# Posts Tagged mass function

## Recent Postings from mass function

### A unified multi-wavelength model of galaxy formation

We present a new version of the GALFORM semi-analytical model of galaxy formation. This brings together several previous developments of GALFORM into a single unified model, including a different initial mass function (IMF) in quiescent star formation and in starbursts, feedback from active galactic nuclei supressing gas cooling in massive halos, and a new empirical star formation law in galaxy disks based on their molecular gas content. In addition, we have updated the cosmology, introduced a more accurate treatment of dynamical friction acting on satellite galaxies, and updated the stellar population model. The new model is able to simultaneously explain both the observed evolution of the K-band luminosity function and stellar mass function, and the number counts and redshift distribution of sub-mm galaxies selected at 850 mu. This was not previously achieved by a single physical model within the LambdaCDM framework, but requires having an IMF in starbursts that is somewhat top-heavy. The new model is tested against a wide variety of observational data covering wavelengths from the far-UV to sub-mm, and redshifts from z=0 to z=6, and is found to be generally successful. These observations include the optical and near-IR luminosity functions, HI mass function, Tully-Fisher relation, fraction of early type galaxies, metallicity-luminosity relation and size-luminosity relation at z=0, as well as far-IR number counts, and far-UV luminosity functions at z ~ 3-6. [abridged]

### Spectro-photometric characterization of high proper motion sources from WISE

The census of the solar neighborhood is almost complete for stars and becoming more complete in the brown dwarf regime. Spectroscopic, photometric and kinematic characterization of nearby objects helps us to understand the local mass function, the binary fraction, and provides new targets for sensitive planet searches. We aim to derive spectral types and spectro-photometric distances of a sample of new high proper motion sources found with the WISE satellite, and obtain parallaxes for those objects that fall within the area observed by the Vista Variables in the V\'ia L\'actea survey (VVV). We used low resolution spectroscopy and template fitting to derive spectral types, multiwavelength photometry to characterize the companion candidates and obtain photometric distances. Multi-epoch imaging from the VVV survey was used to measure the parallaxes and proper motions for three sources. We confirm a new T2 brown dwarf within $\sim$15 pc. We derived optical spectral types for twenty four sources, mostly M dwarfs within 50 pc. We addressed the wide binary nature of sixteen objects found by the WISE mission and previously known high proper motion sources. Six of these are probably members of wide binaries, two of those are new, and present evidence against the physical binary nature of two candidate binary stars found in the literature, and eight that we selected as possible binary systems. We discuss a likely microlensing event produced by a nearby low mass star and a galaxy, that is to occur in the following five years.

### Star Formation triggered by cloud-cloud collisions

We present the results of SPH simulations in which two clouds, each having mass $M_{_{\rm{o}}}\!=\!500\,{\rm M}_{_\odot}$ and radius $R_{_{\rm{o}}}\!=\!2\,{\rm pc}$, collide head-on at relative velocities of $\Delta v_{_{\rm{o}}} =2.4,\;2.8,\;3.2,\;3.6\;{\rm and}\;4.0\,{\rm km}\,{\rm s}^{-1}$. There is a clear trend with increasing $\Delta v_{_{\rm{o}}}$. At low $\Delta v_{_{\rm{o}}}$, star formation starts later, and the shock-compressed layer breaks up into an array of predominantly radial filaments; stars condense out of these filaments and fall, together with residual gas, towards the centre of the layer, to form a single large-$N$ cluster, which then evolves by competitive accretion, producing one or two very massive protostars and a diaspora of ejected (mainly low-mass) protostars; the pattern of filaments is reminiscent of the hub and spokes systems identified recently by observers. At high $\Delta v_{_{\rm{o}}}$, star formation occurs sooner and the shock-compressed layer breaks up into a network of filaments; the pattern of filaments here is more like a spider's web, with several small-$N$ clusters forming independently of one another, in cores at the intersections of filaments, and since each core only spawns a small number of protostars, there are fewer ejections of protostars. As the relative velocity is increased, the {\it mean} protostellar mass increases, but the {\it maximum} protostellar mass and the width of the mass function both decrease. We use a Minimal Spanning Tree to analyse the spatial distributions of protostars formed at different relative velocities.

### A unified model for the spatial and mass distribution of subhaloes

N-body simulations suggest that the substructures that survive inside dark matter haloes follow universal distributions in mass and radial number density. We demonstrate that a simple analytical model can explain these subhalo distributions as resulting from tidal stripping which increasingly reduces the mass of subhaloes with decreasing halo-centric distance. As a starting point, the spatial distribution of subhaloes of any given infall mass is shown to be largely indistinguishable from the overall mass distribution of the host halo. Using a physically motivated statistical description of the amount of mass stripped off individual subhaloes, the model fully describes the joint distribution of subhaloes in final mass, infall mass and radius. As a result, it can be used to predict several derived distributions involving combinations of these quantities including, but not limited to, the universal subhalo mass function, the subhalo spatial distribution, the lensing profile, the dark matter annihilation radiation profile and boost factor. This model clarifies a common confusion when comparing the spatial distributions of galaxies and subhaloes, the so called "anti-bias", as a simple selection effect. We provide a Python code SubGen for populating haloes with subhaloes at http://icc.dur.ac.uk/data/.

### A possible link between the power spectrum of interstellar filaments and the origin of the prestellar core mass function

Two major features of the prestellar CMF are: 1) a broad peak below 1 Msun, presumably corresponding to a mean gravitational fragmentation scale, and 2) a characteristic power-law slope, very similar to the Salpeter slope of the stellar initial mass function (IMF) at the high-mass end. While recent Herschel observations have shown that the peak of the prestellar CMF is close to the thermal Jeans mass in marginally supercritical filaments, the origin of the power-law tail of the CMF/IMF at the high-mass end is less clear. Inutsuka (2001) proposed a theoretical scenario in which the origin of the power-law tail can be understood as resulting from the growth of an initial spectrum of density perturbations seeded along the long axis of filaments by interstellar turbulence. Here, we report the statistical properties of the line-mass fluctuations of filaments in nearby molecular clouds observed with Herschel using a 1-D power spectrum analysis. The observed filament power spectra were fitted by a power-law function $(P_{true}(s) \propto s^{\alpha})$ after removing the effect of beam convolution at small scales. A Gaussian-like distribution of power-spectrum slopes was found centered at -1.6, close to that of the one-dimensional velocity power spectrum generated by subsonic Kolomogorov turbulence (-1.67). An empirical correlation, $P^{0.5}(s_0) \propto <N_{\rm H_2}>^{1.4 \pm 0.1}$, was also found between the amplitude of each filament power spectrum $P(s_0)$ and the mean column density along the filament $<N_{\rm H_2}>$. Finally, the dispersion of line-mass fluctuations along each filament $\sigma_{\rm M_{line}}$ was found to scale with the physical length $L$ of the filament, roughly as $\sigma_{M_{line}} \propto L^{0.7}$. Overall, our results are consistent with the suggestion that the bulk of the CMF/IMF results from the gravitational fragmentation of filaments.

### Push it to the limit: Local Group constraints on high-redshift stellar mass functions for Mstar > 10^5 Msun

We constrain the evolution of the galaxy stellar mass function from 2 < z < 5 for galaxies with stellar masses as low as 10^5 Msun by combining star formation histories of Milky Way satellite galaxies derived from deep Hubble Space Telescope observations with merger trees from the ELVIS suite of N-body simulations. This approach extends our understanding more than two orders of magnitude lower in stellar mass than is currently possible by direct imaging. We find the faint end slopes of the mass functions to be alpha= -1.42(+0.07/-0.05) at z = 2 and alpha = -1.57^(+0.06/-0.06) at z = 5, and show the slope only weakly evolves from z = 5 to z = 0. Our findings are in stark contrast to a number of direct detection studies that suggest slopes as steep as alpha = -1.9 at these epochs. Such a steep slope would result in an order of magnitude too many luminous Milky Way satellites in a mass regime that is observationally complete (Mstar > 2*10^5 Msun at z = 0). The most recent studies from ZFOURGE and CANDELS also suggest flatter faint end slopes that are consistent with our results, but with a lower degree of precision. This work illustrates the strong connections between low and high-z observations when viewed through the lens of LCDM numerical simulations.

### The O- and B-Type Stellar Population in W3: Beyond the High-Density Layer

We present the first results from our survey of the star-forming complex W3, combining VRI photometry with multiobject spectroscopy to identify and characterize the high-mass stellar population across the region. With 79 new spectral classifications, we bring the total number of spectroscopically-confirmed O- and B-type stars in W3 to 105. We find that the high-mass slope of the mass function in W3 is consistent with a Salpeter IMF, and that the extinction toward the region is best characterized by an Rv of approximately 3.6. B-type stars are found to be more widely dispersed across the W3 giant molecular cloud (GMC) than previously realized: they are not confined to the high-density layer (HDL) created by the expansion of the neighboring W4 HII region into the GMC. This broader B-type population suggests that star formation in W3 began spontaneously up to 8--10 Myr ago, although at a lower level than the more recent star formation episodes in the HDL. In addition, we describe a method of optimizing sky subtraction for fiber spectra in regions of strong and spatially-variable nebular emission.

### 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 [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 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 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

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 [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.

### 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.

### Electromagnetic production of pions and confinement phenomenology in Minkowski space [Replacement]

Additional interfering mechanism for generation of QCD resonances is studied. It is proposed that a shape of resonant structure is largely affected by the interference of ordinary resonances with the background quark and gluon loops. For this purpose, the framework of QCD Dyson-Schwinger equations defined and actually solved in Minkowski space is used and the solution for the pion and excited states have been identified. Chiral symmetry is broken dynamically providing nontrivial momentum dependent phase for the dynamical mass function of confined quarks. Within obtained oscillating QCD Green's functions the pion form factor is calculated for timelike momenta. The dip experimentally observed at $\sqrt{s}=1.5GeV$ is explain as a simple effect of such interference.

### 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.

### Constraints on the evolutionary mechanisms of massive galaxies since $z \sim 1$ from their velocity dispersions [Replacement]

Several authors have reported that the dynamical masses of massive compact galaxies ($M_\star \gtrsim 10^{11} \ \mathrm{M_\odot}$, $r_\mathrm{e} \sim 1 \ \mathrm{kpc}$), computed as $M_\mathrm{dyn} = 5.0 \ \sigma_\mathrm{e}^2 r_\mathrm{e} / G$, are lower than their stellar masses $M_\star$. In a previous study from our group, the discrepancy is interpreted as a breakdown of the assumption of homology that underlie the $M_\mathrm{dyn}$ determinations. Here, we present new spectroscopy of six redshift $z \approx 1.0$ massive compact ellipticals from the Extended Groth Strip, obtained with the 10.4 m Gran Telescopio Canarias. We obtain velocity dispersions in the range $161-340 \ \mathrm{km \ s^{-1}}$. As found by previous studies of massive compact galaxies, our velocity dispersions are lower than the virial expectation, and all of our galaxies show $M_\mathrm{dyn} < M_\star$ (assuming a Salpeter initial mass function). Adding data from the literature, we build a sample covering a range of stellar masses and compactness in a narrow redshift range $\mathit{z \approx 1.0}$. This allows us to exclude systematic effects on the data and evolutionary effects on the galaxy population, which could have affected previous studies. We confirm that mass discrepancy scales with galaxy compactness. We use the stellar mass plane ($M_\star$, $\sigma_\mathrm{e}$, $r_\mathrm{e}$) populated by our sample to constrain a generic evolution mechanism. We find that the simulations of the growth of massive ellipticals due to mergers agree with our constraints and discard the assumption of homology.

### 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.