# Posts Tagged mass function

## Recent Postings from mass function

### Explaining the stellar initial mass function with the theory of spatial networks

The distributions of stars and prestellar cores by mass (initial and dense core mass functions, IMF/DCMF) stay among the key factors regulating star formation and are subject of detailed theoretical and observational studies. Results from numerical simulations of star formation qualitatively resemble an observed mass function, a scale free power law with a sharp decline at low masses. However, most analytic IMF theories critically depend on the empirically chosen input spectrum of mass fluctuations which evolve into dense cores and, subsequently, stars. Here we propose a new approach exploiting the techniques from the field of network science. We represent a system of dense cores accreting gas from the surrounding diffuse interstellar medium (ISM) as a spatial network growing by preferential attachment and assume that the ISM density has a self-similar fractal distribution following the Kolmogorov turbulence theory. As opposed to gravoturbulent fragmentation theories, we consider the dense core growth and demonstrate that the power law core mass function emerges independently of the initial distribution of density fluctuations by mass. Our model yields a power law solely defined by the fractal dimensionalities of the ISM and accreting gas. With a proper choice of the low mass cut-off, it reproduces observations over three decades in mass. We also rule out a low mass star dominated bottom-heavy'' IMF in a single star forming region.

### The Mass Distribution of Population III Stars

Extremely metal-poor stars are uniquely informative on the nature of massive Population III stars. Modulo a few elements that vary with stellar evolution, the present-day photospheric abundances observed in extremely metal-poor stars are representative of their natal gas cloud composition. For this reason, the detailed chemistry of extremely metal-poor stars closely reflects the nucleosynthetic yields of supernovae from massive Population III stars. Here we collate detailed chemical abundances of 53 extremely metal-poor stars from the literature and infer the masses of their Population III progenitors. We fit a simple initial mass function to the ensemble of inferred Population III star masses, and find that the mass distribution is well-represented by a powerlaw IMF with an exponent of \$\alpha=2.35^{+0.29}_{-0.24}\$. The inferred maximum progenitor mass for supernovae from massive Population III stars is \$M=87^{+13}_{-33}M_\odot\$, and we find no evidence for a contribution from stars with masses above \$\sim120M_\odot\$. The minimum mass is strongly consistent with the theoretical lower mass limit for Population III Supernovae. We conclude that the IMF for massive Population III stars is consistent with the initial mass function of present-day massive stars and there may well have formed stars much below the supernova mass limit that could have survived to the present day.

### The Mass Distribution of Population III Stars [Replacement]

Extremely metal-poor stars are uniquely informative on the nature of massive Population III stars. Modulo a few elements that vary with stellar evolution, the present-day photospheric abundances observed in extremely metal-poor stars are representative of their natal gas cloud composition. For this reason, the detailed chemistry of extremely metal-poor stars closely reflects the nucleosynthetic yields of supernovae from massive Population III stars. Here we collate detailed chemical abundances of 53 extremely metal-poor stars from the literature and infer the masses of their Population III progenitors. We fit a simple initial mass function to the ensemble of inferred Population III star masses, and find that the mass distribution is well-represented by a powerlaw IMF with an exponent of \$\alpha=2.35^{+0.29}_{-0.24}\$. The inferred maximum progenitor mass for supernovae from massive Population III stars is \$M=87^{+13}_{-33}M_\odot\$, and we find no evidence for a contribution from stars with masses above \$\sim120M_\odot\$. The minimum mass is strongly consistent with the theoretical lower mass limit for Population III Supernovae. We conclude that the IMF for massive Population III stars is consistent with the initial mass function of present-day massive stars and there may well have formed stars much below the supernova mass limit that could have survived to the present day.

### Revisiting the classics: Is [Mg/Fe] a good proxy for galaxy formation time-scales?

In the local Universe, massive early-type galaxies exhibit enhanced [Mg/Fe] ratios, which has been traditionally interpreted as the result of a rapid ($\tau \lesssim 1$ Gyr) collapse. However, recent claims of a non-universal, steep initial mass function call for a revision of this standard interpretation. In the present work we show how the simultaneous consideration of a high [Mg/Fe] and a steep IMF slope would imply unreasonably short ($\tau \sim 7$ Myr) and intense (SFR $\sim 10^{5}$ Msun yr$^{-1}$) formation events for massive early-type galaxies. We discuss possible caveats and explanations to this apparent inconsistency, and we suggest that further IMF determinations, both in the local Universe and at high redshift, are necessary to better understand the problem.

### Stellar Population Effects on the Inferred Photon Density at Reionization

The relationship between stellar populations and the ionizing flux with which they irradiate their surroundings has profound implications for the evolution of the intergalactic medium. We quantify the ionizing flux arising from synthetic stellar populations which incorporate the evolution of interacting binary stars. We determine that these show ionizing flux boosted by 60 per cent at 0.05 < Z < 0.3 Z_sun and a more modest 10-20 per cent at near-Solar metallicities relative to star-forming populations in which stars evolve in isolation. The relation of ionizing flux to observables such as 1500A continuum and ultraviolet spectral slope is sensitive to attributes of the stellar population including age, star formation history and initial mass function. For a galaxy forming 1 M_sun yr^{-1}, observed at > 100 Myr after the onset of star formation, we predict a production rate of photons capable of ionizing hydrogen, N_ion = 1.4 x 10^{53} s^{-1} at Z = Z_sun and 3.5 x 10^{53} s^{-1} at 0.1 Z_sun, assuming a Salpeter-like initial mass function. We evaluate the impact of these issues on the ionization of the intergalactic medium, finding that the known galaxy populations can maintain the ionization state of the Universe back to z ~ 9, assuming that their luminosity functions continue to M_UV = -10, and that constraints on the intergalactic medium at z ~ 2 - 5 can be satisfied with modest Lyman continuum photon escape fractions of 4 - 24 per cent depending on assumed metallicity.

### The VMC Survey. XVIII. Radial dependence of the low-mass, 0.55--0.82 $M_\odot$ stellar mass function in the Galactic globular cluster 47 Tucanae

We use near-infrared observations obtained as part of the {\sl Visible and Infrared Survey Telescope for Astronomy} (VISTA) Survey of the Magellanic Clouds (VMC), as well as two complementary {\sl Hubble Space Telescope} ({\sl HST}) data sets, to study the luminosity and mass functions as a function of clustercentric radius of the main-sequence stars in the Galactic globular cluster 47 Tucanae. The {\sl HST} observations indicate a relative deficit in the numbers of faint stars in the central region of the cluster compared with its periphery, for $18.75\leq m_{\rm F606W}\leq 20.9$ mag (corresponding to a stellar mass range of $0.55<m_\ast/{M_\odot}<0.73$). The stellar number counts at $6.7'$ from the cluster core show a deficit for $17.62\leq m_{\rm F606W}\leq 19.7$ mag (i.e., $0.65<m_\ast/{M_\odot}<0.82$), which is consistent with expectations from mass segregation. The VMC-based stellar mass functions exhibit power-law shapes for masses in the range $0.55<m_\ast/{M_\odot}< 0.82$. These power laws are characterized by an almost constant slope, $\alpha$. The radial distribution of the power-law slopes $\alpha$ thus shows evidence of the importance of both mass segregation and tidal stripping, for both the first- and second-generation stars in 47 Tuc.

### Towards a self-consistent halo model for the nonlinear large-scale structure [Replacement]

The halo model is a theoretically and empirically well-motivated framework for predicting the statistics of the nonlinear matter distribution in the Universe. However, current incarnations of the halo model suffer from two major deficiencies: $(i)$ they do not enforce the stress-energy conservation of matter; $(ii)$ they are not guaranteed to recover exact perturbation theory results on large scales. Here, we provide a formulation of the halo model ("EHM") that remedies both drawbacks in a consistent way, while attempting to maintain the predictivity of the approach. In the formulation presented here, mass and momentum conservation are guaranteed, and results of perturbation theory and the effective field theory can in principle be matched to any desired order on large scales. We find that a key ingredient in the halo model power spectrum is the halo stochasticity covariance, which has been studied to a much lesser extent than other ingredients such as mass function, bias, and profiles of halos. As written here, this approach still does not describe the transition regime between perturbation theory and halo scales realistically, which is left as an open problem. We also show explicitly that, when implemented consistently, halo model predictions do not depend on any properties of low-mass halos that are smaller than the scales of interest.

### Towards a self-consistent halo model for the nonlinear large-scale structure

The halo model is a theoretically and empirically well-motivated framework for predicting the statistics of the nonlinear matter distribution in the Universe. However, current incarnations of the halo model suffer from two major deficiencies: $(i)$ they do not enforce the stress-energy conservation of matter; $(ii)$ they are not guaranteed to recover exact perturbation theory results on large scales. Here, we provide a formulation of the halo model ("EHM") that remedies both drawbacks in a consistent way, while attempting to maintain the predictivity of the approach. In the formulation presented here, mass and momentum conservation are guaranteed, and results of perturbation theory and the effective field theory can in principle be matched to any desired order on large scales. We find that a key ingredient in the halo model power spectrum is the halo stochasticity covariance, which has been studied to a much lesser extent than other ingredients such as mass function, bias, and profiles of halos. As written here, this approach still does not describe the transition regime between perturbation theory and halo scales realistically, which is left as an open problem. We also show explicitly that, when implemented consistently, halo model predictions do not depend on any properties of low-mass halos that are smaller than the scales of interest.

### Effective Window Function for Lagrangian Halos [Replacement]

The window function for the Lagrangian halos is often assumed to be a top hat function. We measure the profile of the Lagrangian halo directly and find that it is more extended than a top hat but less diffuse than a Gaussian. We find that the Lagrangian profile can be described well by an effective window composed of a product of a top hat and a Gaussian window in Fourier space. We also check that the same effective window function together with the scale-dependent excursion set bias parameters fits the Lagrangian cross bias parameter in Fourier space well up to $k R_{\rm Lag} \sim 10$, where $R_{\rm Lag}$ is the Lagrangian size of the halo. The effective window is simple in Fourier space, and there is also an analytic form in real space, thus there is little work in converting from the usual top hat window to the effective window. With the effective window function, all the spectral moments of the power spectrum are finite, thus we have a unified treatment for computing the spectral moments in peak and excursion set peak theories. When the effective window function is used, the resultant excursion set peak mass function is significantly lower compared to that obtained from the mixed window function approach, and hence this causes the excursion set peak mass function to be appreciably lower than the simulation results for halos of mass $\lesssim 10^{14} M_{\odot}/h$. We can interpret this deficit as that only part of the low to medium mass halos can arise directly from peaks, or the current modelling of the collapse of peaks is not sufficient.

### The Bottom-Light Present Day Mass Function of the Peculiar Globular Cluster NGC 6535

Dynamical mass calculations have suggested that the Milky Way globular cluster NGC 6535 belongs to a population of clusters with high mass-to-light ratios, possibly due to a bottom-heavy stellar initial mass function. We use published Hubble Space Telescope data to measure the present day stellar mass function of this cluster within its half-light radius and instead find that it is bottom-light, exacerbating the discrepancy between the dynamical measurement and its known stellar content. The cluster's proximity to the Milky Way bulge and its relatively strong velocity anisotropy are both reasons to be suspicious of the dynamical mass measurement, but we find that neither straightforwardly explains the sense and magnitude of the discrepancy. Although there are alternative potential explanations for the high mass-to-light ratio, such as the presence of large numbers of stellar remnants or dark matter, we find this cluster to be sufficiently perplexing that we now exclude it from a discussion of possible variations in the initial mass function. Because this was the sole known old, Milky Way cluster in the population of high dynamical mass-to-light ratio clusters, some possible explanations for the difference in cluster properties are again open for consideration.

### The Imprint of f(R) Gravity on Non-Linear Structure Formation

We test the imprint of f(R) modified gravity on the halo mass function, using N-body simulations and a theoretical model developed in (Kopp et al. 2013). We find a very good agreement between theory and simulations. We extend the theoretical model to the conditional mass function and apply it to the prediction of the linear halo bias in f(R) gravity. Using the halo model we obtain a prediction for the non-linear matter power spectrum accurate to ~10% at z=0 and up to k=2h/Mpc. We also study halo profiles for the f(R) models and find a deviation from the standard general relativity result up to 40%, depending on the halo masses and redshift. This has not been pointed out in previous analysis. Finally we study the number density and profiles of voids identified in these f(R) N-body simulations. We underline the effect of the bias and the sampling to identify voids. We find significant deviation from GR when measuring the f(R) void profiles with fR0<-10^{-6}.

### Linear response to long wavelength fluctuations using curvature simulations

We study the local response to long wavelength fluctuations in cosmological $N$-body simulations, focusing on the matter and halo power spectra, halo abundance and non-linear transformations of the density field. The long wavelength mode is implemented using an effective curved cosmology and a mapping of time and distances. The method provides an alternative, most probably more precise, way to measure the isotropic halo biases. Limiting ourselves to the linear case, we find generally good agreement between the biases obtained from the curvature method and the traditional power spectrum method at the level of a few percent. We also study the response of halo counts to changes in the variance of the field and find that the slope of the relation between the responses to density and variance differs from the naive derivation assuming a universal mass function by 18%. This has implications for measurements of the amplitude of local non-Gaussianity using scale dependent bias. We also analyze the halo power spectrum and halo-dark matter cross-spectrum response to long wavelength fluctuations and derive second order halo bias from it, as well as the super-sample variance contribution to the galaxy power spectrum covariance matrix.

### The VIMOS Public Extragalactic Redshift Survey (VIPERS). Environmental effects shaping the galaxy stellar mass function

We exploit the first public data release of VIPERS to investigate environmental effects in galaxy evolution between $z\sim0.5$ and $0.9$. The large number of spectroscopic redshifts over an area of about $10\,\mathrm{deg}^2$ provides a galaxy sample with high statistical power. The accurate redshift measurements, with $\sigma_z = 0.00047(1+z_\mathrm{spec})$, allow us to robustly isolate galaxies living in the lowest- and highest-density environments, as defined in terms of spatial 3D density contrast. We estimate the stellar mass function (SMF) of galaxies residing in these two environments, and constrain its high-mass end with unprecedented precision. We find that the galaxy SMF in the densest regions has a different shape than that measured at low densities, with an enhancement of massive galaxies and a hint of a flatter (less negative) slope at $z<0.8$. We normalise each SMF to the comoving volume occupied by the corresponding environment, and relate estimates from different redshift bins. We observe an evolution of the SMF of VIPERS galaxies in high densities, while the low-density one is nearly constant. We compare these results to semi-analytical models and find consistent environmental signatures. We discuss how the halo mass function and fraction of central/satellite galaxies depend on the environments considered, making intrinsic and environmental properties of galaxies physically coupled, and therefore difficult to disentangle. The evolution of our low-density regions is well described by the formalism introduced by Peng et al.~(2010), and is consistent with the idea that galaxies become progressively passive because of internal physical processes. The same formalism could also describe the evolution of the SMF in the high density regions, but only if a significant contribution from dry mergers is considered. [Abridged]

### The initial mass function of young open clusters in the Galaxy: A preliminary result

The initial mass function (IMF) is an essential tool with which to study star formation processes. We have initiated the photometric survey of young open clusters in the Galaxy, from which the stellar IMFs are obtained in a homogeneous way. A total of 16 famous young open clusters have preferentially been studied up to now. These clusters have a wide range of surface densities (log sigma = -1 to 3 [stars pc^2] for stars with mass larger than 5M_sun) and cluster masses (M_cl = 165 to 50,000M_sun), and also are distributed in five different spiral arms in the Galaxy. It is possible to test the dependence of star formation processes on the global properties of individual clusters or environmental conditions. We present a preliminary result on the variation of the IMF in this paper.

### Light versus dark in strong-lens galaxies: Dark matter haloes that are rounder than their stars

We measure the projected density profile, shape and alignment of the stellar and dark matter mass distribution in 11 strong-lens galaxies. We find that the projected dark matter density profile - under the assumption of a Chabrier stellar initial mass function - shows significant variation from galaxy to galaxy. Those with an outermost image beyond $\sim 10$ kpc are very well fit by a projected NFW profile; those with images within 10 kpc appear to be more concentrated than NFW, as expected if their dark haloes contract due to baryonic cooling. We find that over several half-light radii, the dark matter haloes of these lenses are rounder than their stellar mass distributions. While the haloes are never more elliptical than $e_{dm} = 0.2$, their stars can extend to $e_* > 0.2$. Galaxies with high dark matter ellipticity and weak external shear show strong alignment between light and dark; those with strong shear ($\gamma \gtrsim 0.1$) can be highly misaligned. This is reassuring since isolated misaligned galaxies are expected to be unstable. Our results provide a new constraint on galaxy formation models. For a given cosmology, these must explain the origin of both very round dark matter haloes and misaligned strong-lens systems.

### IAU Commission 37 "Star Clusters and Associations" Legacy report

It is widely accepted that stars do not form in isolation but result from the fragmentation of molecular clouds, which in turn leads to star cluster formation. Over time, clusters dissolve or are destroyed by interactions with molecular clouds or tidal stripping, and their members become part of the general field population. Star clusters are thus among the basic building blocks of galaxies. In turn, star cluster populations, from young associations and open clusters to old globulars, are powerful tracers of the formation, assembly, and evolutionary history of their parent galaxies. Although their importance had been recognised for decades, major progress in this area has only become possible in recent years, both for Galactic and extragalactic cluster populations. Star clusters are the observational foundation for stellar astrophysics and evolution, provide essential tracers of galactic structure, and are unique stellar dynamical environments. Star formation, stellar structure, stellar evolution, and stellar nucleosynthesis continue to benefit and improve tremendously from the study of these systems. Additionally, fundamental quantities such as the initial mass function can be successfully derived from modelling either the H-R diagrams or the integrated velocity structures of, respectively, resolved and unresolved clusters and cluster populations. Star cluster studies thus span the fields of Galactic and extragalactic astrophysics, while heavily affecting our detailed understanding of the process of star formation in dense environments.This report highlights science results of the last decade in the major fields covered by IAU Commission 37: Star clusters and associations.

### Stellar and gas dynamical model for tidal disruption events in a quiescent galaxy

A detailed model of the tidal disruption events (TDE) has been constructed using stellar dynamical and gas dynamical inputs that include black hole mass $M_{\bullet}$, specific orbital energy $E$ and angular momentum $J$, star mass $M_{\star}$ and radius $R_{\star}$ and pericenter of the star orbit $r_{p}(E,\hspace{1mm}J,\hspace{1mm}M_{\bullet})$. We have solved the steady state Fokker- Planck equation using the standard loss cone theory for the galactic density profile $\rho (r) \propto r^{-\gamma}$ and stellar mass function $\xi(m)$ where $m=M_{\star}/M_{\odot}$ and obtained the feeding rate of stars to the black hole integrated over the phase space as $\dot{N}_{t} \propto M_{\bullet}^\beta$ where $\beta= -0.3\pm 0.01$ for $M_{\bullet}>10^7 M_{\odot}$ and $\sim 6.8 \hspace{1mm} \times 10^{-5}$ Yr$^{-1}$ for $\gamma=0.7$. Using this we model the in fall rate of the disrupted debris, $\dot{M}(E,\hspace{1mm}J,\hspace{1mm}m,\hspace{1mm}t)$ and discuss conditions for the disk formation and find that the accretion disk is formed almost always for the fiduciary range of the physical parameters. We also find the conditions under which the disk formed from the tidal debris of a given star has a super Eddington accretion phase. We have simulated the light curve profiles in relevant optical g band and soft X-rays for both super and sub Eddington accretion disks as function of $\dot{M}(E,\hspace{1mm}J,\hspace{1mm}t)$. Using this, standard cosmological parameters and mission instrument details, we predict the detectable TDE rates for various forthcoming surveys finally as a function of $\gamma$.

### Stellar and gas dynamical model for tidal disruption events in a quiescent galaxy [Replacement]

A detailed model of the tidal disruption events (TDEs) has been constructed using stellar dynamical and gas dynamical inputs that include black hole (BH) mass $M_{\bullet}$, specific orbital energy $E$ and angular momentum $J$, star mass $M_{\star}$ and radius $R_{\star}$, and the pericenter of the star orbit $r_{p}(E,\hspace{1mm}J,\hspace{1mm}M_{\bullet})$. We solved the steady state Fokker--Planck equation using the standard loss cone theory for the galactic density profile $\rho (r) \propto r^{-\gamma}$ and stellar mass function $\xi(m)$ where $m=M_{\star}/M_{\odot}$ and obtained the feeding rate of stars to the BH integrated over the phase space as $\dot{N}_{t} \propto M_{\bullet}^\beta$, where $\beta= -0.3\pm 0.01$ for $M_{\bullet}>10^7 M_{\odot}$ and $\sim 6.8 \hspace{1mm} \times 10^{-5}$ Yr$^{-1}$ for $\gamma=0.7$. We use this to model the in-fall rate of the disrupted debris, $\dot{M}(E,\hspace{1mm}J,\hspace{1mm}m,\hspace{1mm}t)$, and discuss the conditions for the disk formation, finding that the accretion disk is almost always formed for the fiduciary range of the physical parameters. We also find the conditions under which the disk formed from the tidal debris of a given star with a super Eddington accretion phase. We have simulated the light curve profiles in the relevant optical g band and soft X-rays for both super and sub-Eddington accretion disks as a function of $\dot{M}(E,\hspace{1mm}J,\hspace{1mm}t)$. Using this, standard cosmological parameters, and mission instrument details, we predict the detectable TDE rates for various forthcoming surveys finally as a function of $\gamma$.

### CLASH-VLT: Environment-driven evolution of galaxies in the z=0.209 cluster Abell 209

The analysis of galaxy properties and the relations among them and the environment, can be used to investigate the physical processes driving galaxy evolution. We study the cluster A209 by using the CLASH-VLT spectroscopic data combined with Subaru photometry, yielding to 1916 cluster members down to a stellar mass of 10^{8.6} Msun. We determine: i) the stellar mass function of star-forming and passive galaxies; ii) the intra-cluster light and its properties; iii) the orbits of low- and high-mass passive galaxies; and iv) the mass-size relation of ETGs. The stellar mass function of the star-forming galaxies does not depend on the environment, while the slope found for passive galaxies becomes flatter in the densest region. The color distribution of the intra-cluster light is consistent with the color of passive members. The analysis of the dynamical orbits shows that low-mass passive galaxies have tangential orbits, avoiding small pericenters around the BCG. The mass-size relation of low-mass passive ETGs is flatter than that of high mass galaxies, and its slope is consistent with that of field star-forming galaxies. Low-mass galaxies are also more compact within the scale radius of 0.65 Mpc. The ratio between stellar and number density profiles shows a mass segregation in the center. The comparative analysis of the stellar and total density profiles indicates that this effect is due to dynamical friction. Our results are consistent with a scenario in which the "environmental quenching" of low-mass galaxies is due to mechanisms such as harassment out to R200, starvation and ram-pressure stripping at smaller radii, as supported by the analysis of the mass function, of the dynamical orbits and of the mass-size relation of passive early-types in different regions. Our analyses support the idea that the intra-cluster light is formed through the tidal disruption of subgiant galaxies.

### X-ray galaxy clusters abundance and mass temperature scaling

The abundance of clusters of galaxies is known to be a potential source of cosmological constraints through their mass function. In the present work, we examine the information that can be obtained from the temperature distribution function of X-ray clusters. For this purpose, the mass-temperature ($M$-$T$) relation and its statistical properties are critical ingredients. Using a combination of cosmic microwave background (CMB) data from Planck and our estimations of X-ray cluster abundances, we use Markov chain Monte Carlo (MCMC) techniques to estimate the $\Lambda$CDM cosmological parameters and the mass to X-ray temperature scaling relation simultaneously. We determine the integrated X-ray temperature function of local clusters using flux-limited surveys. A local comprehensive sample was build from the BAX X-ray cluster database, allowing us to estimate the local temperature distribution function above $\sim$1 keV. We model the expected temperature function from the mass function and the $M$-$T$ scaling relation. We then estimate the cosmological parameters and the parameters of the $M$-$T$ relation (calibration and slope) simultaneously. The measured temperature function of local clusters in the range $\sim\!\!1$-$10$ keV is well reproduced once the calibration of the $M$-$T$ relation is treated as a free parameter, and therefore is self-consistent with respect to the $\Lambda$CDM cosmology. The best-fit values of the standard cosmological parameters as well as their uncertainties are unchanged by the addition of clusters data. The calibration of the mass temperature relation, as well as its slope, are determined with $\sim10\%$ statistical uncertainties. This calibration leads to masses that are $\sim\!\!75\%$ larger than X-ray masses used in Planck.

### 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.

### Trans-Dimensional Bayesian Inference for Gravitational Lens Substructures [Replacement]

We introduce a Bayesian solution to the problem of inferring the density profile of strong gravitational lenses when the lens galaxy may contain multiple dark or faint substructures. The source and lens models are based on a superposition of an unknown number of non-negative basis functions (or "blobs") whose form was chosen with speed as a primary criterion. The prior distribution for the blobs' properties is specified hierarchically, so the mass function of substructures is a natural output of the method. We use reversible jump Markov Chain Monte Carlo (MCMC) within Diffusive Nested Sampling (DNS) to sample the posterior distribution and evaluate the marginal likelihood of the model, including the summation over the unknown number of blobs in the source and the lens. We demonstrate the method on two simulated data sets: one with a single substructure, and one with ten. We also apply the method to the g-band image of the "Cosmic Horseshoe" system, and find evidence for more than zero substructures. However, these have large spatial extent and probably only point to misspecifications in the model (such as the shape of the smooth lens component or the point spread function), which are difficult to guard against in full generality.

### 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

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.