ALBERT

Description: We present deep galaxy counts in the K (lambda 2.2 micrometer) band, obtained at the W. M. Kech 10 m telescope. The data reach limiting magnitudes K approximately 24 mag, about 5 times deeper than the deepest published K-band images to date. The counts are performed in three small (approximately 1 min), widely separated high-latitude fields. Extensive Monte Carlo tests were used to derive the comleteness corrections and minimize photometric biases. The counts continue to rise, with no sign of a turnover, down to the limits of our data, with the logarithmic slope of d log N/dm = 0.315 +/- 0.02 between K = 20 and 24 mag. This implies a cumulative surface density of approximately 5 x 10(exp 5) galaxies/sq deg, or approximately 2 x 10(exp 10) over the entire sky, down to K = 24 mag. Our counts are in good agreement with, although slightly lower than, those from the Hawaii Deep Survey by Cowie and collaborators; the discrepancies may be due to the small differences in the aperture corrections. We compare our counts with some of the available theoretical predictions. The data do not require models with a high value of Omega(sub 0), but can be well fitted by models with no (or little) evolution, and cosmologies with a low value of Omega(sub 0). Given the uncertainties in the models, it may be premature to put useful constrains on the value of Omega(sub 0) from the counts alone. Optical-to-IR colors are computed, using CCD data obtaind previously at Palomar. We find a few red galaxies with (r-K) approximately greater than 5 mag, or (i-K) approximately greater than 5 mag; these may be ellipticals at z approximately 1. While the redshift distribution of galaxies in our counts is still unknown, the flux limits reached would allow us to detect unobscured L(sub *) galaxies out to substantial redshifts (z greater than 3?).

Description: Recent numerical investigations have focused attention once more on the role of intermediate shocks in MHD. Four types of intermediate shock are identified using a graphical representation of the MHD Rankine-Hugoniot conditions. This same representation can be used to exhibit the close relationship of intermediate shocks to switch-on shocks and rotational discontinuities. The conditions under which intermediate discontinuities can be found are elucidated. The variations in velocity, pressure, entropy and magnetic-field jumps with upstream parameters in intermediate shocks are exhibited graphically. The evolutionary arguments traditionally advanced against intermediate shocks may fail because the equations of classical MHD are not strictly hyperbolic.

Description: A simplified set of equations is derived that approximates the magnetohydrodynamic (MHD) Navier-Stokes equations for weakly nonlinear disturbances whose speeds are close to the MHD intermediate speed. Its shock structure solutions are then examined. The fast and slow shock solutions are uniquely specified by their Rankine-Hugoniot relations. However, the intermediate shock solutions, which are not unique, are characterized by the integral through the shock of the noncoplanar component of the magnetic field. For situations in which this integral is conserved, the Riemann problem is well defined and predicts the evolution of intermediate shocks. This analysis is substantiated by numerical computations.