measuring the Lense-Thirring precession using a second Lageos satellite

A complete numerical simulation and error analysis was performed for the proposed experiment with the objective of establishing an accurate assessment of the feasibility and the potential accuracy of the measurement of the Lense-Thirring precession. Consideration was given to identifying the error sources which limit the accuracy of the experiment and proposing procedures for eliminating or reducing the effect of these errors. Analytic investigations were conducted to study the effects of major error sources with the objective of providing error bounds on the experiment. The analysis of realistic simulated data is used to demonstrate that satellite laser ranging of two Lageos satellites, orbiting with supplemental inclinations, collected for a period of 3 years or more, can be used to verify the Lense-Thirring precession. A comprehensive covariance analysis for the solution was also developed

Latitudinal extension of low-latitude scintillations measured with a network of GPS receivers

International audienceA latitudinal-distributed network of GPS receivers has been operating within Colombia, Peru and Chile with sufficient latitudinal span to measure the absolute total electron content (TEC) at both crests of the equatorial anomaly. The network also provides the latitudinal extension of GPS scintillations and TEC depletions. The GPS-based information has been supplemented with density profiles collected with the Jicamarca digisonde and JULIA power maps to investigate the background conditions of the nighttime ionosphere that prevail during the formation and the persistence of plasma depletions. This paper presents case-study events in which the latitudinal extension of GPS scintillations, the maximum latitude of TEC depletion detections, and the altitude extension of radar plumes are correlated with the location and extension of the equatorial anomaly. Then it shows the combined statistics of GPS scintillations, TEC depletions, TEC latitudinal profiles, and bottomside density profiles collected between September 2001 and June 2002. It is demonstrated that multiple sights of TEC depletions from different stations can be used to estimate the drift of the background plasma, the tilt of the plasma plumes, and in some cases even the approximate time and location of the depletion onset. This study corroborates the fact that TEC depletions and radar plumes coincide with intense levels of GPS scintillations. Bottomside radar traces do not seem to be associated with GPS scintillations. It is demonstrated that scintillations/depletions can occur when the TEC latitude profiles are symmetric, asymmetric or highly asymmetric; this is during the absence of one crest. Comparison of the location of the northern crest of the equatorial anomaly and the maximum latitude of scintillations reveals that for 90% of the days, scintillations are confined within the boundaries of the 50% decay limit of the anomaly crests. The crests of the anomaly are the regions where the most intense GPS scintillations and the deepest TEC depletions are encountered. In accord with early results, we observe that GPS scintillations/TEC depletions mainly occur when the altitude of the magnetic equator F-region is above 500km. Nevertheless, in many instances GPS scintillations and TEC depletions are observed to exist when the F-layer is well below 500km or to persist when the F-layer undergoes its typical nighttime descent. Close inspection of the TEC profiles during scintillations/depletions events that occur when the equatorial F-layer peak is below 500km altitude reveals that on these occasions the ratio of the crest-to-equator TEC is above 2, and the crests are displaced 10° or more from the magnetic equator. When the equatorial F-layer is above 500km, neither of the two requirements is needed, as the flux tube seems to be inherently unstable. We discuss these findings in terms of the Rayleigh-Taylor instability (RTI) mechanism for flux-tube integrated quantities. We advance the idea that the seeming control that the reverse fountain effect exerts on inhibiting or suppressing GPS scintillations may be related to the redistribution of the density and plasma transport from the crests of the anomaly toward the equatorial region and then to much lower altitudes, and the simultaneous decrease of the F-region altitude. These two effects originate a decrease in the crest/trough ratio and a reduction of the crests separation, making the whole flux tube more stable to the RTI. The correspondence between crest separation, altitude of the equatorial F-region, the onset of depletions, and the altitude (latitude) extension of plumes (GPS scintillations) can be used to track the fate of the density structures

Tight p-fusion frames

Fusion frames enable signal decompositions into weighted linear subspace components. For positive integers p, we introduce p-fusion frames, a sharpening of the notion of fusion frames. Tight p-fusion frames are closely related to the classical notions of designs and cubature formulas in Grassmann spaces and are analyzed with methods from harmonic analysis in the Grassmannians. We define the p-fusion frame potential, derive bounds for its value, and discuss the connections to tight p-fusion frames