arXiv subjects

Joop Schaye

Publications and source records attributed to Joop Schaye.

At least 451 records · Page 25Linked to original sources

arXiv2012

Sample variance and Lyman-alpha forest transmission statistics

We compare the observed probability distribution function of the transmission in the \HI\ Lyman-alpha forest, measured from the UVES 'Large Programme' sample at redshifts z=[2,2.5,3], to results from the GIMIC cosmological simulations. Our measured values for the mean transmission and its PDF are in good agreement with published results. Errors on statistics measured from high-resolution data are typically estimated using bootstrap or jack-knife resampling techniques after splitting the spectra into chunks. We demonstrate that these methods tend to underestimate the sample variance unless the chunk size is much larger than is commonly the case. We therefore estimate the sample variance from the simulations. We conclude that observed and simulated transmission statistics are in good agreement, in particular, we do not require the temperature-density relation to be 'inverted'.

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arXiv2012

Rotation rates, sizes, and star formation efficiencies of a representative population of simulated disc galaxies

We examine the rotation rates, sizes, and star formation (SF) efficiencies of a representative population of simulated disc galaxies extracted from the Galaxies-Intergalactic Medium Interaction Calculation (GIMIC) suite of cosmological hydrodynamic simulations. These simulations include efficient, but energetically feasible supernova feedback, but have not been tuned in any way to produce 'realistic' disc galaxies. Yet, they generate a large number of discs, without requiring extremely high resolution. Over the wide galaxy stellar mass range, 9.0 < log10[Mstar (Msun)] < 10.5, the simulations reproduce the observed Tully-Fisher relation, the rotation curves of disc galaxies in bins of stellar mass, the mass-size relation of disc galaxies, the optical rotation to virial circular velocity ratio (Vopt/Vvir), and the SF efficiencies of disc galaxies as inferred from stacked weak lensing and stacked satellite kinematics observations. They also reproduce the specific star formation rates of ~L* galaxies but predict too low levels of star formation for low-mass galaxies, which is plausibly due to the finite resolution of the simulations. At higher stellar masses, log10[Mstar (\Msun)] > 10.6, the simulated galaxies are too concentrated and have too high SF efficiencies. We conjecture that this shortcoming reflects the neglect of feedback from accreting supermassive black holes in these simulations. We conclude that it is possible to generate a representative population of disc galaxies that reproduces many of the observed trends of local disc galaxies using standard numerical hydrodynamic techniques and a plausible implementation of the "subgrid" astrophysical processes thought to be relevant to galaxy formation.

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arXiv2012

The Origin of Disks and Spheroids in Simulated Galaxies

In the simplest scenario, disk galaxies form predominantly in halos with high angular momentum and quiet recent assembly history, whereas spheroids are the slowly-rotating remnants of repeated merging events. We explore these assumptions using one hundred systems with halo masses similar to that of the Milky Way, identified in a series of cosmological gasdynamical simulations GIMIC. At z=0, the simulated galaxies exhibit a wide variety of morphologies, from dispersion-dominated spheroids to pure disk galaxies. Surprisingly, these morphological features are very poorly correlated with their halo properties: disks form in halos with high and low net spin, and mergers play a negligible role in the formation of spheroid stars, most of which form in-situ. More important to morphology is the coherent alignment of the angular momentum of baryons that accrete over time to form a galaxy. Spheroids tend to form when the spin of newly-accreted gas is misaligned with that of the extant galaxy, leading to the episodic formation of stars with different kinematics that cancel out the net rotation of the system. Disks, on the other hand, form out of gas that flows in with similar angular momentum to that of earlier-accreted material. Gas accretion from a hot corona thus favours disk formation, whereas gas that flows "cold", often along separate, misaligned filaments, favours the formation of spheroids. In this scenario, most spheroids consist of superpositions of stellar components with distinct kinematics, age, and metallicity, an arrangement that might survive to the present day given the paucity of major mergers. Since angular momentum is acquired largely at turnaround, morphology is imprinted early by the interplay of the tidal field and the shape of the material destined to form the galaxy.

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arXiv2012

Properties of gas in and around galaxy haloes

We study the properties of gas inside and around galaxy haloes as a function of radius and halo mass, focussing mostly on z=2, but also showing some results for z=0. For this purpose, we use a suite of large cosmological, hydrodynamical simulations from the OverWhelmingly Large Simulations project. The properties of cold- and hot-mode gas, which we separate depending on whether the temperature has been higher than 10^5.5 K while it was extragalactic, are clearly distinguishable in the outer parts of massive haloes (virial temperatures >> 10^5 K. The differences between cold- and hot-mode gas resemble those between inflowing and outflowing gas. The cold-mode gas is mostly confined to clumpy filaments that are approximately in pressure equilibrium with the diffuse, hot-mode gas. Besides being colder and denser, cold-mode gas typically has a much lower metallicity and is much more likely to be infalling. However, the spread in the properties of the gas is large, even for a given mode and a fixed radius and halo mass, which makes it impossible to make strong statements about individual gas clouds. Metal-line cooling causes a strong cooling flow near the central galaxy, which makes it hard to distinguish gas accreted through the cold and hot modes in the inner halo. Stronger feedback results in larger outflow velocities and pushes hot-mode gas to larger radii. The gas properties evolve as expected from virial arguments, which can also account for the dependence of many gas properties on halo mass. We argue that cold streams penetrating hot haloes are observable as high-column density HI Lyman-alpha absorption systems in sightlines near massive foreground galaxies.

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arXiv2012

Simulating galactic outflows with thermal supernova feedback

Cosmological simulations make use of sub-grid recipes for the implementation of galactic winds driven by massive stars because direct injection of supernova energy in thermal form leads to strong radiative losses, rendering the feedback inefficient. We argue that the main cause of the catastrophic cooling is a mismatch between the mass of the gas in which the energy is injected and the mass of the parent stellar population. Because too much mass is heated, the temperatures are too low and the cooling times too short. We use analytic arguments to estimate, as a function of the gas density and the numerical resolution, the minimum heating temperature that is required for the injected thermal energy to be efficiently converted into kinetic energy. We then propose and test a stochastic implementation of thermal feedback that uses this minimum temperature increase as an input parameter and that can be employed in both particle- and grid-based codes. We use smoothed particle hydrodynamics simulations to test the method on models of isolated disc galaxies in dark matter haloes with total mass 10^10 and 10^12 h^-1 solar masses. The thermal feedback strongly suppresses the star formation rate and can drive massive, large-scale outflows without the need to turn off radiative cooling temporarily. In accord with expectations derived from analytic arguments, for sufficiently high resolution the results become insensitive to the imposed temperature jump and also agree with high-resolution simulations employing kinetic feedback.

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arXiv2012

Absorption signatures of warm-hot gas at low redshift: Broad HI Lyman-Alpha Absorbers

We investigate the physical state of HI absorbing gas at low redshift (z = 0.25) using a subset of cosmological, hydrodynamic simulations from the OWLS project, focusing in particular on broad (b_HI > 40 km/s) HI Lyman-Alpha absorbers (BLAs), which are believed to originate in shock-heated gas in the warm-hot intergalactic medium (WHIM). Our fiducial model, which includes radiative cooling by heavy elements and feedback by supernovae and active galactic nuclei, predicts that by z = 0.25 nearly 60 per cent of the gas mass ends up at densities and temperatures characteristic of the WHIM and we find that half of this fraction is due to outflows. The standard HI observables (distribution of HI column densities N_HI, distribution of Doppler parameters b_HI, b_HI - N_HI correlation) and the BLA line number density predicted by our simulations are in remarkably good agreement with observations. BLAs arise in gas that is hotter, more highly ionised and more enriched than the gas giving rise to typical Lyman-Alpha forest absorbers. The majority of the BLAs arise in warm-hot (log (T/K) ~ 5) gas at low (log Delta < 1.5) overdensities. On average, thermal broadening accounts for at least 60 per cent of the BLA line width, which in turn can be used as a rough indicator of the thermal state of the gas. Detectable BLAs account for only a small fraction of the true baryon content of the WHIM at low redshift. In order to detect the bulk of the mass in this gas phase, a sensitivity at least one order of magnitude better than achieved by current ultraviolet spectrographs is required. We argue that BLAs mostly trace gas that has been shock-heated and enriched by outflows and that they therefore provide an important window on a poorly understood feedback process.

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arXiv2012

Quantifying the effect of baryon physics on weak lensing tomography

We use matter power spectra from cosmological hydrodynamic simulations to quantify the effect of baryon physics on the weak gravitational lensing shear signal. The simulations consider a number of processes, such as radiative cooling, star formation, supernovae and feedback from active galactic nuclei (AGN). Van Daalen et al. (2011) used the same simulations to show that baryon physics, in particular the strong feedback that is required to solve the overcooling problem, modifies the matter power spectrum on scales relevant for cosmological weak lensing studies. As a result, the use of power spectra from dark matter simulations can lead to significant biases in the inferred cosmological parameters. We show that the typical biases are much larger than the precision with which future missions aim to constrain the dark energy equation of state, w_0. For instance, the simulation with AGN feedback, which reproduces X-ray and optical properties of groups of galaxies, gives rise to a ~40% bias in w_0. We demonstrate that the modification of the power spectrum is dominated by groups and clusters of galaxies, the effect of which can be modelled. We consider an approach based on the popular halo model and show that simple modifications can capture the main features of baryonic feedback. Despite its simplicity, we find that our model, when calibrated on the simulations, is able to reduce the bias in w_0 to a level comparable to the size of the statistical uncertainties for a Euclid-like mission. While observations of the gas and stellar fractions as a function of halo mass can be used to calibrate the model, hydrodynamic simulations will likely still be needed to extend the observed scaling relations down to halo masses of 10 ^12 M_sun/h.

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arXiv2012

Neutral hydrogen optical depth near star-forming galaxies at z~2.4 in the Keck Baryonic Structure Survey

[Abridged] We study the interface between galaxies and the intergalactic medium by measuring the absorption by neutral hydrogen in the vicinity of star-forming galaxies at z~2.4. Our sample consists of 679 rest-frame-UV selected galaxies with spectroscopic redshifts that have impact parameters < 2 (proper) Mpc to the line of sight of one of 15 bright, background QSOs. We present the first 2-D maps of the absorption around galaxies, plotting the median Ly-a pixel optical depth as a function of transverse and line of sight, LOS, separation from galaxies. The median optical depth, and hence the median density of atomic hydrogen, drops by more than an order of magnitude around 100 kpc, which is similar to the virial radius of the halos thought to host the galaxies. The median remains enhanced (>3 sigma level) out to at least 2.8 Mpc (i.e. > 9 comoving Mpc). Within 100 (200) kpc, and over \pm 165 km/s, the covering fraction of gas with Ly-a optical depth greater than unity is 100(+0)(-32)% (86(+14)(-18)%). Absorbers with tau(Ly-a)> 0.1 are typically closer to galaxies than random. The mean galaxy overdensity around absorbers increases with the optical depth and also as the length scale over which the galaxy overdensity is evaluated is decreased. Absorbers with tau(Ly-a)~1 reside in regions where the galaxy number density is close to the cosmic mean on scales > 0.25 Mpc. We detect two types of redshift space anisotropies. On scales < 200 km/s, or < 1 Mpc, the absorption is stronger along the LOS than in the transverse direction. This "finger of God" effect may be partly due to redshift errors, but is probably dominated by gas motions within or very close to the halos. On the other hand, on scales of 1.4 - 2.0 Mpc the absorption is compressed along the LOS (>3 sigma significance), which we attribute to large-scale infall (i.e. the Kaiser effect).

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arXiv2012

The XMM Cluster Survey: The interplay between the brightest cluster galaxy and the intra-cluster medium via AGN feedback

Using a sample of 123 X-ray clusters and groups drawn from the XMM-Cluster Survey first data release, we investigate the interplay between the brightest cluster galaxy (BCG), its black hole, and the intra-cluster/group medium (ICM). It appears that for groups and clusters with a BCG likely to host significant AGN feedback, gas cooling dominates in those with Tx > 2 keV while AGN feedback dominates below. This may be understood through the sub-unity exponent found in the scaling relation we derive between the BCG mass and cluster mass over the halo mass range 10^13 < M500 < 10^15Msol and the lack of correlation between radio luminosity and cluster mass, such that BCG AGN in groups can have relatively more energetic influence on the ICM. The Lx - Tx relation for systems with the most massive BCGs, or those with BCGs co-located with the peak of the ICM emission, is steeper than that for those with the least massive and most offset, which instead follows self-similarity. This is evidence that a combination of central gas cooling and powerful, well fuelled AGN causes the departure of the ICM from pure gravitational heating, with the steepened relation crossing self-similarity at Tx = 2 keV. Importantly, regardless of their black hole mass, BCGs are more likely to host radio-loud AGN if they are in a massive cluster (Tx > 2 keV) and again co-located with an effective fuel supply of dense, cooling gas. This demonstrates that the most massive black holes appear to know more about their host cluster than they do about their host galaxy. The results lead us to propose a physically motivated, empirical definition of 'cluster' and 'group', delineated at 2 keV.

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arXiv2012

Hydrodynamical simulations and semi-analytic models of galaxy formation: two sides of the same coin

In this work we develop a new method to turn a state-of-the-art hydrodynamical cosmological simulation of galaxy formation (HYD) into a simple semi-analytic model (SAM). This is achieved by summarizing the efficiencies of accretion, cooling, star formation, and feedback given by the HYD, as functions of the halo mass and redshift. Surprisingly, by turning the HYD into a SAM, we conserve the mass of individual galaxies, with deviations at the level of 0.1 dex, on an object-by-object basis. This is true for all redshifts, and for the mass of stars and gas components, although the agreement reaches 0.2 dex for satellite galaxies at low redshift. We show that the same level of accuracy is obtained even in case the SAM uses only one phase of gas within each galaxy. Moreover, we demonstrate that the formation history of one massive galaxy provides sufficient information for the SAM to reproduce the population of galaxies within the entire cosmological box. The reasons for the small scatter between the HYD and SAM galaxies are: a) The efficiencies are matched as functions of the halo mass and redshift, meaning that the evolution within merger-trees agrees on average. b) For a given galaxy, efficiencies fluctuate around the mean value on time scales of 0.2-2 Gyr. c) The various mass components of galaxies are obtained by integrating the efficiencies over time, averaging out these fluctuations. We compare the efficiencies found here to standard SAM recipes and find that they often deviate significantly. For example, here the HYD shows smooth accretion that is less effective for low mass haloes, and is always composed of hot or dilute gas; cooling is less effective at high redshift; and star formation changes only mildly with cosmic time. The method developed here can be applied in general to any HYD, and can thus serve as a common language for both HYDs and SAM (Abridged).

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arXiv2012

Cold accretion flows and the nature of high column density HI absorption at redshift 3

Simulations predict that galaxies grow primarily through the accretion of gas that has not gone through an accretion shock near the virial radius and that this cold gas flows towards the central galaxy along dense filaments and streams. There is, however, little observational evidence for the existence of these cold flows. We use a large, cosmological, hydrodynamical simulation that has been post-processed with radiative transfer to study the contribution of cold flows to the observed z=3 column density distribution of neutral hydrogen, which our simulation reproduces. We find that nearly all of the HI absorption arises in gas that has remained colder than 10^5.5 K, at least while it was extragalactic. In addition, the majority of the HI is rapidly falling towards a nearby galaxy, with non-negligible contributions from outflowing and static gas. Above a column density of N_HI = 10^17 cm^-2, most of the absorbers reside inside haloes, but the interstellar medium only dominates for N_HI > 10^21 cm^-2. Haloes with total mass below 10^10 Msun dominate the absorption for 10^17 10^17 cm^-2 are closely related to star formation: most of their HI either will become part of the interstellar medium before z=2 or has been ejected from a galaxy at z>3. Cold accretion flows are critical for the success of our simulation in reproducing the observed rate of incidence of damped Lyman-alpha and particularly that of Lyman limit systems. We therefore conclude that cold accretion flows exist and have already been detected in the form of high column density HI absorbers.

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arXiv2011

Global structure and kinematics of stellar haloes in cosmological hydrodynamic simulations

We use the Galaxies-Intergalactic Medium Interaction Calculation (GIMIC) suite of cosmological hydrodynamical simulations to study the global structure and kinematics of stellar spheroids of Milky Way mass disc galaxies. Font et al. have recently demonstrated that these simulations are able to successfully reproduce the satellite luminosity functions and the metallicity and surface brightness profiles of the spheroids of the Milky Way and M31. A key to the success of the simulations is a significant contribution to the spheroid from stars that formed in situ. While the outer halo is dominated by accreted stars, stars formed in the main progenitor of the galaxy dominate at r < ~30 kpc. In the present study we show that this component was primarily formed in a proto-disc at high redshift and was subsequently liberated from the disc by dynamical heating associated with mass accretion. As a consequence of its origin, the in situ component of the spheroid has different kinematics (namely net prograde rotation with respect to the disc) than that of the spheroid component built from the disruption of satellites. In addition, the in situ component has a flattened distribution, that is due in part to its rotation. We make comparisons with measurements of the shape and kinematics of local galaxies, including the Milky Way and M31, and stacked observations of more distant galaxies. We find that the simulated disc galaxies have spheroids of the correct shape (oblate with a median axis ratio of ~0.6 at radii of < ~30 kpc, but note there is significant system-to-system scatter in this quantity) and that the kinematics show evidence for two components (due to in situ vs. accreted), as observed. Our findings therefore add considerable weight to the importance of dissipative processes in the formation of stellar haloes and to the notion of a 'dual stellar halo'.

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arXiv2011

The filling factor of intergalactic metals at redshift z=3

Observations of quasar absorption line systems reveal that the z=3 intergalactic medium (IGM) is polluted by heavy elements down to HI optical depths tau_HI<<10. What is not yet clear, however, is what fraction of the volume needs to be enriched by metals and whether it suffices to enrich only regions close to galaxies in order to reproduce the observations. We use gas density fields derived from large cosmological simulations, together with synthetic quasar spectra and imposed, model metal distributions to investigate what enrichment patterns can reproduce the observed median optical depth of CIV as a function of tau_HI. Our models can only satisfy the observational constraints if the z=3 IGM was primarily enriched by galaxies that reside in low-mass (m_tot<10^10 M_sun) haloes that can eject metals out to distances >10^2 kpc. Galaxies in more massive haloes cannot possibly account for the observations as they are too rare for their outflows to cover a sufficiently large fraction of the volume. Galaxies need to enrich gas out to distances that are much greater than the virial radii of their host haloes. Assuming the metals to be well mixed on small scales, our modeling requires that the fractions of the simulated volume and baryonic mass that are polluted with metals are, respectively, >10% and >50% in order to match observations.

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arXiv2011

Modelling neutral hydrogen in galaxies using cosmological hydrodynamical simulations

The characterisation of the atomic and molecular hydrogen content of high-redshift galaxies is a major observational challenge that will be addressed over the coming years with a new generation of radio telescopes. We investigate this important issue by considering the states of hydrogen across a range of structures within high-resolution cosmological hydrodynamical simulations. Additionally, our simulations allow us to investigate the sensitivity of our results to numerical resolution and to sub-grid baryonic physics (especially feedback from supernovae and active galactic nuclei). We find that the most significant uncertainty in modelling the neutral hydrogen distribution arises from our need to model a self-shielding correction in moderate density regions. Future simulations incorporating radiative transfer schemes will be vital to improve on our empirical self-shielding threshold. Irrespective of the exact nature of the threshold we find that while the atomic hydrogen mass function evolves only mildly from redshift two to zero, the molecular hydrogen mass function increases with increasing redshift, especially at the high-mass end. Interestingly, the weak evolution of the neutral hydrogen mass function is insensitive to the feedback scheme utilised, but the opposite is true for the molecular gas, which is more closely associated with the star formation in the simulations.

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arXiv2011

Disentangling galaxy environment and host halo mass

[Abridged] The properties of observed galaxies and dark matter haloes in simulations depend on their environment. The term environment has been used to describe a wide variety of measures that may or may not correlate with each other. Popular measures of environment include the distance to the N'th nearest neighbour, the number density of objects within some distance, or the mass of the host dark matter halo. We use results from the Millennium simulation and a semi-analytic model for galaxy formation to quantify the relations between environment and halo mass. We show that the environmental parameters used in the observational literature are in effect measures of halo mass, even if they are measured for a fixed stellar mass. The strongest correlation between environment and halo mass arises when the number of objects is counted out to a distance of 1.5-2 times the virial radius of the host halo and when the galaxies/haloes are required to be relatively bright/massive. For observational studies the virial radius is not easily determined, but the number of neighbours out to 1-2 Mpc/h gives a similarly strong correlation. For the distance to the N'th nearest neighbour the correlation with halo mass is nearly as strong provided N>2. We demonstrate that this environmental parameter becomes insensitive to halo mass if it is constructed from dimensionless quantities. This can be achieved by scaling the minimum luminosity/mass of neighbours to that of the object in question and by dividing the distance to a length scale associated with either the neighbour or the galaxy under consideration. We show how such a halo mass independent environmental parameter can be defined for observational and numerical studies. The results presented here will help future studies to disentangle the effects of halo mass and external environment on the properties of galaxies and dark matter haloes.

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arXiv2011

Rest-frame UV line emission from the intergalactic medium at 2<z<5

Rest-frame UV emission lines offer the possibility to directly image the gas around high-redshift galaxies with upcoming optical instruments. We use a suite of large, hydrodynamical simulations to predict the nature and detectability of emission lines from the intergalactic medium at 2<z<5. The brightest emission comes from HI Ly-alpha and the strongest metal line, CIII, is about an order of magnitude fainter, although HI Ly-alpha may be fainter if the gas is self-shielded to the UV background or if dust is important. The highest surface brightness regions for CIV, SiIII, SiIV and OVI are fainter than CIII by factors of a few. The NV and NeVIII lines, as well as HeII H-alpha, are substantially weaker but their maximum surface brightnesses still exceed 100 photon/cm^2/s/sr at z=2 (for 2" pixels). Lower ionisation lines arise in denser and colder gas that produces clumpier emission. The brightest HI Ly-alpha emission arises in highly overdense gas, but the highest surface brightness emission from high-ionisation metal lines traces a wider range of overdensities. Bright metal-line emission traces gas with temperatures close to the peak of the corresponding emissivity curve. While HI Ly-alpha, HeII H-alpha, CIII, SiIII, and SiIV are excellent probes of cold accretion flows and the colder parts of outflows, CIV, NV, OVI, and NeVIII are powerful tracers of the diffuse WHIM and galactic winds. A comparison of results from simulations with varying physical prescriptions demonstrates that the predictions for the brighter metal-line emission are robust to within factors of a few. Several emission lines from the high-redshift IGM will become detectable in the near future, possibly starting with the Cosmic Web Imager on Palomar. MUSE and the Keck Cosmic Web Imager have the potential to revolutionise studies of the interactions between high-redshift galaxies and their environment. (Abridged)

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arXiv2011

Through Thick and Thin - HI Absorption in Cosmological Simulations

We investigate the column density distribution function of neutral hydrogen at redshift z = 3 using a cosmological simulation of galaxy formation from the OverWhelmingly Large Simulations (OWLS) project. The base simulation includes gravity, hydrodynamics, star formation, supernovae feedback, stellar winds, chemodynamics, and element-by-element cooling in the presence of a uniform UV background. Self-shielding and formation of molecular hydrogen are treated in post-processing, without introducing any free parameters, using an accurate reverse ray-tracing algorithm and an empirical relation between gas pressure and molecular mass fraction. The simulation reproduces the observed z = 3 abundance of Ly-A forest, Lyman Limit and Damped Ly-A HI absorption systems probed by quasar sight lines over ten orders of magnitude in column density. Self-shielding flattens the column density distribution for NHI > 10^18 cm-2, while the conversion to fully neutral gas and conversion of HI to H2 steepen it around column densities of NHI = 10^20.3 cm-2 and NHI = 10^21.5 cm-2, respectively.

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arXiv2011

Cosmological simulations of the formation of the stellar haloes around disc galaxies

We use the Galaxies-Intergalactic Medium Interaction Calculation (GIMIC) suite of cosmological hydrodynamical simulations to study the formation of stellar spheroids of Milky Way-mass disc galaxies. The simulations contain accurate treatments of metal-dependent radiative cooling, star formation, supernova feedback, and chemodynamics, and the large volumes that have been simulated yield an unprecedentedly large sample of ~400 simulated L_* disc galaxies. The simulated galaxies are surrounded by low-mass, low-surface brightness stellar haloes that extend out to ~100 kpc and beyond. The diffuse stellar distributions bear a remarkable resemblance to those observed around the Milky Way, M31 and other nearby galaxies, in terms of mass density, surface brightness, and metallicity profiles. We show that in situ star formation typically dominates the stellar spheroids by mass at radii of r < 30 kpc, whereas accretion of stars dominates at larger radii and this change in origin induces a change in slope of the surface brightness and metallicity profiles, which is also present in the observational data. The system-to-system scatter in the in situ mass fractions of the spheroid, however, is large and spans over a factor of 4. Consequently, there is a large degree of scatter in the shape and normalisation of the spheroid density profile within r < 30 kpc (e.g., when fit by a spherical powerlaw profile the indices range from -2.6 to -3.4). We show that the in situ mass fraction of the spheroid is linked to the formation epoch of the system. Dynamically older systems have, on average, larger contributions from in situ star formation, although there is significant system-to-system scatter in this relationship. Thus, in situ star formation likely represents the solution to the longstanding failure of pure accretion-based models to reproduce the observed properties of the inner spheroid.

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