arXiv subjects

Giuseppe Murante

Publications and source records attributed to Giuseppe Murante.

At least 55 records · Page 3Linked to original sources

arXiv2017

On the effect of galactic outflows in cosmological simulations of disc galaxies

We investigate the impact of galactic outflow modelling on the formation and evolution of a disc galaxy, by performing a suite of cosmological simulations with zoomed-in initial conditions of a Milky Way-sized halo. We verify how sensitive the general properties of the simulated galaxy are to the way in which stellar feedback triggered outflows are implemented, keeping initial conditions, simulation code and star formation (SF) model all fixed. We present simulations that are based on a version of the GADGET3 code where our sub-resolution model is coupled with an advanced implementation of Smoothed Particle Hydrodynamics that ensures a more accurate fluid sampling and an improved description of gas mixing and hydrodynamical instabilities. We quantify the strong interplay between the adopted hydrodynamic scheme and the sub-resolution model describing SF and feedback. We consider four different galactic outflow models, including the one introduced by Dalla Vecchia and Schaye (2012) and a scheme that is inspired by the Springel and Hernquist (2003) model. We find that the sub-resolution prescriptions adopted to generate galactic outflows are the main shaping factor of the stellar disc component at low redshift. The key requirement that a feedback model must have to be successful in producing a disc-dominated galaxy is the ability to regulate the high-redshift SF (responsible for the formation of the bulge component), the cosmological infall of gas from the large-scale environment, and gas fall-back within the galactic radius at low redshift, in order to avoid a too high SF rate at $z=0$.

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arXiv2017

Quantitative estimates of the surface habitability of Kepler-452b

Kepler-452b is currently the best example of an Earth-size planet in the habitable zone of a sun-like star, a type of planet whose number of detections is expected to increase in the future. Searching for biosignatures in the supposedly thin atmospheres of these planets is a challenging goal that requires a careful selection of the targets. Under the assumption of a rocky-dominated nature for Kepler-452b, we considered it as a test case to calculate a temperature-dependent habitability index, $h_{050}$, designed to maximize the potential presence of biosignature-producing activity (Silva et al.\ 2016). The surface temperature has been computed for a broad range of climate factors using a climate model designed for terrestrial-type exoplanets (Vladilo et al.\ 2015). After fixing the planetary data according to the experimental results (Jenkins et al.\ 2015), we changed the surface gravity, CO$_2$ abundance, surface pressure, orbital eccentricity, rotation period, axis obliquity and ocean fraction within the range of validity of our model. For most choices of parameters we find habitable solutions with $h_{050}>0.2$ only for CO$_2$ partial pressure $p_\mathrm{CO_2} \lesssim 0.04$\,bar. At this limiting value of CO$_2$ abundance the planet is still habitable if the total pressure is $p \lesssim 2$\,bar. In all cases the habitability drops for eccentricity $e \gtrsim 0.3$. Changes of rotation period and obliquity affect the habitability through their impact on the equator-pole temperature difference rather than on the mean global temperature. We calculated the variation of $h_{050}$ resulting from the luminosity evolution of the host star for a wide range of input parameters. Only a small combination of parameters yield habitability-weighted lifetimes $\gtrsim 2$\,Gyr, sufficiently long to develop atmospheric biosignatures still detectable at the present time.

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arXiv2016

Panchromatic Spectral Energy Distributions of simulated galaxies: results at redshift $z=0$

We present predictions of Spectral Energy Distributions (SEDs), from the UV to the FIR, of simulated galaxies at $z=0$. These were obtained by post-processing the results of an N-body+hydro simulation of a small cosmological volume, that uses the Multi-Phase Particle Integrator (MUPPI) for star formation and stellar feedback, with the GRASIL-3D radiative transfer code, that includes reprocessing of UV light by dust. Physical properties of galaxies resemble observed ones, though with some tension at small and large stellar masses. Comparing predicted SEDs of simulated galaxies with different samples of local galaxies, we find that these resemble observed ones, when normalised at 3.6 $μ$m. A comparison with the Herschel Reference Survey shows that, when binning galaxies in Star Formation Rate (SFR), average SEDs are reproduced to within a factor of $\sim2$ even in normalization, while binning in stellar mass highlights the same tension that is present in the stellar mass -- SFR plane. We use our sample to investigate the correlation of IR luminosity in Spitzer and Herschel bands with several galaxy properties. SFR is the quantity that best correlates with IR light up to $160\ μ$m, while at longer wavelengths better correlations are found with molecular mass and, at $500\ μ$m, with dust mass. However, using the position of the FIR peak as a proxy for cold dust temperature, we assess that heating of cold dust is mostly determined by SFR, with stellar mass giving only a minor contribution. We finally show how our sample of simulated galaxies can be used as a guide to understand the physical properties and selection biases of observed samples.

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arXiv2016

nIFTy galaxy cluster simulations V: Investigation of the Cluster Infall Region

We examine the properties of the galaxies and dark matter haloes residing in the cluster infall region surrounding the simulated $Λ$CDM galaxy cluster studied by Elahi et al. (2016) at z=0. The $1.1\times10^{15}h^{-1}\text{M}_{\odot}$ galaxy cluster has been simulated with eight different hydrodynamical codes containing a variety of hydrodynamic solvers and subgrid schemes. All models completed a dark-matter only, non-radiative and full-physics run from the same initial conditions. The simulations contain dark matter and gas with mass resolution $m_{\text{DM}}=9.01\times 10^8h^{-1}\text{M}_{\odot}$ and $m_{\text{gas}}=1.9\times 10^8h^{-1}\text{M}_{\odot}$ respectively. We find that the synthetic cluster is surrounded by clear filamentary structures that contain ~60% of haloes in the infall region with mass ~$10^{12.5} - 10^{14} h^{-1}\text{M}_{\odot}$, including 2-3 group-sized haloes ($> 10^{13}h^{-1}\text{M}_{\odot}$). However, we find that only ~10% of objects in the infall region are subhaloes residing in haloes, which may suggest that there is not much ongoing preprocessing occurring in the infall region at z=0. By examining the baryonic content contained within the haloes, we also show that the code-to-code scatter in stellar fraction across all halo masses is typically ~2 orders of magnitude between the two most extreme cases, and this is predominantly due to the differences in subgrid schemes and calibration procedures that each model uses. Models that do not include AGN feedback typically produce too high stellar fractions compared to observations by at least ~1 order of magnitude.

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arXiv2016

On the dynamical state of galaxy clusters: insights from cosmological simulations II

Using a suite of cosmology simulations of a sample of $> 120$ galaxy clusters with $\log(M_{DM, vir}) \le 14.5$. We compare clusters that form in purely dark matter run and their counterparts in hydro runs and investigate 4 independent parameters, that are normally used to classify dynamical state. We find that the virial ratio $η$ in hydro-dynamical runs is $\sim 10$ per cent lower than in the DM run, and there is no clear separation between the relaxed and unrelaxed clusters for any parameter. Further, using the velocity dispersion deviation parameter $ζ$, which is defined as the ratio between cluster velocity dispersion $σ$ and the theoretical prediction $σ_t = \sqrt{G M_{total}/R}$, we find that there is a linear correlation between the virial ratio $η$ and this $ζ$ parameter. We propose to use this $ζ$ parameter, which can be easily derived from observed galaxy clusters, as a substitute of the $η$ parameter to quantify the cluster dynamical state.

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arXiv2016

Kinetic AGN Feedback Effects on Cluster Cool Cores Simulated using SPH

We implement novel numerical models of AGN feedback in the SPH code GADGET-3, where the energy from a supermassive black hole (BH) is coupled to the surrounding gas in the kinetic form. Gas particles lying inside a bi-conical volume around the BH are imparted a one-time velocity (10,000 km/s) increment. We perform hydrodynamical simulations of isolated cluster (total mass 10^14 /h M_sun), which is initially evolved to form a dense cool core, having central T<10^6 K. A BH resides at the cluster center, and ejects energy. The feedback-driven fast wind undergoes shock with the slower-moving gas, which causes the imparted kinetic energy to be thermalized. Bipolar bubble-like outflows form propagating radially outward to a distance of a few 100 kpc. The radial profiles of median gas properties are influenced by BH feedback in the inner regions (r<20-50 kpc). BH kinetic feedback, with a large value of the feedback efficiency, depletes the inner cool gas and reduces the hot gas content, such that the initial cool core of the cluster is heated up within a time 1.9 Gyr, whereby the core median temperature rises to above 10^7 K, and the central entropy flattens. Our implementation of BH thermal feedback (using the same efficiency as kinetic), within the star-formation model, cannot do this heating, where the cool core remains. The inclusion of cold gas accretion in the simulations produces naturally a duty cycle of the AGN with a periodicity of 100 Myr.

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arXiv2016

From climate models to planetary habitability: temperature constraints for complex life

In an effort to derive temperature based criteria of habitability for multicellular life, we investigated the thermal limits of terrestrial poikilotherms, i.e. organisms whose body temperature and the functioning of all vital processes is directly affected by the ambient temperature. Multicellular poikilotherms are the most common and evolutionarily ancient form of complex life on earth. The thermal limits for their active metabolism and reproduction are bracketed by the temperature interval 0C<T<50C. The same interval applies to the photosynthetic production of oxygen, an essential ingredient of complex life, and for the generation of atmospheric biosignatures. Analysis of the main mechanisms responsible for the thermal thresholds of terrestrial life suggests that the same mechanisms would apply to other forms of chemical life. We propose a habitability index for complex life, h050, representing the mean orbital fraction of planetary surface that satisfies the temperature limits 0C<T<50C. With the aid of a climate model tailored for the calculation of the surface temperature of Earth-like planets, we calculated h050 as a function of planet insolation S, and atmospheric columnar mass Natm, for a few earth-like atmospheric compositions. By displaying h050 as a function of S and Natm, we built up an atmospheric mass habitable zone (AMHZ) for complex life. At variance with the classic habitable zone, the inner edge of the complex life HZ is not affected by the uncertainties inherent to the calculation of the runaway greenhouse limit. The complex life HZ is significantly narrower than the HZ of dry planets. Our calculations illustrate how changes in ambient conditions dependent on S and Natm, such as temperature excursions and surface dose of secondary particles of cosmic rays, may influence the type of life potentially present at different epochs of planetary evolution inside the AMHZ.

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arXiv2016

nIFTy Galaxy Cluster simulations IV: Quantifying the Influence of Baryons on Halo Properties

Building on the initial results of the nIFTy simulated galaxy cluster comparison, we compare and contrast the impact of baryonic physics with a single massive galaxy cluster, run with 11 state-of-the-art codes, spanning adaptive mesh, moving mesh, classic and modern SPH approaches. For each code represented we have a dark matter only (DM) and non-radiative (NR) version of the cluster, as well as a full physics (FP) version for a subset of the codes. We compare both radial mass and kinematic profiles, as well as global measures of the cluster (e.g. concentration, spin, shape), in the NR and FP runs with that in the DM runs. Our analysis reveals good consistency (<= 20%) between global properties of the cluster predicted by different codes when integrated quantities are measured within the virial radius R200. However, we see larger differences for quantities within R2500, especially in the FP runs. The radial profiles reveal a diversity, especially in the cluster centre, between the NR runs, which can be understood straightforwardly from the division of codes into classic SPH and non-classic SPH (including the modern SPH, adaptive and moving mesh codes); and between the FP runs, which can also be understood broadly from the division of codes into those that include AGN feedback and those that do not. The variation with respect to the median is much larger in the FP runs with different baryonic physics prescriptions than in the NR runs with different hydrodynamics solvers.

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arXiv2016

nIFTY galaxy cluster simulations III: The Similarity & Diversity of Galaxies & Subhaloes

We examine subhaloes and galaxies residing in a simulated LCDM galaxy cluster ($M^{\rm crit}_{200}=1.1\times10^{15}M_\odot/h$) produced by hydrodynamical codes ranging from classic Smooth Particle Hydrodynamics (SPH), newer SPH codes, adaptive and moving mesh codes. These codes use subgrid models to capture galaxy formation physics. We compare how well these codes reproduce the same subhaloes/galaxies in gravity only, non-radiative hydrodynamics and full feedback physics runs by looking at the overall subhalo/galaxy distribution and on an individual objects basis. We find the subhalo population is reproduced to within $\lesssim10\%$ for both dark matter only and non-radiative runs, with individual objects showing code-to-code scatter of $\lesssim0.1$ dex, although the gas in non-radiative simulations shows significant scatter. Including feedback physics significantly increases the diversity. Subhalo mass and $V_{max}$ distributions vary by $\approx20\%$. The galaxy populations also show striking code-to-code variations. Although the Tully-Fisher relation is similar in almost all codes, the number of galaxies with $10^{9}M_\odot/h\lesssim M_*\lesssim 10^{12}M_\odot/h$ can differ by a factor of 4. Individual galaxies show code-to-code scatter of $\sim0.5$ dex in stellar mass. Moreover, strong systematic differences exist, with some codes producing galaxies $70\%$ smaller than others. The diversity partially arises from the inclusion/absence of AGN feedback. Our results combined with our companion papers demonstrate that subgrid physics is not just subject to fine-tuning, but the complexity of building galaxies in all environments remains a challenge. We argue even basic galaxy properties, such as the stellar mass to halo mass, should be treated with errors bars of $\sim0.2-0.4$ dex.

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arXiv2015

Neutral hydrogen in galaxy clusters: impact of AGN feedback and implications for intensity mapping

By means of zoom-in hydrodynamic simulations we quantify the amount of neutral hydrogen (HI) hosted by groups and clusters of galaxies. Our simulations, which are based on an improved formulation of smoothed particle hydrodynamics (SPH), include radiative cooling, star formation, metal enrichment and supernova feedback, and can be split in two different groups, depending on whether feedback from active galactic nuclei (AGN) is turned on or off. Simulations are analyzed to account for HI self-shielding and the presence of molecular hydrogen. We find that the mass in neutral hydrogen of dark matter halos monotonically increases with the halo mass and can be well described by a power-law of the form $M_{\rm HI}(M,z)\propto M^{3/4}$. Our results point out that AGN feedback reduces both the total halo mass and its HI mass, although it is more efficient in removing HI. We conclude that AGN feedback reduces the neutral hydrogen mass of a given halo by $\sim50\%$, with a weak dependence on halo mass and redshift. The spatial distribution of neutral hydrogen within halos is also affected by AGN feedback, whose effect is to decrease the fraction of HI that resides in the halo inner regions. By extrapolating our results to halos not resolved in our simulations we derive astrophysical implications from the measurements of $Ω_{\rm HI}(z)$: halos with circular velocities larger than $\sim25~{\rm km/s}$ are needed to host HI in order to reproduce observations. We find that only the model with AGN feedback is capable of reproducing the value of $Ω_{\rm HI}b_{\rm HI}$ derived from available 21cm intensity mapping observations.

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arXiv2015

How does our choice of observable influence our estimation of the centre of a galaxy cluster? Insights from cosmological simulations

Galaxy clusters are an established and powerful test-bed for theories of both galaxy evolution and cosmology. Accurate interpretation of cluster observations often requires robust identification of the location of the centre. Using a statistical sample of clusters drawn from a suite of cosmological simulations in which we have explored a range of galaxy formation models, we investigate how the location of this centre is affected by the choice of observable - stars, hot gas, or the full mass distribution as can be probed by the gravitational potential. We explore several measures of cluster centre: the minimum of the gravitational potential, which would expect to define the centre if the cluster is in dynamical equilibrium; the peak of the density; the centre of BCG; and the peak and centroid of X-ray luminosity. We find that the centre of BCG correlates more strongly with the minimum of the gravitational potential than the X-ray defined centres, while AGN feedback acts to significantly enhance the offset between the peak X-ray luminosity and minimum gravitational potential. These results highlight the importance of centre identification when interpreting clusters observations, in particular when comparing theoretical predictions and observational data.

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arXiv2015

nIFTy galaxy cluster simulations II: radiative models

We have simulated the formation of a massive galaxy cluster (M$_{200}^{\rm crit}$ = 1.1$\times$10$^{15}h^{-1}M_{\odot}$) in a $Λ$CDM universe using 10 different codes (RAMSES, 2 incarnations of AREPO and 7 of GADGET), modeling hydrodynamics with full radiative subgrid physics. These codes include Smoothed-Particle Hydrodynamics (SPH), spanning traditional and advanced SPH schemes, adaptive mesh and moving mesh codes. Our goal is to study the consistency between simulated clusters modeled with different radiative physical implementations - such as cooling, star formation and AGN feedback. We compare images of the cluster at $z=0$, global properties such as mass, and radial profiles of various dynamical and thermodynamical quantities. We find that, with respect to non-radiative simulations, dark matter is more centrally concentrated, the extent not simply depending on the presence/absence of AGN feedback. The scatter in global quantities is substantially higher than for non-radiative runs. Intriguingly, adding radiative physics seems to have washed away the marked code-based differences present in the entropy profile seen for non-radiative simulations in Sembolini et al. (2015): radiative physics + classic SPH can produce entropy cores. Furthermore, the inclusion/absence of AGN feedback is not the dividing line -as in the case of describing the stellar content- for whether a code produces an unrealistic temperature inversion and a falling central entropy profile. However, AGN feedback does strongly affect the overall stellar distribution, limiting the effect of overcooling and reducing sensibly the stellar fraction.

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arXiv2015

The early phases of galaxy clusters formation in IR: coupling hydrodynamical simulations with GRASIL3D

We compute and study the infrared and sub-mm properties of high redshift ($z \gtrsim 1$) simulated clusters and proto-clusters. The results of a large set of hydro-dynamical zoom-in simulations including active galactic nuclei (AGN) feedback, have been treated with the recently developed radiative transfer code GRASIL-3D, which accounts for the effect of dust reprocessing in an arbitrary geometry. Here, we have slightly generalized the code to adapt it to the present purpose. Then we have post-processed boxes of physical size 2 Mpc encompassing each of the 24 most massive clusters identified at z=0, at several redshifts between 0.5 and 3, producing IR and sub-mm mock images of these regions and SEDs of the radiation coming out from them. While this field is in its infancy from the observational point of view, rapid development is expected in the near future thanks to observations performed in the far IR and sub-mm bands. Notably, we find that in this spectral regime our prediction are little affected by the assumption required by this post-processing, and the emission is mostly powered by star formation rather than accretion onto super massive black hole (SMBH). The comparison with the little observational information currently available, highlights that the simulated cluster regions never attain the impressive star formation rates suggested by these observations. This problem becomes more intriguing taking into account that the brightest cluster galaxies (BCGs) in the same simulations turn out to be too massive. It seems that the interplay between the feedback schemes and the star formation model should be revised, possibly incorporating a positive feedback mode.

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arXiv2015

nIFTy galaxy cluster simulations I: dark matter & non-radiative models

We have simulated the formation of a galaxy cluster in a $Λ$CDM universe using twelve different codes modeling only gravity and non-radiative hydrodynamics (\art, \arepo, \hydra\ and 9 incarnations of GADGET). This range of codes includes particle based, moving and fixed mesh codes as well as both Eulerian and Lagrangian fluid schemes. The various GADGET implementations span traditional and advanced smoothed-particle hydrodynamics (SPH) schemes. The goal of this comparison is to assess the reliability of cosmological hydrodynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be non-radiative. We compare images of the cluster at $z=0$, global properties such as mass, and radial profiles of various dynamical and thermodynamical quantities. The underlying gravitational framework can be aligned very accurately for all the codes allowing a detailed investigation of the differences that develop due to the various gas physics implementations employed. As expected, the mesh-based codes ART and AREPO form extended entropy cores in the gas with rising central gas temperatures. Those codes employing traditional SPH schemes show falling entropy profiles all the way into the very centre with correspondingly rising density profiles and central temperature inversions. We show that methods with modern SPH schemes that allow entropy mixing span the range between these two extremes and the latest SPH variants produce gas entropy profiles that are essentially indistinguishable from those obtained with grid based methods.

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arXiv2014

Properties of barred spiral disks in hydrodynamical cosmological simulations

We present a quantification of the properties of bars in two N-body+SPH cosmological simulations of spiral galaxies, named GA and AqC. The initial conditions were obtained using the zoom-in technique and represent two dark matter (DM) halos of $2-3\times10^{12}\ {\rm M}_\odot$, available at two different resolutions. The resulting galaxies are presented in the companion paper of Murante et al. (2014). We find that the GA galaxy has a bar of length $8.8$ kpc, present at the two resolution levels even though with a slightly different strength. Classical bar signatures (e.g. pattern of streaming motions, high $m=2$ Fourier mode with roughly constant phase) are consistently found at both resolutions. Though a close encounter with a merging satellite at $z\sim0.6$ (mass ratio $1:50$) causes a strong, transient spiral pattern and some heating of the disk, we find that bar instability is due to secular process, caused by a low Toomre parameter $Q\lesssim1$ due to accumulation of mass in the disk. The AqC galaxy has a slightly different history: it suffers a similar tidal disturbance due to a merging satellite at $z\sim0.5$ but with a mass ratio of $1:32$, that triggers a bar in the high-resolution simulation, while at low resolution the merging is found to take place at a later time, so that both secular evolution and merging are plausible triggers for bar instability.

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arXiv2014

Simulating realistic disk galaxies with a novel sub-resolution ISM model

We present results of cosmological simulations of disk galaxies carried out with the GADGET-3 TreePM+SPH code, where star formation and stellar feedback are described using our MUlti Phase Particle Integrator (MUPPI) model. This description is based on simple multi-phase model of the interstellar medium at unresolved scales, where mass and energy flows among the components are explicitly followed by solving a system of ordinary differential equations. Thermal energy from SNe is injected into the local hot phase, so as to avoid that it is promptly radiated away. A kinetic feedback prescription generates the massive outflows needed to avoid the over-production of stars. We use two sets of zoomed-in initial conditions of isolated cosmological halos with masses (2-3) * 10^{12} Msun, both available at several resolution levels. In all cases we obtain spiral galaxies with small bulge-over-total stellar mass ratios (B/T \approx 0.2), extended stellar and gas disks, flat rotation curves and realistic values of stellar masses. Gas profiles are relatively flat, molecular gas is found to dominate at the centre of galaxies, with star formation rates following the observed Schmidt-Kennicutt relation. Stars kinematically belonging to the bulge form early, while disk stars show a clear inside-out formation pattern and mostly form after redshift z=2. However, the baryon conversion efficiencies in our simulations differ from the relation given by Moster et al. (2010) at a 3 sigma level, thus indicating that our stellar disks are still too massive for the Dark Matter halo in which they reside. Results are found to be remarkably stable against resolution. This further demonstrates the feasibility of carrying out simulations producing a realistic population of galaxies within representative cosmological volumes, at a relatively modest resolution.

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arXiv2014

Galactic outflow and diffuse gas properties at z>=1 using different baryonic feedback models

We measure and quantify properties of galactic outflows and diffuse gas at $z \geq 1$ in cosmological hydrodynamical simulations. Our novel sub-resolution model, MUPPI, implements supernova feedback using fully local gas properties, where the wind velocity and mass loading are not given as input. We find the following trends at $z = 2$ by analysing central galaxies having a stellar mass higher than $10^{9} M_{\odot}$. The outflow velocity and mass outflow rate ($\dot{M}_{\rm out}$) exhibit positive correlations with galaxy mass and with the star formation rate (SFR). However, most of the relations present a large scatter. The outflow mass loading factor ($η$) is between $0.2 - 10$. The comparison Effective model generates a constant outflow velocity, and a negative correlation of $η$ with halo mass. The number fraction of galaxies where outflow is detected decreases at lower redshifts, but remains more than $80 \%$ over $z = 1 - 5$. High SF activity at $z \sim 2 - 4$ drives strong outflows, causing the positive and steep correlations of velocity and $\dot{M}_{\rm out}$ with SFR. The outflow velocity correlation with SFR becomes flatter at $z = 1$, and $η$ displays a negative correlation with halo mass in massive galaxies. Our study demonstrates that both the MUPPI and Effective models produce significant outflows at $\sim 1 / 10$ of the virial radius; at the same time shows that the properties of outflows generated can be different from the input speed and mass loading in the Effective model. Our MUPPI model, using local properties of gas in the sub-resolution recipe, is able to develop galactic outflows whose properties correlate with global galaxy properties, and consistent with observations.

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arXiv2014

The effect of AGN feedback on the halo mass function

[Abridged.] We investigate baryon effects on the halo mass function (HMF), with emphasis on the role played by AGN feedback. Halos are identified with both Friends-of-Friends (FoF) and Spherical Overdensity (SO) algorithms. We embed the standard SO algorithm into a memory-controlled frame program and present the {\bf P}ython spher{\bf I}c{\bf A}l {\bf O}verdensity code --- {\small PIAO}. For both FoF and SO halos, the effect of AGN feedback is that of suppressing the HMFs to a level even below that of Dark Matter simulations. The ratio between the HMFs in the AGN and in the DM simulations is $\sim 0.8$ at overdensity $Δ_c=500$, a difference that increases at higher overdensity $Δ_c=2500$, with no significant redshift and mass dependence. A decrease of the halo masses ratio with respect to the DM case induces the decrease of the HMF in the AGN simulation. The shallower inner density profiles of halos in the AGN simulation witnesses that mass reduction is induced by the sudden displacement of gas induced by thermal AGN feedback. We provide fitting functions to describe halo mass variations at different overdensities, which can recover the HMFs with a residual random scatter $\lt 5$ per cent for halo masses larger than $10^{13} ~h^{-1}{\rm M_\odot}$.

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