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Reipurth et al. ( 2007 have supported the predictions made by Kroupa et al. ( 1999 concerning the binary population in the ONC, by uncovering a radially dependent binary fraction in nice agreement with the theoretically expected behaviour. The late-type stellar binary population is therewith quite well understood, over... |
Brown dwarfs (BDs), which extend the mass scale down to 0.01 [MATH] , have been added into the theoretical analysis in Kroupa & Bouvier ( 2003b ); Kroupa et al. ( 2003 This theoretical study of observational data (Close et al. 2003 ; Bouy et al. 2003 |
showed that BDs cannot be understood to be an extension of the stellar mass regime (as is often but wrongly stated). The hypothesis of doing so leads to incompatible statistics on the star-star, star-BD and BD-BD binary fractions, and on their energy distributions. This work showed that BDs must be viewed as a separate... |
TK07 and this contribution are a logical extension of the above findings. Here we repeat parts of the analysis of TK07 with assumed BD-like binary fractions up to 60 % as an upper limit. The clusters we analyse are the ONC ( Muench et al. 2002 ), TA ( Luhman 2004 ; Luhman et al. 2003 ), IC 348 (Luhman et al. 2003 and t... |
IMF basics and computational method The IMFs are constructed from power-law functions similar to that proposed by Salpeter ( 1955 |
[EQUATION] or in bi-logarithmic form [EQUATION] where [MATH] is a normalisation constant and [MATH] While Salpeter found [MATH] , the canonical stellar IMF, [MATH] , is constructed as a two-part-power law after Kroupa ( 2001 with [MATH] for a stellar mass [MATH] |
[MATH] and [MATH] for higher masses. The substellar IMF, [MATH] , is taken to be a single power-law with cluster-dependent exponent [MATH] |
The basic assumption is that a large fraction of binaries remains unresolved since cluster surveys are often performed with wide-field surveys with limited resolution. One may be tempted to use the observed IMF (hereafter [MATH] ) as a direct representation of the true IMF of individual bodies (simply the IMF hereafter... |
Possible approximations to the [MATH] are the system IMF ( [MATH] ), that is the IMF as a function of system mass (see equations 6 to 8 in TK07), and the primary body IMF ( [MATH] ), the IMF as a function of the primary object mass, [MATH] |
[EQUATION] where [MATH] is the total number of objects, [MATH] is the minimum mass of an individual body in the given population, |
[MATH] is the total binary fraction, and [MATH] is the normalised individual-body IMF. In TK07 the [MATH] has been used for the fitting process. However, one may argue that the mass derived from the system luminosity is closer to the mass of the primary star since the luminosity is mainly given by the primary object an... |
To obtain the true IMF from an observed mass distribution a binary correction has to be applied to each native population (i.e. a population of objects that share the same formation history) the cluster consists of. This is done here via the semi-analytical backward-calculation method and [MATH] minimisation against th... |
[EQUATION] and the upper mass limit of the BD-like IMF, [MATH] , are to be fitted, while the lower mass limit of BDs (0.01 [MATH] and of the star-like population (0.07 [MATH] ) is kept constant. Here, the number of BD-like and star-like objects is given by |
[EQUATION] respectively. The IMFs are then transformed into separate primary mass functions. Before being compared to the observational MFs the fitted [MATH] has been smoothed by a Gaussian convolution along the mass axis in order to simulate the error of the mass determination (see TK07 for a more detailed description... |
reaches a minimum. For the Pleiades the BD data do not constrain the power-law index, so fixed power-laws with [MATH] (the canonical value) and [MATH] have been used here. It should be noted that the power-law indices are in rough agreement with the power-law index [MATH] deduced by Bouvier et al. ( 1998 and |
Moraux et al. ( 2003 . Since they use BDs and low-mass stars up to 0.48 [MATH] while only BDs and VLMSs are used in our contribution these values have to be compared with caution. |
The crucial point in performing the binary correction is that the assumed number and mass range of a native population largely affects the resulting [MATH] . If, for example, only one overall population is assumed (as in the traditional star-like scenario for BDs and stars) but there are actually two separate BD-like a... |
The magnitude of the discontinuity, measured as the number ratio of BD-like to star-like objects at the hydrogen-burning mass limit (HBL), |
[MATH] , is given by [EQUATION] If there is no overlap of the fitted BD-like and the star-like population (which is actually the case for the ONC and the Pleiades), |
[MATH] is calculated from extrapolation of the BD-like IMF to the HBL. Since [MATH] depends on the binary fraction among each population, the binary fraction is varied from [MATH] to [MATH] |
in order to include even the most extreme BD binary fraction. The unresolved stellar binary fraction, [MATH] , is set to 0.4 for the ONC, IC 348 and the Pleiades while that of TA is assumed to be 0.8, as in TK07. |
Results 4.1 IMF fitting parameters for different BD binary fractions For illustration, Fig. shows the fitted BD-like and star-like IMFs, [MATH] and [MATH] and the resulting [MATH] for the ONC for an assumed [MATH] (upper panel) and [MATH] (lower panel), both using equal-mass pairing for BD-like binaries and random pair... |
The top panel of Fig. shows the dependency of [MATH] on [MATH] for the ONC, TA and IC 348 (the clusters for which [MATH] has actually been calculated from [MATH] minimisation) for both equal-mass pairing and random pairing. The IMFs have been fitted via the [MATH] . It should be noted that [MATH] for [MATH] for random-... |
The most remarkable feature is that [MATH] remains almost constant for equal-mass pairing in BD-like binaries. For random-pairing |
[MATH] increases with [MATH] in a similar way for all three clusters. A similar growth is found even for equal-mass pairing if [MATH] is used for fitting. For comparison, the constant values assumed for the Pleiades are shown in the lower panel of Fig. |
(straight dashed lines at [MATH] and [MATH] ). The fitting of [MATH] yields values slightly below 0.07 [MATH] for the ONC and the Pleiades. This is probably due to the Gaussian smearing of [MATH] that has been used for smoothing the fit. For TA and IC 348, however, [MATH] is found to be around 0.1 [MATH] and between 0.... |
[MATH] the best-fit [MATH] is about 0.07 for the ONC and the Pleiades while it is about 0.15 for TA and IC 348. It increases for larger [MATH] , reaching about twice these values for the extreme binarity of [MATH] . That is, if a realistic value of |
[MATH] is assumed, we expect about 1 BD-like body per 10 star-like ones for the ONC and the Pleiades, and about 1 BD-like body per 5 star-like bodies for the others. This result is remarkable given that e.g. Slesnick et al. ( 2004 state a higher BD-to-star ratio for the ONC than for TA and IC 348. The result can be int... |
[MATH] would be significantly higher (about 75 %, given the histogram data) for the ONC than suggested by our results. One may criticise the way of assigning a mass to an observed system. In TK07 the model-observed IMF has been created by simply adding the masses of all components, i.e. [MATH] . Because the observed da... |
Instead, a simpler way to at least embrace the real relation is to repeat the analysis (or parts of it) by using the primary mass instead of the system mass. This corresponds to the extreme case that the contribution of less-massive companions is negligible. This method has been used in the present contribution with si... |
4.2 The discontinuity in the low-mass IMF A measure for the discontinuity at the HBL, [MATH] , is given by eq. . For a continuous IMF [MATH] , while values significantly different from 1 indicate a discontinuity. Fig. displays [MATH] as a function of [MATH] . For all clusters [MATH] shows a similar steady increase. The... |
4.3 IMF slope and BD-to-star ratio in relation to the stellar density Certain theories of BD formation (e.g. Bonnell et al. 2008 suggest a dependency of the rate of BD formation on the star-cluster density. Correlating the BD IMF index, [MATH] , and the BD-to-star ratio, [MATH] , against the stellar density, [MATH] , m... |
[MATH] (Martín et al. 2001 [MATH] for IC 348 (Duchêne et al. 1999 , and [MATH] for the ONC (Hillenbrand & Hartmann 1998 . The values of [MATH] found in this study are plotted against [MATH] in Fig. (upper panel). In addition, the BD-to-star ratio, [MATH] , is shown in the lower panel, where |
[EQUATION] The mass limits are chosen in accordance with Kroupa et al. ( 2003 and Thies & Kroupa ( 2007 . The crosses connected with solid lines show the results of our modelling while the open circles with dashed lines are values taken from Luhman ( 2006 (TA), Preibisch et al. ( 2003 (IC 348), and |
Slesnick et al. ( 2004 (ONC). For [MATH] a regression line has been calculated. However, only three clusters have been analysed in this study, and there are large uncertainties. Especially for TA and IC 348 the confidence range is rather large here. Thus, the linear fit is only poorly constrained and well in agreement ... |
Summary A discontinuity in the IMF near the hydrogen burning mass limit appears if the binary properties of BDs and VLMSs on the one hand, and of stars on the other, are taken into account carefully when inferring the true underlying single-object IMF. This implies that BDs and some VLMSs need to be viewed as arising f... |
2.2 , and 4.3 ). Here we have extended the analysis of TK07 for BD-like binary fractions up to 60 % for the Orion Nebula Cluster, the Taurus-Auriga association, IC 348 and the Pleiades by using slight modifications of the techniques introduced in TK07. |
As a main result, we found that the discontinuity that comes about by treating BDs/VLMSs and stars consistently in terms of their observed multiplicity properties remains even for the highest BD binary fraction. These results suggest that the BD binary fraction, [MATH] , is not the dominant origin of the discontinuity ... |
It is re-emphasised that by seeking to mathematically describe the BD and stellar population in terms of the relevant mass- and binary distribution functions, it is unavoidable to mathematically separate BDs and VLMSs from stars. The two resulting mass distributions do not join at the transition mass near 0.08 [MATH] .... |
With this contribution we have quantified how the power-law index of the BD-like IMF and the BD-to-star ratio changes with varying binary fraction of BD-like bodies. The BD-like power-law index, |
[MATH] , remains almost constant if equal-mass pairing of BD-like binaries is assumed, while [MATH] increases somewhat with increasing [MATH] in the case of random pairing over the BD-like mass range. All values of [MATH] are between [MATH] and [MATH] We also find that although the stellar density differs from a few st... |
[MATH] , the resulting [MATH] is constant within the uncertainties. Similarly, the BD-to-star ratio does not show a trend with increasing stellar density. This suggests the star-formation and BD-formation outcome to be rather universal at least within the range of densities probed here. Acknowledgements This project is... |
# Source: arxiv 0808.2645 # Title: DLA kinematics and outflows from starburst galaxies # Sections: all # Downloaded: 2026-03-02T07:58:19.509023+00:00 |
DLA kinematics and outflows from starburst galaxies. Abstract We present results from a numerical study of the multiphase interstellar medium in sub-Lyman-break galaxy protogalactic clumps. Such clumps are abundant at [MATH] and are thought to be a major contributor to damped Ly [MATH] absorption. We model the formatio... |
[MATH] . At lower [MATH] resolution the first signs of the multiphase medium are spotted; however, at this low resolution thermal injection of feedback energy cannot yet create hot expanding bubbles around star-forming regions – instead feedback tends to erase high-density peaks and suppress star formation. At [MATH] |
resolution feedback compresses cold clouds, often without disrupting the ongoing star formation; at the same time a larger fraction of feedback energy is channeled into low-density bubbles and winds. These winds often entrain compact neutral clumps which produce multi-component metal absorption lines. |
Subject headings: galaxies: formation — galaxies: kinematics and dynamics — intergalactic medium 1. introduction Current numerical galaxy formation models can successfully reproduce some of the properties of damped Ly [MATH] absorbers (DLAs), such as the lower end ( [MATH] ) of the column density distribution and the t... |
(Pontzen et al., 2008 ; Razoumov et al., 2007 , the distribution of metals, and the slope of the relation between metallicity and low-ion velocity width which appears to originate in the mass-metallicity relation in the models (Pontzen et al., 2008 . On the other hand, simulations tend to overpredict the number of DLAs... |
In general, the velocity dispersion of neutral gas clouds can come either from the gravitational infall in the process of hierarchical buildup of galaxies, in the form of random velocities of protogalactic clumps (Haehnelt et al., 1998 , or from feedback from stellar winds and supernovae (SNe) (Schaye, 2001 . In fairly... |
halos at [MATH] as much as [MATH] of gas by mass can be in the cold phase surviving the infall (Razoumov et al., 2007 . The corresponding |
[MATH] can account for part of the observed neutral gas velocity dispersion. However, more massive halos are rare at [MATH] , and the fraction of cold gas drops sharply in [MATH] |
halos, leaving us in search of other mechanisms to produce high velocities. Galactic winds driven by the feedback energy from stellar winds and SNe are an obvious candidate (Schaye, 2001 . Star-forming Lyman-break galaxies (LBGs) at [MATH] show evidence for large-scale outflows with typical velocities of hundreds [MATH... |
(Pettini et al., 1998 2001 . In fact, with a simple semi-analytical model McDonald & Miralda-Escudé ( 1999 showed that feedback at the rate [MATH] per [MATH] of halo dark matter mass added to the velocity dispersion of neutral clouds inside virialized halos works out perfectly to explain the observed DLA kinematics. Ho... |
This classical problem (Katz, 1992 has been somewhat alleviated in recent years (Thacker & Couchman, 2000 ; Sommer-Larsen et al., 2003 as it was realized that feedback from young stars can be very efficient at keeping gas in a diluted state preventing it from rapid collapse and conversion into stars. However, even gala... |
[MATH] above [MATH] (Dalla Vecchia & Schaye, 2008 Cosmological simulations must then turn to ad-hoc assumptions about the role of stellar feedback at scales below their resolution limit. Two types of solutions have been popular. The first one is suppressing radiative cooling in the feedback regions for the duration of ... |
(Razoumov et al., 2007 . Since these galaxies extend to larger radii, their outer regions may pick part of the velocity dispersion of the local galaxy group, so that they have slightly less severe kinematics problem (Pontzen et al., 2008 than similar-resolution models which do not suppress radiative cooling. |
The second widespread approach is to use kinetic feedback instead of thermal feedback (Navarro & White, 1993 ; Springel & Hernquist, 2003 ; Dalla Vecchia & Schaye, 2008 usually implemented in particle-based simulations. Although there are several variations of this method, the basic idea is to give a velocity kick to a... |
(Dalla Vecchia & Schaye, 2008 A popular method to circumvent some of the resolution problems that can be combined with either of the above two approaches is to use a sub-resolution multiphase model that describes analytically growth of cold clouds embedded in a hot intercloud medium, star formation (SF) in these clouds... |
(Yepes et al., 1997 ; Springel & Hernquist, 2003 . In such models SF and feedback are self-regulating. However, different phases are not dynamically separated from each other, and therefore by itself such model cannot result in outflows. |
At the other end of the resolution spectrum, detailed models of small patches of galactic disks, usually in the context of the Milky Way galaxy, provide sufficient resolution to study turbulent ISM stirred by SN explosions. Such models resolve hot bubbles driven by individual SNe, fragmentation of shells created by the... |
(e.g., Joung & Mac Low, 2006 . High SF rates in such models naturally lead to galactic outflows, galactic fountains rising to several kpc away from the midplane, and shell fragments raining back onto the disk as intermediate-velocity cold clouds (Joung & Mac Low, 2006 . Such high-resolution simulations can in principle... |
In the past few years it has become possible to extend such high-resolution 3D models to entire galactic disks, albeit at a lower spatial resolution. Tasker & Bryan ( 2006 used adaptive mesh refinement (AMR) models to study the multiphase ISM in a quiescent Milky Way-sized disk galaxy. They employ two SF prescriptions,... |
Saitoh et al. ( 2008 carried out SPH simulations of an isolated gas disk with [MATH] particles to study the effect of various SF prescriptions on the structure of the ISM. Similar to |
Tasker & Bryan ( 2006 2008 , they test both a cosmological [MATH] ) and a high-density ( [MATH] ) SF thresholds, but also vary the SF efficiency [MATH] . Only the high-density threshold models could reproduce the complex multiphase structure of the gas disk, regardless of the value of [MATH] . In these runs the SF rate... |
Ceverino & Klypin ( 2007 developed a realistic prescription for modeling feedback formulating conditions under which simulations would resolve the formation of hot bubbles in the multiphase ISM. Such bubble can only be created if simulations resolve cold dense clouds in which feedback occurs – only in these clouds heat... |
In this paper the approach of Ceverino & Klypin ( 2007 is used to study the formation of winds in high-redshift protogalactic clumps responsible for damped Ly [MATH] absorption. We show that a brief episode of SF in a sub-LBG galaxy that creates a multiphase medium can also drive winds with neutral gas velocity dispers... |
2. Models 2.1. Peak cross-section of DLA absorption The mass range of halos that are the main contributors to the total DLA line density is still debated. Pontzen et al. ( 2008 argue that the main contribution comes from halos in the mass range |
[MATH] . Lower-mass halos have much smaller absorption cross-sections due to heating by the ultraviolet background (UVB), while the number of halos with masses above [MATH] drops sharply. Pontzen et al. ( 2008 point out that their peak at |
[MATH] is probably related to their particular feedback implementation in which cooling is turned off to reproduce the blastwave solution. On the other hand, Nagamine et al. ( 2007 see a peak of DLA absorption shift to higher halo masses with the increased wind strength, reaching [MATH] in the “strong wind” model. |
In our earlier cosmological DLA models (Razoumov et al., 2007 , the most common DLA absorbers are halos in the range [MATH] . At the lower end of this range, absorption is typically dominated by a single galaxy in the halo, while in halos with masses above [MATH] DLAs are commonly associated with one of several protoga... |
[MATH] (Fig. ). Our goal is to model formation of winds in one of these clumps as it undergoes a starburst. For the sake of simplicity, we adopt a fixed gravitational potential with [MATH] and a low [MATH] , but we argue that our results are equally applicable to lower-mass ( [MATH] ) halos with [MATH] |
2.2. Initial setup and grids All simulations in this paper were performed using the AMR hydrodynamical code ENZO (O’Shea et al., 2004 . The computational domain is a 3D periodic box [MATH] on a side covered with a [MATH] |
root grid and up to seven levels of refinement corresponding to [MATH] spatial resolution. A fixed spherical Navarro-Frenk-White DM profile |
[EQUATION] is assumed at the center of the volume, where [MATH] , the concentration parameter [MATH] , and [MATH] . The initial distribution of gas follows an isothermal disk with a temperature of [MATH] and a density |
[EQUATION] (Tasker & Bryan, 2006 . For all models we take [MATH] and [MATH] to approximate a compact star-forming disk at [MATH] . The total mass of the gas disk is then |
[EQUATION] Since our disks are at least 30 times smaller than the side of the box, using a small [MATH] volume is a reasonable approximation; in addition, small perturbations from nearby clumps should be always expected. To resolve the initial disk configuration, inside the central [MATH] region a hierarchy of six cent... |
A cooling function in the temperature range [MATH] is assumed, with heating by the ionizing UVB from Razoumov et al. ( 2006 with self-shielding above [MATH] . Since DLAs at [MATH] have fairly high metallicities at times exceeding solar, for simplicity solar metallicity is assumed throughout all calculations. |
2.3. Star formation and feedback Star formation is modeled with discrete stellar particles that represent a population of stars born in the same cell roughly at the same time and assumed to have the same velocity vector in later evolution. In two of the three runs presented in this paper, we adopt the minimum stellar p... |
[MATH] , and (2) the mass of the gas is larger than the local Jeans mass. In other words, stars will be formed only in cells in which the local Jeans length is unresolved which with our refinement criterion is possible only at the highest AMR level. If a cell is marked as a candidate for SF, we compute the mass of star... |
[MATH] exceeds [MATH] , a stellar particle is created, and the corresponding mass is removed from the gas component. Since our minimum stellar particle mass is very low and would allow us to record individual core-collapse SN events, we adopt instantaneous conversion of gas into stars with [MATH] , unlike, e.g., in Tas... |
Over its lifetime every stellar particle injects feedback energy into the thermal energy of the gas. We use a prescription similar to that of Ceverino & Klypin ( 2007 to include feedback by both stellar winds and type II SNe. Stellar winds supply energy at a constant rate of |
[MATH] for [MATH] after creation of the stellar particle which corresponds to conversion of [MATH] of the rest-mass energy of newly created stars into feedback energy. In addition, during the last 10% of the [MATH] feedback phase, SNe contribute [MATH] per every |
[MATH] of the initial stellar particle mass. This energy is added to the thermal energy of the cell hosting each stellar particle, in discrete [MATH] events spread uniformly over the [MATH] |
interval. In our starburst model most stellar particle masses fall into the range [MATH] , therefore our simulations begin to resolve environmental effect of individual massive stars exploding as SNe. |
In addition to energy, winds and SNe also return mass and metals to the ISM. In our models, energy and mass release into the ISM is strictly synchronized to avoid putting too much energy into regions which have been cleared by winds and/or earlier SNe. We assume that |
[MATH] of the total mass that goes into stars is ejected back into the ISM via winds and SNe. It can be shown that the maximum sound speed in hot bubbles in simulations in which mass and energy are simultaneously released into the same cell cannot exceed |
[EQUATION] where [MATH] is the speed of light, corresponding to the maximum temperature of [MATH] . Actual temperatures in hot bubbles are somewhat lower in the range [MATH] , largely due to expansion and the work performed to compress the ambient medium, and to a much lesser degree due to cooling in the bubble itself.... |
In all our runs the SF efficiency [MATH] is assumed. Many authors have found that the exact value of [MATH] has little impact on the mean SF rates (Stinson et al., 2006 , e.g.) , as long as it is in the range from 0.05 to 1 (see their Fig.14). Moreover, the true efficiency of SF, i.e. the fraction of gas that is eventu... |
In this paper we are using a set of three simulations listed in Table 1: a high-resolution starburst model A1, a high-resolution quiescent disk model A2, and a low-resolution model A3 for which [MATH] was adjusted to produce the highest SF rate. The high-resolution models used 7 levels of AMR in the [MATH] region cente... |
We ran the quiescent model to estimate the effect of star formation on the structure of the ISM and on galactic wind kinematics. There are two ways to reduce the SF rate in our models: increase the SF density threshold [MATH] or increase the minimum stellar particle mass |
[MATH] . Note that in our setup [MATH] is not independent of [MATH] . A star particle is formed only if [MATH] in a cell exceeds [MATH] . For the fiducial value |
[MATH] and [MATH] , the gas mass in a cell allowed to form stars is [EQUATION] Setting [MATH] would result in immediate SF once the density exceeds [MATH] , whereas using a much higher value would delay SF until more gas accumulates in the cell. For the quiescent disk model we use [MATH] . This prescription ultimately ... |
3. Results 3.1. Global ISM morphology Without cooling our disks would be marginally Toomre-unstable. Adding cooling leads to rapid gas accumulation near the galactic midplane and its subsequent fragmentation into cold clumps and warm interclump material. For the initial central disk density [MATH] |
and temperature [MATH] the cooling time is of order of few years leading to gas collapse of the disk onto the midplane on the timescale of [MATH] . Soon thereafter first cold clumps form in which SF begins. By [MATH] high-resolution models start developing a complex ISM morphology characterized by dense clouds and fila... |
(Fig. ) in which [MATH] of the gas in the disk is converted into stars. In the quiescent disk model A2 there is no single starburst phase; the first significant episode of gas conversion into stars takes place well past [MATH] , with intermittent SF throughout the entire run. It is interesting that by the end of simula... |
The morphology of the ISM is clearly affected by feedback from SF as can be seen from the surface density maps in Fig. at [MATH] corresponding to the end of the starburst phase in model A1. By this time in the starburst model a much larger amount of mass and energy have been injected through feedback into the lower-den... |
In our high-resolution models dense clouds are continuously being formed and destroyed by self-gravity, differential rotation, feedback from SF inside the clouds, and interaction with feedback waves coming from nearby star-forming regions. Any single cloud usually survives only for a fraction of its galactic orbital re... |
3.2. Conditions in simulated SF regions We are interested in modeling conditions in the star-forming regions that facilitate launching of galactic winds from thermal feedback only, without suppression of cooling. We will here review a set of criteria necessary to model winds and expanding hot bubbles in the ISM. First ... |
[EQUATION] where [MATH] is the spatial density of young stars, and [MATH] is expected to be in the range [MATH] . If the gas temperature is around [MATH] , cooling |
[MATH] , and heating from SNe cannot counterbalance cooling in any moderate overdensity. On the other hand, at very low temperatures ( [MATH] ) cooling is much less efficient ( [MATH] ), and even at high star-forming cloud densities feedback may be able to heat the gas. Therefore, Ceverino & Klypin ( 2007 argue, it is ... |
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