On changes of the rotation velocities of stable,recurrent sunspots and their interpretation with a flux tube model

The angular rotation velocities of stable, recurrent sunspots were investigated using data from the Greenwich Photoheliographic Results 1940 until 1968. We found constant rotation velocities during the passages on the solar disk with errors of about ±4 m s^–1. During their lifetime these spots show a decreasing braking of their rotation velocities from 0.8 to 0.3 m s^–1 per day. A plausible interpretation is found by assuming the spots to be coupled to a slowly rising subsurface flux tube and a rotation velocity which increases with depth.Mitteilungen aus dem Kiepenheuer-Institut Nr. 201.     

On an analytical framework for voids: their abundances, density profiles and local mass functions

We present a general analytical procedure for computing the number density of voids with radius above a given value within the context of gravitational formation of the large-scale structure of the Universe out of Gaussian initial conditions. To this end, we develop an accurate (under generally satisfied conditions) extension of the unconditional mass function to constrained environments, which allows us both to obtain the number density of collapsed objects of certain mass at any distance from the centre of the void, and to derive the number density of voids defined by collapsed objects. We have made detailed calculations for the spherically averaged mass density and halo number density profiles for particular voids. We also present a formal expression for the number density of voids defined by galaxies of a given type and luminosity. This expression contains the probability for a collapsed object of certain mass to host a galaxy of that type and luminosity (i.e. the conditional luminosity function) as a function of the environmental density. We propose a procedure to infer this function, which may provide useful clues as to the galaxy formation process, from the observed void densities.     

Exact analytic solution for the rotation of a rigid body having spherical ellipsoid of inertia and subjected to a constant torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.     

On the APM power spectrum and the CMB anisotropy: evidence for a phase transition during inflation?

Adams et al. have noted that according to our current understanding of the unification of fundamental interactions, there should have been phase transitions associated with spontaneous symmetry breaking during the inflationary era. This may have resulted in the breaking of scale-invariance of the primordial density perturbation for brief periods. A possible such feature was identified in the power spectrum of galaxy clustering in the automated plate measurement (APM) survey at the scale k  ∼ 0.1  h  Mpc ^− 1 and it was shown that the secondary acoustic peaks in the power spectrum of the cosmic microwave background (CMB) anisotropy should consequently be suppressed. We demonstrate that this prediction is confirmed by the recent Boomerang and Maxima observations, which favour a step-like spectral feature in the range k  ∼ (0.06–0.6)  h  Mpc ^− 1 , independently of the similar previous indication from the APM data. Such a spectral break enables an excellent fit to both APM and CMB data with a baryon density consistent with the big bang nucleosynthesis (BBN) value. It also allows the possibility of a matter-dominated universe with zero cosmological constant, which we show can now account for even the evolution of the abundance of rich clusters.