Pavel Kroupa

Inverse dynamical population synthesis and star formation

We investigate the hypothesis that stars form in aggregates of binary systems and that the dynamical evolution of these aggregates leads to the observed properties of binary stars in the Galactic field. We assume that the initial distribution of periods is flat in logP, where P is the orbital period in days, and 3 7.5. After the cluster with R=0.8pc disintegrates we obtain a population which consists of about 60 per cent binary systems with a period distribution for logP>4 as is observed and in which the G-dwarf binaries have a mass ratio distribution which agrees with the observed distribution. This result indicates that the majority of Galactic field stars may originate from a clustered star formation mode. We invert the orbit depletion function and obtain an approximation to the initial binary star period distribution for star formation in the dominant mode cluster. Comparison with the measured distribution of orbits for pre-main sequence stars suggests that the initial distribution may not depend on the star formation environment. Inverse dynamical population synthesis suggests that the Galactic field stellar mass function may be related to the stellar density at birth in the most common, or dominant, mode of star formation.

Dwarf spheroidal satellite galaxies without dark matter

Abstract Self-consistent simulations of the interaction of initially spherical low-mass satellite galaxies with a massive Galactic dark halo suggest that observed apparent high mass-to-light ratios, ( M L ) obs , in dwarf-spheroidal (dSph) satellites may be obtained through successive and destructive perigalactic passages. The model satellites are disrupted after several perigalactic passages, but orbiting condensations in phase space can clearly be identified as remnants well after this event. An intrinsic ( M L ) true leads to long-lived model remnants that show, as seen from Earth, a tantalizingly close resemblance to observed dSph satellites with ( M L ) obs > 10 . The reason for large ( M L ) obs is that the remnants have non-isotropic velocity dispersions, are non-spherical and are not in dynamical equilibrium. The remnants fade with time (i.e. orbital phase) and ( M L ) obs increases indicating a correlation between brightness and ( M L ) obs as in the observed dSph sample. The observed correlation between central surface brightness and integrated absolute magnitude is also approximately reproduced by model remnants of different dynamical age. A possibly useful method for probing the line-of-sight extension of a dSph galaxy is suggested. If it is true that most if not all dSph satellites are tidally modified remnants without dark matter then it is plausible that their progenitors may have formed as satellite galaxies in tidal tails during possible early merging events.

SUPERBOX – an efficient code for collisionless galactic dynamics

We present SUPERBOX, a particle-mesh code with high resolution sub-grids and an NGP (nearest grid point) force-calculation scheme based on the second derivatives of the potential. SUPERBOX implements a fast low-storage FFT-algorithm, giving the possibility to work with millions of particles on desk-top computers. Test calculations show energy and angular momentum conservation to one part in 10(5) per crossing-time. The effects of grid and numerical relaxation remain negligible, even when these calculations cover a Hubble-time of evolution. As the sub-grids follow the trajectories of individual galaxies, the code allows a highly resolved treatment of interactions in clusters of galaxies, such as high-velocity encounters between elliptical galaxies and the tidal disruption of dwarf galaxies. Excellent agreement is obtained in a comparison with a direct-summation N-body code running on special-purpose GRAPE 3 hardware. The orbital decay of satellite galaxies due to dynamical friction obtained with SUPERBOX agrees with Chandrasekhars treatment when the Coulomb logarithm ln Lambda approximate to 1.5

The Hipparcos proper motion of the Magellanic Clouds

Abstract The proper motion of the Large (LMC) and Small (SMC) Magellanic Cloud using data acquired with the Hipparcos satellite is presented. Hipparcos measured 36 stars in the LMC and 11 stars in the SMC. A correctly weighted mean of the data yields the presently available most accurate values, μαcos(δ) = 1.94±0.29 mas/yr, μδ = −0.14±0.36 mas/yr for the LMC. For the SMC, μαcos(δ) = 1.23±0.84 mas/yr, μδ = −1.21±0.75 mas/yr is obtained, whereby care is taken to exclude likely tidal motions induced by the LMC. Both galaxies are moving approximately parallel to each other on the sky, with the Magellanic Stream trailing behind. The Hipparcos proper motions are in agreement with previous measurements using PPM catalogue data by Kroupa et al. (1994) [MNRAS, 266, 412] and by Jones et al. (1994) [AJ, 107, 1333] using background galaxies in a far-outlying field of the LMC. For the LMC the Hipparcos data suggest a weak rotation signal in a clockwise direction on the sky. Comparison of the Hipparcos proper motion with the proper motion of the field used by Jones et al. (1994) [AJ, 107, 1333], which is about 7.3 kpc distant from the center of the LMC, also suggeests clockwise rotation. Combining the three independent measurments of the proper motion of the LMC and the two independent measurements of the proper motion of the SMC improves the estimate of the proper motion of the LMC and SMC. The corresponding galactocentric space motion vectors are computed. Within the uncertainties, the LMC and SMC are found to be on parallel trajectories. Recent theoretical work concerning the origin of the Magellanic System is briefly reviewed, but a unique model of the Magellanic Stream, for the origin of the Magellanic Clouds, and for the mass distribution in the Galaxy cannot yet be decided upon. Future astrometric space missions are necessary to significantly improve our present knowledge of the space motion of the two most conspicous galactic neighbours of the Milky Way.

Satellite decay in flattened dark matter haloes

We carry out a set of self-consistent N-body calculations to compare the decay rates of satellite dwarf galaxies orbiting a disc galaxy embedded in a dark matter halo (DMH). We consider both spherical and oblate axisymmetric DMHs of aspect ratio qh = 0.6. The satellites are given different initial orbital inclinations, orbital periods and mass. The live flattened DMHs with embedded discs and bulges are set-up using a new fast algorithm, MaGalie (Boily, Kroupa & Penarrubia 2001). We find that the range of survival times of satellites within a flattened DMH becomes � 100% larger than the same satellites within a spherical DMH. In the oblate DMH, satellites on polar orbits have the longest survival time, whereas satellites on coplanar prograde orbits are destroyed most rapidly. The orbital plane of a satellite tilts as a result of anisotropic dynamical friction, causing the satellites orbit to align with the plane of symmetry of the DMH. Polar orbits are not subjected to alignment. Therefore the decay of a satellites in an axisymmetric DMH may provide a natural explanation for the observed lack of satellites within 0 30 ◦ of their host galaxys disc (Holmberg 1969; Zaritsky & Gonzalez 1999). The computations furthermore indicate that the evolution of the orbital eccen- tricity e is highly dependent of its initial value e(t = 0) and the DMHs shape. We also discuss some implications of flattened DMHs for satellite debris streams.

The theoretical mass-magnitude relation of low-mass stars and its metallicity dependence

We investigate the dependence of theoretically generated mass - (absolute magnitude) relations on stellar models. Using up to date physics we compute models in the mass range 0.1 [Fe/H] > -2.3) shows a maximum in -dm/dM_bol, which moves to brighter bolometric magnitudes with decreasing metallicity. The change in location of the maximum, as a function of [Fe/H], follows the location of structure in luminosity functions for stellar populations with different metal abundances. This structure seen in all observed stellar populations can be accounted for by the mass--luminosity relation.

Dynamical friction in flattened systems: a numerical test of Binney's approach

We carry out a set of self-consistent N-body calculations to investigate how important the velocity anisotropy in non-spherical dark matter haloes is for dynamical friction. For this purpose, we allow satellite galaxies to orbit within flattened and live dark matter haloes (DMHs) and compare the resulting orbit evolution with a semi-analytic code. This code solves the equation of motion of the same satellite orbits with mass loss and assumes the same DMH, but either employs Chandrasekhars dynamical friction formula, which does not incorporate the velocity anisotropy, or Binneys description of dynamical friction in anisotropic systems. In the numerical and the two semi-analytic models, the satellites are given different initial orbital inclinations and orbital eccentricities, whereas the parent galaxy is composed of a DMH with aspect ratio qh= 0.6. We find that Binneys approach successfully describes the overall satellite decay and orbital inclination decrease for the whole set of orbits, with an averaged discrepancy of less than 4 per cent in orbital radius during the first three orbits. If Chandrasekhars expression is used instead, the discrepancy increases to 20 per cent. Binneys treatment therefore appears to provide a significantly improved treatment of dynamical friction in anisotropic systems. The velocity anisotropy of the DMH velocity distribution function leads to a significant decrease with time of the inclination of non-polar satellite orbits. But, at the same time, it reduces the difference in decay times between polar and coplanar orbits evident in a flattened DMH when the anisotropic DMH velocity distribution function is not taken into account explicitly. Our N-body calculations furthermore indicate that polar orbits survive about 1.6 times longer than coplanar orbits and that the orbital eccentricity e remains close to its initial value if satellites decay slowly towards the galaxy centre. However, orbits of rapidly decaying satellites modelled with the semi-analytic code show a strong orbital circularization () not present in the N-body computations.

Unification of the nearby and photometric stellar luminosity functions

We introduce a model Galactic field low-mass stellar population that has a proportion of binary systems as observed, with a mass ratio distribution consistent with observational constraints. The model single star and system luminosity function agrees with the nearby and the Malmquist corrected photometric luminosity function, respectively. We tabulate the model luminosity functions in the photometric V-, I- and K-bands, and in bolometric magnitudes. Unresolved binary systems are thus a natural explanation for the difference between the nearby and photometric luminosity functions. A local overdensity of faint stars needs not be postulated to account for the difference, and is very unlikely. We stress that the nearby luminosity function can only be used to weakly constrain the stellar mass function below

Efficient N-body realisations of axisymmetric galaxies and halos

0.5\,M_\odot

MODEST-2: a summary

, because of the small sample size. The photometric luminosity function can only be used to put lower limits on the stellar mass function because most binary systems are not resolved. However, taken together the nearby and photometric stellar luminosity function data do not imply a mass function with a peak at a mass of