Buildup of Magnetic Shear and Free Energy During Flux Emergence and Cancellation

We examine a simulation of flux emergence and cancellation, which shows a complex sequence of processes that accumulate free magnetic energy in the solar corona essential for the eruptive events such as coronal mass ejections (CMEs), filament eruptions and flares. The flow velocity at the surface and in the corona shows a consistent shearing pattern along the polarity inversion line (PIL), which together with the rotation of the magnetic polarities, builds up the magnetic shear. Tether-cutting reconnection above the PIL then produces longer sheared magnetic field lines that extend higher into the corona, where a sigmoidal structure forms. Most significantly, reconnection and upward energy-flux transfer are found to occur even as magnetic flux is submerging and appears to cancel at the photosphere. A comparison of the simulated coronal field with the corresponding coronal potential field graphically shows the development of nonpotential fields during the emergence of the magnetic flux and formation of sunspots

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Abundance of moderate-redshift clusters in the Cold + Hot dark matter model

Using a set of \pppm simulation which accurately treats the density evolution of two components of dark matter, we study the evolution of clusters in the Cold + Hot dark matter (CHDM) model. The mass function, the velocity dispersion function and the temperature function of clusters are calculated for four different epochs of $z\le 0.5$. We also use the simulation data to test the Press-Schechter expression of the halo abundance as a function of the velocity dispersion $\sigma_v$. The model predictions are in good agreement with the observational data of local cluster abundances ($z=0$). We also tentatively compare the model with the Gunn and his collaborators' observation of rich clusters at $z\approx 0.8$ and with the x-ray luminous clusters at $z\approx 0.5$ of the {\it Einstein} Extended Medium Sensitivity Survey. The important feature of the model is the rapid formation of clusters in the near past: the abundances of clusters of \sigma_v\ge 700\kms and of \sigma_v\ge 1200 \kms at $z=0.5$ are only 1/4 and 1/10 respectively of the present values ($z=0$). Ongoing ROSAT and AXAF surveys of distant clusters will provide sensitive tests to the model. The abundance of clusters at $z\approx 0.5$ would also be a good discriminator between the CHDM model and a low-density flat CDM model both of which show very similar clustering properties at $z=0$.Comment: 21 pages + 6 figures (uuencoded version of the PS files), Steward Preprints No. 118

Constraining Dark Energy by Combining Cluster Counts and Shear-Shear Correlations in a Weak Lensing Survey

We study the potential of a large future weak-lensing survey to constrain dark energy properties by using both the number counts of detected galaxy clusters (sensitive primarily to density fluctuations on small scales) and tomographic shear-shear correlations (restricted to large scales). We use the Fisher matrix formalism, assume a flat universe and parameterize the equation of state of dark energy by w(a)=w_0+w_a(1-a), to forecast the expected statistical errors from either observable, and from their combination. We show that the covariance between these two observables is small, and argue that therefore they can be regarded as independent constraints. We find that when the number counts and the shear-shear correlations (on angular scales l < 1000) are combined, an LSST (Large Synoptic Survey Telescope)-like survey can yield statistical errors on (Omega_DE, w_0, w_a) as tight as (0.003, 0.03, 0.1). These values are a factor of 2-25 better than using either observable alone. The results are also about a factor of two better than those from combining number counts of galaxy clusters and their power spectrum.Comment: 17 pages, 5 figures, 10 tables, submitted to PR