# Posts Tagged mass function

## Recent Postings from mass function

### Horizon Run 4 Simulation: Coupled Evolution of Galaxies and Large-scale Structures of the Universe

The Horizon Run 4 is a cosmological $N$-body simulation designed for the study of coupled evolution between galaxies and large-scale structures of the Universe, and for the test of galaxy formation models. Using $6300^3$ gravitating particles in a cubic box of $L_{\rm box} = 3150 ~h^{-1}{\rm Mpc}$, we build a dense forest of halo merger trees to trace the halo merger history with a halo mass resolution scale down to $M_s = 2.7 \times 10^{11} h^{-1}{\rm M_\odot}$. We build a set of particle and halo data, which can serve as testbeds for comparison of cosmological models and gravitational theories with observations. We find that the FoF halo mass function shows a substantial deviation from the universal form with tangible redshift evolution of amplitude and shape. At higher redshifts, the amplitude of the mass function is lower, and the functional form is shifted toward larger values of $\ln (1/\sigma)$. We also find that the baryonic acoustic oscillation feature in the two-point correlation function of mock galaxies becomes broader with a peak position moving to smaller scales and the peak amplitude decreasing for increasing directional cosine $\mu$ compared to the linear predictions. From the halo merger trees built from halo data at 75 redshifts, we measure the half-mass epoch of halos and find that less massive halos tend to reach half of their current mass at higher redshifts. Simulation outputs including snapshot data, past lightcone space data, and halo merger data are available at http://sdss.kias.re.kr/astro/Horizon-Run4/.

### Horizon Run 4 Simulation: Coupled Evolution of Galaxies and Large-scale Structures of the Universe [Replacement]

The Horizon Run 4 is a cosmological $N$-body simulation designed for the study of coupled evolution between galaxies and large-scale structures of the Universe, and for the test of galaxy formation models. Using $6300^3$ gravitating particles in a cubic box of $L_{\rm box} = 3150 ~h^{-1}{\rm Mpc}$, we build a dense forest of halo merger trees to trace the halo merger history with a halo mass resolution scale down to $M_s = 2.7 \times 10^{11} h^{-1}{\rm M_\odot}$. We build a set of particle and halo data, which can serve as testbeds for comparison of cosmological models and gravitational theories with observations. We find that the FoF halo mass function shows a substantial deviation from the universal form with tangible redshift evolution of amplitude and shape. At higher redshifts, the amplitude of the mass function is lower, and the functional form is shifted toward larger values of $\ln (1/\sigma)$. We also find that the baryonic acoustic oscillation feature in the two-point correlation function of mock galaxies becomes broader with a peak position moving to smaller scales and the peak amplitude decreasing for increasing directional cosine $\mu$ compared to the linear predictions. From the halo merger trees built from halo data at 75 redshifts, we measure the half-mass epoch of halos and find that less massive halos tend to reach half of their current mass at higher redshifts. Simulation outputs including snapshot data, past lightcone space data, and halo merger data are available at http://sdss.kias.re.kr/astro/Horizon-Run4/.

### Effects of ghost dark energy perturbations on the evolution of spherical overdensities

While in the standard cosmological model the accelerated expansion of the Universe is explained by invoking the presence of the cosmological constant term, it is still unclear the true origin of this stunning observational fact. It is therefore interesting to explore alternatives to the simplest scenario, in particular by assuming a more general framework where the fluid responsible of the accelerated expansion is characterised by a time-dependant equation of state. Usually these models, dubbed dark energy models, are purely phenomenological, but in this work we concentrate on a theoretically justified model, the ghost dark energy model. Within the framework of the spherical collapse model, we evaluate effects of dark energy perturbations both at the linear and non-linear level and transfer these results into an observable quantity, the mass function, by speculatively taking into account contributions of dark energy to the mass of the halos. We showed that the growth rate is higher in ghost models and that perturbations enhance the number of structures with respect to the $\Lambda$CDM model, with stronger effects when the total mass takes into account dark energy clumps.

### Effects of ghost dark energy perturbations on the evolution of spherical overdensities [Cross-Listing]

While in the standard cosmological model the accelerated expansion of the Universe is explained by invoking the presence of the cosmological constant term, it is still unclear the true origin of this stunning observational fact. It is therefore interesting to explore alternatives to the simplest scenario, in particular by assuming a more general framework where the fluid responsible of the accelerated expansion is characterised by a time-dependant equation of state. Usually these models, dubbed dark energy models, are purely phenomenological, but in this work we concentrate on a theoretically justified model, the ghost dark energy model. Within the framework of the spherical collapse model, we evaluate effects of dark energy perturbations both at the linear and non-linear level and transfer these results into an observable quantity, the mass function, by speculatively taking into account contributions of dark energy to the mass of the halos. We showed that the growth rate is higher in ghost models and that perturbations enhance the number of structures with respect to the $\Lambda$CDM model, with stronger effects when the total mass takes into account dark energy clumps.

### Effects of Cosmic String Velocities and the Origin of Globular Clusters

With the hypothesis that cosmic string loops act as seeds for globular clusters in mind, we study the role that velocities of these strings will play in determining the mass distribution of globular clusters. Loops with high enough velocities will not form compact and roughly spherical objects and can hence not be the seeds for globular clusters. We compute the expected number density and mass function of globular clusters as a function of both the string tension and the peak loop velocity, and compare the results with the observational data on the mass distribution of globular clusters in our Milky Way. We determine the critical peak string loop velocity above which the agreement between the string loop model for the origin of globular clusters (neglecting loop velocities) and observational data is lost.

### Effects of Cosmic String Velocities and the Origin of Globular Clusters [Cross-Listing]

With the hypothesis that cosmic string loops act as seeds for globular clusters in mind, we study the role that velocities of these strings will play in determining the mass distribution of globular clusters. Loops with high enough velocities will not form compact and roughly spherical objects and can hence not be the seeds for globular clusters. We compute the expected number density and mass function of globular clusters as a function of both the string tension and the peak loop velocity, and compare the results with the observational data on the mass distribution of globular clusters in our Milky Way. We determine the critical peak string loop velocity above which the agreement between the string loop model for the origin of globular clusters (neglecting loop velocities) and observational data is lost.

### Effects of Cosmic String Velocities and the Origin of Globular Clusters [Cross-Listing]

With the hypothesis that cosmic string loops act as seeds for globular clusters in mind, we study the role that velocities of these strings will play in determining the mass distribution of globular clusters. Loops with high enough velocities will not form compact and roughly spherical objects and can hence not be the seeds for globular clusters. We compute the expected number density and mass function of globular clusters as a function of both the string tension and the peak loop velocity, and compare the results with the observational data on the mass distribution of globular clusters in our Milky Way. We determine the critical peak string loop velocity above which the agreement between the string loop model for the origin of globular clusters (neglecting loop velocities) and observational data is lost.

### Effects of Cosmic String Velocities and the Origin of Globular Clusters [Cross-Listing]

With the hypothesis that cosmic string loops act as seeds for globular clusters in mind, we study the role that velocities of these strings will play in determining the mass distribution of globular clusters. Loops with high enough velocities will not form compact and roughly spherical objects and can hence not be the seeds for globular clusters. We compute the expected number density and mass function of globular clusters as a function of both the string tension and the peak loop velocity, and compare the results with the observational data on the mass distribution of globular clusters in our Milky Way. We determine the critical peak string loop velocity above which the agreement between the string loop model for the origin of globular clusters (neglecting loop velocities) and observational data is lost.

### The white dwarf population of NGC 6397

NGC 6397 is one of the most interesting, well observed and theoretically studied globular clusters. The existing wealth of observations allows us to study the reliability of the theoretical white dwarf cooling sequences of low metallicity progenitors,to determine its age and the percentage of unresolved binaries, and to assess other important characteristics of the cluster, like the slope of the initial mass function, or the fraction of white dwarfs with hydrogen deficient atmospheres. We present a population synthesis study of the white dwarf population of NGC 6397. In particular, we study the shape of the color-magnitude diagram, and the corresponding magnitude and color distributions. We do this using an up-to-date Monte Carlo code that incorporates the most recent and reliable cooling sequences and an accurate modeling of the observational biases. We find a good agreement between our theoretical models and the observed data. In particular, we find that this agreement is best for those cooling sequences that take into account residual hydrogen burning. This result has important consequences for the evolution of progenitor stars during the thermally-pulsing asymptotic giant branch phase, since it implies that appreciable third dredge-up in low-mass, low-metallicity progenitors is not expected to occur. Using a standard burst duration of 1.0 Gyr, we obtain that the age of the cluster is 12.8+0.50-0.75 Gyr. Larger ages are also compatible with the observed data, but then realistic longer durations of the initial burst of star formation are needed to fit the luminosity function. We conclude that a correct modeling of the white dwarf opulation of globular clusters, used in combination with the number counts of main sequence stars provides an unique tool to model the properties of globular clusters.

### Substellar Objects in Nearby Young Clusters (SONYC) IX: The planetary-mass domain of Chamaeleon-I and updated mass function in Lupus-3

Substellar Objects in Nearby Young Clusters — SONYC — is a survey program to investigate the frequency and properties of substellar objects in nearby star-forming regions. We present new spectroscopic follow-up of candidate members in Chamaeleon-I (~2 Myr, 160 pc) and Lupus 3 (~1 Myr, 200 pc), identified in our earlier works. We obtained 34 new spectra (1.5 – 2.4 mum, R~600), and identified two probable members in each of the two regions. These include a new probable brown dwarf in Lupus 3 (NIR spectral type M7.5 and Teff=2800 K), and an L3 (Teff=2200 K) brown dwarf in Cha-I, with the mass below the deuterium-burning limit. Spectroscopic follow-up of our photometric and proper motion candidates in Lupus 3 is almost complete (>90%), and we conclude that there are very few new substellar objects left to be found in this region, down to 0.01 – 0.02 MSun and Av \leq 5. The low-mass portion of the mass function in the two clusters can be expressed in the power-law form dN/dM \propto M^{-\alpha}, with \alpha~0.7, in agreement with surveys in other regions. In Lupus 3 we observe a possible flattening of the power-law IMF in the substellar regime: this region seems to produce fewer brown dwarfs relative to other clusters. The IMF in Cha-I shows a monotonic behavior across the deuterium-burning limit, consistent with the same power law extending down to 4 – 9 Jupiter masses. We estimate that objects below the deuterium-burning limit contribute of the order 5 – 15% to the total number of Cha-I members.

### Substellar Objects in Nearby Young Clusters (SONYC) IX: The planetary-mass domain of Chamaeleon-I and updated mass function in Lupus-3 [Replacement]

Substellar Objects in Nearby Young Clusters — SONYC — is a survey program to investigate the frequency and properties of substellar objects in nearby star-forming regions. We present new spectroscopic follow-up of candidate members in Chamaeleon-I (~2 Myr, 160 pc) and Lupus 3 (~1 Myr, 200 pc), identified in our earlier works. We obtained 34 new spectra (1.5 – 2.4 mum, R~600), and identified two probable members in each of the two regions. These include a new probable brown dwarf in Lupus 3 (NIR spectral type M7.5 and Teff=2800 K), and an L3 (Teff=2200 K) brown dwarf in Cha-I, with the mass below the deuterium-burning limit. Spectroscopic follow-up of our photometric and proper motion candidates in Lupus 3 is almost complete (>90%), and we conclude that there are very few new substellar objects left to be found in this region, down to 0.01 – 0.02 MSun and Av \leq 5. The low-mass portion of the mass function in the two clusters can be expressed in the power-law form dN/dM \propto M^{-\alpha}, with \alpha~0.7, in agreement with surveys in other regions. In Lupus 3 we observe a possible flattening of the power-law IMF in the substellar regime: this region seems to produce fewer brown dwarfs relative to other clusters. The IMF in Cha-I shows a monotonic behavior across the deuterium-burning limit, consistent with the same power law extending down to 4 – 9 Jupiter masses. We estimate that objects below the deuterium-burning limit contribute of the order 5 – 15% to the total number of Cha-I members.

### The universality of the virial halo mass function and models for non-universality of other halo definitions

The abundance of galaxy clusters can constrain both the geometry and structure growth in our Universe. However, this probe could be significantly complicated by recent claims of nonuniversality — non-trivial dependences with respect to the cosmological model and redshift. In this work we analyse the dependance of the mass function on the way haloes are identified and establish if this can cause departures from universality. In order to explore this dependance, we use a set of different dark matter only cosmological simulations (Le SBARBINE simulations), with the latest cosmological parameters from the Planck collaboration; this first suite of simulations is followed by a lower resolution set carry out with different cosmological parameters. We identify dark matter haloes using a Spherical Overdensity algorithm with varying overdensity thresholds (virial, 2000$\rho_c$, 1000$\rho_c$, 500$\rho_c$, 200$\rho_c$ and 200$\rho_b$) at all redshifts. We notice that, when expressed in term of the rescaled variable $\nu$, the mass function for virial haloes can be considered universal as a function of redshift and cosmology, while this is clearly not the case for the other considered overdensities. We provide fitting functions for the halo mass function parameters as a function of density, that allow to predict, with a few percent accuracy, the halo mass function for a wide range of halo definitions, redshifts and cosmological models. We then present how the departures from universality associated with other halo definitions can be derived by combining the universality of the virial definition with the expected shape of the density profile of halos.

### Outflows in Sodium Excess Objects

van Dokkum and Conroy revisited the unexpectedly strong Na I lines at 8200 A found in some giant elliptical galaxies and interpreted it as evidence for unusually bottom-heavy initial mass function. Jeong et al. later found a large population of galaxies showing equally-extraordinary Na D doublet absorption lines at 5900 A (Na D excess objects: NEOs) and showed that their origins can be different for different types of galaxies. While a Na D excess seems to be related with the interstellar medium (ISM) in late-type galaxies, smooth-looking early-type NEOs show little or no dust extinction and hence no compelling sign of ISM contributions. To further test this finding, we measured the doppler components in the Na D lines. We hypothesized that ISM would have a better (albeit not definite) chance of showing a blueshift doppler departure from the bulk of the stellar population due to outflow caused by either star formation or AGN activities. Many of the late-type NEOs clearly show blueshift in their Na D lines, which is consistent with the former interpretation that the Na D excess found in them is related with star formation-caused gas outflow. On the contrary, smooth-looking early-type NEOs do not show any notable doppler component, which is also consistent with the interpretation of Jeong et al. that the Na D excess in early-type NEOs is likely not related with ISM activities but is purely stellar in origin.

### The Next Generation Virgo Cluster Survey. IX. Estimating the Efficiency of Galaxy Formation on the Lowest-Mass Scales

The Next Generation Virgo Cluster Survey has recently determined the luminosity function of galaxies in the core of the Virgo cluster down to unprecedented magnitude and surface brightness limits. Comparing simulations of cluster formation to the derived central stellar mass function, we attempt to estimate the stellar-to-halo-mass ratio (SHMR) for dwarf galaxies, as it would have been before they fell into the cluster. This approach ignores several details and complications, e.g., the contribution of ongoing star formation to the present-day stellar mass of cluster members, and the effects of adiabatic contraction and/or violent feedback on the subhalo and cluster potentials. The final results are startlingly simple, however; we find that the trends in the SHMR determined previously for bright galaxies appear to extend down in a scale-invariant way to the faintest objects detected in the survey. These results extend measurements of the formation efficiency of field galaxies by two decades in halo mass, or five decades in stellar mass, down to some of the least massive dwarf galaxies known, with stellar masses of $\sim 10^5 M_\odot$.

### On the Localisation of 4-Dimensional Brane-World Black Holes II: the general case [Cross-Listing]

We perform a comprehensive analysis of a number of scalar field theories in a attempt to find analytically 5-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the 5-dimensional metric tensor that allows for time-dependence, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen, non-isotropic in 5 dimensions, energy-momentum tensor, solutions that have the form of a Schwarzschild-(Anti)de Sitter or Reissner-Nordstrom type of solution do emerge, however, the resulting profile of the mass-function along the bulk coordinate, when allowed, is not the correct one to eliminate the bulk singularities.

### On the Localisation of 4-Dimensional Brane-World Black Holes II: the general case [Cross-Listing]

We perform a comprehensive analysis of a number of scalar field theories in a attempt to find analytically 5-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the 5-dimensional metric tensor that allows for time-dependence, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen, non-isotropic in 5 dimensions, energy-momentum tensor, solutions that have the form of a Schwarzschild-(Anti)de Sitter or Reissner-Nordstrom type of solution do emerge, however, the resulting profile of the mass-function along the bulk coordinate, when allowed, is not the correct one to eliminate the bulk singularities.

### On the Localisation of 4-Dimensional Brane-World Black Holes II: the general case [Cross-Listing]

We perform a comprehensive analysis of a number of scalar field theories in a attempt to find analytically 5-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the 5-dimensional metric tensor that allows for time-dependence, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen, non-isotropic in 5 dimensions, energy-momentum tensor, solutions that have the form of a Schwarzschild-(Anti)de Sitter or Reissner-Nordstrom type of solution do emerge, however, the resulting profile of the mass-function along the bulk coordinate, when allowed, is not the correct one to eliminate the bulk singularities.

### On the Localisation of 4-Dimensional Brane-World Black Holes II: the general case

We perform a comprehensive analysis of a number of scalar field theories in a attempt to find analytically 5-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the 5-dimensional metric tensor that allows for time-dependence, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen, non-isotropic in 5 dimensions, energy-momentum tensor, solutions that have the form of a Schwarzschild-(Anti)de Sitter or Reissner-Nordstrom type of solution do emerge, however, the resulting profile of the mass-function along the bulk coordinate, when allowed, is not the correct one to eliminate the bulk singularities.

### Mass distributions of star clusters for different star formation histories in a galaxy cluster environment

Clusters of galaxies usually contain rich populations of globular clusters (GCs). We investigate how different star formation histories (SFHs) shape the final mass distribution of star clusters. We assume that every star cluster population forms during a formation epoch of length dt at a constant star-formation rate (SFR). The mass distribution of such a population is described by the embedded cluster mass function (ECMF), which is a pure power law extending to an upper limit M_max. Since the SFR determines M_max, the ECMF implicitly depends on the SFR. Starting with different SFHs, each SFH is divided into formation epochs of length dt at different SFRs. The requested mass function arises from the superposition of the star clusters of all formation epochs. An improved optimal sampling technique is introduced that allows generating number and mass distributions, both of which accurately agree with the ECMF. Moreover, for each SFH the distribution function of all involved SFRs, F(SFR), is computed. For monotonically decreasing SFHs, F(SFR) always follows a power law. With F(SFR), we develope the theory of the integrated galactic embedded cluster mass function (IGECMF). It describes the distribution function of birth stellar masses of star clusters that accumulated over a formation episode much longer than dt. The IGECMF indeed reproduces the mass distribution of star clusters created according to the superposition principle. Interestingly, all considered SFHs lead to a turn-down with increasing star cluster mass in their respective IGECMFs. In the past, a turn-down at the high-mass end has been observed for GC systems in different galaxy clusters and in the cluster initial mass function. This behavior can be explained naturally if the observed star cluster ensembles are superpositions of several individual star cluster populations that formed at different times at different SFRs.

### The mass function of hydrogen-rich white dwarfs: robust observational evidence for a distinctive high-mass excess near 1Msun

The mass function of hydrogen-rich atmosphere white dwarfs has been frequently found to reveal a distinctive high-mass excess near 1Msun. However, a significant excess of massive white dwarfs has not been detected in the mass function of the largest white dwarf catalogue to date from the Sloan Digital Sky Survey. Hence, whether a high-mass excess exists or not has remained an open question. In this work we build the mass function of the latest catalogue of data release 10 SDSS hydrogen-rich white dwarfs, including the cool and faint population (i.e. effective temperatures 6,000 <~ Teff <~ 12,000 K, equivalent to 12 mag <~ Mbol <~ 13 mag). We show that the high-mass excess is clearly present in our mass function, and that it disappears only if the hottest (brightest) white dwarfs (those with Teff >~ 12,000 K, Mbol <~ 12 mag) are considered. This naturally explains why previous SDSS mass functions failed at detecting a significant excess of high-mass white dwarfs. Thus, our results provide additional and robust observational evidence for the existence of a distinctive high-mass excess near 1Msun. We investigate possible origins of this feature and argue that the most plausible scenario that may lead to an observed excess of massive white dwarfs is the merger of the degenerate core of a giant star with a main sequence or a white dwarf companion during or shortly after a common envelope event.

### Revisiting the Dynamical Case for a Massive Black Hole in IC10 X-1

The relative phasing of the X-ray eclipse ephemeris and optical radial velocity (RV) curve for the X-ray binary IC10 X-1 suggests the He[$\lambda$4686] emission-line originates in a shadowed sector of the stellar wind that avoids ionization by X-rays from the compact object. The line attains maximum blueshift when the wind is directly toward us at mid X-ray eclipse, as is also seen in Cygnus X-3. If the RV curve is unrelated to stellar motion, evidence for a massive black hole evaporates because the mass function of the binary is unknown. The reported X-ray luminosity, spectrum, slow QPO, and broad eclipses caused by absorption/scattering in the WR wind are all consistent with either a low-stellar-mass BH or a NS. For a NS, the centre of mass lies inside the WR envelope whose motion is then far below the observed 370 km/s RV amplitude, while the velocity of the compact object is as high as 600 km/s. The resulting 0.4\% doppler variation of X-ray spectral lines could be confirmed by missions in development. These arguments also apply to other putative BH binaries whose RV and eclipse curves are not yet phase-connected. Theories of BH formation and predicted rates of gravitational wave sources may need revision.

### Bondi-Hoyle-Littleton accretion and the upper mass stellar IMF

We report on a series of numerical simulations of gas clouds with self-gravity forming sink particles, adopting an isothermal equation of state to isolate the effects of gravity from thermal physics on the resulting sink mass distributions. Simulations starting with supersonic velocity fluctuations develop sink mass functions with a high-mass power-law tail $dN/d\log M \propto M^{\Gamma}$, $\Gamma = -1 \pm 0.1$, independent of the initial Mach number of the velocity field. Similar results but with weaker statistical significance hold for a simulation starting with initial density fluctuations. This mass function power-law dependence agrees with the asymptotic limit found by Zinnecker assuming Bondi-Hoyle-Littleton (BHL) accretion, even though the mass accretion rates of individual sinks show significant departures from the predicted $\mdot \propto M^2$ behavior. While BHL accretion is not strictly applicable due to the complexity of the environment, we argue that the final mass functions are the result of a {\em relative} $M^2$ dependence resulting from gravitationally-focused accretion. Our simulations may show the power-law mass function particularly clearly compared with others because our adoption of an isothermal equation of state limits the effects of thermal physics in producing a broad initial fragmentation spectrum; $\Gamma \rightarrow -1$ is an asymptotic limit found only when sink masses grow well beyond their initial values. While we have purposely eliminated many additional physical processes (radiative transfer, feedback) which can affect the stellar mass function, our results emphasize the importance of gravitational focusing for massive star formation.

### The Finslerian compact star model

We construct a toy model for compact stars based on the Finslerian structure of spacetime. By assuming a particular mass function, we find an exact solution of the Finsler-Einstein field equations with an anisotropic matter distribution. The solutions are revealed to be physically interesting and pertinent for the explanation of compact stars.

### New insights on the Galactic Bulge Initial Mass Function [Replacement]

We have derived the Galactic bulge initial mass function of the SWEEPS field in the mass range 0.15 $< M/M_{\odot}<$ 1.0, using deep photometry collected with the Advanced Camera for Surveys on the Hubble Space Telescope. Observations at several epochs, spread over 9 years, allowed us to separate the disk and bulge stars down to very faint magnitudes, F814W $\sim$ 26 mag, with a proper-motion accuracy better than 0.5 mas/yr. This allowed us to determine the initial mass function of the pure bulge component uncontaminated by disk stars for this low-reddening field in the Sagittarius window. In deriving the mass function, we took into account the presence of unresolved binaries, errors in photometry, distance modulus and reddening, as well as the metallicity dispersion and the uncertainties caused by adopting different theoretical color-temperature relations. We found that the Galactic bulge initial mass function can be fitted with two power laws with a break at M $\sim$ 0.56 $M_{\odot}$, the slope being steeper ($\alpha$ = -2.41$\pm$0.50) for the higher masses, and shallower ($\alpha$ = -1.25$\pm$0.20) for the lower masses. In the high-mass range, our derived mass function agrees well with the mass function derived for other regions of the bulge. In the low-mass range however, our mass function is slightly shallower, which suggests that separating the disk and bulge components is particularly important in the low-mass range. The slope of the bulge mass function is also similar to the slope of the mass function derived for the disk in the high-mass regime, but the bulge mass function is slightly steeper in the low-mass regime. We used our new mass function to derive stellar M/L values for the Galactic bulge and we obtained 2.1 $<M/L_{F814W}<$ 2.4 and 3.1 $< M/L_{F606W}<$ 3.6 according to different assumptions on the slope of the IMF for masses larger than 1 $M_{\odot}$.

### New insights on the Galactic Bulge Initial Mass Function

We have derived the Galactic bulge initial mass function of the SWEEPS field down to 0.15 $M_{\odot}$, using deep photometry collected with the Advanced Camera for Surveys on the Hubble Space Telescope. Observations at several epochs, spread over 9 years, allowed us to separate the disk and bulge stars down to very faint magnitudes, $F814W \approx$ 26 mag, with a proper-motion accuracy better than 0.5 mas/yr (20 km/s). This allowed us to determine the initial mass function of the pure bulge component uncontaminated by disk stars for this low-reddening field in the Sagittarius window. In deriving the mass function, we took into account the presence of unresolved binaries, errors in photometry, distance modulus and reddening, as well as the metallicity dispersion and the uncertainties caused by adopting different theoretical color-temperature relations. We found that the Galactic bulge initial mass function can be fitted with two power laws with a break at $M \sim$ 0.56 $M_{\odot}$, the slope being steeper ($\alpha = -2.41\pm$0.50) for the higher masses, and shallower ($\alpha = -1.25\pm$0.20) for the lower masses. In the high-mass range, our derived mass function agrees well with the mass function derived for other regions of the bulge. In the low-mass range however, our mass function is slightly shallower, which suggests that separating the disk and bulge components is particularly important in the low-mass range. The slope of the bulge mass function is also similar to the slope of the mass function derived for the disk in the high-mass regime, but the bulge mass function is slightly steeper in the low-mass regime. We used our new mass function to derive stellar mass–to–light values for the Galactic bulge and we found $M/L_{F814W} =$ 2.2$\pm$0.3 and $M/L_{F606W} =$ 3.2$\pm$0.5.

### The Copernicus Complexio: a high-resolution view of the small-scale Universe

We introduce Copernicus Complexio (COCO), a high-resolution cosmological N-body simulation of structure formation in the $\Lambda$cdm model. COCO follows an approximately spherical region of radius $\sim 17.4h^{-1}$Mpc, in which the particle mass is $1.1 \times 10^5h^{-1}M_{\odot}$, embedded in a much larger periodic cube followed at lower resolution. Thus, the resolution in the inner volume is 60 times better than in the Millennium-II simulation. COCO gives the dark matter halo mass function over eight orders of magnitude in halo mass; it forms $\sim 60$ halos of galactic size, each resolved with about 10 million particles. The concentration-mass relation of COCO halos deviates from a single power law for masses $M_{200}<$a few$\times 10^{8}h^{-1}M_{\odot}$, where it flattens in agreement with results by Sanchez-Conde et al. We confirm the power-law character of the subhalo mass function, $\overline N(>\mu)\propto\mu^{-s}$, down to a reduced subhalo mass $M_{sub}/M_{200}\equiv\mu=10^{-6}$, with a best-fit power-law index, $s=0.94$, for hosts of mass $\langle M_{200}\rangle=10^12h^{-1}M_{\odot}$, increasing very slowly with host mass. The host-mass invariance of the reduced maximum circular velocity function of subhaloes, $\nu\equiv V_{max}/V_{200}$, hinted at in previous simulations, is clearly demonstrated over five orders of magnitude in host mass. Similarly, we find that the average, normalized radial distribution of subhaloes is approximately universal (i.e. independent of subhalo mass), as previously suggested by the Aquarius simulations of individual halos. Finally, we find that at fixed physical subhalo size, subhaloes in lower mass hosts typically have lower central densities than those in higher mass hosts.

### Simulating the shocks in the dissociative galaxy cluster Abell 1758N

Major mergers between massive clusters have a profound effect in the intracluster gas, which may be used as a probe of the dynamics of structure formation at the high end of the mass function. An example of such a merger is observed at the northern component of Abell 1758, comprised of two massive sub-clusters separated by approximately 750 kpc. One of the clusters exhibits an offset between the dark matter and the intracluster gas. We aim to determine whether it is possible to reproduce the specific morphological features of this cluster by means of a major merger. We perform dedicated SPH (smoothed particle hydrodynamics) N-body simulations in an attempt to simultaneously recover several observed features of Abell 1758, such as the X-ray morphology and the separation between the two peaks in the projected galaxy luminosity map. We propose a specific scenario for the off-axis collision of two massive clusters. This model adequately reproduces several observed features and suggests that Abell 1758 is seen approximately 0.4 Gyr after the first pericentric passage, and that the clusters are already approaching their maximum separation. This means that their relative velocity is as low as 380 km/s. At the same time, the simulated model entails shock waves of ~4500 km/s, which are currently undetected presumably due to the low-density medium. We explain the difference between these velocities and argue that the predicted shock fronts, while plausible, cannot be detected from currently available data.

### Galactic Chemical Evolution: Stellar Yields and the Initial Mass Function

We present a set of 144 galactic chemical evolution models applied to a Milky Way analogue, computed using four sets of low and intermediate star nucleosynthetic yields, six massive star yield compilations, and six functional forms for the initial mass function. The integrated or true yields for each combination are derived. A comparison is made between a grid of multiphase chemical evolution models computed with these yield combinations and empirical data drawn from the Milky Way’s disc, including the solar neighbourhood. By means of a chi2 methodology, applied to the results of these multiphase models, the best combination of stellar yields and initial mass function capable of reproducing these observations is identified.

### Biases in the determination of dynamical parameters of star clusters: today and in the Gaia era

The structural and dynamical properties of star clusters are generally derived by means of the comparison between steady-state analytic models and the available observables. With the aim of studying the biases of this approach, we fitted different analytic models to simulated observations obtained from a suite of direct N-body simulations of star clusters in different stages of their evolution and under different levels of tidal stress to derive mass, mass function and degree of anisotropy. We find that masses can be under/over-estimated up to 50% depending on the degree of relaxation reached by the cluster, the available range of observed masses and distances of radial velocity measures from the cluster center and the strength of the tidal field. The mass function slope appears to be better constrainable and less sensitive to model inadequacies unless strongly dynamically evolved clusters and a non-optimal location of the measured luminosity function are considered. The degree and the characteristics of the anisotropy developed in the N-body simulations are not adequately reproduced by popular analytic models and can be detected only if accurate proper motions are available. We show how to reduce the uncertainties in the mass, mass-function and anisotropy estimation and provide predictions for the improvements expected when Gaia proper motions will be available in the near future.

### The initial mass function of a massive relic galaxy [Replacement]

Massive relic galaxies formed the bulk of their stellar component before z~2 and have remained unaltered since then. Therefore, they represent a unique opportunity to study in great detail the frozen stellar population properties of those galaxies that populated the primitive Universe. We have combined optical to near-infrared line-strength indices in order to infer, out to 1.5 Reff, the IMF of the nearby relic massive galaxy NGC 1277. The IMF of this galaxy is bottom-heavy at all radii, with the fraction of low-mass stars being at least a factor of two larger than that found in the Milky Way. The excess of low-mass stars is present throughout the galaxy, while the velocity dispersion profile shows a strong decrease with radius. This behaviour suggests that local velocity dispersion is not the only driver of the observed IMF variations seen among nearby early-type galaxies. In addition, the excess of low-mass stars shown in NGC 1277 could reflect the effect on the IMF of dramatically different and intense star formation processes at z~2, compared to the less extreme conditions observed in the local Universe.

### Cosmological simulations with disformally coupled symmetron fields

We use N-body simulations to study the matter distribution in disformal gravity. The disformal model studied here is a conformally coupled symmetron field with an additional exponential disformal term. We conduct cosmological simulations with the aim to find the impact of the new disformal terms in the matter power spectrum, halo mass function and radial profile of the scalar field. This is done by calculating the disformal geodesic equation and the equation of motion for the scalar field, then implementing them into the N-body code ISIS, which is a modified gravity version of the code RAMSES. The presence of a conformal symmetron field increases both the power spectrum and mass function compared to standard gravity on small scales. Our main result is that the newly added disformal terms tend to counteract this effects and can make the evolution slightly closer to standard gravity. We finally show that the disformal terms give rise to oscillations of the scalar field in the centre of the dark matter haloes.

### Cosmological simulations with disformally coupled symmetron fields [Cross-Listing]

We use N-body simulations to study the matter distribution in disformal gravity. The disformal model studied here is a conformally coupled symmetron field with an additional exponential disformal term. We conduct cosmological simulations with the aim to find the impact of the new disformal terms in the matter power spectrum, halo mass function and radial profile of the scalar field. This is done by calculating the disformal geodesic equation and the equation of motion for the scalar field, then implementing them into the N-body code ISIS, which is a modified gravity version of the code RAMSES. The presence of a conformal symmetron field increases both the power spectrum and mass function compared to standard gravity on small scales. Our main result is that the newly added disformal terms tend to counteract this effects and can make the evolution slightly closer to standard gravity. We finally show that the disformal terms give rise to oscillations of the scalar field in the centre of the dark matter haloes.

### Cosmological simulations with disformally coupled symmetron fields [Cross-Listing]

We use N-body simulations to study the matter distribution in disformal gravity. The disformal model studied here is a conformally coupled symmetron field with an additional exponential disformal term. We conduct cosmological simulations with the aim to find the impact of the new disformal terms in the matter power spectrum, halo mass function and radial profile of the scalar field. This is done by calculating the disformal geodesic equation and the equation of motion for the scalar field, then implementing them into the N-body code ISIS, which is a modified gravity version of the code RAMSES. The presence of a conformal symmetron field increases both the power spectrum and mass function compared to standard gravity on small scales. Our main result is that the newly added disformal terms tend to counteract this effects and can make the evolution slightly closer to standard gravity. We finally show that the disformal terms give rise to oscillations of the scalar field in the centre of the dark matter haloes.

### Cosmological simulations with disformally coupled symmetron fields [Cross-Listing]

We use N-body simulations to study the matter distribution in disformal gravity. The disformal model studied here is a conformally coupled symmetron field with an additional exponential disformal term. We conduct cosmological simulations with the aim to find the impact of the new disformal terms in the matter power spectrum, halo mass function and radial profile of the scalar field. This is done by calculating the disformal geodesic equation and the equation of motion for the scalar field, then implementing them into the N-body code ISIS, which is a modified gravity version of the code RAMSES. The presence of a conformal symmetron field increases both the power spectrum and mass function compared to standard gravity on small scales. Our main result is that the newly added disformal terms tend to counteract this effects and can make the evolution slightly closer to standard gravity. We finally show that the disformal terms give rise to oscillations of the scalar field in the centre of the dark matter haloes.

### The density variance - Mach number relation in isothermal and non-isothermal adiabatic turbulence [Replacement]

The density variance – Mach number relation of the turbulent interstellar medium is relevant for theoretical models of the star formation rate, efficiency, and the initial mass function of stars. Here we use high-resolution hydrodynamical simulations with grid resolutions of up to 1024^3 cells to model compressible turbulence in a regime similar to the observed interstellar medium. We use Fyris Alpha, a shock-capturing code employing a high-order Godunov scheme to track large density variations induced by shocks. We investigate the robustness of the standard relation between the logarithmic density variance (sigma_s^2) and the sonic Mach number (M) of isothermal interstellar turbulence, in the non-isothermal regime. Specifically, we test ideal gases with diatomic molecular (gamma = 7/5) and monatomic (gamma = 5/3) adiabatic indices. A periodic cube of gas is stirred with purely solenoidal forcing at low wavenumbers, leading to a fully-developed turbulent medium. We find that as the gas heats in adiabatic compressions, it evolves along the relationship in the density variance – Mach number plane, but deviates significantly from the standard expression for isothermal gases. Our main result is a new density variance – Mach number relation that takes the adiabatic index into account: sigma_s^2 = ln {1+b^2*M^[(5*gamma+1)/3]} and provides good fits for b*M <= 1. A theoretical model based on the Rankine-Hugoniot shock jump conditions is derived, sigma_s^2 = ln {1+(gamma+1)*b^2*M^2/[(gamma-1)*b^2*M^2+2]}, and provides good fits also for b*M > 1. We conclude that this new relation for adiabatic turbulence may introduce important corrections to the standard relation, if the gas is not isothermal.

### The density variance - Mach number relation in isothermal and non-isothermal adiabatic turbulence

The density variance – Mach number relation of the turbulent interstellar medium is relevant for theoretical models of the star formation rate, efficiency, and the initial mass function of stars. Here we use high-resolution hydrodynamical simulations with grid resolutions of up to 1024^3 cells to model compressible turbulence in a regime similar to the observed interstellar medium. We use Fyris Alpha, a shock-capturing code employing a high-order Godunov scheme to track large density variations induced by shocks. We investigate the robustness of the standard relation between the logarithmic density variance (sigma_s^2) and the sonic Mach number (M) of isothermal interstellar turbulence, in the non-isothermal regime. Specifically, we test ideal gases with diatomic molecular (gamma = 7/5) and monatomic (gamma = 5/3) adiabatic indices. A periodic cube of gas is stirred with purely solenoidal forcing at low wavenumbers, leading to a fully-developed turbulent medium. We find that as the gas heats in adiabatic compressions, it evolves along the relationship in the density variance – Mach number plane, but deviates significantly from the standard expression for isothermal gases. Our main result is a new density variance – Mach number relation that takes the adiabatic index into account: sigma_s^2 = ln {1+b^2*M^[(5*gamma+1)/3]} and provides good fits for b*M <= 1. A theoretical model based on the Rankine-Hugoniot shock jump conditions is derived, sigma_s^2 = ln {1+(gamma+1)*b^2*M^2/[(gamma-1)*b^2*M^2+2]}, and provides good fits also for b*M > 1. We conclude that this new relation for adiabatic turbulence may introduce important corrections to the standard relation, if the gas is not isothermal.

### Nonminimal Macroscopic Models of a Scalar Field Based on Microscopic Dynamics. II. Transport Equations

The article proposes generalizations of the macroscopic model of plasma of scalar charged particles to the cases of inter-particle interaction with multiple scalar fields and negative effective masses of these particles. The model is based on the microscopic dynamics of a particle at presence of scalar fields. The theory is managed to be generalized naturally having strictly reviewed a series of its key positions depending on a sign of particle masses. Thereby, it is possible to remove the artificial restriction contradicting the more fundamental principle of action functional additivity. Additionally, as a condition of internal consistency of the theory, particle effective mass function is found.

### Tidal Downsizing Model. III. Planets from sub-Earths to Brown Dwarfs: structure and metallicity preferences [Replacement]

We present population synthesis calculations of the Tidal Downsizing (TD) hypothesis for planet formation. Our models address the following observations: (i) most abundant planets being Super Earths; (ii) cores more massive than $\sim 5-15 M_\oplus$ are enveloped by massive atmospheres; (iii) the frequency of occurrence of close-in gas giant planets correlates strongly with metallicity of the host star; (iv) no such correlation is found for sub-Neptune planets; (v) presence of massive cores in giant planets; (vi) gas giant planets are over-abundant in metals compared to their host stars; (vii) this over-abundance decreases with planet’s mass; (viii) a deep valley in the planet mass function between masses of $\sim 10-20 M_\oplus$ and $\sim 100 M_\oplus$. A number of observational predictions distinguish the model from Core Accretion: (a) composition of the massive cores is always dominated by rocks not ices; (b) the core mass function is smooth with no minimum at $\sim 3 M_\oplus$ and has no ice-dominated cores; (c) gas giants beyond 10 AU are insensitive to the host star metallicity; (d) objects more massive than $\sim 10 M_{\rm Jup}$ do not correlate or even anti-correlate with metallicity. The latter prediction is consistent with observations of low mass stellar companions. TD can also explain formation of planets in close binary systems. TD model is a viable alternative to the Core Accretion scenario in explaining many features of the observed population of exoplanets.

### Tidal Downsizing Model. III. Planets from sub-Earths to Brown Dwarfs: structure and metallicity preferences

We present improved population synthesis calculations in the context of the Tidal Downsizing (TD) hypothesis for planet formation. Our models provide natural explanations and/or quantitative match to exoplanet observations in the following categories: (i) most abundant planets being super-Earths; (ii) cores more massive than $\sim 5-15 M_\oplus$ are enveloped by massive metal-rich atmospheres; (iii) the frequency of occurrence of close-in gas giant planets correlates strongly with metallicity of the host star; (iv) no such correlation is found for sub-Neptune planets; (v) presence of massive cores in giant planets; (vi) the composition of gas giant planets is over-abundant in metals compared to their host stars; (vii) this over-abundance decreases with planet’s mass, as observed; (viii) a deep valley in the planet mass function between masses of $\sim 10-20 M_\oplus$ and $\sim 100 M_\oplus$. We provide a number of observational predictions distinguishing the model from Core Accretion: (a) composition of the massive cores is dominated by rocks not ices; (b) the core mass function is smooth with no minimum at $\sim 3 M_\oplus$ and a rollover (rather than rise) below $\sim 1 M_\oplus$; (c) gas giants beyond 10 AU are insensitive to the host star metallicity. Objects more massive than $\sim 10 M_{\rm Jup}$ do not correlate or even anti-correlate with metallicity of the host star, which is consistent with observations showing that brown dwarf/ low mass stellar companions do not correlate/anti-correlate with metallicity of the primary star. One mismatch of the model and exoplanet observations is in the ratio of directly imaged to close-in giant planets, which is a factor $\sim 10$ too high. This however may well be a deficiency of the simple disc model we use. We conclude that TD model is a viable alternative to CA in explaining the observed population of exoplanets (abridged).

### Evolution of Mass Functions of Coeval Stars through Wind Mass Loss and Binary Interactions

Accurate determinations of stellar mass functions and ages of stellar populations are crucial to much of astrophysics. We analyse the evolution of stellar mass functions of coeval main sequence stars including all relevant aspects of single- and binary-star evolution. We show that the slope of the upper part of the mass function in a stellar cluster can be quite different to the slope of the initial mass function. Wind mass loss from massive stars leads to an accumulation of stars which is visible as a peak at the high mass end of mass functions, thereby flattening the mass function slope. Mass accretion and mergers in close binary systems create a tail of rejuvenated binary products. These blue straggler stars extend the single star mass function by up to a factor of two in mass and can appear up to ten times younger than their parent stellar cluster. Cluster ages derived from their most massive stars that are close to the turn-off may thus be significantly biased. To overcome such difficulties, we propose the use of the binary tail of stellar mass functions as an unambiguous clock to derive the cluster age because the location of the onset of the binary tail identifies the cluster turn-off mass. It is indicated by a pronounced jump in the mass function of old stellar populations and by the wind mass loss peak in young stellar populations. We further characterise the binary induced blue straggler population in star clusters in terms of their frequency, binary fraction and apparent age.

### Towards accurate rescaling of a halo mass function

We propose a new method of calculating a dark matter halo mass function based on the rescaling of a mass function measured in simulations. Our tests show that the accuracy almost linearly depends on the difference of the cosmological parameters and amounts to few percent in the case of WMAP5 and PLANCK parameters.

### Structural properties of artificial halos in non-standard dark matter simulations

Artificial fragmentation of the matter density field causes the formation of spurious groups of particles in N-body simulations of non-standard Dark Matter (DM) models which are characterized by a small scale cut-off in the linear matter power spectrum. These spurious halos alter the prediction of the mass function in a range of masses where differences among DM models are most relevant to observational tests. Using a suite of high resolution simulations we show that the contamination of artificial groups of particles significantly affect the statistics of halo spin, shape and virial state parameters. We find that spurious halos have systematically larger spin values, are highly elliptical or prolate and significantly deviate from virial equilibrium. These characteristics allow us to detect the presence of spurious halos even in non-standard DM models for which the low-mass end of the mass function remains well behaved. We show that selecting halos near the virial equilibrium provides a simple and effective method to remove the bulk of spurious halos from numerical halo catalogs and consistently recover the halo mass function at low masses.

### Structural properties of artificial halos in non-standard dark matter simulations [Replacement]

Artificial fragmentation of the matter density field causes the formation of spurious groups of particles in N-body simulations of non-standard Dark Matter (DM) models which are characterized by a small scale cut-off in the linear matter power spectrum. These spurious halos alter the prediction of the mass function in a range of masses where differences among DM models are most relevant to observational tests. Using a suite of high resolution simulations we show that the contamination of artificial groups of particles significantly affect the statistics of halo spin, shape and virial state parameters. We find that spurious halos have systematically larger spin values, are highly elliptical or prolate and significantly deviate from virial equilibrium. These characteristics allow us to detect the presence of spurious halos even in non-standard DM models for which the low-mass end of the mass function remains well behaved. We show that selecting halos near the virial equilibrium provides a simple and effective method to remove the bulk of spurious halos from numerical halo catalogs and consistently recover the halo mass function at low masses.

### Comparisons between different techniques for measuring mass segregation

We examine the performance of four different methods which are used to measure mass segregation in star-forming regions: the radial variation of the mass function $\mathcal{M}_{\rm MF}$; the minimum spanning tree-based $\Lambda_{\rm MSR}$ method; the local surface density $\Sigma_{\rm LDR}$ method; and the $\Omega_{\rm GSR}$ technique, which isolates groups of stars and determines whether the most massive star in each group is more centrally concentrated than the average star. All four methods have been proposed in the literature as techniques for quantifying mass segregation, yet they routinely produce contradictory results as they do not all measure the same thing. We apply each method to synthetic star-forming regions to determine when and why they have shortcomings. When a star-forming region is smooth and centrally concentrated, all four methods correctly identify mass segregation when it is present. However, if the region is spatially substructured, the $\Omega_{\rm GSR}$ method fails because it arbitrarily defines groups in the hierarchical distribution, and usually discards positional information for many of the most massive stars in the region. We also show that the $\Lambda_{\rm MSR}$ and $\Sigma_{\rm LDR}$ methods can sometimes produce apparently contradictory results, because they use different definitions of mass segregation. We conclude that only $\Lambda_{\rm MSR}$ measures mass segregation in the classical sense (without the need for defining the centre of the region), although $\Sigma_{\rm LDR}$ does place limits on the amount of previous dynamical evolution in a star-forming region.

### The SINFONI Nearby Elliptical Lens Locator Survey: Discovery of two new low-redshift strong lenses and implications for the initial mass function in giant early-type galaxies

We present results from a blind survey to identify strong gravitational lenses among the population of low-redshift early-type galaxies. The SINFONI Nearby Elliptical Lens Locator Survey (SNELLS) uses integral-field infrared spectroscopy to search for lensed emission line sources behind massive lens candidates at $z$<0.055. From 27 galaxies observed, we have recovered one previously-known lens (ESO325-G004) at $z$=0.034, and discovered two new systems, at $z$=0.031 and $z$=0.052. All three lens galaxies have high velocity dispersions (\sigma>300 km/s) and \alpha-element abundances ([Mg/Fe]>0.3). From the lensing configurations we derive total J-band mass-to-light ratios of 1.8$\pm$0.1, 2.1$\pm$0.1 and 1.9$\pm$0.2 within the $\sim$2 kpc Einstein radius. Correcting for estimated dark-matter contributions, and comparing to stellar population models with a Milky Way (Kroupa) initial mass function (IMF), we determine the "mass excess factor", \alpha. Assuming the lens galaxies have "old" stellar populations (10$\pm$1 Gyr), the average IMF mass factor is $\langle\alpha\rangle$=1.10$\pm$0.08$\pm$0.10, where the first error is random and the second is systematic. If we instead fit the stellar populations from 6dF optical survey spectra, all three galaxies are consistent with being old, but the age errors are 3-4 Gyr, due to limited signal-to-noise. The IMF constraints are therefore looser in this case, with $\langle\alpha\rangle$ = $1.23^{+0.16}_{-0.13}\pm{0.10}$. Our results are thus consistent with a Kroupa IMF (\alpha=1.00) on average, and strongly reject very heavy IMFs with \alpha>2. A Salpeter IMF (\alpha=1.55) is inconsistent at the 3.5$\sigma$ level if the galaxies are old, but cannot be excluded using age constraints derived from the currently-available optical spectra.

### I. Apples to apples $A^2$: photometric redshift predictions for next-generation surveys

This is the first of a series of papers where we compare the expected performance of two of the largest stage IV next-generation surveys in the optical and infrared (LSST and Euclid), with a particular focus on cluster surveys. In this first paper, we introduce the mock catalogues we have utilized in this work, an N-body simulation+semi-analytical cone with a posterior modification with PhotReal, a technique which modifies the original photometry to make it more realistic by using an empirical library of spectral templates. We have confirmed the reliability of the mock catalogue by comparing the obtained color-magnitude relation, the luminosity and mass function and the angular correlation function with those of real data. We also analyze the behavior of the expected photometric redshifts for each different survey, in terms of photometric redshift resolution, photometric redshift bias and fraction of outliers. In addition, we discuss the benefits of using the BPZ \emph{odds} photometric redshift quality parameter to select the best quality data of the sample. We find that very deep near infrared surveys such as Euclid will provide very good performance ($\Delta z/(1+z) \sim 0.025-0.053$) down to H$\sim$24 AB mag and up to redshift $\sim 3$ depending on the optical observations available from the ground whereas extremely deep optical surveys such as LSST will obtain an overall lower photometric redshift resolution ($\Delta z/(1+z) \sim 0.045$) down to $i\sim27.5$ AB mag, being substantially improved ($\Delta z/(1+z) \sim 0.035$) if we restrict the sample down to i$\sim$24 AB mag. We highlight the fact that those numbers can be improved substantially by selecting a subsample of galaxies with the best quality photometric redshifts. We finally discuss the impact that these surveys will have for the community in terms of photometric redshift legacy once the data is available. (Abridged)

### Hydrogen Reionization in the Illustris universe [Replacement]

Hydrodynamical simulations of galaxy formation such as the Illustris simulations have progressed to a state where they approximately reproduce the observed stellar mass function from high to low redshift. This in principle allows self-consistent models of reionization that exploit the accurate representation of the diffuse gas distribution together with the realistic growth of galaxies provided by these simulations, within a representative cosmological volume. In this work, we apply and compare two radiative transfer algorithms implemented in a GPU-accelerated code to the $106.5\,{\rm Mpc}$ wide volume of Illustris in postprocessing in order to investigate the reionization transition predicted by this model. We find that the first generation of galaxies formed by Illustris is just about able to reionize the universe by redshift $z\sim 7$, provided quite optimistic assumptions about the escape fraction and the resolution limitations are made. Our most optimistic model finds an optical depth of $\tau\simeq 0.065$, which is in very good agreement with recent Planck 2015 determinations. Furthermore, we show that moment-based approaches for radiative transfer with the M1 closure give broadly consistent results with our angular-resolved radiative transfer scheme. In our favoured fiducial model, 20\% of the hydrogen is reionized by redshift $z=9.20$, and this rapidly climbs to 80\% by redshift $z=6.92$. It then takes until $z=6.24$ before 99\% of the hydrogen is ionized. On average, reionization proceeds inside-out’ in our models, with a size distribution of reionized bubbles that progressively features regions of ever larger size while the abundance of small bubbles stays fairly constant.

### Hydrogen Reionization in the Illustris Universe

Hydrodynamical simulations of galaxy formation such as the Illustris simulations have progressed to a state where they approximately reproduce the observed stellar mass function from high to low redshift. This in principle allows self-consistent models of reionization that exploit the accurate representation of the diffuse gas distribution together with the realistic growth of galaxies provided by these simulations, within a representative cosmological volume. In this work, we apply and compare two radiative transfer algorithms implemented in a GPU-accelerated code to the $106.5\,{\rm Mpc}$ wide volume of Illustris in postprocessing in order to investigate the reionization transition predicted by this model. We find that the first generation of galaxies formed by Illustris is just about able to reionize the universe by redshift $z\sim 7$, provided quite optimistic assumptions about the escape fraction and the resolution limitations are made. Our most optimistic model finds an optical depth of $\tau\simeq 0.065$, which is in very good agreement with recent Planck 2015 determinations. Furthermore, we show that moment-based approaches for radiative transfer with the M1 closure give broadly consistent results with our angular-resolved radiative transfer scheme as far as the global reionization history is concerned. We also confirm earlier findings that the reduced speed-of-light approximation introduces non-neglibible inaccuracies. In our favoured fiducial model, 20% of the hydrogen is reionized by redshift $z=9.20$, and this rapidly climbs to 80% by redshift $z=6.92$. It then takes until $z=6.24$ before 99% of the hydrogen is ionized. On average, reionization proceeds inside-out’ in our models, with a size distribution of reionized bubbles that progressively features regions of ever larger size while the abundance of small bubbles stays fairly constant.

### Comparing halo bias from abundance and clustering

We model the abundance of haloes in the $\sim(3 \ \text{Gpc}/h)^3$ volume of the MICE Grand Challenge simulation by fitting the universal mass function with an improved Jack-Knife error covariance estimator that matches theory predictions. We present unifying relations between different fitting models and new predictions for linear ($b_1$) and non-linear ($c_2$ and $c_3$) halo clustering bias. Different mass function fits show strong variations in their overall poor performance when including the low mass range ($M_h \lesssim 3 \ 10^{12} \ M_{\odot}/h$) in the analysis, which indicates noisy friends-of-friends halo detection given the MICE resolution ($m_p \simeq 3 \ 10^{10} \ M_{\odot}$/h). Together with fits from the literature we find an overall variance in the amplitudes of around $10%$ in the low mass and up to $50%$ in the high mass (galaxy cluster) range ($M_h > 10^{14} \ M_{\odot}/h$). These variations propagate into a $10%$ change in $b_1$ predictions and a $50%$ change in $c_2$ or $c_3$. Despite these strong variations we find tight universal relations between $b_1$ and $c_2$ or $c_3$ for $b_1\gtrsim 1.5$ for which we provide simple fits. Their dependence on the mass function fit increases moderately for smaller $b_1$. Excluding low mass haloes, different models fitted with reasonable goodness in this analysis, show percent level agreement in their $b_1$ predictions, but are systematically $5-10%$ lower than the bias directly measured with two-point halo-mass clustering. This result confirms previous findings on larger volumes (and larger masses). Inaccuracies in the bias predictions propagate into the prediction of bias ratios at two redshifts, which would lead to $5-10%$ errors in growth measurements. They also affect any HOD fitting or (cluster) mass calibration from clustering measurements.

### Comparing halo bias from abundance and clustering [Replacement]

We model the abundance of haloes in the $\sim(3 \ \text{Gpc}/h)^3$ volume of the MICE Grand Challenge simulation by fitting the universal mass function with an improved Jack-Knife error covariance estimator that matches theory predictions. We present unifying relations between different fitting models and new predictions for linear ($b_1$) and non-linear ($c_2$ and $c_3$) halo clustering bias. Different mass function fits show strong variations in their performance when including the low mass range ($M_h \lesssim 3 \ 10^{12} \ M_{\odot}/h$) in the analysis. Together with fits from the literature we find an overall variation in the amplitudes of around $10$% in the low mass and up to $50$% in the high mass (galaxy cluster) range ($M_h > 10^{14} \ M_{\odot}/h$). These variations propagate into a $10$% change in $b_1$ predictions and a $50$% change in $c_2$ or $c_3$. Despite these strong variations we find universal relations between $b_1$ and $c_2$ or $c_3$ for which we provide simple fits. Excluding low mass haloes, different models fitted with reasonable goodness in this analysis, show percent level agreement in their $b_1$ predictions, but are systematically $5-10$% lower than the bias directly measured with two-point halo-mass clustering. This result confirms previous findings derived from smaller volumes (and smaller masses). Inaccuracies in the bias predictions lead to $5-10$% errors in growth measurements. They also affect any HOD fitting or (cluster) mass calibration from clustering measurements.