------------------------------------------------------------------------ ms-revised-version.tex MNRAS, in press From: Ralf Klessen Date: Mon, 20 Nov 2006 09:36:10 +0100 X-Mailer: Apple Mail (2.752.3) X-MailScanner-Information: Please contact postmaster@aoc.nrao.edu for more information X-MailScanner: Found to be clean X-MailScanner-SpamCheck: not spam, SpamAssassin (score=0, required 5, autolearn=disabled) X-MailScanner-From: rklessen@ita.uni-heidelberg.de X-Spam-Status: No --Apple-Mail-2-1020976908 Content-Transfer-Encoding: 7bit Content-Type: text/plain; charset=US-ASCII; delsp=yes; format=flowed %astro-ph/ %http://www.blackwell-synergy.com/doi/abs/10.1111/j. 1745-3933.2006.00258.x --Apple-Mail-2-1020976908 Content-Transfer-Encoding: 7bit Content-Type: application/octet-stream; x-unix-mode=0644; name=ms-revised-version.tex Content-Disposition: attachment; filename=ms-revised-version.tex \documentclass[useAMS,usenatbib]{mn2e} \usepackage{epsf,rotating,color} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %\usepackage{txfonts} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % latex draft-mnras-04.tex ; dvips -o draft-mnras-04.ps draft-mnras-04 ; ps2pdf draft-mnras-04.ps \title[IMF in the Galactic Centre and Starburst Regions]{ The Stellar Mass Spectrum in Warm and Dusty Gas: Deviations from Salpeter in the Galactic Centre and in Circum-Nuclear Starburst Regions} \author[Klessen, Spaans, \& Jappsen]{Ralf S.\ Klessen$^{1,2}$, %\thanks{E-mail: rklessen@ita.uni-heidelberg.de} Marco Spaans$^3$, Anne-Katharina Jappsen$^{2,4}$\\ {$^1$Zentrum f\"ur Astronomie der Universit\"at Heidelberg, Institut f\"ur Theoretische Astrophysik, Albert-\"Uberle-Str.\ 2,}\\ {~ 69120 Heidelberg, Germany}\\ {$^2$Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany} \\ {$^3$Kapteyn Astronomical Institute, P.O. Box 800, 9700 AV Groningen, The Netherlands}\\ {$^4$Canadian Institute for Theoretical Astrophysics, McLennan Physics Labs, 60 St. George Street,}\\{~ University of Toronto, Toronto, ON M5S 3H860, Canada} } \begin{document} % \def\araa{{\em ARAA}} %\def\aas{{\em Astron.\ Astrophys.\ Suppl.\ Ser.}} \def\aj{{\em AJ}} %\def\anap{{\em Ann.\ Astrophys.}} %{\em Annales d'Astrophysique} %\def\an{{\em Astron. Nach.}} \def\apj{{\em ApJ}} \def\apjl{{\em ApJ}} \def\apjs{{\em ApJS}} \def\aap{{\em A\&A}} \def\apss{{\em Astrophys.\ Space Science}} \def\baas{{\em Bull.\ Amer.\ Astron.\ Soc.}} \def\bain{{\em Bull.\ Astron.\ Inst.\ Netherlands}} \def\fcp{{\em Fund.\ Cosm.\ Phys.}} \def\jcam{{\em J.\ Comput.\ Appl.\ Math.}} \def\jcp{{\em J.\ Comput.\ Phys.}} \def\jfm{{\em J.\ Fluid Mech.}} \def\mnras{{\em MNRAS}} \def\nat{{\em Nature}} \def\pta{{\em Phil.\ Trans.\ A.}} \def\ptp{{\em Prog.\ Theo.\ Phys.}} \def\prd{{\em Phys.\ Rev.\ D}} \def\pre{{\em Phys.\ Rev.\ E}} \def\prl{{\em Phys.\ Rev.\ Lett.}} \def\prsa{{\em Proc.\ R.\ Soc.\ London A}} \def\pasj{{\em Pub.\ Astron.\ Soc.\ Japan}} \def\pasp{{\em PASP}} \def\pfl{{\em Phys.\ Fluids}} \def\ppl{{\em Phys.\ Plasmas}} \def\rpp{{\em Rep.\ Prog.\ Phys.}} \def\rmp{{\em Rev.\ Mod.\ Phys.}} \def\zp{{\em Z.\ Phys.}} \def\za{{\em Z.\ Astrophys.}} \date{Received sooner; accepted later} \pagerange{\pageref{firstpage}--\pageref{lastpage}} \pubyear{2006} \maketitle \label{firstpage} \begin{abstract} % %% Understanding the origin of stellar masses is a key problem in %% astrophysics. In the solar neighborhood, the mass distribution of %% stars follows a seemingly universal pattern. In the centre of the %% Milky Way, however, there are indications for strong deviations and %% similar may hold for starburst galaxies in the distant universe. We %% perform ab-initio hydrodynamic calculations of stellar birth in a %% circum-nuclear starburst region and compare these to the solar %% neighborhood. We show that under extreme environmental conditions %% the stellar mass spectrum is expected to be dominated by massive %% stars and discuss possible implications for galaxy formation and %% evolution. %% Understanding the origin of stellar masses is a key problem in astrophysics. In the solar neighborhood, the mass distribution of stars follows a seemingly universal pattern. In the centre of the Milky Way, however, there are indications for strong deviations and the same may be true for the nuclei of distant starburst galaxies. Here we present the first numerical hydrodynamical calculations of stars formed in a molecular region with chemical and thermodynamic properties similar to those of warm and dusty circum-nuclear starburst regions. The resulting IMF is top-heavy with a peak at $\sim 15$ $M_\odot$, a sharp turn-down below $\sim 7$ $M_\odot$ and a power-law decline at high masses. We find a natural explanation for our results in terms of the temperature dependence of the Jeans mass, with collapse occuring at a temperature of $\sim 100$ K and an H$_2$ density of a few $\times 10^5$ cm$^{-3}$, and discuss possible implications for galaxy formation and evolution. % \end{abstract} \begin{keywords} stars: formation -- hydrodynamics -- turbulence -- equation of state -- Galaxy: centre -- galaxies: starburst \end{keywords} %\firstsection % if your document starts with a section, % remove some space above using this command. \section{Introduction} Identifying the physical processes that determine the masses of stars and their statistical distribution, the initial mass function (IMF), is a fundamental problem in star-formation research. It is central to much of modern astrophysics, with implications ranging from cosmic re-ionisation and the formation of the first galaxies, over the evolution and structure of our own Milky Way, down to the build-up of planets and planetary systems. % which have been discovered in abundance in the past decade. Near the Sun the number density of stars as a function of mass has a peak at a characteristic stellar mass of a few tenths of a solar mass, below which it declines steeply, and for masses above one solar mass it follows a power-law with an exponent $dN/d{\log}m \propto m^{-1.3}$. Within a radius of several kpc %from the Sun this distribution shows surprisingly little variation (Salpeter 1955; Scalo 1998; Kroupa 2001; Kroupa 2002; Chabrier 2003). This has prompted the suggestion that the distribution of stellar masses at birth is a truly universal function, which often is referred to as the Salpeter IMF, although note that the original Salpeter (1955) estimate was a pure power-law fit without characteristic mass scale. On the other hand, there is increasing evidence that the IMF close to the centre of our Milky Way (Stolte et al.\ 2002, 2005, Nayakshin \& Sunyaev 2005, Paumard et al.\ 2006) and the neighboring Andromeda galaxy (Bender et al.\ 2005) is dominated by massive rather than low-mass stars. For the circum-nuclear starburst regions in more distant galaxies, very similar IMF deviations are subject to continuing debate (e.g., Scalo 1990, Elmegreen 2005). %% If true, this would have important consequences %% for our understanding of the early universe and for galaxy evolution %% from high redshifts to present times (10). However, no conclusion has yet been reached, and it appears timely to examine the problem from a theoretical point of view. We approach the problem by means of self-consistent hydrodynamical calculations of fragmentation and star formation in interstellar gas where chemical and thermodynamical properties are described by a realistic equation of state (EOS). We focus on the most extreme environmental conditions such as occur in the nuclear regions of massive star-forming spiral galaxies. There the inferred dust and gas temperatures, gas densities and star formation rates typically exceed the solar-neighborhood values by factors of 3, 10 and $\ge 100$, respectively (e.g.\ Ott et al.\ 2005; Israel 2005; Aalto et al.\ 2002; Spinoglio et al.\ 2002). Consequently, it has long been speculated that such conditions lead to deviations from the Salpeter IMF (e.g., Scalo 1990, Elmegreen 2005). %Our study shows that this is indeed expected to be the case. \begin{figure*} \centerline{% \epsfxsize=0.90\textwidth\epsffile{figure1.ps} %\epsfxsize=0.33\textwidth\epsffile{imf_200h_from_162_004_x_z.eps} %\epsfxsize=0.33\textwidth\epsffile{imf_200h_from_162_007_002_002_x_z.eps} %\epsfxsize=0.33\textwidth\epsffile{imf_200h_from_162_007_002_009_004_003_x_z.eps} } \vspace*{0.4cm} \caption{Column density distribution of the gas projected along the three principal axes of the system after 3.5 million years of evolution when 15\% of the gas is converted into protostars (sink particles). Their location is indicated by black dots.} \label{fig:2D-plot} \end{figure*} \section{Model} Stars and star clusters form through the interplay between self-gravity on the one side and turbulence, magnetic fields, and thermal pressure on the other %, so-called gravoturbulent fragmentation (for recent reviews see Larson 2003; Mac~Low \& Klessen 2004; Ballesteros-Paredes et al.\ 2006). The supersonic turbulence ubiquitously observed in interstellar gas clouds can create strong density fluctuations with gravity taking over in the densest and most massive regions. Collapse sets in to build up stars and star clusters. Turbulence plays a dual role. On global scales it provides support, %and counterbalances gravity, on local scales it provokes collapse. Stellar birth is thus intimately linked to the dynamic behavior of the parental gas cloud, which governs when and where star formation sets in (as illustrated in Figure \ref{fig:2D-plot}). The chemical and thermodynamic properties of interstellar clouds play a key role in this process. In particular, the value of the polytropic exponent $\gamma$, when adopting an EOS of the form $P\propto\rho^\gamma$, strongly influences the compressibility of density condensations as well as the temperature of the gas. The EOS thus determines the amount of clump fragmentation, and so directly relates to the IMF (V\'azquez-Semadeni et al.\ 1996) with values of $\gamma$ larger than unity leading to little fragmentation and high mass cores (Li, Klessen, \& Mac~Low 2003; Jappsen et al.\ 2005). The stiffness of the EOS in turn depends strongly on the ambient metallicity, density and infrared background radiation field produced by warm dust grains. The EOS thus varies considerably in different galactic environments (see Spaans \& Silk 2000, 2005 for a detailed account). For the circum-nuclear starburst regions that are the subject here we assume a cosmic ray ionisation rate of $3\times 10^{-15}$ s$^{-1}$, solar relative abundances (Asplund et al.\ 2004; Jenkins 2004) and an overall metallicity of two times solar (Barthel 2005). A velocity dispersion $\Delta V_{\rm tur}=5$ km/s is adopted to take the larger input of kinetic energy (e.g.\ through supernovae) into account. The dust temperature inside the model clouds is set by a fiducial background star formation rate of $100\,$M$_\odot$ yr$^{-1}$/kpc$^{2}$ which causes dust grains to be at temperatures of about $T_d=30 - 90\,$K, depending on the amount of shielding. Gas temperatures range from $T_g = 40 - 140\,$K, over a density range of $10^4 - 10^7\,$cm$^{-3}$. These values are consistent with gas and dust temperatures determined for circum-nuclear starburst regions (Klaas et al.\ 1997; Aalto et al.\ 2002; Spinoglio et al.\ 2002; Ott et al.\ 2005; Israel 2005). \begin{figure} \centerline{\epsfxsize=0.45\textwidth\epsffile{figure2.ps}} %\centerline{\epsfxsize=0.40\textwidth\epsffile{spaans-EOS-3.ps}} \caption{Starburst EOS adopted from Spaans \& Silk (2005).} \label{fig:starburst-EOS} \end{figure} Figure \ref{fig:starburst-EOS} shows the resulting polytropic exponent as a function of density. The main feature is the $\gamma > 1$ peak around $n = 10^4\ $cm$^3$. This peak implies that the gas warms up as it is compressed and it is caused mainly by strong photon trapping in opaque H$_2$O and CO lines in the metal-rich nuclear gas. That is, the large optical depth in the cooling lines suppresses the cooling efficiency. Also, warm dust ($T > 40\,$K), heated by the ambient stars, causes H$_2$O collisional de-excitation heating through far-infrared pumping (Takahashi, Hollenbach \& Silk, 1983; Spaans \& Silk 2005), which adds to the gas-dust heating. Cosmic-ray heating rate is elevated by a high supernova rate, as expected for nuclear starburst regions (Bradford et al.\ 2003). %% shows the resulting dependence of the polytropic exponent on %% density. Its main feature is the $\gamma >1$ peak around a few %% $\times 10^4$ cm$^{-3}$. This peak implies that the gas warms up as it %% is compressed and it is caused mainly by strong photon trapping in %% opaque H$_2$O and CO lines (Spaans \& Silk 2000, 2005). Also, warm %% dust ($>40$ K) causes H$_2$O collisional de-excitation heating through %% far-infrared pumping (Takahashi, Hollenbach \& Silk 1983; Spaans \& %% Silk 2005), which adds to the gas-dust and cosmic-ray heating rates at %% these densities. Adopting this EOS we follow the dynamical evolution of the star-forming gas using smoothed particle hydrodynamics (SPH). This is a Lagrangian method to solve the equations of hydrodynamics, where the fluid is represented by an ensemble of particles, and flow quantities are obtained by averaging over an appropriate subset of SPH particles (Monaghan 2005). The method is able to resolve high density contrasts as particles are free to move, and so the particle concentration increases naturally in high-density regions. The performance and convergence properties of SPH are well understood and tested against analytic models and other numerical schemes in the context of astrophysical flows (see, e.g., Mac~Low et al.\ 1998; Lombardi et al.\ 1999; Klessen et al.\ 2000; O'Shea et al.\ 2005; Ballesteros-Paredes et al.\ 2006). Artificial fragmentation can be ruled out, as long as the mass within one smoothing volume remains less than half the critical mass for gravitational collapse (Bate \& Burkert 1997; Hubber, Goodwin, \& Whitworth 2005). We use the publically available parallel code GADGET (Springel et al.\ 2001). It is modified to replace high-density cores with sink particles (Bate, Bonnell, \& Price 1995) that can accrete gas from their surroundings while keeping track of mass and momentum. This enables us to follow the dynamic evolution of the system over many local free-fall timescales. We identify sink particles as the direct progenitors of individual stars. For a more detailed account of the method and a discussion of its convergence properties we refer the reader to Klessen et al.\ (2000) and Jappsen et al.\ (2005). \begin{figure*} \centerline{\epsfxsize=0.45\textwidth\epsffile{figure3a.ps}\epsfxsize=0.45\textwidth\epsffile{figure3b.ps}} \caption{ {\em (a)} Mass spectrum of gravitational condensations in the starburst calculation at a time when 15\% of the gas is converted into collapsed objects (which we identify as direct progenitors of individual stars). To guide the eye, we indicate a slope -1.0 and the Salpeter slope -1.3 with dotted lines. The mass function in our simulated starburst environment shows a broad peak in the range $10\,$M$_{\odot}-25\,$M$_{\odot}$ and falls off for larger masses. It is thus top-heavy compared to the IMF in the solar neighborhood (Salpeter 1955; Kroupa 2002; Chabrier 2003). {\em (b)} Mass spectrum of collapsed objects in a calculation focusing on nearby molecular clouds (see Jappsen et al.\ 2005). It agrees well with the IMF in the solar vicinity. For comparison we overplot the functional forms proposed by Kroupa (2002) with dashed lines and by Chabrier (2003) with dotted lines. Our two calculations differ mainly in the adopted EOS, i.e.\ in the chemical and thermodynamic state of the star forming gas, other parameters are comparable. %% %% Mass spectrum of protostellar objects in a simulation %% focusing on a starburst environment. The size of the considered %% molecular cloud region is $11.14\,$pc and it contains %% $80\,000\,$M$_{\odot}$. The system is depicted at a time when 15\% of %% the gas is converted to stars. The mean mass of the distribution %% lies at 15 $M_\odot$. The nominal resolution limit is $1\,$M$_{\odot}$. } \label{fig:starburst-IMF} \end{figure*} We focus on a cubic volume of 11.2$\,$pc in size, which contains $80,000\,$M$_{\odot}$ of gas and has an initial mean particle density $n = 10^3\,$cm$^{_3}$ at a temperature of $21\,$K. Above the characteristic density $n = 10^4\,$cm$^{-3}$ where $\gamma$ is at a maximum, the temperature quickly reaches values of $\sim 100\,$K. This set-up is chosen to describe the typical environment within the central regions of an actively star-forming galaxy such as our own Milky Way or NGC$\,$253. In such galaxies, high-density gas with $n > 10^5\,$cm$^{-3}$, as traced by HCN, typically has a filamentary structure with very low filling factor, while the bulk of the gas is at $n \approx 10^3\,$cm$^{-3}$ (Morris \& Serabyn 1996; H\"uttemeister et al.\ 1993; Israel \& Baas 2003), exactly as found at the end of our simulation (see Figure \ref{fig:2D-plot}). We stop the calculation at a star formation efficiency SFE $\approx 15$\%, when roughly 1/6 of the total gas mass has turned into gravitationally collapsed condensations (i.e.\ sink particles, which we identify as direct progenitors of individual young stars). %% For typical molecular clouds in the solar vicinity less %% than a few percent of their mass takes part in star formation (Myers %% et al.\ 1986). However, in circum-nuclear starburst regions this star %% formation efficiency (SFE) can be higher by as much as an order of %% magnitude (Mooney \& Solomon 1988). %% Throughout the simulation we drive turbulence continuously on large scales, with wave numbers $k$ in the range $1 \le k \le 2$ (see Mac~Low 1999) to yield a constant turbulent Mach number $\mathcal{M}_{\mathrm{rms}}\approx 5$. The particle number is $N=8\,000\,000$. This is thus one of the highest-resolution star-formation calculations done with SPH, with a total CPU time of $8 \times 10^4$ hours. %% The star formation %% efficiency, i.e.\ the total fraction of gas turned into stars at the %% end of the simulation, is about 15\%. The critical density for sink particle formation is $n_c = 10^7\,$cm$^{-3}$, with a sink particle radius of 0.015$\,$pc. The mass of individual SPH particles is $m=0.01\,$M$_{\odot}$, which is sufficient to resolve the minimum Jeans mass in the system $M_{\rm J} \approx 1.5\,$M$_{\odot}$. Except for the EOS and the particle number, the numerical set-up is identical to the study by Jappsen et al.\ (2005). We have performed a second run for a region of 5.7$\,$pc with 4 times less mass, eight times fewer particles and a sink particle radius of 0.02 pc that has reached a SFE $\sim 36$\%. %% {\sl %% For SFE $>10$\%, the resulting %% mass spectrum in the two regions are statistically indistinguishable %% and no longer change with time. We are thus allowed to consider the %% results of the two simulations in combination. %% } \section{Result and Physical Interpretation} We find that in the considered star-forming region, the mass spectrum of collapsed objects is biased towards high masses. The resulting IMF has a broad peak at $\sim 15\,$M$_{\odot}$ followed by an approximate power-law fall-off with a slope in the range -1.0 to -1.3. Furthermore, there is a clear deficit of stars below $7\,$M$_{\odot}$. This is illustrated in Figure \ref{fig:starburst-IMF}a. We contrast this finding with the result from a simulation appropriate for the physical conditions in star forming regions near the Sun (from Jappsen et al.\ 2005), where $\gamma$ changes from 0.7 to 1.1 at an H$_2$ density of a few $\times 10^5\,$cm$^{-3}$. As expected, Figure \ref{fig:starburst-IMF}b shows a mass spectrum that is very similar to the IMF in the solar neighborhood (Kroupa 2002; Chabrier 2003). These striking differences are caused by the very disparate chemical and thermodynamic state of the star forming gas in the two simulations, since all other parameters are very similar. Our results thus support the hypothesis that for extreme environmental conditions as inferred for the centres of most spiral galaxies or more general for IR-luminous circum-nuclear starburst regions the IMF is indeed expected to be top-heavy. %% Note, %% that the strong shear motions close to the Galactic centre may be able %% to mimic the EOS effects discussed here, as shear adds stability and %% thus requires larger Jeans masses for collapse to occur. However, the %% Arches cluster is bound, i.e. this shear field may not play a dominant %% role in the inner parts of the cluster. There is a natural explanation for our results in terms of the temperature dependence of the Jeans mass $M_{\rm J}$. Compared to a mean temperature of $10\,$K for dense molecular gas in the Milky Way, gravitationally collapsing gas in our simulations has a temperature of $\sim 100\,$K and an H$_2$ density of a few $\times 10^5$ cm$^{-3}$. As the critical mass for gravitational collapse scales as $M_{\rm J} \propto T^{1.5}$, this boosts $M_{\rm J}$ from $0.3\,$M$_\odot$ at $10\,$K to about 10$\,$M$_\odot$ at $100\,$K (see also Klessen \& Burkert 2000, Bonnell, Clarke, \& Bate 2006). This temperature may seem high, but is quite consistent with molecular cloud observations in the Galactic centre (e.g. H\"uttemeister et al.\ 1993) or with high-density ($n>10^4\,$cm$^{-3}$) NH$_3$ data in the starburst centre of NGC253 (Ott et al.\ 2005). We also note, that this Jeans mass scaling argument is supported by recent observations in more nearby high-mass star-forming regions. For example, in M17 at a distance of 1.6$\,$kpc from the Sun, the mass spectrum of prestellar cores, which are the direct progenitors of individual stars, peaks at at $\sim 4\,$M$_{\odot}$ at an ambient temperature of $30\,$K (Reid \& Wilson 2006). This is well above the corresponding peak in low-mass star-forming regions (e.g.\ Motte, Andr{\'e}, \& Neri 1998). %% In principle, %% the formation of multiple stellar systems (28) and protostellar %% feedback (29), which our numerical method cannot resolve, may diminish %% the final stellar masses. Still, even in the extreme case that half of %% the collapsing mass is redistributed or removed, deviations from the %% standard IMF will persist. \section{Discussion} Our mass spectrum is in good agreement with the IMF estimates in the Galactic centre by Stolte et al.\ (2002, 2005), Nayakshin et al. (2005), and Paumard et al.\ (2006). For example, Stolte et al.\ (2002, 2005) find for the Arches cluster a clear deficit of stars below $7\,$M$_\odot$. This is consistent with our result in the sense that the ambient densities and temperatures found in the Galactic centre are similarly elevated (Helfer \& Blitz 1996) as in the circum-nuclear starburst environment we consider. We stress that the turn-down in our model IMF at masses below 10$\,$M$_\odot$ is a direct consequence of the stiff EOS for densities $n$ above a few$\times 10^3\,$cm$^{-3}$ through the Jeans mass temperature dependence, and is not caused by resolution effects. Our two simulations resolve masses down to $\sim 2\,$M$_\odot$ and $\sim 1\,$M$_\odot$, respectively, and our least massive stars (i.e.\ sink particles) are well above this limit. Rather, the effective Jeans mass at $T\sim 100$K and densities of $\sim 10^5-10^6$ cm$^{-3}$ prevent the formation of low-mass stars. When interpreting our simulation results, there are several caveats that need to be kept in mind. First, our numerical model does not include shear. Strong shear motions may mimic the EOS effects discussed here, as shear adds stability and thus requires larger Jeans masses for collapse to occur. However, the Arches cluster is bound. Thus the Galactic centre shear field cannot play a dominant role in the inner parts of the cluster. Second, our numerical model does not take the effects of magnetic fields into account, which may be of considerable strength in the Galactic centre (Yusef-Zadeh \& Morris 1987, but also see Roy 2004 for lower estimates). However, even if there is a rough equipartition between kinetic and magnetic energy, the chemical and thermodynamic properties of the gas are not strongly affected. Our results will still hold at least qualitatively, in the sense that an extreme environment leads to deviatiations from the standard Salpeter IMF. Third, the use of sink particles does not permit us to resolve close binary systems. Massive stars in the solar vicinity are almost always members of a binary or higher-order multiple stellar system (e.g.\ Vanbeveren et al.\ 1998). If this trend holds also for starburst environments, then the peak of the stellar IMF will lie below the value reported here. For instance, if each unresolved sink particle in our calculation separates into a binary star, in a statistical sense our mass spectrum needs to be shifted to lower masses by a factor of 0.5. Finally, protostellar feedback may locally affect the accretion onto individual protostars. In this case the mass content of the sink particle may only poorly reflect the mass that ends up in a star. However, even in the extreme case that half the mass is removed by feedback during collapse (for estimates, see Yorke \& Sonnhalter 2002; Krumholz, McKee, \& Klein 2005), deviations from the standard IMF will still persist. For typical molecular clouds in the Milky less than a few percent of their mass takes part in star formation (e.g.\ Myers et al.\ 1986) and this fraction goes up by a factor of a few for cluster-forming cores (e.g.\ Lada \& Lada 2003). A number of observations (Paglione et al. 1997; Mooney \& Solomon 1988) indicate that starburst systems like NGC253 and M82, and luminous infrared galaxies in general, have a larger fraction of their interstellar gas mass at high densities (Gao \& Solomon 2004). Consequently, their SFE's are up by as much as an order of magnitude. Our simulations cover this range and the statistics of our mass spectra do not change above a SFE $\sim 10$\% in both runs. Hence, the precise SFE that pertains to a starburst environment does not influence our results as long as it is larger than 10\%. The computed star formation rate (SFR), defined as the change in mass with time of the sink particles, is typically $860\, M_\odot$ yr$^{-1}/$kpc$^2$ for a SFE $>10$\% and when normalised to a surface area of $1\,$kpc$^2$, which is roughly the size scale of the nuclear region inside a starburst galaxy. This number lies well within the fiducial range of $50 - 1000\,M_\odot$yr$^{-1}/$kpc$^2$ inferred for most starburst systems (e.g.\ Kennicutt 1998, Scoville \& Wilson 2004). When turning to distant starburst galaxies in the early universe, the low-mass cut-off at $7\ $M$_{\odot}$ seen in the simulated local starburst region seems at first glance difficult to reconcile with the mass-to-light ratio and the stellar population synthesis models inferred from global observations (Kaufmann et al.\ 2003). However, we emphasise again, that we are focusing on an extreme case and on a clearly localised, isolated region only. In reality these extreme (warm and dusty) environmental conditions will not apply to all regions inside a starburst galaxy. There will be pockets of colder gas with different ($\gamma < 1$) EOS that are less exposed to radiation (Spaans \& Silk 2000) and that behave like Galactic star-forming regions. Under these conditions the studies by Jappsen et al.\ (2005) and Larson (2005) indicate that a normal, Salpeter-like IMF results. This also suggests that the relative contribution of the extreme IMF found in this work can be connected directly to the observations. The fraction of molecular gas at densities $> 10^4$ cm$^{-3}$ that enjoys temperatures larger than $50\,$K should be a strong indicator of deviations from a Salpeter IMF. Future work will address the issue of stellar population matching and will compare our results with observed M/L ratios and warm, high density gas mass estimates. \begin{thebibliography}{99} \bibitem[]{01}Aalto, S., Polatidis, A.G., H\"uttemeister, S., Curran, S.J., 2002, A\&A, 381, 783 \bibitem[]{02}Asplund, M., Grevesse, N., \& Sauval, J., 2005, in Cosmic Abundances as Records of Stellar Evolution and Nucleosynthesis, eds.\ T.\ G.\ Barnes \& F.\ N.\ Bash, ASP Conference Series, 336, 25 \bibitem[]{03} Ballesteros-Paredes, J., Klessen, R.\ S., Mac~Low, M.-M., V{\'a}zquez-Semadeni, E., 2006, in { Protostars and Planets V}, eds.\ B.\ Reipurth, D.\ Jewitt, \& K.\ Keil (University of Arizona Press, Tucson) (astro-ph/0603357) \bibitem[]{04} Ballesteros-Paredes, J., Gazol, A., Kim, J., Klessen, R.\ S., Jappsen, A.-K., Tejero, E., 2006, ApJ, 637, 384 \bibitem[]{05}Barthel, P.D., 2005, In: Proceedings of the dusty and molecular universe: a prelude to Herschel and ALMA,ed. A.\ Wilson. ESA SP-577, 41 \bibitem[]{06} Bate, M.\ R., Burkert, A., 1997, MNRAS, 288, 1060 \bibitem[{{Bate} {et~al.}(1995){Bate}, {Bonnell}, \& {Price}}]{BAT95} {Bate}, M.~R., {Bonnell}, I.~A., \& {Price}, N.~M. 1995, \mnras, 277, 362 \bibitem[]{07} Bender, R., et al., 2005, ApJ, 631, 280 \bibitem[]{08}{Benson}, P.~J. \& {Myers}, P.~C. 1989, ApJS, 71, 89 %% \bibitem[{{Benz}(1990)}]{BEN90} %% {Benz}, W. 1990, in {\em Numerical Modelling of Nonlinear Stellar Pulsations %% Problems and Prospects}, ed. J.~R. Buchler (Dordrecht: Kluwer), 269 \bibitem[]{09} Bonnell, I.\ A., Clarke, C.\ J., Bate, M.\ R., 2006, \mnras,368, 1296 \bibitem[]{10} Bradford, C.\ M., Nikola, T., Stacey, G.\ J., Bolatto, A.\ D., Jachson, J.\ M., Savage, M.\ L., Davidson, J.\ A., Higdon, S.\ J., 2003, ApJ, 586, 644 \bibitem[]{11}Bunker, A., Stanway, E., Ellis, R., McMahon, R., Eyles, L., Lacy, M., 2005, astro-ph/0508271 \bibitem[]{12}Chabrier, G., PASP, 115, 763 - 795 \bibitem[Elmegreen(2004)]{2004astro.ph.11193E} Elmegreen, B.~G.\ 2004, in Starbursts: from 30 Doradus to Lyman Break Galaxies, eds. R.\ de Grijs \& R.\ M.\ Gonzales Delgado (Kluwer), in press (astro-ph/0411193 ) \bibitem[]{13}Elmegreen, B.\ G., 2005, Astrophys.\ \& Space Lib., 329, 57 \bibitem[]{14}Gao, Y., Solomon, P.M., 2004, ApJS, 152, 63 \bibitem[]{15}Helfer, T.T., Blitz, L., 1996, BAAS, 28, 954 \bibitem[]{16} Hubber, D.\ A., Goodwin, S.\ P., Whitworth, A.\ P., 2005, MNRAS, in press (astro-ph/0512247) \bibitem[]{17} H\"uttemeister, S., Wilson, T.\ L., Bania, T.\ M., Martin-Pintado, J., 1993, A\&A, 280, 255 \bibitem[]{18}Israel, F.P., 2005, Ap\&SS, 295, 171 \bibitem[]{19}Israel, F.\ P., Baas, F., 2003, A\&A, 404, 495 \bibitem[{{Jappsen} {et~al.}(2005){Jappsen}, {Klessen}, {Larson}, Y., \& {Mac Low}}]{JKLLM05} {Jappsen}, A.-K., {Klessen}, R.~S., {Larson}, R.~B., Y., L., \& {Mac Low}, M.-M. 2004, \aap, 435, 611 \bibitem[]{20}Jenkins, E.B., in Origin and Evolution of the Elements, p.\ 339 \bibitem[]{21}Kaufmann, G., Heckman, T.M., White, S.D.M., Charlot, S., et al., 2003, MNRAS, 341, 33 \bibitem[]{22}Kennicutt, R.\ C., 1998, ARAA, 36, 189 - 231 \bibitem[]{23}Klaas, U., Haas, M., Heinrichsen, I., \& Schulz, B., 1997, A\&A, 325, L21 \bibitem[{{Klessen} {et~al.}(2000){Klessen}, {Heitsch}, \& {Mac Low}}]{KLE00b} {Klessen}, R.~S., {Heitsch}, F., \& {Mac Low}, M.-M. 2000, ApJ, 535, 887 \bibitem[{{Kroupa}(2001)}]{KRO01b} {Kroupa}, P. 2001, \mnras, 322, 231 \bibitem[{{Kroupa}(2002)}]{KRO02} {Kroupa}, P. 2002, Science, 295, 82 - 91 \bibitem[]{24}Krumholz, M.\ R., McKee, C.\ F., Klein, R.\ I., 2005, ApJ, 618, L33 - L36 \bibitem[]{25}Lada, C.J., \& Lada, E.A., 2003, ARA\&A, 41, 57 \bibitem[{{Larson}(2003)}]{LAR03} {Larson}, R.~B. 2003, Rep.~Prog.~Phys., 66, 1651 \bibitem[]{26} Larson, R.\ B. 2005, MNRAS, 359, 211 - 222 \bibitem[{{Li} {et~al.}(2003){Li}, {Klessen}, \& {Mac Low}}]{LI03} {Li}, Y., {Klessen}, R.~S., \& {Mac Low}, M.-M. 2003, ApJ, 592, 975 \bibitem[]{s7} Lombardi, J.\ C., Sills, A., Rasio, F.\ A., Shapiro, S.\ L., 1999, J.\ Comput.\ Phys., 152, 687 \bibitem[{{Mac Low}(1999)}]{MAC99} {Mac Low}, M.-M. 2004, ApJ, 524, 169 \bibitem[{{Mac Low} \& {Klessen}(2004)}]{MAC04} {Mac Low}, M.-M. \& {Klessen}, R.~S., 2004, Rev.~Mod.~Phys., 76, 125 \bibitem[]{28} Mac Low, M.-M., Klessen, R.~S., Burkert, A., Smith M.\ D., 1998, PRL, 80, 2754 \bibitem[]{29}Madau, P., Ferguson, H.C., Dickinson, M.E., Giavalisco, M., Steidel, C.C., Fruchter, A., 1996, MNRAS, 283, 1388 %% \bibitem[]{30} Meyer, M.R., Greissl, J., Kenworthy, M., \& McCarthy, D., %% 2004, in IMF at 50: The Initial Mass Function 50 Years Later, %% eds. E.\ Corbelli, F.\ Palla, \& H.\ Zinnecker, Kluwer, 245 \bibitem[]{31} Myers, P.~C., Dame, T.~M., Thaddeus, P., Cohen, R.~S., Silverberg, R.~F., Dwek, E., \& Hauser, M.~G., 1986, ApJ, 301, 398 %\bibitem[{{Monaghan}(1992)}]{MON92} %{Monaghan}, J.~J. 1992, \araa, 30, 543 \bibitem[{{Monaghan}(2005)}]{MON05} {Monaghan}, J.~J. 2005, {\em Prog.\ Rep.\ Phys.} 68, 1703 \bibitem[]{32}Mooney, T.J., Solomon, P.M., 1988, ApJ, 334, L51 \bibitem[]{33} Morris, M., Serabyn, E., 1996, AARA, 34, 645 \bibitem[]{34} Motte, F., Andr{\'e}, P., Neri, R., 1998, A\&A, 336, 150 \bibitem[]{35}Myers, P.C., Dame, T.M., Thaddeus, P., Cohen, R.S., Silverberg, R.F., Dwek, E., Hauser, M.G., 1986, ApJ, 301, 398 \bibitem[]{36}Nayakshin, S, Sunyaev, R., 2005, MNRAS, 364, L23 \bibitem[]{37} O'Shea, B.\ W., Nagamine, K., Springel, V., Hernquist, L., Norman, M.\ L., 2005, ApJS, 160, 1 \bibitem[]{38}Ott, J., Weiss, A., Henkel, C., Walter, F., 2005, ApJ, 629, 767 \bibitem[]{39}Paglione, T.\ A.\ D., Jackson, J.M., Ishizuki, S., 1997, ApJ, 484, 656 \bibitem[]{40}Paumard, T., et al., 2006, ApJ,643, 1011 \bibitem[]{41} Reid, M.\ A., Wilson, C.\ D., 2006, ApJ, 644, 990 \bibitem[]{42} Roy, S., 2004, BASI, 32, 205 %\bibitem[]{43}Rodriquez-Fernandez, N.J., Combes, F., Martin-Pintado, J., 2004, in 'Semaine de l'Astrophysique Francaise', eds.\ Combes et al., p.\ 475 \bibitem[{{Salpeter}(1955)}]{SAL55} {Salpeter}, E.~E. 1955, ApJ, 121, 161 \bibitem[{{Scalo}(1998)}]{SCA98} {Scalo}, J. 1998, in ASP Conf. Ser. 142: {\em The Stellar Initial Mass Function}, ed. G. Gilmore \& D. Howell (San Francisco: Astron. Soc. Pac.), 201 \bibitem[]{44}Scalo, J., 1990, in Astrophys.\ \& Space Lib., 160, 125 \bibitem[]{45}Scoville, N.Z., \& Wilson, C.D., 2004, ASPC, 322, 245 \bibitem[{{Spaans} \& {Silk}(2000)}]{SPA00} {Spaans}, M. \& {Silk}, J. 2000, ApJ, 538, 115 \bibitem[]{SPA05}Spaans, M. \& Silk, 2005, ApJ, 626, 644 \bibitem[]{46}Spinoglio, L., Andreani, P., \& Malkan, M.A., 2002, ApJ, 572, 105 \bibitem[{{Springel} {et~al.}(2001){Springel}, {Yoshida}, \& {White}}]{SPR01} {Springel}, V., {Yoshida}, N., \& {White}, S.~D.~M. 2001, New Astronomy, 6, 79 \bibitem[]{47} Stolte, A., Grebel, E.\ K., Brandner, W., Figer, D.\ F., 2002, \aap, 394, 459 \bibitem[]{48}Stolte, A., Brandner, W., Grebel, E.K., Lenzen, R., Lagrange, A.-M., 2005, ApJ, 628, L113 \bibitem[Stolte et al.(2003)]{2003ASPC..287..433S} Stolte, A., Grebel, E.~K., Brandner, W., \& Figer, D.~F.\ 2003, ASP Conf.~Ser.~287: Galactic Star Formation Across the Stellar Mass Spectrum, 287, 433 \bibitem[]{49}Takahashi, T., Hollenbach, D.J., \& Silk, J.,1983, ApJ, 275, 145 %\bibitem{kitsionas_vazquez03} V\'{a}zquez-Semadeni, E., % Ballesteros-Paredes, J., Klessen, R.~S., 2003, ApJ, 585, L131 \bibitem[]{50}Vanbeveren, D., De Loore, C., \& Van Rensbergen, W., 1998, A\&ARv, 9, 63 \bibitem[]{VAZ96}V\'azquez-Semadeni, E., Passot, T., \& Pouquet, A., 1996, ApJ, 473, 881 \bibitem[]{51}Yorke, H.\ W., Sonnhalter, C., 2002, ApJ, 569, 846 - 862 \bibitem[]{52}Yusef-Zadeh, F, \& Morris, M., 1987, AJ, 94, 1178 \end{thebibliography} \label{lastpage} \end{document} --Apple-Mail-2-1020976908 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=ISO-8859-1; delsp=yes; format=flowed Ralf Klessen Institut f=FCr Theoretische Astrophysik / Zentrum f=FCr Astronomie der =20= Universit=E4t Heidelberg Albert-=DCberle-Str. 2, 69120 Heidelberg, Germany phone: +49 6221 54 8978 / fax: +49 6221 54 4221 web: http://www.ita.uni-heidelberg.de/~ralf --Apple-Mail-2-1020976908--