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Jan Pflamm-Altenburg

Publications and source records attributed to Jan Pflamm-Altenburg.

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Gas surface density, star formation rate surface density, and the maximum mass of young star clusters in a disk galaxy. II. The grand-design galaxy M51

We analyze the relationship between maximum cluster mass, and surface densities of total gas (Sigma_gas), molecular gas (Sigma_H_2), neutral gas (Sigma_HI) and star formation rate (Sigma_SFR) in the grand design galaxy M51, using published gas data and a catalog of masses, ages, and reddenings of more than 1800 star clusters in its disk, of which 223 are above the cluster mass distribution function completeness limit. We find for clusters older than 25 Myr that M_3rd, the median of the 5 most massive clusters, is proportional to Sigma_HI^0.4. There is no correlation with Sigma_gas, Sigma_H2, or Sigma_SFR. For clusters younger than 10 Myr, M_3rd is proportional to Sigma_HI^0.6, M_3rd is proportional to Sigma_gas^0.5; there is no correlation with either Sigma_H_2 or Sigma_SFR. The results could hardly be more different than those found for clusters younger than 25 Myr in M33. For the flocculent galaxy M33, there is no correlation between maximum cluster mass and neutral gas, but M_3rd is proportional to Sigma_gas^3.8; M_3rd is proportional to Sigma_H_2^1.2; M_3rd proportional to Sigma_SFR^0.9. For the older sample in M51, the lack of tight correlations is probably due to the combination of the strong azimuthal variations in the surface densities of gas and star formation rate, and the cluster ages. These two facts mean that neither the azimuthal average of the surface densities at a given radius, nor the surface densities at the present-day location of a stellar cluster represent the true surface densities at the place and time of cluster formation. In the case of the younger sample, even if the clusters have not yet traveled too far from their birthsites, the poor resolution of the radio data compared to the physical sizes of the clusters results in measured Sigmas that are likely quite diluted compared to the actual densities relevant for the formation of the clusters.

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The stellar and sub-stellar IMF of simple and composite populations

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.

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Gas surface density, star formation rate surface density, and the maximum mass of young star clusters in a disk galaxy. I. The flocculent galaxy M33

We analyze the relationship between maximum cluster mass, M_max, and surface densities of total gas (Sigma_gas), molecular gas (Sigma_H2) and star formation rate (Sigma_SFR) in the flocculent galaxy M33, using published gas data and a catalog of more than 600 young star clusters in its disk. By comparing the radial distributions of gas and most massive cluster masses, we find that M_max is proportional to Sigma_gas^4.7, M_max is proportional Sigma_H2^1.3, and M_max is proportional to Sigma_SFR^1.0. We rule out that these correlations result from the size of sample; hence, the change of the maximum cluster mass must be due to physical causes.

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Low-mass X-ray binaries indicate a top-heavy stellar initial mass function in ultra compact dwarf galaxies

It has been shown before that the high mass-to-light ratios of ultra compact dwarf galaxies (UCDs) can be explained if their stellar initial mass function (IMF) was top-heavy, i.e. that the IMF was skewed towards high mass stars. In this case, neutron stars and black holes would provide unseen mass in the UCDs. In order to test this scenario with an independent method, we use data on which fraction of UCDs has a bright X-ray source. These X-ray sources are interpreted as low-mass X-ray binaries (LMXBs), i.e. binaries where a neutron star accretes matter from an evolving low-mass star. We find that LMXBs are indeed up to 10 times more frequent in UCDs than expected if the IMF was invariant. The top-heavy IMF required to account for this overabundance is the same as needed to explain the unusually high mass-to-light ratios of UCDs and a top-heavy IMF appears to be the only simultaneous explanation for both findings. Furthermore, we show that the high rate of type II supernovae (SNII) in the star-burst galaxy Arp 220 suggests a top-heavy IMF in that system. This finding is consistent with the notion that star-burst galaxies are sites where UCDs are likely to be formed and that the IMF of UCDs is top-heavy. It is estimated that the IMF becomes top-heavy whenever the star formation rate per volume surpasses 0.1 Solar masses per year and cubic parsec in pc-scale regions.

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Do all O stars form in star clusters?

The question whether or not massive stars can form in isolation or only in star clusters is of great importance for the theory of (massive) star-formation as well as for the stellar initial mass function of whole galaxies (IGIMF-theory). While a seemingly easy question it is rather difficult to answer. Several physical processes (e.g. star-loss due to stellar dynamics or gas expulsion) and observational limitations (e.g. dust obscuration of young clusters, resolution) pose severe challenges to answer this question. In this contribution we will present the current arguments in favour and against the idea that all O stars form in clusters.

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Top-heavy integrated galactic stellar initial mass functions (IGIMFs) in starbursts

Star formation rates (SFR) larger than 1000 Msun/ yr are observed in extreme star bursts. This leads to the formation of star clusters with masses > 10^6 Msun in which crowding of the pre-stellar cores may lead to a change of the stellar initial mass function (IMF). Indeed, the large mass-to-light ratios of ultra-compact dwarf galaxies and recent results on globular clusters suggest the IMF to become top-heavy with increasing star-forming density. We explore the implications of top-heavy IMFs in these very massive and compact systems for the integrated galactic initial mass function (IGIMF), which is the galaxy-wide IMF, in dependence of the star-formation rate of galaxies. The resulting IGIMFs can have slopes, alpha_3, for stars more massive than about 1 Msun between 1.5 and the Salpeter slope of 2.3 for an embedded cluster mass function (ECMF) slope (beta) of 2.0, but only if the ECMF has no low-mass clusters in galaxies with major starbursts. Alternatively, beta would have to decrease with increasing SFR >10 Msun/ yr such that galaxies with major starbursts have a top-heavy ECMF. The resulting IGIMFs are within the range of observationally deduced IMF variations with redshift.

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Accretion-regulated star formation in late-type galaxies

We develop a four-phase galaxy evolution model in order to study the effect of accretion of extra-galactic gas on the star formation rate (SFR) of a galaxy. Pure self-regulated star formation of isolated galaxies is replaced by an accretion-regulated star formation mode. The SFR settles into an equlibrium determined entirely by the gas accretion rate on a Gyr time scale.

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Applications of the IGIMF-theory to the astrophysics of galaxies

The functional form of the galaxy-wide stellar initial mass function is of fundamental importance for understanding galaxies. So far this stellar initial mass function has been assumed to be identical to the IMF observed directly in star clusters. But because stars form predominantly in embedded groups rather than uniformly distributed over the whole galaxy, the galaxy-wide IMF needs to be calculated by adding all IMFs of all embedded groups. This integrated galactic stellar initial mass function (IGIMF) is steeper than the canonical IMF and steepens with decreasing SFR, leading to fundamental new insights and understanding of star forming properties of galaxies. This contribution reviews the existing applications of the IGIMF theory to galactic astrophysics, while the parallel contribution by Weidner, Pflamm-Altenburg & Kroupa (this volume) introduces the IGIMF theory.

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The galaxy-wide IMF - from star clusters to galaxies

Over the past years observations of young and populous star clusters have shown that the stellar initial mass function (IMF) can be conveniently described by a two-part power-law with an exponent alpha_2 = 2.3 for stars more massive than about 0.5 Msol and an exponent of alpha_1 = 1.3 for less massive stars. A consensus has also emerged that most, if not all, stars form in stellar groups and star clusters, and that the mass function of these can be described as a power-law (the embedded cluster mass function, ECMF) with an exponent beta ~2. These two results imply that the integrated galactic IMF (IGIMF) for early-type stars cannot be a Salpeter power-law, but that they must have a steeper exponent. An application to star-burst galaxies shows that the IGIMF can become top-heavy. This has important consequences for the distribution of stellar remnants and for the chemo-dynamical and photometric evolution of galaxies. In this contribution the IGIMF theory is described, and the accompanying contribution by Pflamm-Altenburg, Weidner & Kroupa (this volume) documents the applications of the IGIMF theory to galactic astrophysics.

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Two step ejection of massive stars and the issue of their formation in isolation

In this paper we investigate the combined effect of massive binary ejection from star clusters and a second acceleration of a massive star during a subsequent supernova explosion. We call this the "two-step-ejection" scenario. The main results are: i) Massive field stars produced via the two-step-ejection process can not in the vast majority of cases be traced back to their parent star clusters. These stars can be mistakenly considered as massive stars formed in isolation. ii) The expected O star fraction produced via the two-step-ejection process is of the order of 1-4 per cent, in quantitative agreement with the observed fraction of candidates for isolated-O-star formation. iii) Stars ejected via the two-step-ejection process can get a higher final velocity (up to 1.5-2 times higher) than the pre-supernova velocity of the massive-star binary.

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The fundamental gas depletion and stellar-mass buildup times of star forming galaxies

Stars do not form continuously distributed over star forming galaxies. They form in star clusters of different masses. This nature of clustered star formation is taken into account in the theory of the integrated galactic stellar initial mass function (IGIMF) in which the galaxy-wide IMF (the IGIMF) is calculated by adding all IMFs of young star clusters. For massive stars the IGIMF is steeper than the universal IMF in star clusters and steepens with decreasing SFR which is called the IGIMF-effect. The current SFR and the total Halpha luminosity of galaxies therefore scale non-linearly in the IGIMF theory compared to the classical case in which the galaxy-wide IMF is assumed to be constant and identical to the IMF in star clusters. We here apply for the first time the revised SFR-L_Halpha relation on a sample of local volume star forming galaxies with measured Halpha luminosities. The fundamental results are: i) the SFRs of galaxies scale linearly with the total galaxy neutral gas mass, ii) the gas depletion time scales of dwarf irregular and large disk galaxies are about 3 Gyr implying that dwarf galaxies do not have lower star formation efficiencies than large disk galaxies, and iii) the stellar mass buildup times of dwarf and large galaxies are only in agreement with downsizing in the IGIMF context, but contradict downsizing within the traditional framework that assumes a constant galaxy-wide IMF.

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Clustered star formation as a natural explanation of the Halpha cutoff in disc galaxies

Star formation is mainly determined by the observation of H$α$ radiation which is related to the presence of short lived massive stars. Disc galaxies show a strong cutoff in H$α$ radiation at a certain galactocentric distance which has led to the conclusion that star formation is suppressed in the outer regions of disc galaxies. This is seemingly in contradiction to recent UV observations (Boissier et al., 2007) that imply disc galaxies to have star formation beyond the Halpha cutoff and that the star-formation-surface density is linearly related to the underlying gas surface density being shallower than derived from Halpha luminosities (Kennicutt, 1998). In a galaxy-wide formulation the clustered nature of star formation has recently led to the insight that the total galactic Halpha luminosity is non-linearly related to the galaxy-wide star formation rate (Pflamm-Altenburg et al., 2007d). Here we show that a local formulation of the concept of clustered star formation naturally leads to a steeper radial decrease of the Halpha surface luminosity than the star-formation-rate surface density in quantitative agreement with the observations, and that the observed Halpha cutoff arises naturally.

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Recurrent gas accretion by massive star clusters, multiple stellar populations and mass thresholds for spherical stellar systems

We explore the gravitational influence of pressure supported stellar systems on the internal density distribution of a gaseous environment. We conclude that compact massive star clusters with masses >= 10^6 M_sun act as cloud condensation nuclei and are able to accrete gas recurrently from a warm interstellar medium which may cause further star formation events and account for multiple stellar populations in the most massive globular and nuclear star clusters. The same analytical arguments can be used to decide whether an arbitrary spherical stellar system is able to keep warm or hot interstellar material or not. These mass thresholds coincide with transition masses between pressure supported galaxies of different morphological types.

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On the origin of complex stellar populations in star clusters

The existence of complex stellar populations in some star clusters challenges the understanding of star formation. E.g. the ONC or the sigma Orionis cluster host much older stars than the main bulk of the young stars. Massive star clusters (omega Cen, G1, M54) show metallicity spreads corresponding to different stellar populations with large age gaps. We show that (i) during star cluster formation field stars can be captured and (ii) very massive globular clusters can accrete gas from a long-term embedding inter stellar medium and restart star formation.

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Converting Halpha luminosities into SFRs

Star-formation rates (SFRs) of galaxies are commonly calculated by converting the measured Halpha luminosities (L_Halpha) into current SFRs. This conversion is based on a constant initial mass function (IMF) independent of the total SFR. As recently recognised the maximum stellar mass in a star cluster is limited by the embedded total cluster mass and, in addition, the maximum embedded star cluster mass is constrained by the current SFR. The combination of these two relations leads to an integrated galaxial initial stellar mass function (IGIMF, the IMF for the whole galaxy) which is steeper in the high mass regime than the constant canonical IMF, and is dependent on the SFR of the galaxy. Consequently, the L_Halpha-SFR relation becomes non-linear and flattens for low SFRs. Especially for dwarf galaxies the SFRs can be underestimated by up to three orders of magnitude. We revise the existing linear L_Halpha-SFR relations using our IGIMF notion. These are likely to lead to a revision of the cosmological star formation histories. We also demonstrate that in the case of the Sculptor dwarf irregular galaxies the IGIMF-formalism implies a linear dependence of the total SFR on the total galaxy gas mass. A constant gas depletion time scale of a few Gyrs results independently of the galaxy gas mass with a reduced scatter compared to the conventional results. Our findings are qualitatively independent of the explicit choice of the IGIMF details and challenges current star formation theory in dwarf galaxies.

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Converting H$α$ Luminosities into Star Formation Rates

The recent finding that the IGIMF (integrated galaxial initial stellar mass function) composed of all newly formed stars in all young star clusters has, in dependence of the SFR, a steeper slope in the high mass regime than the underlying canonical IMF of each star cluster offers new insights into the galactic star formation process: The classical linear relation between the SFR and the produced H$α$ luminosity is broken and SFRs are always underestimated. Our new relation is likely to lead to a revision of the cosmological SFH.

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Captured older stars as the reason for apparently prolonged star formation in young star clusters

The existence of older stars within a young star cluster can be interpreted to imply that star formation occurs on time scales longer than a free-fall time of a pre-cluster cloud core. Here the idea is explored that these older stars are not related to the star formation process forming the young star cluster but rather that the orbits of older field stars are focused by the collapsing pre-cluster cloud core. Two effects appear: The focussing of stellar orbits leads to an enhancement of the density of field stars in the vicinity of the centre of the young star cluster. And due to the time-dependent potential of the forming cluster some of these stars can get bound gravitationally to the cluster. These stars exhibit similar kinematical properties as the newly formed stars and can not be distinguished from them on the basis of radial-velocity or proper-motion surveys. Such contaminations may lead to a wrong apparent star-formation history of a young cluster. In the case of the ONC the theoretical number of gravitationally bound older low-mass field stars agrees with the number of observed older low-mass stars.

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