H. J. G. L. M. Lamers

Mass-loss predictions for O and B stars as a function of metallicity

We have calculated a grid of massive star wind models and mass-loss rates for a wide range of metal abundances between 1=100 Z=Z 10. The calculation of this grid completes the Vink et al. (2000) mass-loss recipe with an additional parameter Z. We have found that the exponent of the power law dependence of mass loss vs. metallicity is constant in the range between 1/30 Z=Z 3. The mass-loss rate scales as _ M / Z 0:85 v1 p with p = 1:23 for stars with Te > 25 000 K, and p = 1:60 for the B supergiants with Te 25 000 K, and _ M / Z 0:64 for B supergiants with Te < 25 000 K. Although it is derived that the exponent of the mass loss vs. metallicity dependence is constant over a large range in Z, one should be aware of the presence of bi-stability jumps at specic temperatures. Here the character of the line driving changes drastically due to recombinations of dominant metal species resulting in jumps in the mass loss. We have investigated the physical origins of these jumps and have derived formulae that combine mass loss recipes for both sides of such jumps. As observations of dierent galaxies show that the ratio Fe/O varies with metallicity, we make a distinction between the metal abundance Z derived on the basis of iron or oxygen lines. Our mass-loss predictions are successful in explaining the observed mass-loss rates for Galactic and Small Magellanic Cloud O- type stars, as well as in predicting the observed Galactic bi-stability jump. Hence, we believe that our predictions are reliable and suggest that our mass-loss recipe be used in future evolutionary calculations of massive stars at dierent metal abundance. A computer routine to calculate mass loss is publicly available.

The Star Cluster Population of M51: II. Age distribution and relations among the derived parameters

We use archival Hubble Space Telescope observations of broad-band images from the ultraviolet (F255W- filter) through the near infrared (NICMOS F160W-filter) to study the star cluster population of the interacting spiral galaxy M51. We obtain age, mass, extinction, and effective radius estimates for 1152 star clusters in a region of � 7.3 × 8.1 kpc centered on the nucleus and extending into the outer spiral arms. In this paper we present the data set and exploit it to determine the age distribution and relationships among the fundamental parameters (i.e. age, mass, effective radius). We show the critical dependence of the age distribution on the sample selection, and confirm that using a constant mass cut-off, above which the sample is complete for the entire age range of interest, is essential. In particular, in this sample we are complete only for masses above 5×10 4 M⊙ for the last 1 Gyr. Using this dataset we find: i) that the cluster formation rate seems to have had a large increase � 50-70 Myr ago, which is coincident with the suggested second passage of its companion, NGC 5195, ii) a large number of extremely young (< 10 Myr) star clusters, which we interpret as a population of unbound clusters of which a large majority will disrupt within the next �10 Myr, and iii) that the distribution of cluster sizes can be well approximated by a power-law with exponent, � = 2.2 ± 0.2, which is very similar to that of Galactic globular clusters, indicating that cluster disruption is largely independent of cluster radius. In addition, we have used this dataset to search for correlations among the derived parameters. In particular, we do not find any strong trends between the age and mass, mass and effective radius, nor between the galactocentric distance and effective radius. There is, however, a strong correlation between the age of a cluster and its extinction, with younger clusters being more heavily reddened than older clusters.We present the age and mass distribution of star clusters in M51. The structural parameters are found by fitting cluster evolution models to the spectral energy distribution consisting of 8 HST-WFPC2 pass bands. There is evidence for a burst of cluster formation at the moment of the second encounter with the companion NGC5195 (50-100 Myr ago) and a hint for an earlier burst (400-500 Myr ago). The cluster IMF has a power law slope of -2.1. The disruption time of clusters is extremely short (< 100 Myr for a 10^4 Msun cluster).

Star cluster disruption by giant molecular clouds

We investigate encounters between giant molecular clouds (GMCs) and star clusters. We propose a single expression for the energy gain of a cluster due to an encounter with a GMC, valid for all encounter distances and GMC properties. This relation is verified with N-body simulations of cluster-GMC encounters, where the GMC is represented by a moving analytical potential. Excellent agreement is found between the simulations and the analytical work for fractional energy gains of Delta E/vertical bar E-0 vertical bar < 10, where vertical bar E-0 vertical bar is the initial total cluster energy. The fractional mass loss from the cluster scales with the fractional energy gain as (Delta M/M-0) = f(Delta E/vertical bar E-0 vertical bar), where f similar or equal to 0.25. This is because a fraction 1 - f of the injected energy goes to the velocities of escaping stars, that are higher than the escape velocity. We therefore suggest that the disruption time of clusters, t(dis), is best defined as the time needed to bring the cluster mass to zero, instead of the time needed to inject the initial cluster energy. We derive an expression for t(dis) based on the mass loss from the simulations, taking into account the effect of gravitational focusing by the GMC. Assuming spatially homogeneous distributions of clusters and GMCs with a relative velocity dispersion of sigma(cn), we find that clusters lose most of their mass in relatively close encounters with high relative velocities (similar to 2 sigma(cn)). The disruption time depends on the cluster mass (M-c) and half-mass radius (r(h)) as t(dis) = 2.0 S(M-c/10(4) M-circle dot)(3.75 pc/r(h))(3) Gyr, with S equivalent to 1 for the solar neighbourhood and S scales with the surface density of individual GMCs (Sigma(n)) and the global GMC density (rho(n)) as S proportional to (Sigma(n)rho(n))(-1). Combined with the observed relation between r(h) and M-c, that is, r(h) proportional to M-c(lambda), t(dis) depends on M-c as t(dis)proportional to M-c(gamma). The index gamma is then defined as gamma= 1 - 3 lambda. The observed shallow relation between cluster radius and mass (e.g. lambda similar or equal to 0.1), makes the value of the index gamma = 0.7 similar to that found from observations and from simulations of clusters dissolving in tidal fields (gamma similar or equal to 0.62). The constant of 2.0 Gyr, which is the disruption time of a 10(4) M circle dot cluster in the solar neighbourhood, is about a factor of 3.5 shorter than that found from earlier simulations of clusters dissolving under the combined effect of Galactic tidal field and stellar evolution. It is somewhat higher than the observationally determined value of 1.3 Gyr. It suggests, however, that the combined effect of tidal field and encounters with GMCs can explain the lack of old open clusters in the solar neighbourhood. GMC encounters can also explain the (very) short disruption time that was observed for star clusters in the central region of M51, since there rho(n) is an order of magnitude higher than that in the solar neighbourhood.

Star cluster formation and disruption time-scales - I. An empirical determination of the disruption time of star clusters in four galaxies

We have derived the disruption times of star clusters from cluster samples of four galaxies, M51, M33, the Small Magellanic Cloud (SMC) and the solar neighbourhood. If the disruption time of clusters in a galaxy depends only on their initial mass as t d i s (yr) = t d i s 4 (M c l /10 4 M O .) γ , and if the cluster formation rate is constant, then the mass and age distributions of the observed clusters will each be given by double power-law relations. For clusters of low mass or young age the power law depends on the fading of the clusters below the detection limit due to the evolution of the stars. For clusters of high mass and old age the power law depends on the disruption time of the clusters. The samples of clusters in M51 and M33, observed with HST-WFPC2, indeed show the predicted double power-law relations in both their mass and age distributions. The values of t d i s 4 and y can be derived from these relations. For the cluster samples of the SMC and the solar neighbourhood, taken from the literature, only the age distribution is known. This also shows the characteristic double power-law behaviour, which allows the determination of t d i s 4 and y in these galaxies. The values of y are the same in the four galaxies within the uncertainty, and the mean value is y = 0.62 ′ 0.06. However, the disruption time t d i s 4 of a cluster of 10 4 M O . is very different in the different galaxies. The clusters in the SMC have the longest disruption time, t d i s 4 ≃ 8 x 10 9 yr, and the clusters at 1-3 kpc from the nucleus of M51 have the shortest disruption time of t d i s 4 ≃ 4 x 10 7 yr. The disruption time of clusters 1-5 kpc from the nucleus of M33 is t d i s 4 ≃ 1.3 x 10 8 yr and for clusters within 1 kpc from the Sun we find t d i s 4 ≃ 1.0 × 10 9 yr.

Clusters in the inner spiral arms of M 51: The cluster IMF and the formation history

We present the results of an analysis of the HST-WFPC2 observations of the interacting galaxy M51. From the observations in 5 broadband filters (UBVRI) and two narrowband filters (Hα and (OIII)) we study the cluster population in a region of 3.2 ×3.2 kpc 2 in the inner spiral arms of M51, at a distance of about 1 to 3 kpc from the nucleus. We found 877 cluster candidates and we derived their ages, initial masses and extinctions by means of a comparison between the observed spectral energy distribution and the predictions from cluster synthesis models for instantaneous star formation and solar metallicity. The lack of (OIII) emission in even the youngest clusters with strong Hα emission, indicates the absence of the most massive stars and suggests a mass upper limit of about 25 to 30 M� . The mass versus age distribution of the clusters shows a drastic decrease in the number of clusters with age, much more severe than can be expected on the basis of evolutionary fading of the clusters. This indicates that cluster dispersion is occurring on a timescale of 10 Myr or longer. The cluster initial mass function has been derived from clusters younger than 10 Myr by a linear regression fit of the cumulative mass distribution. This results in an exponent α = −dlogN(M)/dlog (M) = 2.1 ± 0.3 in the range of 2.5 × 10 3 2 × 10 4 M� . In the restricted range of 2.5 × 10 3 < M < 2 × 10 4 Mwe find α = 2.0 ± 0.05. This exponent is very similar to the value derived for clusters in the interacting Antennae galaxies, and to the exponent of the mass distribution of the giant molecular clouds in our Galaxy. To study the possible effects of the interaction of M51 with its companion NGC 5195 about 400 Myr ago, which triggered a huge starburst in the nucleus, we determined the cluster formation rate as a function of time for clusters with an initial mass larger than 10 4 M� . There is no evidence for a peak in the cluster formation rate at around 200 to 400 Myr ago within 2 σ accuracy, i.e. within a factor two. The formation rate of the detected clusters decreases strongly with age by about a factor 10 2 between 10 Myr and 1 Gyr. For clusters older than about 150 Myr this is due to the evolutionary fading of the clusters below the detection limit. For clusters younger than 100 Myr this is due to the dispersion of the clusters, unless one assumes that the cluster formation rate has been steadily increasing with time from 1 Gyr ago to the present time.

Stellar clusters in M83: formation, evolution, disruption and the influence of the environment

We study the stellar cluster population in two adjacent fields in the nearby, face-on spiral galaxy M83 using multiwavelength Wide Field Camera 3/Hubble Space Telescope imaging. After automatic det ...

Systematic uncertainties in the analysis of star cluster parameters based on broad-band imaging observations

High-resolution Hubble Space Telescope (HST) imaging observations of star cluster systems provide a very interesting and useful alternative for stellar population analyses to spectroscopic studies with 8m-class telescopes. Here, we assess the systematic uncertainties in (young) cluster age, mass, and – to a lesser extent – extinction and metallicity determinations, based on broad-band imaging observations with the HST. Our aim here is to intercompare the results obtained using a variety of commonly used modelling techniques, specifically with respect to our own extensively tested multi-dimensional approach. Any significant differences among the resulting parameters are due to the details of the various, independently developed modelling techniques used, rather than to the stellar population models themselves. Despite the model uncertainties and the selection effects inherent to most methods used, we find that the peaks in the relative age and mass distributions of a given young (. 10 9 yr) cluster system can be derived relatively robustly and consistently, to accuracies of σt ≡ �h log(Age/yr)i ≤ 0.35 and σM ≡ �h log(Mcl/M⊙)i ≤ 0.14, respectively, assuming Gaussian distributions in cluster ages and masses for reasons of simplicity. The peaks in the relative mass distributions can be obtained with a higher degree of confidence than those in the relative age distributions, as exemplified by the smaller spread among the peak values of the mass distributions derived. This implies that mass determinations are mostly insensitive to the approach adopted. We reiterate that as extensive a wavelength coverage as possible is required to obtain robust and internally consistent age and mass estimates for the individual objects, with reasonable uncertainties. Finally, we conclude that the actual filter systems used for the observations should be used for constructing model colours, instead of using conversion equations, to achieve more accurate derivations of ages and masses.

Maximum mass-loss rates of line-driven winds of massive stars: The effect of rotation and an application to eta Carinae

We investigate the effect of rotation on the maximum mass-loss rate due to an optically-thin radiatively-driven wind according to a formalism which takes into account the possible presence of any instability at the base of the wind that might increase the mass-loss rate. We include the Von Zeipel effect and the oblateness of the star in our calculations. We determine the maximum surface-integrated mass that can be lost from a star by line driving as a function of rotation for a number of relevant stellar models of massive OB stars with luminosities in the range of 5.0 < log (L/L ○. ) < 6.0. We also determine the corresponding maximum loss of angular momentum. We find that rotation increases the maximum mass-loss rate by a moderate factor for stars far from the Eddington limit as long as the ratio of equatorial to critical velocity remains below 0.7. For higher ratios, however, the temperature, flux and Eddington factor distributions change considerably over the stellar surface such that extreme mass loss is induced. Stars close to the Eddington-Gamma limit suffer extreme mass loss already for a low equatorial rotation velocity. We compare the maximum mass-loss rates as a function of rotation velocity with other predicted relations available in the literature which do not take into account possible instabilities at the stellar surface and we find that the inclusion thereof leads to extreme mass loss at much lower rotation rates. We present a scaling law to predict maximum mass-loss rates. Finally, we provide a mass-loss model for the LBV η Carinae that is able to explain the large observed current mass-loss rate of ∼10 -3 M ○. yr -1 but that leads to too low wind velocities compared to those derived from observations.

The orbiting stellar ultraviolet spectrophotometer S59 in ESRO's TD-1A satellite

The ultraviolet stellar spectrophotometer S59 of the Utrecht Astronomical Institute uses the stabilization properties of the ESRO TD-1A satellite. This spacecraft scans the sky along eliptic meridians with an orbital precession of one degree per day, thus covering the whole celestial sphere in half a year. This property is combined with a tracking system which points the spectrophotometer during four minutes at stars of sufficient brightness. During this time interval the ultraviolet stellar spectrum is scanned with a resolution of 1.7 Å in three bands of about 100 Å, around 2110, 2545 and 2825 Å. The optical, mechanical and electronic properties of the instrument and its tracking system are described in some detail, as well as the optical and technical performance in laboratory tests and in orbit. Some results obtained during the first half year of operation are briefly described.

On the nature of pre-main sequence candidate stars in the Large Magellanic Cloud

We investigate a sample of 18 Large Magellanic Cloud Herbig Ae/Be candidate stars looking at their (1) spectral types (2) brightness variability mechanism and (3) near infra-red JHK emission. We find that the majority of the target stars have Hα emission, are of spectral type early- to mid-B and lack strong JHK excess emission. Their Balmer decrements are found to be similar to that of Galactic Be stars in general. Their erratic brightness variability is evaluated by using the observed optical color excess and the color gradient from the light curves and is subsequently interpreted as being due to variable dust obscuration or variable bf-ff emission from circumstellar ionized gas. For approximately half of the target stars in our sample the type of variability seems to be dissimilar to the mechanism involving bound-free and free-free emission, but could be interpreted as caused by variable dust obscuration, as we have proposed in earlier studies. It is therefore suggested that they are pre-main sequence objects, despite the fact that they nearly all lack thermal dust emission in the near infra-red; mid/far infra-red observations for these objects are warranted. One star is observed to have JHK excess emission and an inspection of its 7.5 year MACHO light curve confirms its erratic photometric behavior. The object displays deep photometric minima with a quasi-period of 191.3 days, as generally seen in the Galactic pre-main sequence subgroup of the UX Orionis stars.