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Christopher F. McKee

Publications and source records attributed to Christopher F. McKee.

At least 55 records · Page 3Linked to original sources

Radiatively Efficient Magnetized Bondi Accretion

We have carried out a numerical study of the effect of large scale magnetic fields on the rate of accretion from a uniform, isothermal gas onto a resistive, stationary point mass. Only mass, not magnetic flux, accretes onto the point mass. The simulations for this study avoid complications arising from boundary conditions by keeping the boundaries far from the accreting object. Our simulations leverage adaptive refinement methodology to attain high spatial fidelity close to the accreting object. Our results are particularly relevant to the problem of star formation from a magnetized molecular cloud in which thermal energy is radiated away on time scales much shorter than the dynamical time scale. Contrary to the adiabatic case, our simulations show convergence toward a finite accretion rate in the limit in which the radius of the accreting object vanishes, regardless of magnetic field strength. For very weak magnetic fields, the accretion rate first approaches the Bondi value and then drops by a factor ~ 2 as magnetic flux builds up near the point mass. For strong magnetic fields, the steady-state accretion rate is reduced by a factor ~ 0.2 β^{1/2} compared to the Bondi value, where βis the ratio of the gas pressure to the magnetic pressure. We give a simple expression for the accretion rate as a function of the magnetic field strength. Approximate analytic results are given in the Appendixes for both time-dependent accretion in the limit of weak magnetic fields and steady-state accretion for the case of strong magnetic fields.

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A Universal, Local Star Formation Law in Galactic Clouds, Nearby Galaxies, High-Redshift Disks, and Starbursts

[abridged] While observations of Local Group galaxies show a very simple, local star formation law in which the star formation rate per unit area in each patch of a galaxy scales linearly with the molecular gas surface density, recent observations of both Milky Way molecular clouds and high redshift galaxies apparently show a more complicated relationship, in which regions of equal surface density can form stars at quite different rates. These data have been interpreted as implying either that different star formation laws apply in different circumstances, that the star formation law is sensitive to large-scale galaxy properties rather than local properties, or that there are high density thresholds for star formation. Here we collate resolved observations of Milky Way molecular clouds, kpc-scale observations of Local Group galaxies, and unresolved observations of both disk and starburst galaxies in the local universe and at high redshift. We show that all of these data are in fact consistent with a simple, local, volumetric star formation law. The apparent variations stem from the fact that the observed objects have a wide variety of 3D size scales and degrees of internal clumping, so even at fixed gas column density the regions being observed can have wildly varying volume densities. We provide a simple theoretical framework to remove this projection effect, and we show that all the data, from small Solar neighborhood clouds with masses ~10^3 Msun to sub-mm galaxies with masses ~10^11 Msun, fall on a single star formation law in which the SFR is simply ~1% of the molecular gas mass per local free-fall time. In contrast, proposed star formation laws in which the star formation timescale is set by the galactic rotation period or the SFR is linearly proportional to the gas mass above some density threshold fail to match at least some of the data.

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A Stable, Accurate Methodology for High Mach Number, Strong Magnetic Field MHD Turbulence with Adaptive Mesh Refinement: Resolution and Refinement Studies

Performing a stable, long duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and Constrained Transport EMF averaging schemes that can meet this challenge, and using this strategy, we have developed a new Adaptive Mesh Refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma $β_0$ of 0.1 as initial conditions; our code is shown to be stable for simulations with higher Mach numbers ($M_rms = 17.3$) and smaller plasma beta ($β_0 = 0.0067$) as well. Our results show that the quality of the turbulence simulation is generally related to the volume-averaged refinement. Our AMR simulations show that the turbulent dissipation coefficient for supersonic MHD turbulence is about 0.5, in agreement with unigrid simulations.

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Sub-Alfvenic Non-Ideal MHD Turbulence Simulations with Ambipolar Diffusion: III. Implications for Observations and Turbulent Enhancement

Ambipolar diffusion (AD) is believed to be a crucial process for redistributing magnetic flux in the dense molecular gas that occurs in regions of star formation. We carry out numerical simulations of this process in regions of low ionization using the heavy ion approximation. The simulations are for regions of strong field (plasma β=0.1) and mildly supersonic turbulence (M=3, corresponding to an Alfven mach number of 0.67). The velocity power spectrum of the neutral gas changes from an Iroshnikov-Kraichnan spectrum in the case of ideal MHD to a Burgers spectrum in the case of a shock-dominated hydrodynamic system. The magnetic power spectrum shows a similar behavior. We use a 1D radiative transfer code to post-process our simulation results; the simulated emission from the CS J=2-1 and H13CO+ J=1-0 lines shows that the effects of AD are observable in principle. Linewidths of ions are observed to be less than those of neutrals, and we confirm previous suggestions that this is due to AD. We show that AD is unlikely to affect the Chandrasekhar-Fermi method for inferring field strengths unless the AD is stronger than generally observed. Finally, we present the first fully 3D study of the enhancement of AD by turbulence, finding that AD is accelerated by factor 2-4.5 for non self-gravitating systems with the level of turbulence we consider.

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Radiation-Hydrodynamic Simulations of Massive Star Formation with Protostellar Outflows

We report the results of a series of AMR radiation-hydrodynamic simulations of the collapse of massive star forming clouds using the ORION code. These simulations are the first to include the feedback effects protostellar outflows, as well as protostellar radiative heating and radiation pressure exerted on the infalling, dusty gas. We find that that outflows evacuate polar cavities of reduced optical depth through the ambient core. These enhance the radiative flux in the poleward direction so that it is 1.7 to 15 times larger than that in the midplane. As a result the radiative heating and outward radiation force exerted on the protostellar disk and infalling cloud gas in the equatorial direction are greatly diminished. The simultaneously reduces the Eddington radiation pressure barrier to high-mass star formation and increases the minimum threshold surface density for radiative heating to suppress fragmentation compared to models that do not include outflows. The strength of both these effects depends on the initial core surface density. Lower surface density cores have longer free-fall times and thus massive stars formed within them undergo more Kelvin contraction as the core collapses, leading to more powerful outflows. Furthermore, in lower surface density clouds the ratio of the time required for the outflow to break out of the core to the core free-fall time is smaller, so that these clouds are consequently influenced by outflows at earlier stages of collapse. As a result, outflow effects are strongest in low surface density cores and weakest in high surface density one. We also find that radiation focusing in the direction of outflow cavities is sufficient to prevent the formation of radiation pressure-supported circumstellar gas bubbles, in contrast to models which neglect protostellar outflow feedback.

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Radiation-Hydrodynamic Simulations of the Formation of Orion-Like Star Clusters I. Implications for the Origin of the Initial Mass Function

One model for the origin of typical galactic star clusters such as the Orion Nebula Cluster (ONC) is that they form via the rapid, efficient collapse of a bound gas clump within a larger, gravitationally-unbound giant molecular cloud. However, simulations in support of this scenario have thus far have not included the radiation feedback produced by the stars; radiative simulations have been limited to significantly smaller or lower density regions. Here we use the ORION adaptive mesh refinement code to conduct the first ever radiation-hydrodynamic simulations of the global collapse scenario for the formation of an ONC-like cluster. We show that radiative feedback has a dramatic effect on the evolution: once the first ~10-20% of the gas mass is incorporated into stars, their radiative feedback raises the gas temperature high enough to suppress any further fragmentation. However, gas continues to accrete onto existing stars, and, as a result, the stellar mass distribution becomes increasingly top-heavy, eventually rendering it incompatible with the observed IMF. Systematic variation in the location of the IMF peak as star formation proceeds is incompatible with the observed invariance of the IMF between star clusters, unless some unknown mechanism synchronizes the IMFs in different clusters by ensuring that star formation is always truncated when the IMF peak reaches a particular value. We therefore conclude that the global collapse scenario, at least in its simplest form, is not compatible with the observed stellar IMF. We speculate that processes that slow down star formation, and thus reduce the accretion luminosity, may be able to resolve the problem.

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The Global Evolution of Giant Molecular Clouds II: The Role of Accretion

We present virial models for the global evolution of giant molecular clouds. Focusing on the presence of an accretion flow, and accounting for the amount of mass, momentum, and energy supplied by accretion and star formation feedback, we are able to follow the growth, evolution, and dispersal of individual giant molecular clouds. Our model clouds reproduce the scaling relations observed in both galactic and extragalactic clouds. We find that accretion and star formation contribute contribute roughly equal amounts of turbulent kinetic energy over the lifetime of the cloud. Clouds attain virial equilibrium and grow in such a way as to maintain roughly constant surface densities, with typical surface densities of order 50 - 200 Msun pc^-2, in good agreement with observations of giant molecular clouds in the Milky Way and nearby external galaxies. We find that as clouds grow, their velocity dispersion and radius must also increase, implying that the linewidth-size relation constitutes an age sequence. Lastly, we compare our models to observations of giant molecular clouds and associated young star clusters in the LMC and find good agreement between our model clouds and the observed relationship between H ii regions, young star clusters, and giant molecular clouds.

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The Protostellar Luminosity Function

The protostellar luminosity function (PLF) is the present-day luminosity function of the protostars in a region of star formation. It is determined using the protostellar mass function (PMF) in combination with a stellar evolutionary model that provides the luminosity as a function of instantaneous and final stellar mass. As in McKee & Offner (2010), we consider three main accretion models: the Isothermal Sphere model, the Turbulent Core model, and an approximation of the Competitive Accretion model. We also consider the effect of an accretion rate that tapers off linearly in time and an accelerating star formation rate. For each model, we characterize the luminosity distribution using the mean, median, maximum, ratio of the median to the mean, standard deviation of the logarithm of the luminosity, and the fraction of very low luminosity objects. We compare the models with bolometric luminosities observed in local star forming regions and find that models with an approximately constant accretion time, such as the Turbulent Core and Competitive Accretion models, appear to agree better with observation than those with a constant accretion rate, such as the Isothermal Sphere model. We show that observations of the mean protostellar luminosity in these nearby regions of low-mass star formation suggest a mean star formation time of 0.3$\pm$0.1 Myr. Such a timescale, together with some accretion that occurs non-radiatively and some that occurs in high-accretion, episodic bursts, resolves the classical "luminosity problem" in low-mass star formation, in which observed protostellar luminosities are significantly less than predicted. An accelerating star formation rate is one possible way of reconciling the observed star formation time and mean luminosity.

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Metallicity and the Universality of the IMF

The stellar initial mass function (IMF), along with the star formation rate, is one of the fundamental properties that any theory of star formation must explain. An interesting feature of the IMF is that it appears to be remarkably universal across a wide range of environments. Particularly, there appears to be little variation in either the characteristic mass of the IMF or its high-mass tail between clusters with different metallicities. Previous attempts to understand this apparent independence of metallicity have not accounted for radiation feedback from high-mass protostars, which can dominate the energy balance of the gas in star-forming regions. We extend this work, showing that the fragmentation of molecular gas should depend only weakly on the amount of dust present, even when the primary heating source is radiation from massive protostars. First, we report a series of core collapse simulations using the ORION AMR code that systematically vary the dust opacity and show explicitly that this has little effect on the temperature or fragmentation of the gas. Then, we provide an analytic argument for why the IMF varies so little in observed star clusters, even as the metallicity varies by a factor of 100.

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IRAS 15099-5856: Remarkable Mid-Infrared Source with Prominent Crystalline Silicate Emission Embedded in the Supernova Remnant MSH15-52

We report new mid-infrared observations of the remarkable object IRAS 15099-5856 using the space telescopes AKARI and Spitzer, which demonstrate the presence of prominent crystalline silicate emission in this bright source. IRAS 15099-5856 has a complex morphology with a bright central compact source (IRS1) surrounded by knots, spurs, and several extended (~4') arc-like filaments. The source is seen only at >= 10 um. The Spitzer MIR spectrum of IRS1 shows prominent emission features from Mg-rich crystalline silicates, strong [Ne II] 12.81 um and several other faint ionic lines. We model the MIR spectrum as thermal emission from dust and compare with the Herbig Be star HD 100546 and the luminous blue variable R71, which show very similar MIR spectra. Molecular line observations reveal two molecular clouds around the source, but no associated dense molecular cores. We suggest that IRS1 is heated by UV radiation from the adjacent O star Muzzio 10 and that its crystalline silicates most likely originated in a mass outflow from the progenitor of the supernova remnant (SNR) MSH 15-52. IRS1, which is embedded in the SNR, could have been shielded from the SN blast wave if the progenitor was in a close binary system with Muzzio 10. If MSH15-52 is a remnant of Type Ib/c supernova (SN Ib/c), as has been previously proposed, this would confirm the binary model for SN Ib/c. IRS1 and the associated structures may be the relics of massive star death, as shaped by the supernova explosion, the pulsar wind and the intense ionizing radiation of the embedded O star.

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What Phase of the Interstellar Medium Correlates with the Star Formation Rate?

Nearby spiral galaxies show an extremely tight correlation between tracers of molecular hydrogen (H_2) in the interstellar medium (ISM) and tracers of recent star formation, but it is unclear whether this correlation is fundamental or accidental. In the galaxies that have been surveyed to date, H_2 resides predominantly in gravitationally bound clouds cooled by carbon monoxide (CO) molecules, but in galaxies of low metal content the correlations between bound clouds, CO, and H_2 break down, and it is unclear if the star formation rate will then correlate with H_2 or with some other quantity. Here we show that star formation will continue to follow H_2 independent of metallicity. This is not because H_2 is directly important for cooling, but instead because the transition from predominantly atomic hydrogen (HI) to H_2 occurs under the same conditions as a dramatic drop in gas temperature and Bonnor-Ebert mass that destabilizes clouds and initiates collapse. We use this model to compute how star formation rate will correlate with total gas mass, with mass of gas where the hydrogen is H_2, and with mass of gas where the carbon is CO in galaxies of varying metallicity, and show that preliminary observations match the trend we predict.

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An Initial Mass Function for Individual Stars in Galactic Disks: I. Constraining the Shape of the IMF

We derive a semi-empirical galactic initial mass function (IMF) from observational constraints. We assume that the star formation rate in a galaxy can be expressed as the product of the IMF, $ψ(m)$, which is a smooth function of mass $m$ (in units of \msun), and a time- and space-dependent total rate of star formation per unit area of galactic disk. The mass dependence of the proposed IMF is determined by five parameters: the low-mass slope $γ$, the high-mass slope $-Γ$, the characteristic mass $m_{ch}$ (which is close to the mass $m_{\rm peak}$ at which the IMF turns over), and the lower and upper limits on the mass, $m_l$ (taken to be 0.004) and $m_u$ (taken to be 120). The star formation rate in terms of number of stars per unit area of galactic disk per unit logarithmic mass interval, is proportional to $m^{-Γ} \left\{1-\exp\left[{-(m/m_{ch})^{γ+Γ}}\right]\right\}$, where $\cal N_*$ is the number of stars, $m_l<m<m_u$ is the range of stellar masses. The values of $γ$ and $\emch$ are derived from two integral constraints: i) the ratio of the number density of stars in the range $m=0.1-0.6$ to that in the range $m=0.6-0.8$ as inferred from the mass distribution of field stars in the local neighborhood, and ii) the ratio of the number of stars in the range $m=0.08 - 1$ to the number of brown dwarfs in the range $m=0.03-0.08$ in young clusters. The IMF satisfying the above constraints is characterized by the parameters $γ=0.51$ and $\emch=0.35$ (which corresponds to $m_{\rm peak}=0.27$). This IMF agrees quite well with the Chabrier (2005) IMF for the entire mass range over which we have compared with data, but predicts significantly more stars with masses $< 0.03\, M_\odot$; we also compare with other IMFs in current use.

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Regulation of Star Formation Rates in Multiphase Galactic Disks: a Thermal/Dynamical Equilibrium Model

We develop a model for regulation of galactic star formation rates Sigma_SFR in disk galaxies, in which ISM heating by stellar UV plays a key role. By requiring simultaneous thermal and (vertical) dynamical equilibrium in the diffuse gas, and star formation at a rate proportional to the mass of the self-gravitating component, we obtain a prediction for Sigma_SFR as a function of the total gaseous surface density Sigma and the density of stars + dark matter, rho_sd. The physical basis of this relationship is that thermal pressure in the diffuse ISM, which is proportional to the UV heating rate and therefore to Sigma_SFR, must adjust to match the midplane pressure set by the vertical gravitational field. Our model applies to regions where Sigma < 100 Msun/pc^2. In low-Sigma_SFR (outer-galaxy) regions where diffuse gas dominates, the theory predicts Sigma_SFR \propto Sigma (rho_sd)^1/2. The decrease of thermal equilibrium pressure when Sigma_SFR is low implies, consistent with observations, that star formation can extend (with declining efficiency) to large radii in galaxies, rather than having a sharp cutoff. The main parameters entering our model are the ratio of thermal pressure to total pressure in the diffuse ISM, the fraction of diffuse gas that is in the warm phase, and the star formation timescale in self-gravitating clouds; all of these are (in principle) direct observables. At low surface density, our model depends on the ratio of the mean midplane FUV intensity (or thermal pressure in the diffuse gas) to the star formation rate, which we set based on Solar neighborhood values. We compare our results to recent observations, showing good agreement overall for azimuthally-averaged data in a set of spiral galaxies. For the large flocculent spiral galaxies NGC 7331 and NGC 5055, the correspondence between theory and observation is remarkably close.

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Sub-Alfvenic Non-Ideal MHD Turbulence Simulations with Ambipolar Diffusion: II. Comparison with Observation, Clump Properties, and Scaling to Physical Units

Ambipolar diffusion is important in redistributing magnetic flux and in damping Alfven waves in molecular clouds. The importance of ambipolar diffusion on a length scale $\ell$ is governed by the ambipolar diffusion Reynolds number, $\rad=\ell/\lad$, where $\lad$ is the characteristic length scale for ambipolar diffusion. The logarithmic mean of the AD Reynolds number in a sample of 15 molecular clumps with measured magnetic fields (Crutcher 1999) is 17, comparable to the theoretically expected value. We identify several regimes of ambipolar diffusion in a turbulent medium, depending on the ratio of the flow time to collision times between ions and neutrals; the clumps observed by Crutcher (1999) are all in the standard regime of ambipolar diffusion, in which the neutrals and ions are coupled over a flow time. We have carried out two-fluid simulations of ambipolar diffusion in isothermal, turbulent boxes for a range of values of $\rad$. The mean Mach numbers were fixed at $\calm=3$ and $\ma=0.67$; self-gravity was not included. We study the properties of overdensities--i.e., clumps--in the simulation and show that the slope of the higher-mass portion of the clump mass spectrum increases as $\rad$ decreases, which is qualitatively consistent with Padoan et al. (2007)'s finding that the mass spectrum in hydrodynamic turbulence is significantly steeper than in ideal MHD turbulence. For a value of $\rad$ similar to the observed value, we find a slope that is consistent with that of the high-mass end of the Initial Mass Function for stars. However, the value we find for the spectral index in our ideal MHD simulation differs from theirs, presumably because our simulations have different initial conditions. This suggests that the mass spectrum of the clumps in the Padoan et al. (2007) turbulent fragmentation model for the IMF depends on the environment, which would conflict with evidence ...

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The Protostellar Mass Function

The protostellar mass function (PMF) is the Present-Day Mass Function of the protostars in a region of star formation. It is determined by the initial mass function weighted by the accretion time. The PMF thus depends on the accretion history of protostars and in principle provides a powerful tool for observationally distinguishing different protostellar accretion models. We consider three basic models here: the Isothermal Sphere model (Shu 1977), the Turbulent Core model (McKee & Tan 2003), and an approximate representation of the Competitive Accretion model (Bonnell et al. 1997, 2001a). We also consider modified versions of these accretion models, in which the accretion rate tapers off linearly in time. Finally, we allow for an overall acceleration in the rate of star formation. At present, it is not possible to directly determine the PMF since protostellar masses are not currently measurable. We carry out an approximate comparison of predicted PMFs with observation by using the theory to infer the conditions in the ambient medium in several star-forming regions. Tapered and accelerating models generally agree better with observed star-formation times than models without tapering or acceleration, but uncertainties in the accretion models and in the observations do not allow one to rule out any of the proposed models at present. The PMF is essential for the calculation of the Protostellar Luminosity Function, however, and this enables stronger conclusions to be drawn (Offner & McKee 2010).

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Metal-Ion Absorption in Conductively Evaporating Clouds

We present computations of the ionization structure and metal-absorption properties of thermally conductive interface layers that surround evaporating warm spherical clouds, embedded in a hot medium. We rely on the analytical formalism of Dalton & Balbus to calculate the temperature profile in the evaporating gas, and explicitly solve the time-dependent ionization equations for H, He, C, N, O, Si, and S in the interface. We include photoionization by an external field. We estimate how departures from equilibrium ionization affect the resonance-line cooling efficiencies in the evaporating gas, and determine the conditions for which radiative losses may be neglected in the solution for the evaporation dynamics and temperature profile. Our results indicate that non-equilibrium cooling significantly increases the value of the saturation parameter at which radiative losses begin to affect the flow dynamics. As applications we calculate the ion fractions and projected column densities arising in the evaporating layers surrounding dwarf-galaxy-scale objects that are also photoionized by metagalactic radiation. We compare our results to the UV metal-absorption column densities observed in local highly-ionized metal-absorbers, located in the Galactic corona or intergalactic medium. Conductive interfaces significantly enhance the formation of high-ions such as C^3+, N^4+, and O^5+ relative to purely photoionized clouds, especially for clouds embedded in a high-pressure corona. However, the enhanced columns are still too low to account for the O VI columns (~1e14 cm^-2) observed in the local high-velocity absorbers. We find that O VI columns larger than ~1e13 cm^-2 cannot be produced in evaporating clouds. Our results do support the conclusion of Savage & Lehner, that absorption due to evaporating O VI likely occurs in the local interstellar medium, with characteristic columns of ~1e13 cm^-2.

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The Dark Molecular Gas

The mass of molecular gas in an interstellar cloud is often measured using line emission from low rotational levels of CO, which are sensitive to the CO mass, and then scaling to the assumed molecular hydrogen H_2 mass. However, a significant H_2 mass may lie outside the CO region, in the outer regions of the molecular cloud where the gas phase carbon resides in C or C+. Here, H_2 self-shields or is shielded by dust from UV photodissociation, where as CO is photodissociated. This H_2 gas is "dark" in molecular transitions because of the absence of CO and other trace molecules, and because H_2 emits so weakly at temperatures 10 K < T < 100 K typical of this molecular component. This component has been indirectly observed through other tracers of mass such as gamma rays produced in cosmic ray collisions with the gas and far-infrared/submillimeter wavelength dust continuum radiation. In this paper we theoretically model this dark mass and find that the fraction of the molecular mass in this dark component is remarkably constant (~ 0.3 for average visual extinction through the cloud with mean A_V ~ 8) and insensitive to the incident ultraviolet radiation field strength, the internal density distribution, and the mass of the molecular cloud as long as mean A_V, or equivalently, the product of the average hydrogen nucleus column and the metallicity through the cloud, is constant. We also find that the dark mass fraction increases with decreasing mean A_V, since relatively more molecular H_2 material lies outside the CO region in this case.

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Radiation Feedback, Fragmentation, and the Environmental Dependence of the Initial Mass Function

The fragmentation of star-forming interstellar clouds, and the resulting stellar initial mass function (IMF), is strongly affected by the temperature structure of the collapsing gas. Since radiation feedback from embedded stars can modify this as collapse proceeds, feedback plays an important role in determining the IMF. However, the effects and importance of radiative heating are likely to depend strongly on the surface density of the collapsing clouds, which determines both their effectiveness at trapping radiation and the accretion luminosities of the stars forming within them. In this paper we report a suite of adaptive mesh refinement radiation-hydrodynamic simulations using the ORION code in which we isolate the effect of column density on fragmentation by following the collapse of clouds of varying column density while holding the mass, initial density and velocity structure, and initial virial ratio fixed. We find that radiation does not significantly modify the overall star formation rate or efficiency, but that it suppresses fragmentation more and more as cloud surface densities increase from those typical of low mass star-forming regions like Taurus, through the typical surface density of massive star-forming clouds in the Galaxy, up to conditions found only in super star clusters. In regions of low surface density, fragmentation during collapse leads to the formation of small clusters rather than individual massive star systems, greatly reducing the fraction of the stellar population with masses >~ 10 Msun. Our simulations have important implications for the formation of massive stars and the universality of the IMF.

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