M giants are among the longest-period pulsating stars which is why their studies were traditionally restricted to analyses of low-precision visual observations, and more recently, accurate ground-based data. Here we present an overview of M giant variability on a wide range of time-scales (hours to years), based on analysis of thirteen quarters of Kepler longcadence observations (one point per every 29.4 minutes), with a total time-span of over 1000 days. About two-thirds of the sample stars have been selected from the ASAS-North survey of the Kepler field, with the rest supplemented from a randomly chosen M giant control sample.We first describe the correction of the light curves from different quarters, which was found to be essential. We use Fourier analysis to calculate multiple frequencies for all stars in the sample. Over 50 stars show a relatively strong signal with a period equal to the Kepleryear and a characteristic phase dependence across the whole field-of-view. We interpret this as a so far unidentified systematic effect in the Kepler data. We discuss the presence of regular patterns in the distribution of multiple periodicities and amplitudes. In the period-amplitude plane we find that it is possible to distinguish between solar-like oscillations and larger amplitude pulsations which are characteristic for Mira/SR stars. This may indicate the region of the transition between two types of oscillations as we move upward along the giant branch.

This paper discusses a new method to generate self-coherent initial conditions for young substructured stellar cluster. The expansion of a uniform system allows stellar sub-structures (clumps) to grow from fragmentation modes by adiabatic cooling. We treat the system mass elements as stars, chosen according to a Salpeter mass function, and the time-evolution is performed with a collisional N-body integrator. This procedure allows to create a fully-coherent relation between the clumps' spatial distribution and the underlying velocity field. The cooling is driven by the gravitational field, as in a cosmological Hubble-Lemaître flow. The fragmented configuration has a 'fractal'like geometry but with a self-grown velocity field and mass profile. We compare the characteristics of the stellar population in clumps with that obtained from hydrodynamical simulations and find a remarkable correspondence between the two in terms of the stellar content and the degree of spatial mass-segregation. In the fragmented configuration, the IMF power index is ≈ 0.3 lower in clumps in comparison to the field stellar population, in agreement with observations in the Milky Way. We follow in time the dynamical evolution of fully fragmented and sub-virial configurations, and find a soft collapse, leading rapidly to equilibrium (timescale of 1 Myr for a ∼ 10 4 M ⊙ system). The low-concentration equilibrium implies that the dynamical evolution including massive stars is less likely to induce direct collisions and the formation of exotic objects. Low-mass stars already ejected from merging clumps are depleted in the end-result stellar clusters, which harbour a top-heavy stellar mass function.

We explore with collisional gravitational N-body models the evolution of binary stars in initially fragmented and globally subvirial clusters of stars. Binaries are inserted in the (initially) clumpy configurations so as to match the observed distributions of the field-binary-stars' semimajor axes a and binary fraction versus primary mass. The dissolution rate of wide binaries is very high at the start of the simulations, and is much reduced once the clumps are eroded by the global infall. The transition between the two regimes is sharper as the number of stars N is increased, from N = 1.5 k up to 80 k. The fraction of dissolved binary stars increases only mildly with N, from ≈15 per cent to ≈25 per cent for the same range in N. We repeated the calculation for two initial system mean number densities of 6 per pc 3 (low) and 400 per pc 3 (high). We found that the longer free-fall time of the low-density runs allows for prolonged binary-binary interactions inside clumps and the formation of very tight (a ≈ 0.01 au) binaries by exchange collisions. This is an indication that the statistics of such compact binaries bear a direct link to their environment at birth. We also explore the formation of wide (a 5 × 10 4 au) binaries and find a low (≈0.01 per cent) fraction mildly bound to the central star cluster. The high-precision astrometric mission Gaia could identify them as outflowing shells or streams.