The current knowledge on the stellar IMF is documented. It appears to become top-heavy when the star-formation rate density surpasses about 0.1Msun/(yr pc^3) on a pc scale and it may become increasingly bottom-heavy with increasing metallicity and in
increasingly massive early-type galaxies. It declines quite steeply below about 0.07Msun with brown dwarfs (BDs) and very low mass stars having their own IMF. The most massive star of mass mmax formed in an embedded cluster with stellar mass Mecl correlates strongly with Mecl being a result of gravitation-driven but resource-limited growth and fragmentation induced starvation. There is no convincing evidence whatsoever that massive stars do form in isolation. Various methods of discretising a stellar population are introduced: optimal sampling leads to a mass distribution that perfectly represents the exact form of the desired IMF and the mmax-to-Mecl relation, while random sampling results in statistical variations of the shape of the IMF. The observed mmax-to-Mecl correlation and the small spread of IMF power-law indices together suggest that optimally sampling the IMF may be the more realistic description of star formation than random sampling from a universal IMF with a constant upper mass limit. Composite populations on galaxy scales, which are formed from many pc scale star formation events, need to be described by the integrated galactic IMF. This IGIMF varies systematically from top-light to top-heavy in dependence of galaxy type and star formation rate, with dramatic implications for theories of galaxy formation and evolution.
The non-thermal jet emission in active galactic nuclei covers several orders of magnitude in the frequency range. Hence the observational approach needs multi-wavelength (MWL) campaigns collecting data in the radio, optical, UV, X-rays, high energy u
ntil the Very High Energy (VHE) gamma-ray band. MAGIC, a system of two 17 m diameter telescopes at the Roque de los Muchachos observatory on the canary island La Palma, actively participates and organizes MWL observations on known and newly discovered VHE sources. In these proceedings we report the latest results of extra-galactic observations with MAGIC, which gained new insights in time variability studies and jet emission models.
We describe a scenario for the topology of the magnetic field in penumbrae that accounts for recent observations showing upflows, downflows, and reverse magnetic polarities. According to our conjecture, short narrow magnetic loops fill the penumbral
photosphere. Flows along these arched field lines are responsible for both the Evershed effect and the convective transport. This scenario seems to be qualitatively consistent with most existing observations, including the dark cores in penumbral filaments reported by Scharmer et al. Each bright filament with dark core would be a system of two paired convective rolls with the dark core tracing the common lane where the plasma sinks down. The magnetic loops would have a hot footpoint in one of the bright filament and a cold footpoint in the dark core. The scenario fits in most of our theoretical prejudices (siphon flows along field lines, presence of overturning convection, drag of field lines by downdrafts, etc). If the conjecture turns out to be correct, the mild upward and downward velocities observed in penumbrae must increase upon improving the resolution. This and other observational tests to support or disprove the scenario are put forward.
We describe a scenario for the sunspot magnetic field topology that may account for recent observations of upflows and downflows in penumbrae. According to our conjecture, short narrow magnetic loops fill the penumbral volume. Flows along these field
lines are responsible for both the Evershed effect and the convective transport. This scenario seems to be qualitatively consistent with most existing observations, including the dark cores in penumbral filaments reported by Scharmer et al. Each bright filament with dark core would be a system of two paired convective rolls with the dark core tracing the lane where the plasma sinks down. The magnetic loops would have a hot footpoint in one of the bright filament and a cold footpoint in the dark core. The scenario also fits in most of our theoretical prejudices (siphon flows along field lines, presence of overturning convection, drag of field lines by downdrafts, etc). If the conjecture turns out to be correct, the mild upward and downward velocities observed in penumbrae must increase upon improvement of the current spatial resolution. This and other observational tests to support or disprove the proposed scenario are put forward.
By applying the standard adiabatic approximation and using the accurate analytical expression for the corresponding local chemical potential obtained in our previous work [Phys. Rev. A textbf{75}, 063610 (2007)] we derive an effective 1D equation tha
t governs the axial dynamics of mean-field cigar-shaped condensates with repulsive interatomic interactions, accounting accurately for the contribution from the transverse degrees of freedom. This equation, which is more simple than previous proposals, is also more accurate. Moreover, it allows treating condensates containing an axisymmetric vortex with no additional cost. Our effective equation also has the correct limit in both the quasi-1D mean-field regime and the Thomas-Fermi regime and permits one to derive fully analytical expressions for ground-state properties such as the chemical potential, axial length, axial density profile, and local sound velocity. These analytical expressions remain valid and accurate in between the above two extreme regimes. Following the same procedure we also derive an effective 2D equation that governs the transverse dynamics of mean-field disk-shaped condensates. This equation, which also has the correct limit in both the quasi-2D and the Thomas-Fermi regime, is again more simple and accurate than previous proposals. We have checked the validity of our equations by numerically solving the full 3D Gross-Pitaevskii equation.
