# Posts Tagged mass function

## Recent Postings from mass function

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

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

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

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

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

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

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

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

### Cosmological simulations with disformally coupled symmetron fields

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

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

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

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

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

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

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

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

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 [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.

### 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

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

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

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

### Towards accurate rescaling of a halo mass function

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

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

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

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

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

### Comparisons between different techniques for measuring mass segregation

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

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

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

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

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

### Hydrogen Reionization in the Illustris Universe

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

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

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

### Comparing halo bias from abundance and clustering

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

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

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

### The MLP Distribution: A Modified Lognormal Power-Law Model for the Stellar Initial Mass Function

This work explores the mathematical properties of a distribution introduced by Basu & Jones (2004), and applies it to model the stellar initial mass function (IMF). The distribution arises simply from an initial lognormal distribution, requiring that each object in it subsequently undergoes exponential growth but with an exponential distribution of growth lifetimes. This leads to a modified lognormal with a power-law tail (MLP) distribution, which can in fact be applied to a wide range of fields where distributions are observed to have a lognormal-like body and a power-law tail. We derive important properties of the MLP distribution, like the cumulative distribution, the mean, variance, arbitrary raw moments, and a random number generator. These analytic properties of the distribution can be used to facilitate application to modeling the IMF. We demonstrate how the MLP function provides an excellent fit to the IMF compiled by Chabrier (2005) and how this fit can be used to quickly identify quantities like the mean, median, and mode, as well as number and mass fractions in different mass intervals.

### Baryon impact on the halo mass function: Fitting formulae and implications for cluster cosmology

We calibrate the halo mass function accounting for halo baryons and present fitting formulae for spherical overdensity masses $M_{500\textrm c}$, $M_{200\textrm c}$, and $M_{200\textrm m}$. We use the hydrodynamical Magneticum simulations, which are well suited because of their high resolution and large cosmological volumes of up to $\sim2$ Gpc$^3$. Baryonic effects globally decrease the masses of galaxy clusters, which, at given mass, results in a decrease of their number density. This effect vanishes at high redshift $z\sim2$ and for high masses $\gtrsim 5\times10^{14}M_\odot$. We perform cosmological analyses of three idealized approximations to the cluster surveys by the South Pole Telescope (SPT), Planck, and eROSITA. For the SPT-like and the Planck-like samples, we find that the impact of baryons on the cosmological results is negligible. In the eROSITA-like case, we find that neglecting the baryonic impact leads to an underestimate of $\Omega_\textrm m$ by about 0.01, which is comparable to the expected uncertainty from eROSITA. We compare our mass function fits with the literature. In particular, in the analysis of our Planck-like sample, results obtained using our mass function are shifted by $\Delta(\sigma_8)\simeq0.05$ with respect to results obtained using the Tinker et al. (2008) fit. This shift represents a large fraction of the observed difference between the latest results from Planck clusters and CMB anisotropies, and the tension is essentially removed. We discuss biases that can be introduced through inadequate mass function parametrizations that introduce false cosmological sensitivity. Additional work to calibrate the halo mass function is therefore crucial for progress in cluster cosmology.

### The High-Mass Stellar Initial Mass Function in M31 Clusters

We have undertaken the largest systematic study of the high-mass stellar initial mass function (IMF) to date using the optical color-magnitude diagrams (CMDs) of 85 resolved, young (4 Myr < t < 25 Myr), intermediate mass star clusters (10^3-10^4 Msun), observed as part of the Panchromatic Hubble Andromeda Treasury (PHAT) program. We fit each cluster’s CMD to measure its mass function (MF) slope for stars >2 Msun. For the ensemble of clusters, the distribution of stellar MF slopes is best described by $\Gamma=+1.45^{+0.03}_{-0.06}$ with a very small intrinsic scatter. The data also imply no significant dependencies of the MF slope on cluster age, mass, and size, providing direct observational evidence that the measured MF represents the IMF. This analysis implies that the high-mass IMF slope in M31 clusters is universal with a slope ($\Gamma=+1.45^{+0.03}_{-0.06}$) that is steeper than the canonical Kroupa (+1.30) and Salpeter (+1.35) values. Using our inference model on select Milky Way (MW) and LMC high-mass IMF studies from the literature, we find $\Gamma_{\rm MW} \sim+1.15\pm0.1$ and $\Gamma_{\rm LMC} \sim+1.3\pm0.1$, both with intrinsic scatter of ~0.3-0.4 dex. Thus, while the high-mass IMF in the Local Group may be universal, systematics in literature IMF studies preclude any definitive conclusions; homogenous investigations of the high-mass IMF in the local universe are needed to overcome this limitation. Consequently, the present study represents the most robust measurement of the high-mass IMF slope to date. We have grafted the M31 high-mass IMF slope onto widely used sub-solar mass Kroupa and Chabrier IMFs and show that commonly used UV- and Halpha-based star formation rates should be increased by a factor of ~1.3-1.5 and the number of stars with masses >8 Msun are ~25% fewer than expected for a Salpeter/Kroupa IMF. [abridged]

### The Massive Star Population of Cygnus OB2

We have compiled a significantly updated and comprehensive census of massive stars in the nearby Cygnus OB2 association by gathering and homogenising data from across the literature. The census contains 169 primary OB stars, including 52 O-type stars and 3 Wolf-Rayet stars. Spectral types and photometry are used to place the stars in a Hertzprung-Russell diagram, which is compared to both non-rotating and rotating stellar evolution models, from which stellar masses and ages are calculated. The star formation history and mass function of the association are assessed, and both are found to be heavily influenced by the evolution of the most massive stars to their end states. We find that the mass function of the most massive stars is consistent with a universal’ power-law slope of Gamma = 1.3. The age distribution inferred from stellar evolutionary models with rotation and the mass function suggest the majority of star formation occurred more or less continuously between 1 and 7 Myr ago, in agreement with studies of low- and intermediate mass stars in the association. We identify a nearby young pulsar and runaway O-type star that may have originated in Cyg OB2 and suggest that the association has already seen its first supernova. Finally we use the census and mass function to calculate the total mass of the association of 16500^+3800_-2800 Msun, at the low end, but consistent with, previous estimates of the total mass of Cyg OB2. Despite this Cyg OB2 is still one of the most massive groups of young stars known in our Galaxy making it a prime target for studies of star formation on the largest scales.

### The Massive Star Population of Cygnus OB2 [Replacement]

We have compiled a significantly updated and comprehensive census of massive stars in the nearby Cygnus OB2 association by gathering and homogenising data from across the literature. The census contains 169 primary OB stars, including 52 O-type stars and 3 Wolf-Rayet stars. Spectral types and photometry are used to place the stars in a Hertzprung-Russell diagram, which is compared to both non-rotating and rotating stellar evolution models, from which stellar masses and ages are calculated. The star formation history and mass function of the association are assessed, and both are found to be heavily influenced by the evolution of the most massive stars to their end states. We find that the mass function of the most massive stars is consistent with a universal’ power-law slope of Gamma = 1.3. The age distribution inferred from stellar evolutionary models with rotation and the mass function suggest the majority of star formation occurred more or less continuously between 1 and 7 Myr ago, in agreement with studies of low- and intermediate mass stars in the association. We identify a nearby young pulsar and runaway O-type star that may have originated in Cyg OB2 and suggest that the association has already seen its first supernova. Finally we use the census and mass function to calculate the total mass of the association of 16500^+3800_-2800 Msun, at the low end, but consistent with, previous estimates of the total mass of Cyg OB2. Despite this Cyg OB2 is still one of the most massive groups of young stars known in our Galaxy making it a prime target for studies of star formation on the largest scales.

### Radio-X-ray Synergy to discover and Study Jetted Tidal Disruption Events

Observational consequences of tidal disruption of stars (TDEs) by supermassive black holes (SMBHs) can enable us to discover quiescent SMBHs, constrain their mass function, study formation and evolution of transient accretion disks and jet formation. A couple of jetted TDEs have been recently claimed in hard X-rays, challenging jet models, previously applied to $\gamma$-ray bursts and active galactic nuclei. It is therefore of paramount importance to increase the current sample. In this paper, we find that the best strategy is not to use up-coming X-ray instruments alone, which will yield between several (e-Rosita) and a couple of hundreds (Einstein Probe) events per year below redshift one. We rather claim that a more efficient TDE hunter will be the Square Kilometer Array (SKA) operating {\it in survey mode} at 1.4 GHz. It may detect up to several hundreds of events per year below $z \sim 2.5$ with a peak rate of a few tens per year at $z\approx 0.5$. Therefore, even if the jet production efficiency is {\it not } $100\%$ as assumed here, the predicted rates should be large enough to allow for statistical studies. The characteristic TDE decay of $t^{-5/3}$, however, is not seen in radio, whose flux is quite featureless. {\it Identification} therefore requires localization and prompt repointing by higher energy instruments. If radio candidates would be repointed within a day by future X-ray observatories (e.g. Athena and LOFT-like missions), it will be possible to detect up to $\approx 400$ X-ray counterparts, almost up to redshift $2$. The shortcome is that only for redshift below $\approx 0.4$ the trigger times will be less than 10 days from the explosion. In this regard the X-ray surveys are better suited to probe the beginning of the flare, and are therefore complementary to SKA.

### Scale-dependent bias from an inflationary bispectrum: the effect of a stochastic moving barrier

With the advent of large scale galaxy surveys, constraints on primordial non-Gaussianity (PNG) are expected to reach ${\cal O}(f_\text{NL}) \sim 1$. In order to fully exploit the potential of these future surveys, a deep theoretical understanding of the signatures imprinted by PNG on the large scale structure of the Universe is necessary. In this paper, we explore the effect of a stochastic moving barrier on the amplitude of the non-Gaussian bias induced by local quadratic PNG. We show that, in the peak approach to halo clustering, the amplitude of the non-Gaussian bias will generally differ from the peak-background split prediction unless the barrier is flat and deterministic. For excursion set peaks with a square-root barrier, which reproduce reasonably well the linear bias $b_1$ and mass function $\bar{n}_\text{h}$ of SO haloes, the non-Gaussian bias amplitude is $\sim 40$% larger than the peak-background split expectation $d\ln\bar{n}_\text{h}/d\ln\sigma_8$ for haloes of mass $\sim 10^{13} {\it h}^{-1}M_\odot$ at $z=0$. Furthermore, we argue that the effect of PNG on squeezed configurations of the halo bispectrum differs significantly from that predicted by standard local bias approaches. Our predictions can be easily confirmed, or invalidated, with N-body simulations.

### Scale-dependent bias from an inflationary bispectrum: the effect of a stochastic moving barrier [Replacement]

With the advent of large scale galaxy surveys, constraints on primordial non-Gaussianity (PNG) are expected to reach ${\cal O}(f_\text{NL}) \sim 1$. In order to fully exploit the potential of these future surveys, a deep theoretical understanding of the signatures imprinted by PNG on the large scale structure of the Universe is necessary. In this paper, we explore the effect of a stochastic moving barrier on the amplitude of the non-Gaussian bias induced by local quadratic PNG. We show that, in the peak approach to halo clustering, the amplitude of the non-Gaussian bias will generally differ from the peak-background split prediction unless the barrier is flat and deterministic. For excursion set peaks with a square-root barrier, which reproduce reasonably well the linear bias $b_1$ and mass function $\bar{n}_\text{h}$ of SO haloes, the non-Gaussian bias amplitude is $\sim 40$% larger than the peak-background split expectation $d\ln\bar{n}_\text{h}/d\ln\sigma_8$ for haloes of mass $\sim 10^{13} {\it h}^{-1}M_\odot$ at $z=0$. Furthermore, we argue that the effect of PNG on squeezed configurations of the halo bispectrum differs significantly from that predicted by standard local bias approaches. Our predictions can be easily confirmed, or invalidated, with N-body simulations.

### Biases in the inferred mass-to-light ratio of globular clusters: no need for variations in the stellar mass function [Replacement]

From a study of the integrated light properties of 200 globular clusters (GCs) in M31, Strader et al. found that the mass-to-light ratios are lower than what is expected from simple stellar population (SSP) models with a canonical’ stellar initial mass function (IMF), with the discrepancy being larger at high metallicities. We use dynamical multi-mass models, that include a prescription for equipartition, to quantify the bias in the inferred dynamical mass as the result of the assumption that light follows mass. For a universal IMF and a metallicity dependent present day mass function we find that the inferred mass from integrated light properties systematically under estimates the true mass, and that the bias is more important at high metallicities, as was found for the M31 GCs. We show that mass segregation and a flattening of the mass function have opposing effects of similar magnitude on the mass inferred from integrated properties. This makes the mass-to-light ratio as derived from integrated properties an inadequate probe of the low-mass end of the stellar mass function. There is, therefore, no need for variations in the IMF, nor the need to invoke depletion of low-mass stars, to explain the observations. Finally, we find that the retention fraction of stellar-mass black holes (BHs) is an equally important parameter in understanding the mass segregation bias. We speculatively put forward to idea that kinematical data of GCs can in fact be used to constrain the total mass in stellar-mass BHs in GCs.

### Biases in the inferred mass-to-light ratio of globular clusters: no need for variations in the stellar mass function

From a study of the integrated light properties of 200 globular clusters (GCs) in M31, Strader et al. found that the mass-to-light ratios are lower than what is expected from simple stellar population (SSP) models with a `canonical’ stellar initial mass function (IMF), with the discrepancy being larger at high metallicities. We use dynamical multi-mass models, that include a prescription for equipartition, to quantify the bias in the inferred dynamical mass as the result of the assumption that light follows mass. For a universal IMF and a metallicity dependent present day mass function we find that the inferred mass from integrated light properties systematically under estimates the true mass, and that the bias is more important at high metallicities, as was found for the M31 GCs. We show that mass segregation and a flattening of the mass function have opposing effects of similar magnitude on the mass inferred from integrated properties. This makes the mass-to-light ratio as derived from integrated properties an inadequate probe of the low-mass end of the stellar mass function. There is, therefore, no need for variations in the IMF, nor the need to invoke depletion of low-mass stars, to explain the observations. Finally, we find that the retention fraction of stellar-mass black holes (BHs) is an equally important parameter in understanding the mass segregation bias. We speculatively put forward to idea that kinematical data of GCs can in fact be used to constrain the total mass in stellar-mass BHs in GCs.

### SKA as a powerful hunter of jetted Tidal Disruption Events

Observational consequences of the tidal disruption of stars by supermassive black holes (SMBHs) can enable us to discover quiescent SMBHs and constrain their mass function. Moreover, observing jetted TDEs (from previously non-active galaxies) provides us with a new means of studying the early phases of jet formation and evolution in an otherwise "pristine" environment. Although several (tens) TDEs have been discovered since 1999, only two jetted TDEs have been recently discovered in hard X-rays, and only one, Swift J1644+57, has a precise localization which further supports the TDE interpretation. These events alone are not sufficient to address those science issues, which require a substantial increase of the current sample. Despite the way they were discovered, the highest discovery potential for {\em jetted} TDEs is not held by current and up-coming X-ray instruments, which will yield only a few to a few tens events per year. In fact, the best strategy is to use the Square Kilometer Array to detect TDEs and trigger multi-wavelength follow-ups, yielding hundreds candidates per year, up to $z \sim 2$. Radio and X-ray synergy, however, can in principle constrain important quantities such as the absolute rate of jetted TDEs, their jet power, bulk Lorentz factor, the black hole mass function, and perhaps discover massive black holes (MBH) with $<10^{5} M_{\odot}$. Finally, when comparing SKA results with information from optical surveys like LSST, one can more directly constrain the efficiency of jet production.

### Towards a fully consistent Milky Way disc model - III. Constraining the initial mass function

We use our vertical Milky Way disc model together with Galaxia to create mock observations of stellar samples in the solar neighbourhood. We compare these to the corresponding volume complete observational samples of dereddened and binary accounted data from Hipparcos and the Catalogue of Nearby Stars. Sampling the likelihood in the parameter space we determine a new fiducial IMF considering constraints from dwarf and giant stars. The resulting IMF observationally backed in the range from 0.5 to 10 Msun is a two slope broken power law with -1.49 +- 0.08 for the low mass slope, a break at 1.39 +- 0.05 Msun and a high mass slope of -3.02 +- 0.06. The Besancon group also converging to a similar IMF even though their observational sample being quite different to ours shows that the forward modelling technique is a powerful diagnostic to test theoretical concepts like the local field star IMF.

### Characterizing the Brown Dwarf Formation Channels from the Initial Mass Function and Binary-star Dynamics [Replacement]

The stellar initial mass function (IMF) is a key property of stellar populations. There is growing evidence that the classical star-formation mechanism by the direct cloud fragmentation process has difficulties reproducing the observed abundance and binary properties of brown dwarfs and very-low-mass stars. In particular, recent analytical derivations of the stellar IMF exhibit a deficit of brown dwarfs compared to observational data. Here we derive the residual mass function of brown dwarfs as an empirical measure of the brown dwarf deficiency in recent star-formation models with respect to observations and show that it is compatible with the substellar part of the Thies-Kroupa IMF and the mass function obtained by numerical simulations. We conclude that the existing models may be further improved by including a substellar correction term that accounts for additional formation channels like disk or filament fragmentation. The term "peripheral fragmentation" is introduced here for such additional formation channels. In addition, we present an updated analytical model of stellar and substellar binarity. The resulting binary fraction and the dynamically evolved companion mass-ratio distribution are in good agreement with observational data on stellar and very-low-mass binaries in the Galactic field, in clusters, and in dynamically unprocessed groups of stars if all stars form as binaries with stellar companions. Cautionary notes are given on the proper analysis of mass functions and the companion mass-ratio distribution and the interpretation of the results. The existence of accretion disks around young brown dwarfs does not imply that these form just like stars in direct fragmentation.

### Characterizing the brown dwarf formation channels from the IMF and binary-star dynamics

The stellar initial mass function (IMF) is a key property of stellar populations. There is growing evidence that the classical star-formation mechanism by the direct cloud fragmentation process has difficulties to reproduce the observed abundance and binary properties of brown dwarfs and very-low-mass stars. In particular, recent analytical derivations of the stellar IMF exhibit a deficit of brown dwarfs compared to observational data. Here we derive the residual mass function of brown dwarfs as an empirical measure of the brown dwarf deficiency in recent star-formation models with respect to observations and show that it is compatible with the substellar part of the Thies-Kroupa-IMF and the mass function obtained by numerical simulations. We conclude that the existing models may be further improved by including a substellar correction term accounting for additional formation channels like disk or filament fragmentation. The term "peripheral fragmentation" is introduced here for such additional formation channels. In addition, we present an updated analytical model of stellar and substellar binarity. The resulting binary fraction as well as the dynamically evolved companion mass-ratio distribution are in good agreement with observational data on stellar and very-low-mass binaries in the Galactic field, in clusters, and in dynamically unprocessed groups of stars if all stars form as binaries with stellar companions. Cautionary notes are given on the proper analysis of mass functions and the companion-mass-ratio distribution and the interpretation of the results. The existence of accretion disks around young brown dwarfs does not imply these form just like stars in direct fragmentation.

### Further evidence for a time-dependent initial mass function in massive early-type galaxies

Spectroscopic analyses of gravity-sensitive line strengths give growing evidence towards an excess of low-mass stars in massive early-type galaxies (ETGs). Such a scenario requires a bottom-heavy initial mass function (IMF). However, strong constraints can be imposed if we take into account galactic chemical enrichment. We extend the analysis of Weidner et al. and consider the functional form of bottom-heavy IMFs used in recent works, where the high-mass end slope is kept fixed to the Salpeter value, and a free parameter is introduced to describe the slope at stellar masses below some pivot mass scale (M<MP=0.5Msun). We find that no such time-independent parameterisation is capable to reproduce the full set of constraints in the stellar populations of massive ETGs – resting on the assumption that the analysis of gravity-sensitive line strengths leads to a mass fraction at birth in stars with mass M<0.5Msun above 60%. Most notably, the large amount of metal-poor gas locked in low-mass stars during the early, strong phases of star formation results in average stellar metallicities [M/H]<-0.6, well below the solar value. The conclusions are unchanged if either the low-mass end cutoff, or the pivot mass are left as free parameters, strengthening the case for a time-dependent IMF.

### A Dynamical Study of the Black Hole X-ray Binary Nova Muscae 1991 [Replacement]

We present a dynamical study of the Galactic black hole binary system Nova Muscae 1991 (GS/GRS 1124-683). We utilize 72 high resolution Magellan Echellette (MagE) spectra and 72 strictly simultaneous V-band photometric observations; the simultaneity is a unique and crucial feature of this dynamical study. The data were taken on two consecutive nights and cover the full 10.4-hour orbital cycle. The radial velocities of the secondary star are determined by cross-correlating the object spectra with the best-match template spectrum obtained using the same instrument configuration. Based on our independent analysis of five orders of the echellette spectrum, the semi-amplitude of the radial velocity of the secondary is measured to be K_2 = 406.8+/-2.7 km/s, which is consistent with previous work, while the uncertainty is reduced by a factor of 3. The corresponding mass function is f(M) = 3.02+/-0.06 M_\odot. We have also obtained an accurate measurement of the rotational broadening of the stellar absorption lines (v sin i = 85.0+/-2.6 km/s) and hence the mass ratio of the system q = 0.079+/-0.007. Finally, we have measured the spectrum of the non-stellar component of emission that veils the spectrum of the secondary. In a future paper, we will use our veiling-corrected spectrum of the secondary and accurate values of K_2 and q to model multi-color light curves and determine the systemic inclination and the mass of the black hole.

### A Dynamical Study of the Black Hole X-ray Binary Nova Muscae 1991

We present a dynamical study of the Galactic black hole binary system Nova Muscae 1991 (GS/GRS 1124-683). We utilize 72 high resolution Magellan Echellette (MagE) spectra and 72 strictly simultaneous V-band photometric observations; the simultaneity is a unique and crucial feature of this dynamical study. The data were taken on two consecutive nights and cover the full 10.4-hour orbital cycle. The radial velocities of the secondary star are determined by cross-correlating the object spectra with the best-match template spectrum obtained using the same instrument configuration. Based on our independent analysis of five orders of the echellette spectrum, the semi-amplitude of the radial velocity of the secondary is measured to be K_2 = 406.8+/-2.2 km/s, which is consistent with previous work, while the uncertainty is reduced by a factor of 3. The corresponding mass function is f(M) = 3.02+/-0.05 M_\odot. We have also obtained an accurate measurement of the rotational broadening of the stellar absorption lines (v sin i = 80.9+/-1.3 km/s) and hence the mass ratio of the system q = 0.070+/-0.003. Finally, we have measured the spectrum of the non-stellar component of emission that veils the spectrum of the secondary. In a future paper, we will use our veiling-corrected spectrum of the secondary and accurate values of K_2 and q to model multi-color light curves and determine the systemic inclination and the mass of the black hole.

### Statistics of the end of turnaround-scale structure formation in Lambda CDM cosmology

In $\Lambda$CDM cosmology, structure formation is halted shortly after dark energy dominates the mass/energy budget of the Universe. A manifestation of this effect is that in such a cosmology the turnaround radius –the non-expanding mass shell furthest away from the center of a structure– has an upper bound. Recently, a new, local, test for the existence of dark energy in the form of a cosmological constant was proposed based on this turnaround bound. In this work, we build upon this proposal, and we further examine the advantages of studying the end of structure formation at the turnaround scale. Using the Press-Schechter formalism, we calculate the mass function of turnaround structures at various cosmic epochs, including the present one and an infinite time into the future. We find that structures at turnaround scales have in practice stopped forming already today, and consequently, the turnaround radii of structures must be very close to the maximum predicted value. We find that a mass scale of $m \sim 10^{13} M_{\odot}$ separates turnaround structures with qualitative different cosmological evolution: smaller structures are no longer readjusting their mass distribution inside the turnaround scale, they asymptotically approach their ultimate abundance from higher values, and they are common enough to have, at some epoch, experienced major mergers with structures of comparable mass; larger structures exhibit the opposite behavior. We argue that this mass scale is optimal for searches of possible violations of the maximum turnaround radius limit through high-precision determinations of masses and, independently, turnaround radii.

### Small Scale Clustering of Late Forming Dark Matter

We perform a study of the non-linear clustering of matter in the Late Forming Dark Matter (LFDM) scenario in which dark matter results from the transition of non-minimally coupled scalar field from radiation to collisionless matter. A distinct feature of this model is the presence of a damped oscillatory cut-off in the linear matter power spectrum at small scales. We use a suite of high-resolution N-body simulations to study the imprints of LFDM on the non-linear matter power spectrum, the halo mass function and the halo density profiles. The model satisfies high-redshift matter power spectrum constraints from Lyman-$\alpha$ forest measurements. We find suppressed abundance of low mass halos ($\sim 10^{9}-10^{10}$ h$^{-1}$ M$_\odot$) at all redshifts compared to a vanilla $\Lambda$CDM model. Furthermore, in this mass range we find significant deviations with respect to predictions from the Sheth-Tormen mass function. Halos with mass $M\gtrsim 10^{11}$ h$^{-1}$ M$_\odot$ show minor departures of the density profiles from $\Lambda$CDM expectations, while smaller mass halos are less dense consistent with the fact that they form later than their $\Lambda$CDM counterparts.

### Small scale clustering of late forming dark matter [Replacement]

We perform a study of the non-linear clustering of matter in the Late Forming Dark Matter (LFDM) scenario in which dark matter results from the transition of non-minimally coupled scalar field from radiation to collisionless matter. A distinct feature of this model is the presence of a damped oscillatory cut-off in the linear matter power spectrum at small scales. We use a suite of high-resolution N-body simulations to study the imprints of LFDM on the non-linear matter power spectrum, the halo mass function and the halo density profiles. The model satisfies high-redshift matter power spectrum constraints from Lyman-$\alpha$ forest measurements. We find suppressed abundance of low mass halos ($\sim 10^{9}-10^{10}$ h$^{-1}$ M$_\odot$) at all redshifts compared to a vanilla $\Lambda$CDM model. Furthermore, in this mass range we find significant deviations with respect to predictions from the Sheth-Tormen mass function. Halos with mass $M\gtrsim 10^{11}$ h$^{-1}$ M$_\odot$ show minor departures of the density profiles from $\Lambda$CDM expectations, while smaller mass halos are less dense consistent with the fact that they form later than their $\Lambda$CDM counterparts.

### The galaxy stellar mass function at 3.5<z<7.5 in the CANDELS/UDS, GOODS-South, and HUDF fields

The galaxy stellar mass function (GSMF) at high-z provides key information on star-formation history and mass assembly in the young Universe. We aimed to use the unique combination of deep optical/NIR/MIR imaging provided by HST, Spitzer and the VLT in the CANDELS-UDS, GOODS-South, and HUDF fields to determine the GSMF over the redshift range 3.5<z<7.5. We utilised the HST WFC3/IR NIR imaging from CANDELS and HUDF09, reaching H~27-28.5 over a total area of 369 arcmin2, in combination with associated deep HST ACS optical data, deep Spitzer IRAC imaging from the SEDS programme, and deep Y and K-band VLT Hawk-I images from the HUGS programme, to select a galaxy sample with high-quality photometric redshifts. These have been calibrated with more than 150 spectroscopic redshifts in the range 3.5<z<7.5, resulting in an overall precision of sigma_z/(1+z)~0.037. We have determined the low-mass end of the high-z GSMF with unprecedented precision, reaching down to masses as low as M*~10^9 Msun at z=4 and ~6×10^9 Msun at z=7. We find that the GSMF at 3.5<z<7.5 depends only slightly on the recipes adopted to measure the stellar masses, namely the photo-z, the SFHs, the nebular contribution or the presence of AGN on the parent sample. The low-mass end of the GSMF is steeper than has been found at lower redshifts, but appears to be unchanged over the redshift range probed here. Our results are very different from previous GSMF estimates based on converting UV galaxy luminosity functions into mass functions via tight M/L relations. Integrating our evolving GSMF over mass, we find that the growth of stellar mass density is barely consistent with the time-integral of the SFR density over cosmic time at z>4. These results confirm the unique synergy of the CANDELS+HUDF, HUGS, and SEDS surveys for the discovery and study of moderate/low-mass galaxies at high redshifts.

### Chiral-symmetry breaking and confinement in Minkowski space

We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form factor in relativistic impulse approximation, and the results are presented and compared with the experimental data from JLab.

### The initial mass function and star formation law in the outer disc of NGC 2915

Using Hubble Space Telescope (HST) ACS/WFC data we present the photometry and spatial distribution of resolved stellar populations in the outskirts of NGC 2915, a blue compact dwarf with an extended HI disc. These observations reveal an elliptical distribution of red giant branch stars, and a clumpy distribution of main-sequence stars that correlate with the HI gas distribution. We constrain the upper-end initial mass function (IMF) and determine the star formation law (SFL) in this field, using the observed main-sequence stars and an assumed constant star formation rate. Previously published H{\alpha} observations of the field, which show one faint HII region, are used to provide further constraints on the IMF. We find that the main-sequence luminosity function analysis alone results in a best-fitting IMF with a power-law slope {\alpha}=-2.85 and upper-mass limit M$_\rm{u}$ = 60 M$_\odot$. However, if we assume that all H{\alpha} emission is confined to HII regions then the upper-mass limit is restricted to M$_\rm{u}$ $\le$20 M$_\odot$. For the luminosity function fit to be correct we have to discount the H{\alpha} observations implying significant diffuse ionized gas or escaping ionizing photons. Combining the HST photometry with HI imaging we find the SFL has a power law index $N=1.53 \pm 0.21$. Applying these results to the entire outer HI disc indicates that it contributes 11–28% of the total recent star formation in NGC 2915, depending on whether the IMF is constant within the disc or varies from the centre to the outer region.

### New Phantom and non-Phantom Wormhole Solutions with Generic Cosmological Constant

There are a number of reasons to study wormholes with generic cosmological constant $\Lambda$. Recent observations indicate that present accelerating expansion of the universe demands $\Lambda>0$. On the other hand, some extended theories of gravitation such as supergravity and superstring theories posses vacuum states with $\Lambda<0$. Even within the framework of general relativity, a negative cosmological constant permits black holes with horizons topologically different from the usual spherical ones. These solutions are convertible to wormhole solutions by adding some exotic matter. In this paper, the phantom and non-phantom matter wormhole solutions in the presence of cosmological constant are studied. By constructing a specific class of shape functions, mass function, energy density and pressure profiles which support such a geometry are obtained. It is shown that for having such a geometry, the wormhole throat $r_0$, the cosmological constant $\Lambda$ and the equation of state parameter $\omega$ should satisfy two specific conditions. The possibility of setting different values for the parameters of the model helps us to find exact solutions for the metric functions, mass functions and energy-momentum profiles. At last, the volume integral quantifier, which provides useful information about the total amount of energy condition violating matter is discussed briefly.

### Asymptotically Flat Wormhole Solutions in a Generic Cosmological Constant Background [Replacement]

There are a number of reasons to study wormholes with generic cosmological constant $\Lambda$. Recent observations indicate that present accelerating expansion of the universe demands $\Lambda>0$. On the other hand, some extended theories of gravitation such as supergravity and superstring theories posses vacuum states with $\Lambda<0$. Even within the framework of general relativity, a negative cosmological constant permits black holes with horizons topologically different from the usual spherical ones. These solutions are convertible to wormhole solutions by adding some exotic matter. In this paper, the asymptotically flat wormhole solutions in a generic cosmological constant background are studied. By constructing a specific class of shape functions, mass function, energy density and pressure profiles which support such a geometry are obtained. It is shown that for having such a geometry, the wormhole throat $r_0$, the cosmological constant $\Lambda$ and the equation of state parameter $\omega$ should satisfy two specific conditions. The possibility of setting different values for the parameters of the model helps us to find exact solutions for the metric functions, mass functions and energy-momentum profiles. At last, the volume integral quantifier, which provides useful information about the total amount of energy condition violating matter is discussed briefly.

### Finding the First Cosmic Explosions. IV. 90 - 140 M$_{\odot}$ Pair-Instability Supernovae

Population III stars that die as pair-instability supernovae are usually thought to fall in the mass range of 140 – 260 M$_{\odot}$. But several lines of work have now shown that rotation can build up the He cores needed to encounter the pair instability at stellar masses as low as 90 $_{\odot}$. Depending on the slope of the initial mass function of Population III stars, there could be 4 – 5 times as many stars from 90 – 140 $_{\odot}$ in the primordial universe than in the usually accepted range. We present numerical simulations of the pair-instability explosions of such stars performed with the MESA, FLASH and RAGE codes. We find that they will be visible to supernova factories such as Pan-STARRS and LSST in the optical out to z $\sim$ 1 – 2 and to JWST and the 30 m-class telescopes in the NIR out to $z \sim$ 7 – 10. Such explosions will thus probe the stellar populations of the first galaxies and cosmic star formation rates in the era of cosmological reionization. These supernovae are also easily distinguished from more massive pair-instability explosions, underscoring the fact that there is far greater variety to the light curves of these events than previously understood.

### The chemical signature of surviving Population III stars in the Milky Way

Cosmological simulations of Population (Pop) III star formation suggest that the primordial initial mass function may have extended to sub-solar masses. If Pop III stars with masses < 0.8 M_Sun did form, then they should still be present in the Galaxy today as either main sequence or red giant stars. To date, however, despite searches for metal-poor stars in both the halo and the bulge of the Milky Way, no primordial stars have been identified. It has long been recognized that the initial metal-free nature of primordial stars could be masked due to accretion of metal-enriched material from the interstellar medium (ISM) over the course of their long lifetimes. Here we point out that while gas accretion from the ISM may readily occur, the accretion of dust from the ISM can be prevented due to the pressure of the radiation emitted from low-mass stars. This implies a possible unique chemical signature for stars polluted only via accretion, namely an enhancement in gas phase elements relative to those in the dust phase. Using Pop III stellar models, we outline the conditions in which this signature could be exhibited, and we derive the expected signature for the case of accretion from the local ISM. Intriguingly, due to the large fraction of iron depleted into dust relative to that of carbon and other elements, this signature is similar to that observed in many of the so-called carbon-enhanced metal-poor (CEMP) stars. We therefore suggest that some fraction of the observed CEMP stars may, in fact, be accretion-polluted Pop III stars. We find, more broadly, that this effect could also be at play in accretion flows onto protostars, implying that it may also impact the chemical signatures of second generation (Pop II) stars.