Henny J. G. L. M. Lamers

Introduction to Stellar Winds

Preface 1. Historical overview 2. Observations of stellar winds 3. Basic concepts: isothermal winds 4. Basic concepts: non-isothermal winds 5. Coronal winds 6. Sound wave driven winds 7. Dust driven winds 8. Line driven winds 9. Magnetic rotator theory 10. Alfven wave driven winds 11. Outflowing disks from rotating stars 12. Winds colliding with the interstellar medium 13. The effects of mass loss on stellar evolution 14. Problems Appendices Bibliography Object index Index.

What are the mass-loss rates of O stars ?

Empirical mass-loss rates of 28 luminous galactic OB stars are derived from thermal radio emission and from Hα recombination radiation. The velocity fields of all stars had previously been analyzed in the IUE ultraviolet spectral region. The results of these ultraviolet line-profile analyses (shape of the velocity law and terminal velocity) are combined with the radio and Hα data for a precise and consistent determination of the stellar mass-loss rates. It is found that radio and Hα rates agree within the observational errors. This suggests that significant clumping in the wind is unlikely due to the very different radius of origin of radio and Hα radiation within the wind

An analytical description of the disruption of star clusters in tidal fields with an application to Galactic open clusters

We present a simple analytical description of the disruption of star clusters in a tidal field. The cluster disruption time, defined as tdis = {dln M/dt} −1 , depends on the mass M of the cluster as tdis = t0(M/M� ) γ with γ = 0.62 for clusters in a tidal field, as shown by empirical studies of cluster samples in different galaxies and by N-body simulations. Using this simple description we derive an analytic expression for the way in which the mass of a cluster decreases with time due to stellar evolution and disruption. The result agrees very well with those of detailed N-body simulations for clusters in the tidal field of our galaxy. The analytic expression can be used to predict the mass and age histograms of surviving clusters for any cluster initial mass function and any cluster formation history. The method is applied to explain the age distribution of the open clusters in the solar neighbourhood within 600 pc, based on a new cluster sample that appears to be unbiased within a distance of about 1 kpc. From a comparison between the observed and predicted age distributions in the age range between 10 Myr to 3 Gyr we find the following results: (1) The disruption time of a 10 4 Mcluster in the solar neighbourhood is about 1.3 ± 0.5 Gyr. This is a factor of 5 shorter than that derived from N-body simulations of clusters in the tidal field of the galaxy. Possible reasons for this discrepancy are discussed. (2) The present star formation rate in bound clusters within 600 pc of the Sun is 5.9 ± 0.8 × 10 2 MMyr −1 , which corresponds to a surface star formation rate of bound clusters of 5.2 ± 0.7 × 10 −10 Myr −1 pc −2 . (3) The age distribution of open clusters shows a bump between 0.26 and 0.6 Gyr when the cluster formation rate was 2.5 times higher than before and after. (4) The present star formation rate in bound clusters is about half that derived from the study of embedded clusters. The difference suggests that about half of the clusters in the solar neighbourhood become unbound within about 10 Myr. (5) The most massive clusters within 600 pc had an initial mass of about 3 × 10 4 M� . This is in agreement with the statistically expected value based on a cluster initial mass function with a slope of −2, even if the physical upper mass limit for cluster formation is as high as 10 6 M� .

Star cluster formation and evolution in nearby starburst galaxies — II. Initial conditions

We use the ages, masses and metallicities of the rich young star cluster systems in the nearby starburst galaxies NGC 3310 and NGC 6745 to derive their cluster formation histories and subsequent evolution. We further expand our analysis of the systematic uncertainties involved in the use of broad-band observations to derive these parameters (Paper I) by examining the effects of a priori assumptions on the individual cluster metallicities. The age (and metallicity) distributions of both the clusters in the circumnuclear ring in NGC 3310 and of those outside the ring are statistically indistinguishable, but there is a clear and significant excess of higher-mass clusters in the ring compared to the non-ring cluster sample; it is likely that the physical conditions in the starburst ring may be conducive for the formation of higher-mass star clusters, on average, than in the relatively more quiescent environment of the main galactic disc. For the NGC 6745 cluster system we derive a median age of � 10 Myr. NGC 6745 contains a significant population of high-mass “super star clusters”, with masses in the range 6.5 . log(Mcl/M⊙) . 8.0. This detection supports the scenario that such objects form preferentially in the extreme environments of interacting galaxies. The age of the cluster populations in both NGC 3310 and NGC 6745 is significantly lower than their respective characteristic cluster disruption time-scales, respectively log(t dis /yr) = 8.05 and 7.75, for 10 4 M⊙ clusters. This allows us to obtain an independent estimate of the initial cluster mass function slope, � = 2.04(±0.23) +0.13 −0.43 for NGC 3310, and 1.96(±0.15) ± 0.19 for NGC 6745, respectively, for masses Mcl & 10 5 M⊙ and Mcl & 4 × 10 5 M⊙. These mass function slopes are consistent with those of other

Hierarchical star formation in M51: Star/cluster complexes

We report on a study of young star cluster complexes in the spiral galaxy M 51. Recent studies have confirmed that star clusters do not form in isolation, but instead tend to form in larger groupings or complexes. We use HST broad and narrow band images (from both WFPC2 and ACS), along with BIMA-CO observations to study the properties and investigate the origin of these complexes. We find that the complexes are all young (<10 Myr), have sizes between ∼85 and ∼240 pc, and have masses between 3–30 × 10 4 M� . Unlike that found for isolated young star clusters, we find a strong correlation between the complex mass and radius, namely M ∝ R 2.33±0.19 . This is similar to that found for giant molecular clouds (GMCs). By comparing the mass-radius relation of GMCs in M 51 to that of the complexes we can estimate the star formation efficiency within the complexes, although this value is heavily dependent on the assumed CO-to-H2 conversion factor. The complexes studied here have the same surface density distribution as individual young star clusters and GMCs. If star formation within the complexes is proportional to the gas density at that point, then the shared mass-radius relation of GMCs and complexes is a natural consequence of their shared density profiles. We briefly discuss possibilities for the lack of a mass-radius relation for young star clusters. We note that many of the complexes show evidence of merging of star clusters in their centres, suggesting that larger star clusters can be produced through the build up of smaller clusters.

Disruption time scales of star clusters in different galaxies

The observed average lifetime of the population of star clusters in the Solar Neighbourhood, the Small Magellanic Cloud and in selected regions of M 51 and M 33 is compared with simple theoretical predictions and with the results of N-body simulations. The empirically derived lifetimes (or disruption times) of star clusters depend on their initial mass as tdis emp ∝ Mcl 0.60 in all four galaxies. N-body simulations have shown that the predicted disruption time of clusters in a tidal field scales as tdis pred ∝ t 0.75 rh t 0.25 cr ,w heretrh is the initial half-mass relaxation time and tcr is the crossing time for a cluster in equilibrium. We show that this can be approximated accurately by tdis pred ∝ M 0.62 cl for clusters in the mass range of about 10 3 to 10 6 M � ,i n excellent agreement with the observations. Observations of clusters in different extragalactic environments show that tdis also depends on the ambient density in the galaxies where the clusters reside. Linear analysis predicts that the disruption time will depend on the ambient density of the cluster environment as tdis ∝ ρ −1/2 amb . This relation is consistent with N-body simulations. The empirically derived disruption times of clusters in the Solar Neighbourhood, in the SMC and in M 33 agree with these predictions. The best fitting expression for the disruption time is tdis = Cenv(Mcl/10 4 M� ) 0.62 (ρamb/Mpc −3 ) −0.5 where Mcl is the initial mass of the cluster and Cenv � 300−800 Myr. The disruption times of star clusters in M 51 within 1−5 kpc from the nucleus, is shorter than predicted by about an order of magnitude. This discrepancy might be due to the strong tidal field variations in M 51, caused by the strong density contrast between the spiral arms and interarm regions, or to the disruptive forces from giant molecular clouds.

Chemical Composition and Origin of Nebulae around Luminous Blue Variables

We use the analysis of the heavy element abundances (C, N, O, S) in circumstellar nebulae around luminous blue variables to infer the evolutionary phase in which the material has been ejected. We concentrate on four aspects. (1) We discuss the diUerent eUects that may have changed the gas composition of the nebula since it was ejected: mixing with the swept up gas from the wind-blown bubble, mixing with the gas from the faster wind of the central star, and depletion by CO and dust. (2) We calculate the expected abundance changes at the stellar surface due to envelope convection in the red supergiant phase. We show that this depends strongly on the total amount of mass that was lost prior to the onset of the envelope convection. If the observed LBV nebulae are ejected during the red supergiant phase, the abundances of the LBV nebulae require a signi—cantly smaller amount of mass to be lost than assumed in the evolutionary calculations of Meynet et al. (3) We calculate the changes in the surface composition during the main-sequence phase by rotation-induced mixing. If the nebulae are ejected at the end of the main-sequence phase, the abundances in LBV nebulae are compatible with mixing times between 5 ] 106 and 1 ] 107 yr. These values are reasonable, considering the high rotational velocities of mainsequence O-stars. The existence of ON stars supports this scenario. (4) The predicted He/H ratio in the nebulae, derived from the observed N/O ratios, are signi—cantly smaller than the current observed photospheric values of their central stars. This indicates that either (1) the nebula was ejected from a star that had an abundance gradient in its envelope or (2) that fast mixing on a timescale of 104 yr must have occurred in the stars immediately after the nebula was ejected. Combining various arguments, we show that the LBV nebulae are ejected during the blue supergiants phase and that the stars have not gone through a red supergiant phase. The chemical enhancements are due to rotation-induced mixing, and the ejection is possibly triggered by near-critical rotation. During the ejection, the out—ow was optically thick, which resulted in a large eUective radius and a low eUective temperature. This explains why the observed properties of the dust around LBVs closely resemble the properties of dust formed around red supergiants.

ACS imaging of star clusters in M 51 : I. Identification and radius distribution

Context. Size measurements of young star clusters are valuable tools to put constraints on the formation and early dynamical evolution of star clusters. Aims. We use HST/ACS observations of the spiral galaxy M51 in F435W, F555W and F814W to select a large sample of star clusters with accurate effective radius measurements in an area covering the complete disc ofM51.We present the dataset and study the radius distribution and relations between radius, colour, arm/interarm region, galactocentric distance, mass and age. Methods. We select a sample of 7698 (F435W), 6846 (F555W) and 5024 (F814W) slightly resolved clusters and derive their effective radii (Reff) by fitting the spatial profiles with analytical models convolved with the point spread function. The radii of 1284 clusters are studied in detail. Results. We find cluster radii between 0.5 and ∼10 pc, and one exceptionally large cluster candidate with Reff = 21.6 pc. The median Reff is 2.1 pc. We find 70 clusters in our sample which have colours consistent with being old GC candidates and we find 6 new “faint fuzzy” clusters in, or projected onto, the disc of M51. The radius distribution can not be fitted with a power law similar to the one for star-forming clouds. We find an increase in Reff with colour as well as a higher fraction of clusters with B−V >∼ 0.05 in the interarm regions. We find a correlation between Reff and galactocentric distance (RG) of the formReff ∝ R0.12±0.02 G , which is considerably weaker than the observed correlation for old Milky Way GCs. We find weak relations between cluster luminosity and radius: Reff ∝ L0.15±0.02 for the interarm regions and Reff ∝ L−0.11±0.01 for the spiral arm regions, but we do not observe a correlation between cluster mass and radius. Conclusions. The observed radius distribution indicates that shortly after the formation of the clusters from a fractal gas, the radii of the clusters have changed in a non-uniform way. We find tentative evidence suggesting that clusters in spiral arms are more compact.

Clusters in the solar neighbourhood: how are they destroyed?

We predict the survival time of initially bound star clusters in the solar neighbourhood taking into account: (1) stellar evolution, (2) tidal stripping, (3) shocking by spiral arms and (4) encounters with giant molecular clouds. We find that the predicted dissolution time is tdis = 1.7(Mi/104 M )0.67 Gyr for clusters in the mass range of 102 <Mi <105 M . The resulting predicted shape of the logarithmic age distribution agrees very well with the empirical one, derived from a complete sample of clusters in the solar neighbourhood within 600 pc. The required scaling factor implies a star formation rate of 4 × 102 M Myr−1 within 600 pc from the Sun or a surface formation rate of 3.5 × 10−10 M yr−1 pc−2 for stars in bound clusters with an initial mass in the range of 102 to 3 × 104 M .

Modelling the formation and evolution of star cluster populations in galaxy simulations

The formation and evolution of star cluster populations are related to the galactic environment. Cluster formation is governed by processes acting on galactic scales, and star cluster disruption is driven by the tidal field. In this paper, we present a self-consistent model for the formation and evolution of star cluster populations, for which we combine an N-body/smoothed particle hydrodynamics galaxy evolution code with semi-analytical models for star cluster evolution. The model includes star formation, feedback, stellar evolution and star cluster disruption by two-body relaxation and tidal shocks. The model is validated by a comparison to N-body simulations of dissolving star clusters. We apply the model by simulating a suite of nine isolated disc galaxies and 24 galaxy mergers. The evolutionary histories of individual clusters in these simulations are discussed to illustrate how the environment of clusters changes in time and space. It is found that the variability of the disruption rate with time and space affects the properties of star cluster populations. In isolated disc galaxies, the mean age of the clusters increases with galactocentric radius. The combined effect of clusters escaping their dense formation sites (‘cluster migration’) and the preferential disruption of clusters residing in dense environments (‘natural selection’) implies that the mean disruption rate of the population decreases with cluster age. This affects the slope of the cluster age distribution, which becomes a function of the star formation rate density (star formation rate per unit volume). The evolutionary histories of clusters in a galaxy merger vary widely and determine which clusters survive the merger. Clusters that escape into the stellar halo experience low disruption rates, while clusters orbiting near the starburst region of a merger are disrupted on short time-scales due to the high gas density. This impacts the age distributions and the locations of the surviving clusters at all times during a merger. The paper includes a discussion of potential improvements for the model and a brief exploration of possible applications. We conclude that accounting for the interplay between the formation, disruption and orbital histories of clusters enables a more sophisticated interpretation of observed properties of cluster populations, thereby extending the role of cluster populations as tracers of galaxy evolution.