The origin of grand minima in the sunspot cycle

One of the most striking aspects of the 11-year sunspot cycle is that there have been times in the past when some cycles went missing, a most well-known example of this being the Maunder minimum during 1645-1715. Analyses of cosmogenic isotopes (C14 and Be10) indicated that there were about 27 grand minima in the last 11,000 yr, implying that about 2.7% of the solar cycles had conditions appropriate for forcing the Sun into grand minima. We address the question how grand minima are produced and specifically calculate the frequency of occurrence of grand minima from a theoretical dynamo model. We assume that fluctuations in the poloidal field generation mechanism and the meridional circulation produce irregularities of sunspot cycles. Taking these fluctuations to be Gaussian and estimating the values of important parameters from the data of last 28 solar cycles, we show from our flux transport dynamo model that about 1-4% of the sunspot cycles may have conditions suitable for inducing grand minima.Comment: Accepted for publication in Physical Review Letter

The Origin of Solar Activity in the Tachocline

Solar active regions, produced by the emergence of tubes of strong magnetic field in the photosphere, are restricted to within 35 degrees of the solar equator. The nature of the dynamo processes that create and renew these fields, and are therefore responsible for solar magnetic phenomena, are not well understood. We analyze the magneto-rotational stability of the solar tachocline for general field geometry. This thin region of strong radial and latitudinal differential rotation, between the radiative and convective zones, is unstable at latitudes above 37 degrees, yet is stable closer to the equator. We propose that small-scale magneto-rotational turbulence prevents coherent magnetic dynamo action in the tachocline except in the vicinity of the equator, thus explaining the latitudinal restriction of active regions. Tying the magnetic dynamo to the tachocline elucidates the physical conditions and processes relevant to solar magnetism.Comment: 10 pages, 1 figure, accepted for publication in ApJ

Interpolation Properties and SAT-based Model Checking

Craig interpolation is a widespread method in verification, with important applications such as Predicate Abstraction, CounterExample Guided Abstraction Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model checking techniques based on interpolation require collections of interpolants to satisfy particular properties, to which we refer as "collectives"; they do not hold in general for all interpolation systems and have to be established for each particular system and verification environment. Nevertheless, no systematic approach exists that correlates the individual interpolation systems and compares the necessary collectives. This paper proposes a uniform framework, which encompasses (and generalizes) the most common collectives exploited in verification. We use it for a systematic study of the collectives and of the constraints they pose on propositional interpolation systems used in SAT-based model checking

Lifting CDCL to template-based abstract domains for program verification

The success of Conflict Driven Clause Learning (CDCL) for Boolean satisfiability has inspired adoption in other domains. We present a novel lifting of CDCL to program analysis called Abstract Conflict Driven Learning for Programs (ACDLP). ACDLP alternates between model search, which performs over-approximate deduction with constraint propagation, and conflict analysis, which performs under-approximate abduction with heuristic choice. We instantiate the model search and conflict analysis algorithms with an abstract domain of template polyhedra, strictly generalizing CDCL from the Boolean lattice to a richer lattice structure. Our template polyhedra can express intervals, octagons and restricted polyhedral constraints over program variables. We have implemented ACDLP for automatic bounded safety verification of C programs. We evaluate the performance of our analyser by comparing with CBMC, which uses Boolean CDCL, and Astrée, a commercial abstract interpretation tool. We observe two orders of magnitude reduction in the number of decisions, propagations, and conflicts as well as a 1.5x speedup in runtime compared to CBMC. Compared to Astrée, ACDLP solves twice as many benchmarks and has much higher precision. This is the first instantiation of CDCL with a template polyhedra abstract domain

The Magnetic Sun: Reversals and Long-Term Variations

A didactic introduction to current thinking on some aspects of the solar dynamo is given for geophysicists and planetary scientists.Comment: 17 pages, 9 figures; Space Science Rev., in pres

A Comparison of Solar Cycle Variations in the Equatorial Rotation Rates of the Sun's Subsurface, Surface, Corona, and Sunspot Groups

Using the Solar Optical Observing Network (SOON) sunspot-group data for the period 1985-2010, the variations in the annual mean equatorial-rotation rates of the sunspot groups are determined and compared with the known variations in the solar equatorial-rotation rates determined from the following data: i) the plasma rotation rates at 0.94Rsun, 0.95Rsun,...,1.0Rsun measured by Global Oscillation Network Group (GONG) during the period 1995-2010, ii) the data on the soft X-ray corona determined from Yohkoh/SXT full disk images for the years 1992-2001, iii) the data on small bright coronal structures (SBCS) which were traced in Solar and Heliospheric Observatory (SOHO)/EIT images during the period 1998-2006, and iv) the Mount Wilson Doppler-velocity measurements during the period 1986-2007. A large portion (up to approximate 30 deg latitude) of the mean differential-rotation profile of the sunspot groups lies between those of the internal differential-rotation rates at 0.94Rsun and 0.98Rsun.The variation in the yearly mean equatorial-rotation rate of the sunspot groups seems to be lagging that of the equatorial-rotation rate determined from the GONG measurements by one to two years.The amplitude of the latter is very small.The solar-cycle variation in the equatorial-rotation rate of the solar corona closely matches that determined from the sunspot-group data.The variation in the equatorial-rotation rate determined from the Mount Wilson Doppler-velocity data closely resembles the corresponding variation in the equatorial-rotation rate determined from the sunspot-group data that included the values of the abnormal angular motions (> 3 deg per day) of the sunspot groups. Implications of these results are pointed out.Comment: 22 pages, 10 figures, accepted by Solar Physic

Seismology of the Sun : Inference of Thermal, Dynamic and Magnetic Field Structures of the Interior

Recent overwhelming evidences show that the sun strongly influences the Earth's climate and environment. Moreover existence of life on this Earth mainly depends upon the sun's energy. Hence, understanding of physics of the sun, especially the thermal, dynamic and magnetic field structures of its interior, is very important. Recently, from the ground and space based observations, it is discovered that sun oscillates near 5 min periodicity in millions of modes. This discovery heralded a new era in solar physics and a separate branch called helioseismology or seismology of the sun has started. Before the advent of helioseismology, sun's thermal structure of the interior was understood from the evolutionary solution of stellar structure equations that mimicked the present age, mass and radius of the sun. Whereas solution of MHD equations yielded internal dynamics and magnetic field structure of the sun's interior. In this presentation, I review the thermal, dynamic and magnetic field structures of the sun's interior as inferred by the helioseismology.Comment: To be published in the proceedings of the meeting "3rd International Conference on Current Developments in Atomic, Molecular, Optical and Nano Physics with Applications", December 14-16, 2011, New Delhi, Indi

Active region formation through the negative effective magnetic pressure instability

The negative effective magnetic pressure instability operates on scales encompassing many turbulent eddies and is here discussed in connection with the formation of active regions near the surface layers of the Sun. This instability is related to the negative contribution of turbulence to the mean magnetic pressure that causes the formation of large-scale magnetic structures. For an isothermal layer, direct numerical simulations and mean-field simulations of this phenomenon are shown to agree in many details in that their onset occurs at the same depth. This depth increases with increasing field strength, such that the maximum growth rate of this instability is independent of the field strength, provided the magnetic structures are fully contained within the domain. A linear stability analysis is shown to support this finding. The instability also leads to a redistribution of turbulent intensity and gas pressure that could provide direct observational signatures.Comment: 19 pages, 10 figures, submitted to Solar Physic

Photospheric and Subphotospheric Dynamics of Emerging Magnetic Flux

Magnetic fields emerging from the Sun's interior carry information about physical processes of magnetic field generation and transport in the convection zone. Soon after appearance on the solar surface the magnetic flux gets concentrated in sunspot regions and causes numerous active phenomena on the Sun. This paper discusses some properties of the emerging magnetic flux observed on the solar surface and in the interior. A statistical analysis of variations of the tilt angle of bipolar magnetic regions during the emergence shows that the systematic tilt with respect to the equator (the Joy's law) is most likely established below the surface. However, no evidence of the dependence of the tilt angle on the amount of emerging magnetic flux, predicted by the rising magnetic flux rope theories, is found. Analysis of surface plasma flows in a large emerging active region reveals strong localized upflows and downflows at the initial phase of emergence but finds no evidence for large-scale flows indicating future appearance a large-scale magnetic structure. Local helioseismology provides important tools for mapping perturbations of the wave speed and mass flows below the surface. Initial results from SOHO/MDI and GONG reveal strong diverging flows during the flux emergence, and also localized converging flows around stable sunspots. The wave speed images obtained during the process of formation of a large active region, NOAA 10488, indicate that the magnetic flux gets concentrated in strong field structures just below the surface. Further studies of magnetic flux emergence require systematic helioseismic observations from the ground and space, and realistic MHD simulations of the subsurface dynamics.Comment: 21 pages, 15 figures, to appear in Space Science Review