Abstract We use hydrodynamical simulations from the OWLS project to investigate the dependence of the physical properties of galaxy populations at redshift 2 on metal-line cooling and feedback from star formation and active galactic nuclei (AGN). We find that if the sub-grid feedback from star formation is implemented kinetically, the feedback is only efficient if the initial wind velocity exceeds a critical value. This critical velocity increases with galaxy mass and also if metal-line cooling is included. This suggests that radiative losses quench the winds if their initial velocity is too low. If the feedback is efficient, then the star formation rate is inversely proportional to the amount of energy injected per unit stellar mass formed (which is proportional to the initial mass loading for a fixed wind velocity). This can be understood if the star formation is self-regulating, i.e. if the star formation rate (and thus the gas fraction) increase until the outflow rate balances the inflow rate. Feedback from AGN is efficient at high masses, while increasing the initial wind velocity with gas pressure or halo mass allows one to generate galaxy-wide outflows at all masses. Matching the observed galaxy mass function requires efficient feedback. In particular, the predicted faint-end slope is too steep unless we resort to highly mass loaded winds for low-mass objects. Such efficient feedback from lowmass galaxies (M * ≪ 10 10 M ⊙ ) also reduces the discrepancy with the observed specific star formation rates, which are higher than predicted unless the feedback transitions from highly efficient to inefficient just below M * ∼ 5 × 10 9 M ⊙ . formation can be predicted by means of high-resolution gravitational N-body simulations. The distribution of DM haloes derived from these simulations agrees very well with observations. The formation and evolution of galaxies is, however, much less well understood. Modeling the baryonic component is much more difficult than simulating the DM due to the collisional nature of the gas and the wealth of phenomena that need to be taken into account (cooling, star formation, feedback, etc.). There are two popular approaches to tackle this challenging c 2013 RAS task. In semi-analytic models, simple descriptions of the behaviour of the baryonic component, as a function of the DM halo mass, merging history and environment, describe the evolution of gas and stars (e.g. Kauffmann et al. 1999; Somerville & Primack 1999; Cole et al. 2000) . The freedom to choose functional forms and parameter values combined with the ability to run large numbers of models, ensure that reproducing observations is usually within reach. While this approach has great advantages, such as the ability to make mock galaxy surveys that are sufficiently realistic to reveal observational biases, there are also significant drawbacks. The large number of parameters can make it difficult to identify the key physical processes. More importantly, the ability to reproduce observations with a model that uses unphysical functional forms or unrealistic parameter values to describe physical processes can easily result in erroneous conclusions and misplaced confidence. Complimentary to the semi-analytic models are models in which no explicit functional forms are assumed for physical processes. The so-called 'abundance matching' techniques link theoretically constructed dark matter halo populations to observed galaxy populations. These techniques rely on few assumptions, such as a correspondence between galaxy luminosity and dark matter halo mass (e.g. Kravtsov et al. 2004; Vale & Ostriker 2004) . Although such models are relatively easy to construct and give a potentially robust match between dark matter properties and galaxy observables, all baryonic processes that govern galaxy formation are hidden in the assumed correspondence, so even though the consequences of galaxy formation physics can be characterised, it can not be probed directly. The other approach is to follow both the dark matter (DM) and the baryonic components by hydrodynamic simulation. While the DM is nearly always simulated using particles, baryons can either be modeled with Eulerian methods (discretizing the volume in an (adaptive) grid, e.g. Ryu et al. 1990; Cen et al. 1990) or using the Lagrangian approach also used for the DM (discretizing the mass using particles, e.g. Evrard 1988; Hernquist & Katz 1989; Thomas & Couchman 1992) . Here, the freedom is limited to the parametrization of unresolved sub-grid processes. The high computational expense associated with full numerical simulations and the reduced level of freedom in the sub-grid modelling mean that, thus far, numerical simulations have been much less successful in reproducing observations of galaxy populations than semi-analytic models. Compared with the semi-analytic method, the advantages of the simulation approach include the much reduced (though still present) risk of getting the right answers for the wrong reasons, the ability to ask more detailed questions due to the tremendous increase in resolution, and the fact that not only galaxies, but also the intergalactic medium (IGM) is modeled. Following the baryonic component in direct simulation is numerically expensive. There is therefore a trade-off between simulated volume and numerical resolution. Whereas in this work we will simulate a representative cosmological volume, in order to get a large sample of galaxies, other works use a zoom-in technique to obtain high resolution in a couple of regions of interest (typically a handful of galaxies), e.g. Agertz et al. (2009) ; Ceverino et al. (2010 Ceverino et al. ( , 2012 . Such simulations, through their higher resolution, justify the use of more detailed physical models, at the price of a much smaller sample of simulated galaxies. As many processes related to the baryons are not (well) resolved by even the highest resolution simulations, they are dealt with in the so-called sub-grid models. Among these are radiative cooling, the temperature and pressure of the multiphase gas at high densities (in the rest of the paper loosely called "the interstellar medium (ISM)") and the formation of stars, the energy and momentum fed back by these stars into the ISM/intra-cluster medium (ICM)/IGM, stellar mass loss and the growth of supermassive black holes and associated feedback processes. In this work, we employ cosmological, hydrodynamical simulations to investigate a number of basic baryonic properties of haloes, including: the (specific) star formation rate (SFR); the stellar, gas and baryon fractions; the gas-consumption timescale and the galaxy stellar mass function. Reproducing observations in detail is not the main goal of this paper and so we have not attempted to tune our models or to optimize the sub-grid implementations to match any particular data-set. Instead, we focus on understanding how different physical mechanisms shape the galaxy population. We make use of a subset of the simulations from the OverWhelmingly Large Simulations project OWLS , a large (∼ 50 simulations) set of cosmological, smoothed particle hydrodynamics (SPH) simulations, each of the same volume of the universe, run with a wide variety of different prescriptions for subgrid physical processes. The large variety of input physics in the OWLS runs allows us to investigate properties of haloes and their relation to the physical and numerical parameters. In this paper, we investigate the effect of feedback from star formation and from accreting supermassive black holes, as well as metal-line cooling. In a companion paper (Haas et al. 2013 , hereafter Paper II) we investigate the effects of the assumed cosmology, the reionization history, the treatment of the unresolved, multiphase ISM, the assumed star-formation law and the stellar initial mass function. These ingredients are all present in the simulations presented here, but the parameters are not varied. A subset of these simulations have been used by Sales et al. (2009 Sales et al. ( , 2010 to investigate the dependence of the angular momentum and sizes of galaxies on the various feedback ingredients. This work (together with Paper II) complements that of Schaye et al. (2010) , where the cosmic star formation histories predicted by the OWLS models were analyzed. The global SFR density can be decomposed into a DM halo mass function, which is determined by the cosmology, and the statistical distribution of the SFR as a function of halo mass. Here we will study the latter, which is astrophysically more relevant than the global SFR density as it removes the main effect of cosmology (the mass function) and allows us to investigate how the effects of the various baryonic processes vary with mass. Whilst we will add a dimension to the work of Schaye et al. (2010) by investigating the dependence on mass, we will remove another one in order to keep the scope of the study manageable. Thus, we limit ourselves to z = 2 and to the highresolution series presented in Schaye et al. (2010) (these runs were halted at this redshift). This paper is structured as follows: In Sec. 2 we describe the reference simulation used in this study (Sec. 2.1), how we define and extract haloes (Sec. 2.2) and how we compare the simulations to observations (Sec. 2.3). In Sec. 3 we describe how the properties of the galaxies in our reference simulation depend on both halo mass (Sec. 3.1) and galaxy stellar mass (Sec. 3.2). In Sec 4 we describe how galaxy properties depend upon the physics included in the simulation. In this paper we consider the effects of: metal-line cooling (Sec. 4.1), constant-energy supernova (SN) winds (Sec. 4.2), the effect of a top-heavy IMF in high-density gas (Sec. 4.3), "momentum-driven" winds (Sec. 4.4), winds decoupled from the hydrodynamics (Sec. 4.5), thermally coupled SN-driven winds (Sec. 4.6), and the effect of feedback from active galactic nuclei (AGN) (Sec. 4.7). Finally, in Sec. 5 we summarize our findings and conclude. In Appendix A we study the numerical convergence of our results using simulations of different volumes and with different numerical resolution while in Appendix B we show that our results are insensitive to our particular choice of halo finder. NUMERICAL TECHNIQUES For a detailed discussion of the full set of OWLS models we refer the reader to Schaye et al. (2010) . Here we briefly summarize the reference model. Throughout this paper we refer to this reference simulation as 'REF'. The reference simulation We ran our simulations in periodic boxes of 25 co-moving h −1 Mpc with 512 3 dark matter and baryonic particles (which originally are collisional 'gas' particles, but can be converted into collisionless 'star' particles in the course of the simulation). We evolved the particles using an extended version of the N-Body Tree/SPH code Gadget3 (last described in Springel 2005 M ⊙ for baryons (initially; the baryonic particle masses change in the course of the simulation due to mass transfer from stars back to the gaseous phase). In Appendix A we show that our results are reasonably well converged with respect to the resolution and box size of the simulation. The gravitational softening length is initially fixed at 1/25 the inter-particle spacing in co-moving coordinates (1.95 co-moving h −1 kpc), but below z = 2.91 it is wilsonjamie@example.org h −1 kpc in proper units. The reference simulation cmbfast (Seljak & Zaldarriaga 1996) was used to generate initial conditions, that were evolved forward in time using the Zel'Dovich (1970) approximation from an initial glass-like state. The simulation is started at z = 127. The value of the cosmological parameters are Ω m = 0.238, Ω Λ = 0.762, Ω b = 0.0418, h = 0.73, σ 8 = 0.74 and n s = 0.951. These values are derived from the WMAP 3-yr data and largely consistent 1 with the 7-yr WMAP data (Komatsu et al. 2011 ). Because we will study the relative differences between different subgrid models, the actual values of the cosmological parameters are not of major importance. The variation in sub-grid physics implementations is the main power of the OWLS set of simulations. The rest of this paper deals with variations of the sub-grid models for SN and AGN feedback, and their influence on the galaxy population. Therefore, we will first describe the parameters and subgrid models used in the reference simulation. The reference simulation The simulation explicitly follows the 11 elements H, He, C, N, O, Ne, Mg, Si, S, Ca and Fe. Radiative cooling and heating are calculated element-by-element in the presence of the Cosmic Microwave Background and the Haardt & Madau (2001) model for the UV/X-ray background radiation from quasars and galaxies, as described in Wiersma et al. (2009a) . In these calculations, the gas is assumed to be in photo-ionization equilibrium and optically thin. The reference simulation In the centers of haloes the pressure is so high that the gas is expected to be in multiple phases, with cold and dense molecular clouds embedded in a warmer, more tenuous gas. This multiphase structure is not resolved by our simulations (and the simulations lack the physics to describe these phases), so we impose a polytropic effective equation of state for particles with densities n H > 10 −1 cm −3 . These particles are also assumed to be star forming, as this is the density required to form a cold interstellar gas phase in the disk plane (under the assumption of hydrostatic equilibrium in the disk, this central density corresponds to a column density in Hydrogen of ∼ 10 21 cm −2 Schaye 2004). We set the pressure of these particles to P ∝ ρ γ eff , where γ eff is the polytropic index and ρ is the physical proper mass density of the gas. In order to prevent spurious fragmentation due to a lack of numerical resolution we set γ eff = 4/3, as then the ratio of the Jeans length to the SPH kernel and the Jeans mass are independent of density . The normalization of the polytropic equation of state is such that for atomic gas with primordial composition, the energy per unit mass corresponds to 10 4 K, namely (P/k = 1.08 × 10 3 K cm −3 for n H = 10 The reference simulation ). The implementation of star formation is stochastic, as described in , with a pressure dependent SFR, obtained from local hydrostatic equilibrium and the observed Kennicutt-Schmidt law (KS-law Kennicutt 1998) . The reference simulation For the same 11 elements that we use for the cooling, we follow the production by AGB stars and by Type Ia and Type II (including Type Ib,c) SNe, as described in Wiersma et al. (2009b) . The star particles are assumed to be simple stellar populations (SSPs) with a Chabrier (2003) initial mass function (IMF). SN feedback is implemented kinetically. After a short delay of 30 Myr, corresponding to the maximum lifetime of stars that end their lives as core-collapse SNe, newly formed star particles inject kinetic energy into their surroundings by kicking a fraction of their SPH neighbours in random directions. Each SPH neighbour i of a newly formed star particle j has a probability of ηm j / N ngb i=1 m i of receiving a kick with a velocity v w . Our reference model uses η = 2 and v w = 600 km/s, which for our assumed IMF corresponds to ∼ 40% of the available energy from SNe being injected as winds (where all stars more massive than 6M ⊙ are assumed to explode in a SN with 10 51 ergs of energy). See Table 1 for the parameters that are varied in this paper. Halo identification Haloes are identified using a Friends-of-Friends (FoF) algorithm, which links together all dark matter particles which are closer to each other than the linking parameter (b = 0.2 times the mean interparticle distance). FoF identifies iso-overdensity contours of δ ≡ (ρ −ρ)/ρ ≃ 3/(2πb 3 ) ≃ 60 (Davis et al. 1985; Lacey & Cole 1994) . Baryonic particles are linked to their nearest dark matter particle and belong to the same group, if any. Halo identification Following the convergence tests presented in Appendix A, we only include haloes that contain at least 100 star particles when considering halo properties as a function of stellar mass and we use a minimum of 2000 dark matter particles when we plot properties against halo mass. These two cuts produce nearly identical halo samples in the reference simulation and ensure that only well resolved haloes are considered. In Appendix B we confirm that our results are robust to changes in the definition of halo mass used. Physical properties of haloes (e.g. stellar mass and SFR) are just the sum of the properties of all constituent particles (in case of fractions like baryon fraction and specific SFR, it is the ratio of the sums of numerator and denominator). Halo identification Whenever we show the correlation between two halo properties, the plot consists of lines that connect the medians of bins evenly spaced in the quantity plotted along the horizontal axis. Each Table 1 . Overview of the simulations and the input physics that is varied in this paper. Bold face indicates departures from the reference model. The first column gives the name of the simulation; the second column denotes the type of SN feedback, either kinetic, thermal or none. The third column shows the wind velocity for kinetic feedback models (the circular velocity is defined as v c = √ GM vir /R vir and the velocity dispersion σ is related to the gravitational potential Φ: σ = √ −Φ/2); the fourth column indicates, for kinetic feedback models, the wind mass loading. The fifth column indicates whether the winds are decoupled from the hydrodynamics, the sixth column indicates whether metal-dependent cooling is followed in the simulation and the seventh column indicates the stellar IMF(s). The eighth column shows which simulations include AGN feedback and the last column specifies the section in which each simulation is discussed. Name Kinetic bin contains at least 30 data points. If there are fewer than 30 points in a given bin, it is extended until it includes 30 objects. The last bin may contain between 0 and 30 objects. We bin the data starting from the high-mass end. There, the difference in mass for two consecutive haloes is much larger than at the low-mass end, and in this way we are sure that the value of the mass at the high-mass end of the plots is always the mean of the mass of the 15th and 16th most massive systems. Comparing simulations to observations In this section we describe how we compare our simulated galaxy population to observed stellar masses and SFRs. To convert observationally inferred stellar masses and SFRs from the cosmology assumed in the literature to our cosmology, we multiply them by the square of the ratio of luminosity distances, Comparing simulations to observations The subscripts 'our cosm' and 'obs cosm' denote our cosmology and the cosmology under which the observations are transformed into masses/SFRs, respectively. Using the observational data sets compared to in this paper, this ratio varies from very close to 1 to ∼ 2.6. Comparing simulations to observations Note that we are using FoF halos, so all satellites are added to the central galaxy. We show in Appendix B that it makes very little difference to treat the satellites separately. Comparing simulations to observations We compare our simulated SFRs to those observed by Daddi et al. (2007) , who measured obscured and unobscured star formation by taking SFRs from both the UV and IR for K-selected sBzK galaxies (star forming, see Daddi et al. 2004) in the GOODS fields at z ∼ 2. The median of the observed SFR as a function of stellar mass is well fit by SFR = 250 × (M * /10 11 M ⊙ ) 0.9 . The IMF assumed in the observations is the Salpeter (1955) IMF, whereas our stellar masses and SFRs are based on the Chabrier (2003) IMF. We therefore divide the observationally inferred SFRs by a factor 1.65, which is the asymptotic (reached after only 10 8 yr) ratio of the number of ionizing photons per unit stellar mass predicted by Bruzual & Charlot (2003) for a constant SFR. Comparing simulations to observations For stellar masses, the IMF conversion factor is more sensitive to the age of the population and the observed rest-frame wavelength. As the light in most wavelength bands is dominated by massive stars and the high-mass ends of both the Salpeter and Chabrier IMFs are power laws with very similar power law indices, we use the same factor of 1.65 as we used for the SFRs. For very old populations observed in red wavelength bands (tracing stellar continua rather than dust emission) the conversion factor should be different. We verified that the K-band mass-to-light ratio is about a factor 1.65 smaller for a Chabrier than for a Salpeter IMF for SSPs and constantly star forming populations, for the full range of ages and metallicities available in the Bruzual & Charlot (2003) population synthesis package. We therefore also divide by a factor of 1.65 to convert stellar masses from the Salpeter to the Chabrier IMF. Comparing simulations to observations We compare to the galaxy stellar mass function of Marchesini et al. (2009) , a combined sample, using the deep nearinfrared Multi-wavelength Survey by Yale-Chile, the Faint Infrared Extragalactic Survey and the Great Observatories Origins Deep Survey-Chandra Deep Field South surveys at z ∼ 2. Specifically, we compare to the 1/V max results of Marchesini et al. (2009) , including all of their uncertainties, with the exception of bottomlight IMFs. The reason for this choice is that models with bottomlight IMFs dominate the systematic errors and represent a more extreme assumption than the variations in the other quantities. Additionally, theoretical justifications for using bottom-light IMFs exist, thus far, only at high redshift (Davé 2008; van Dokkum 2008; Wilkins et al. 2008) . We obtain the error bars on the observed data points by considering all of the sources of random errors included in the observational data points, which include: Poisson errors on the number counts, cosmic variance and the random er-rors from the use of photometric redshifts. We add the sources of random error in quadrature and, in addition, linearly add the maximum of the systematic errors in the same mass bins, just as Marchesini et al. (2009) . The systematic errors include the systematic component in the errors from photometric redshifts, errors arising from different population synthesis packages (Marchesini et al. (2009) tested Bruzual & Charlot 2003; Maraston 2005, Charlot & Bruzual, in prep.) , varying the metallicities of the stellar populations, and the use of different extinction curves (Milky Way from Allen 1976, SMC from Prevot et al. 1984 , Bouchet et al. 1985 and Calzetti et al. 2000 . Comparing simulations to observations Because our redshift of interest (z = 2) corresponds to the boundary between two of the redshift bins of Marchesini et al. (2009) , which are 1.3 < z < 2 and 2 < z < 3, we weigh the averaging to the sizes of the redshift intervals (weights 1.2 Gyr and 0.8 Gyr respectively), which gives results consistent with the z = 2 results of the Newfirm Medium-Band Survey (Marchesini et al. 2010) . Additionally, the observed mass bins are not exactly the same size in both redshift intervals, although the differences are very small. Observed mass bins are of size 0.3 dex (at 1.3 < z < 2) and 0.29 dex (at 2 < z < 3). We interpolate the observed mass bins to a constant size of 0.3 dex. The resulting 1/V max estimate of the analysis of Marchesini et al. (2009) is shown as the yellow shaded regions in the bottom-right panels of Fig. 1 , and Figs. 3 -9, labelled (I). Marchesini et al. (2009) use a diet Kroupa IMF, for which the correction factor to our Chabrier IMF is very small (∼ 1.03, diet Kroupa being slightly more massive for the same flux). As this number is also derived from population synthesis packages, which come along with their own uncertainties, we chose not to convert masses for the small difference in IMFs. We do correct the masses for the difference in luminosity distances as described earlier. Number densities also need to be converted, as the volume at a given redshift is different for different angular diameter and co-moving distances. Therefore, the number density (φ * ) is corrected for the ratio of volume elements (which is a function of the assumed cosmology). Comparing simulations to observations When we compare our simulated galaxies to observations of the molecular gas mass in galaxies, we use a sub-set of the compilation used in Genzel et al. (2010) . As their total range of redshifts is very large, we chose to use only the two sub-sets directly above and below z = 2. The near-IR long-slit Hα sample from Erb et al. (2006) contains 11 galaxies with a mean redshift of 2.3 and is originally drawn from the BX selected sample of Steidel et al. (2004) and Reddy et al. (2005) . The 4 galaxies with a mean redshift of 1.5 that we include are star-forming BzK galaxies from Daddi et al. (2008 Daddi et al. ( , 2010 . For both samples the molecular gas masses come from CO measurements with the Plateau de Bure interferometer and the stellar masses come from optical/UV SED fitting, under the assumption of a Chabrier IMF. We therefore only have to correct for the difference in luminosity distance, as explained above. Our simulations do not explicitly calculate the molecular fraction in the high-density gas. Nevertheless, the galaxies we compare to are at the very highest stellar mass end of our simulated galaxies. For those galaxies the molecular gas fraction (by mass) is thought to be very high due to high pressures in the ISM, so we assume that all gas on the imposed equation of state is molecular. A recent study by Narayanan et al. (2012) suggests that with an improved conversion factor from CO to H 2 , gas fractions of these galaxies are likely somewhat lower than quoted by Genzel et al. (2010) . Fig. 1 shows, as a function of total halo mass the nine different galaxy properties we consider in this paper: medians of stellar mass fraction ( PHYSICAL PROPERTIES OF SIMULATED GALAXIES AS A FUNCTION OF DARK MATTER HALO MASS and gas mass fraction ( f gas, halo = (M gas, total − M ISM )/M tot , panel E). Then, as a function of stellar mass: medians of the molecular gas mass in the ISM (panel F), specific SFR (sSFR = SFR/M * , panel G), the inverse of the gas consumption timescale (SFR/M ISM , panel H) and galaxy number density (the galaxy stellar mass function, panel I). PHYSICAL PROPERTIES OF SIMULATED GALAXIES AS A FUNCTION OF DARK MATTER HALO MASS In each panel of Fig. 1 we show the properties of the galaxies in the reference simulation with a black curve. The blue curves show results from the simulations analyzed in Paper II, which include changes in the cosmology, ISM physics, star-formation law and IMF. The red curves show the simulations discussed in this paper (see section 4), which comprise changes in the feedback processes that are modeled. The red and blue lines are included in Fig. 1 to give a visual impression of the magnitude of the effects that we are considering. Here, we note that the magnitude of the differences between simulated galaxy properties due to uncertainties in the sub-grid physics are larger than the differences that arise from changing the hydrodynamics method from SPH to a (moving-) mesh code (Springel 2010) , as e.g. shown by Vogelsberger et al. (2012) ; Kereš et al. (2012) and Scannapieco et al. (2012) . The relative accuracy of different numerical techniques can nevertheless be important, but an investigation of this issue falls outside the scope of this paper. PHYSICAL PROPERTIES OF SIMULATED GALAXIES AS A FUNCTION OF DARK MATTER HALO MASS The error bar in the lower right corner of each panel (except the stellar mass function in panel H) indicates the typical scatter of galaxies around the median in the reference simulation. The error bar is a mass-weighted (by halo mass in panels A-E and by stellar mass in panels F-H) mean σ tot of the standard deviation of all galaxies in all bins σ bin : σ tot = bins σ bin M bin / bins M bin . We note that in all panels this scatter is dominated by the lower mass bins, where the scatter is typically much larger (and the bins are smaller and thus more numerous), and possibly partly due to resolution effects. Also, at the high mass end the 'scatter' in the data is partially caused by the (almost exclusively positively sloped) relation between the dependent variable and mass. The scatter of galaxies around the median is typically smaller than the difference between the median relations in the most extreme simulations. A difference between two simulations that is smaller than the scatter is nevertheless still meaningful. PHYSICAL PROPERTIES OF SIMULATED GALAXIES AS A FUNCTION OF DARK MATTER HALO MASS In the remainder of this section we describe and explain the trends seen in the properties of the galaxies in the reference simulation, and comment briefly on the effects of the physics variations. Note that the first five panels (galaxy properties as a function of DM halo mass) and the last four panels (galaxy properties as a function of stellar mass) are resolved down to slightly different resolution limits, as discussed in Appendix A. Properties as a function of halo mass In panel (A) of Fig. 1 we plot the stellar mass fraction as a function of total halo mass. Stellar mass and total mass are tightly (and almost linearly) correlated so differences between the models are emphasized by plotting the ratio of the masses. In the reference model, the fraction of the total mass locked into stars increases smoothly as a function of halo mass, from ∼1% in the smallest resolved haloes In Sec. 4 we consider subsets of simulations in more detail. In the first five panels we show, as function of total halo mass, medians of stellar mass fraction ( Properties as a function of halo mass and gas fraction ( f gas, halo = (M gas, total − M ISM )/M tot , panel E). The next four panels show, as a function of stellar mass, medians of the molecular gas mass in the ISM (panel F), specific SFR (sSFR = SFR/M * , panel G), the inverse of the gas consumption timescale (SFR/M ISM , panel H) and galaxy number density (the galaxy stellar mass function, panel I). As described in the text, we show medians in bins along the horizontal axes for all haloes that satisfy the convergence criteria that apply to that specific panel. The horizontal, dashed line in panel (C) shows the universal baryon fraction for our chosen cosmology, the data points in panel (F) show a sub-set of the compilation studied in Genzel et al. (2010) , the dotted black line in panel (G) shows the stellar mass -sSFR relation from the GOODS field (Daddi et al. 2007 ) and the shaded yellow region in panel (I) shows the galaxy stellar mass function of Marchesini et al. (2009) . The error bars in the lower right corners show the mass-weighted mean scatter of galaxies in the reference simulation, as explained in the text. Properties as a function of halo mass (log 10 (M tot /M ⊙ ) ∼ 10.5), to 4% in the highest mass haloes. It is difficult to make a quantitative comparison with galaxy formation efficiencies quoted in much of the literature (e.g. Guo et al. 2010) , as the definition of halo mass used in this study is different from the spherical overdensity halo definitions used in these works, but the qualitative trend is the same. As we move towards higher halo masses, a fractionally larger proportion of the mass is locked into stars. It is clear from inspection of panel (A) that the changes in physics considered in this paper (red curves) have a large effect on the M halo − M * relation (much bigger than the simulations discussed in Paper II; blue curves). We discuss the reasons for this sensitivity in Sec. 4. The one simulation that is a strong outlier, with much higher stellar mass at fixed halo mass, is the simulation that neglects SN feedback and, as such, contains no mechanism to prevent the catastrophic cooling of gas into stars. Most observational studies do not go out as far as z = 2 and rely on extrapolations beyond the observed galaxy population, especially at the low mass end. Yang et al. (2012) study the stellar mass -halo mass relation around z = 2, but their lowest observed point is at M halo ∼ 10 12 M ⊙ , which is our very highest mass bin. At that mass, the reference simulation slightly overpredicts the mass in stars (a factor of ∼ 2), as expected from the inefficient SN feedback that will be discussed at length below. Some simulations with very efficient feedback underproduce stars at M halo ∼ 10 12 M ⊙ , as compared to these subhalo abundance matching techniques. Properties as a function of halo mass In panel (B) we show the integrated SFR inside haloes as a function of their total mass. In all simulations the SFR is an increasing function of halo mass in the mass range probed here (10.5 < log 10 (M tot /M ⊙ ) < 12.0). As in panel (A), the vast majority of the physics variations considered in Paper II have very little effect, but the variations discussed here are very important. This implies that the sub-grid physics employed to model the ISM, other than that related to feedback, does not affect the large-scale, stellar properties of the galaxies. The outlier among the red curves in this panel is again the simulation that neglects SN feedback, which shows that feedback is an important component of the sub-grid models. Properties as a function of halo mass Panel (C) shows the baryon fractions of the haloes as a function of halo mass. The universal baryon fraction appropriate for our default cosmology (Ω b /Ω m = 0.18) is over-plotted as a horizontal, dashed line. In the default simulation, feedback processes are able to eject baryons from the halo very easily in low-mass haloes, leading to low baryon fractions (0.6 dex below universal) for M tot ∼ 10 10.5 M ⊙ , whereas they become gradually less efficient as the halo mass increases. Again, the physics changes presented in this paper have a much more significant effect on this relation than those discussed in Paper II. Panels (D) and (E) show the fraction of the mass that is in gas in the ISM (which is sensitive to the physics variations in Paper II) and the rest of the gas in the haloes, respectively. In general, both are increasing functions of the total mass. Properties as a function of stellar mass The mass in the ISM as a function of the galaxy stellar mass is slightly sub-linear, as depicted in panel (F). This reflects the fact that at higher masses, gas is more efficiently transformed into stars. Our simulations slightly under-predict the molecular gas mass as a function of stellar mass when compared to the sub-sample of the galaxies studied by Genzel et al. (2010) . Properties as a function of stellar mass Both the stellar mass (panel A) and SFR (panel B) of galaxies are correlated almost linearly with halo mass, suggesting, that there is a linear relation between the stellar mass and the SFR. This linear trend masks important differences between the simulations, so to examine galaxy properties in more detail, we use the galaxy specific SFR (sSFR=SFR/M * ). Properties as a function of stellar mass Panel (G) shows the median sSFR as a function of galaxy stellar mass. In this panel, the black, dotted line shows the observations of Daddi et al. (2007) . The scatter in the data is not shown, but is constant at approximately 0.2 dex. The scatter in the simulation data points is similar, although somewhat smaller (∼ 0.1 to 0.15 dex). We plot the observed relation over the mass range that is observed, and do not extrapolate beyond there. Properties as a function of stellar mass The trend seen in the simulations is such that at low masses the sSFR is an increasing function of mass, but at ∼ 10 10 M ⊙ the trend reverses and the sSFR decreases with increasing stellar mass. At the highest masses the relation is declining more steeply than observed. As discussed in Sec. 3.1, most of the physics variations discussed in this paper have little effect on the integrated stellar properties of the haloes. The underestimate of the SFR is likely connected to the underestimate of molecular mass shown in panel (F). Properties as a function of stellar mass Because SFRs are expected to be more strongly influenced by the mass of available star-forming gas than by the amount of stars already formed, we define a second normalized SFR, the ratio of the galaxy SFR to its star-forming gas mass. This is the inverse of the time needed to convert the present reservoir of star forming gas into stars, assuming that the present SFR is maintained. We plot the inverse of the gas consumption time scale as a function of stellar mass in panel (H). The gas consumption time is a monotonically decreasing function of stellar mass in the simulations. In the cores of the more massive haloes, gas reaches higher densities and pressure, so gas is converted more efficiently into stars. Properties as a function of stellar mass In panel (I) we examine the galaxy stellar mass function: the number density of galaxies as a function of their stellar mass. The yellow, shaded regions show the data from Marchesini et al. (2009) . When the observational uncertainties are taken into account, most of the simulated mass functions fall well within the observed range. We note that, at low masses, our simulated stellar mass function is steeper than most faint-end slopes of derived Schechter function parametrizations at similar redshifts (e.g. Conselice et al. 2005; Marchesini et al. 2009 Marchesini et al. , 2010 , but that this discrepancy exists largely outside the range of stellar masses where the mass function has been observed. Newer results are complete down to only slightly lower masses (e.g. Mortlock et al. 2011 , who are complete down to 10 9.5 M ⊙ ). Our simulation box size is too small to form the rare objects that populate the exponential cutoff of the stellar mass function. Properties as a function of stellar mass Comparing the behaviour of the reference simulation between panels (G) and (I) reveals an interesting behaviour: although the galaxy sSFR is a factor of a few too low at z = 2 over the observed range, the simulations form enough galaxies of all masses, and possibly too many low-mass systems (a similar behaviour was also noted by Choi & Nagamine 2012) . This may indicate that the observations are not internally consistent, such that the integral of observed SFRs do not add up to the observed current stellar mass after correcting for stellar mass loss. A perhaps more likely explanation is that galaxy formation in the simulation is too efficient in low mass systems at high redshift and that other physics variations are required to flatten the stellar mass function and to get the SFRs at z = 2 to agree with observed values. A graphical representation of a galaxy in a halo of 10 12.5 M ⊙ in 15 of our simulations at redshift 2. The colour coding denotes the gas density in a slice of 100 h −1 kpc thickness, divided by the mean density of the universe. All frames are 100 co-moving h −1 kpc on a side and are centered on the position of the galaxy in the 'REF' simulation. All frames have a thickness of 100 co-moving h −1 kpc. The orientation of the line of sight is along the z-axis, which is almost perfectly aligned with the angular momentum vector of all material inside 10% of the virial radius of this galaxy in the 'REF' simulation. It is clear that different feedback prescriptions can have a large effect on the size of the galactic disk. Note that 'WML4' is not included here. That simulation is also discussed in Paper II, and it is included there. ISOLATING THE EFFECTS OF THE INPUT PHYSICS In this section we discuss each of the variations of the input physics. Table 1 A graphical representation of the gas density of a galaxy formed in a representative set of models is shown in Fig. 2 . The galaxy resides in a halo of total mass ∼ 10 12.5 M ⊙ . It was first identified in the 'REF' simulation, where its position (defined as the centre of mass of all particles within 10% of the virial radius) is determined. The line of sight is along the z-axis, which is almost perfectly aligned with the angular momentum vector of the gas within 10% of the virial radius (cos(φ) = 0.994). For the other simulations the image is centered on the same position, showing the remarkable similarity in the positions and orientations of the galaxies. It is immediately clear that changing the feedback model can have a large effect on the galaxy morphology. Going so far as almost completely destroying the galaxy disk in the strongest cases ('AGN' and 'DBLIMFV1618'). Metal-line cooling In this set of simulations we investigate how gas cooling through metal lines affects the galaxy population. Metal-line cooling is the dominant mechanism by which enriched gas can cool in the temperature range 10 5 K < T < 10 6 K (e.g. Wiersma et al. 2009a) . Metals are also the main coolants for gas at temperatures well below 10 4 K, but we do not include those phases of the ISM in these simulations. If gas shock heats to high temperatures while accreting onto galaxies, neglecting metal-line cooling will greatly decrease the supply of gas that can cool out of haloes to fuel the galaxy (see van de Voort et al. 2011 , for a comprehensive discussion of galaxy fueling in these simulations). In order to isolate these effects we compare the 'REF' simulation to one in which cooling through metal-lines was switched off ('NOZCOOL'), and to a further simulation in which both cooling through metal-lines and SN feedback were switched off ('NOZCOOL NOSN'). The morphology of a typical massive galaxy in these simulations can be seen in Fig. 2 . Turning off metal-line cooling reduces the extent of the gaseous disk in this massive system as less gas cools out of the halo into the galaxy. Neglecting SN feedback leads to a hugely centrally concentrated galaxy as there is no mechanism to eject low-angular momentum material or to stop the fragmentation, and associated angular momentum losses. Metal-line cooling To isolate the effect of metal-line cooling, we can compare the 'REF' simulation (solid, black curve) to the 'NOZCOOL' simulation (dotted, red curve) in Fig. 3 . Panel (B) of Fig. 3 shows the effect of metal-line cooling on the SFRs of galaxies. In general, metal-line cooling increases SFRs, because cooling rates increase with increasing metallicities. The magnitude of the differences between the simulations increases with halo mass because both the fraction of gas that is shock heated when it enters the galaxy (e.g. Birnboim & Dekel 2003; Kereš et al. 2005; Ocvirk et al. 2008; van de Voort et al. 2011 ) and the halo virial temperature increase with mass, making the effect of metal-cooling more pronounced. The same trends are evident in other gas properties as a function of halo mass and stellar mass. Without metal-line cooling, less gas is able to cool onto the galaxy (panel D), and hence stellar masses (panel A) are lower. Metal-line cooling As a function of stellar mass, we see that sSFRs are higher (panel G) and gas consumption timescales are shorter (panel H) in the 'REF' than in the 'NOZCOOL' simulation, as gas can cool more quickly into the galaxy when metal-line cooling is allowed, leading to higher gas densities and more efficient star formation. At high masses, winds are inefficient and more metal-rich gas piles up, increasing the difference between the simulations. The stellar mass functions of the two simulations (panel I) are almost identical up to M star = 10 9.5 M ⊙ , but above this mass the 'NOZCOOL' simulation lies systematically 0.1-0.2 dex below 'REF'. This occurs because the normalization of the M star − M tot relation is decreased in 'NOZ-COOL', and so a given stellar mass corresponds to a larger, rarer halo. Turning our attention now to the effect of SN feedback by comparing the 'NOZCOOL' simulation (dotted, red curve) to the 'NOZCOOL NOSN' simulation (dashed, blue curve), we see that neglecting SN feedback leads to dramatic changes in the galaxy population as with no energy injection there is no process that can prevent gas from cooling directly into the galaxy. Metal-line cooling Notably, panel (C) demonstrates that, unlike all of the other simulations we consider, 'NOZCOOL NOSN' has baryon fractions above the universal value. This is due to the fact that star formation and cooling allow more gas to be pulled into the potential well of the galaxy. Non-radiative simulations predict baryon fractions of ∼ 0.8 times the universal value (Crain et al. 2007 , but see Kravtsov et al. 2005 who find a value much closer to one in a nonradiative mesh-based simulation), as pressure support forces more gas outside of haloes. Metal-line cooling Interestingly, we note that (unlike all of the other simulations considered here), the slope of the M star − sSFR relation (panel G) in the 'NOZCOOL NOSN' has an almost identical slope to that observed, although with a normalization that is lower by a factor of approximately two. That the slope of the observed M star − sSFR relation is so similar to that of the simulation without feedback may indicate that perhaps feedback is ineffective at high galaxy masses, as is the case for the reference simulation above 10 10 M ⊙ (see also Paper II). The similarity to the observed relation is striking. The galaxies in the observations are selected to be star forming, so one would naively expect the star formation in those galaxies to be regulated by feedback. Winds with constant energy per unit stellar mass formed Winds driven by feedback from star formation have become a fundamental ingredient of the galaxy formation picture by preventing too much gas from being locked into stars. In the 'REF' simulation, such winds are assumed to be driven by SNe and are implemented kinetically. That is, the effect of SNe is to 'kick' some amount of gas. This model contains two free parameters: the initial mass-loading η =Ṁ wind /Ṁ * and the initial wind velocity v w , which remain essentially unconstrained. We therefore compare a series of four simulations that use the same SN energy per unit stellar mass formed (i.e. ηv 2 w is the same as for 'REF'), but distribute it differently between the velocity and mass loading. The mass loadings in the four simulations are 1, 2 (i.e. 'REF'), 4 and 8, with corresponding velocities of 848, 600, 424 and 300 km/s, respectively. The parameters of the wind model are contained in the simulation name. For example, the simulation 'WML1V848' uses a mass-loading of 1 and a wind velocity of 848 km s −1 . A fifth simulation with kinetic feedback with the same feedback energy, 'WDENS', uses a wind velocity that scales in proportion to the local gas sound-speed (∝ ρ 1/6 ) and a mass loading that scales such that the total injected energy is constant (∝ ρ −1/3 ). The normalization of the parameters in the 'WDENS' simulation is such that the wind velocity and mass loading are the same as in the reference model if the gas density equals the star formation threshold, i.e. n H = 0.1 cm −3 . For illustrative purposes, we also consider a simulation in which the available SN energy relative to 'REF' is doubled (by doubling the mass-loading to 4 and keeping the wind velocity the same). This simulation is termed 'WML4'. Winds with constant energy per unit stellar mass formed We first compare the set of simulations in which we hold the amount of SN energy that is injected per unit stellar mass constant, but vary how the energy is distributed between the initial mass loading and wind velocity. We show in Fig. 4 that the simulation with the highest wind velocity ('WML1V848; red, dotted curve) suppresses SF much more effectively in high-mass objects than the simulations with lower wind velocities (e.g. 'WML8V300'). However, at low galaxy masses, this trend reverses and it is the simulations with the lowest wind velocities that suppress SF most efficiently (panels A, B and D). At the low-mass end, the amount of suppression is
{'paper_id': '54038403', 'title': 'Physical properties of simulated galaxy populations at z=2 - I. Effect of metal-line cooling and feedback from star formation and AGN', 's2_url': 'https://api.semanticscholar.org/CorpusID:54038403', 'source': 'S2ORC'}