# Posts Tagged mass function

## Recent Postings from mass function

### Lower mass normalization of the stellar initial mass function for dense massive early-type galaxies at z ~ 1.4

This paper aims at understanding if the normalization of the stellar initial mass function (IMF) of massive early-type galaxies (ETGs) varies with cosmic time and/or with mean stellar mass density Sigma (M*/2\pi Re^2). For this purpose we have collected a sample of 18 dense (Sigma>2500 M_sun/pc^2) ETGs at 1.2<z<1.6 with available velocity dispersion sigma_e. We have constrained their mass-normalization by comparing their true stellar masses (M_true) derived through virial theorem, hence IMF independent, with those inferred through the fit of the photometry assuming a reference IMF (M_ref). Adopting the virial estimator as proxy of the true stellar mass, we have assumed for these ETGs zero dark matter (DM). However, dynamical models and numerical simulations of galaxy evolution have shown that the DM fraction within Re in dense high-z ETGs is negligible. We have considered the possible bias of virial theorem in recovering the total masses and have shown that for dense ETGs the virial masses are in agreement with those derived through more sophisticated dynamical models. The variation of the parameter $\Gamma$ = M_true/M_ref with sigma_e shows that, on average, dense ETGs at <z> = 1.4 follow the same IMF-sigma_e trend of typical local ETGs, but with a lower mass-normalization. Nonetheless, once the IMF-sigma_e trend we have found for high-z dense ETGs is compared with that of local ETGs with similar Sigma and sigma_e, they turn out to be consistent. The similarity between the IMF-sigma_e trends of dense high-z and low-z ETGs over 9 Gyr of evolution and their lower mass-normalization with respect to the mean value of local ETGs suggest that, independently on formation redshift, the physical conditions characterizing the formation of a dense spheroid lead to a mass spectrum of new formed stars with an higher ratio of high- to low-mass stars with respect to the IMF of normal local ETGs.

### A theoretical calculation of microlensing signatures caused by free-floating planets towards the Galactic bulge

Free-floating planets are recently drawing a special interest of the scientific community. Gravitational microlensing is up to now the exclusive method for the investigation of free-floating planets, including their spatial distribution function and mass function. In this work, we examine the possibility that the future Euclid space-based observatory may allow to discover a substantial number of microlensing events caused by free-floating planets. Based on latest results about the free-floating planet mass function in the mass range $[10^{-5}, 10^{-2}]M_{\odot}$, we calculate the optical depth towards the Galactic bulge as well as the expected microlensing rate and find that Euclid may be able to detect hundreds to thousands of these events per month. Making use of a synthetic population, we also investigate the possibility of detecting parallax effect in simulated microlensing events due to free-floating planets and find a significant efficiency for the parallax detection that turns out to be around 30%.

### Reconstructing the initial mass function of disc-bulge Galactic globular clusters from N-body simulations

We propose an evolutionary model to describe the dynamical evolution of star cluster systems in tidal fields, in which we calibrated the parametric equations defining the model by running direct N-body simulations of star clusters with a wide range of initial masses and set of orbital parameters, living within the external tidal field generated by a disc-like galaxy. We derived a new method to solve numerically the evolutionary equations, allowing us to infer constraints on the mass of a star cluster from its age, present-day mass, orbital parameters and external gravitational potential. The result has been applied to the metal-rich subsample of Galactic globular clusters, being a good representation of a disc-bulge population. We reconstructed the initial mass function of these objects from the present-day mass function, finding that a lognormal distribution is well preserved during the evolution of the globular cluster system. The evolution of a power-law initial mass function has been evaluated, confirming that it transforms into a lognormal distribution of the cluster masses within an Hubble time. Our results are consistent with a formation scenario in which metal-rich Galactic globular clusters formed from giant molecular clouds in high-pressure regions during the early phases of the evolution of the Galactic disc and bulge.

### Stability of AdS in Einstein Gauss Bonnet Gravity [Cross-Listing]

Recently it has been argued that in Einstein gravity Anti-de Sitter spacetime is unstable against the formation of black holes for a large class of arbitrarily small perturbations. We examine the effects of including a Gauss-Bonnet term. In five dimensions, spherically symmetric Einstein-Gauss-Bonnet gravity has two key features: Choptuik scaling exhibits a radius gap, and the mass function goes to a finite value as the horizon radius vanishes. These suggest that black holes will not form dynamically if the total mass/energy content of the space-time is too small, thereby restoring the stability of AdS spacetime. We support this claim with numerical simulations and uncover a rich structure in horizon radii and formation times as a function of perturbation amplitude.

### Stability of AdS in Einstein Gauss Bonnet Gravity

Recently it has been argued that in Einstein gravity Anti-de Sitter spacetime is unstable against the formation of black holes for a large class of arbitrarily small perturbations. We examine the effects of including a Gauss-Bonnet term. In five dimensions, spherically symmetric Einstein-Gauss-Bonnet gravity has two key features: Choptuik scaling exhibits a radius gap, and the mass function goes to a finite value as the horizon radius vanishes. These suggest that black holes will not form dynamically if the total mass/energy content of the space-time is too small, thereby restoring the stability of AdS spacetime. We support this claim with numerical simulations and uncover a rich structure in horizon radii and formation times as a function of perturbation amplitude.

### Stability of AdS in Einstein Gauss Bonnet Gravity [Replacement]

Recently it has been argued that in Einstein gravity Anti-de Sitter spacetime is unstable against the formation of black holes for a large class of arbitrarily small perturbations. We examine the effects of including a Gauss-Bonnet term. In five dimensions, spherically symmetric Einstein-Gauss-Bonnet gravity has two key features: Choptuik scaling exhibits a radius gap, and the mass function goes to a finite value as the horizon radius vanishes. These suggest that black holes will not form dynamically if the total mass/energy content of the space-time is too small, thereby restoring the stability of AdS spacetime. We support this claim with numerical simulations and uncover a rich structure in horizon radii and formation times as a function of perturbation amplitude.

### Stability of AdS in Einstein Gauss Bonnet Gravity [Replacement]

Recently it has been argued that in Einstein gravity Anti-de Sitter spacetime is unstable against the formation of black holes for a large class of arbitrarily small perturbations. We examine the effects of including a Gauss-Bonnet term. In five dimensions, spherically symmetric Einstein-Gauss-Bonnet gravity has two key features: Choptuik scaling exhibits a radius gap, and the mass function goes to a finite value as the horizon radius vanishes. These suggest that black holes will not form dynamically if the total mass/energy content of the space-time is too small, thereby restoring the stability of AdS spacetime. We support this claim with numerical simulations and uncover a rich structure in horizon radii and formation times as a function of perturbation amplitude.

### Variations of the stellar initial mass function in the progenitors of massive early-type galaxies and in extreme starburst environments

We examine variations of the stellar initial mass function (IMF) in extreme environments within the formalism derived by Hennebelle \& Chabrier. We focus on conditions encountered in progenitors of massive early type galaxies and starburst regions. We show that, when applying the concept of turbulent Jeans mass as the characteristic mass for fragmentation in a turbulent medium, instead of the standard thermal Jeans mass for purely gravitational fragmentation, the peak of the IMF in such environments is shifted towards smaller masses, leading to a bottom-heavy IMF, as suggested by various observations. In very dense and turbulent environments, we predict that the high-mass tail of the IMF can become even steeper than the standard Salpeter IMF, with a limit for the power law exponent $\alpha\simeq -2.7$, in agreement with recent observational determinations. This steepening is a direct consequence of the high densities and Mach values in such regions but also of the time dependence of the fragmentation process, as incorporated in the Hennebelle-Chabrier theory. We provide analytical parametrizations of these IMFs in such environments, to be used in galaxy evolution calculations. We also calculate the star formation rates and the mass-to-light ratios expected under such extreme conditions and show that they agree well with the values inferred in starburst environments and massive high-redshift galaxies. This reinforces the paradigm of star formation as being a universal process, i.e. the direct outcome of gravitationally unstable fluctuations in a density field initially generated by large scale shock-dominated turbulence. This globally enables us to infer the variations of the stellar IMF and related properties for atypical galactic conditions.

### The Galaxy Cosmological Mass Function

We study the galaxy cosmological mass function (GCMF) in a semi-empirical relativistic approach using observational data provided by galaxy redshift surveys. Starting from the theory of Ribeiro & Stoeger (2003, arXiv:astro-ph/0304094) between the mass-to-light ratio, the selection function obtained from the luminosity function (LF) data and the luminosity density, the average luminosity $L$ and the average galactic mass $\mathcal{M}_g$ are computed in terms of the redshift. $\mathcal{M}_g$ is also alternatively estimated by a method that uses the galaxy stellar mass function (GSMF). Comparison of these two forms of deriving the average galactic mass allows us to infer a possible bias introduced by the selection criteria of the survey. We used the FORS Deep Field galaxy survey sample of 5558 galaxies in the redshift range $0.5 < z < 5.0$ and its LF Schechter parameters in the B-band, as well as this sample’s stellar mass-to-light ratio and its GSMF data. Assuming ${\mathcal{M}_{g_0}} \approx 10^{11} \mathcal{M}_\odot$ as the local value of the average galactic mass, the LF approach results in $L_{B} \propto (1+z)^{(2.40 \pm 0.03)}$ and $\mathcal{M}_g \propto (1+z)^{(1.1\pm0.2)}$. However, using the GSMF results produces $\mathcal{M}_g \propto (1+z)^{(-0.58 \pm 0.22)}$. We chose the latter result as it is less biased. We then obtained the theoretical quantities of interest, such as the differential number counts, to calculate the GCMF, which can be fitted by a Schechter function. The derived GCMF follows theoretical predictions in which the less massive objects form first, being followed later by more massive ones. In the range $0.5 < z < 2.0$ the GCMF has a strong variation that can be interpreted as a higher rate of galaxy mergers or as a strong evolution in the star formation history of these galaxies.

### The Galaxy Cosmological Mass Function [Cross-Listing]

We study the galaxy cosmological mass function (GCMF) in a semi-empirical relativistic approach using observational data provided by galaxy redshift surveys. Starting from the theory of Ribeiro & Stoeger (2003, arXiv:astro-ph/0304094) between the mass-to-light ratio, the selection function obtained from the luminosity function (LF) data and the luminosity density, the average luminosity $L$ and the average galactic mass $\mathcal{M}_g$ are computed in terms of the redshift. $\mathcal{M}_g$ is also alternatively estimated by a method that uses the galaxy stellar mass function (GSMF). Comparison of these two forms of deriving the average galactic mass allows us to infer a possible bias introduced by the selection criteria of the survey. We used the FORS Deep Field galaxy survey sample of 5558 galaxies in the redshift range $0.5 < z < 5.0$ and its LF Schechter parameters in the B-band, as well as this sample’s stellar mass-to-light ratio and its GSMF data. Assuming ${\mathcal{M}_{g_0}} \approx 10^{11} \mathcal{M}_\odot$ as the local value of the average galactic mass, the LF approach results in $L_{B} \propto (1+z)^{(2.40 \pm 0.03)}$ and $\mathcal{M}_g \propto (1+z)^{(1.1\pm0.2)}$. However, using the GSMF results produces $\mathcal{M}_g \propto (1+z)^{(-0.58 \pm 0.22)}$. We chose the latter result as it is less biased. We then obtained the theoretical quantities of interest, such as the differential number counts, to calculate the GCMF, which can be fitted by a Schechter function. The derived GCMF follows theoretical predictions in which the less massive objects form first, being followed later by more massive ones. In the range $0.5 < z < 2.0$ the GCMF has a strong variation that can be interpreted as a higher rate of galaxy mergers or as a strong evolution in the star formation history of these galaxies.

### Spectroscopic evidence for a low-mass black hole in SWIFT J1753.5-0127

The black hole (BH) candidate SWIFT J1753.5-0127 has remained active since the onset of its 2005 outburst. Emission lines in the optical spectrum were observed at the very beginning of the outburst, but since then the spectrum has been featureless making a precise BH mass estimation impossible. Here we present results from our optical and UV observations of SWIFT J1753.5-0127 taken in 2012-2013. Our new observations show extremely broad, double-peaked emission lines in the optical and UV spectra. The optical data also show narrow absorption and emission features with nearly synchronous and significant Doppler motions. A radial velocity study of these lines which we associate with the secondary star, yields a semi-amplitude of K_2=382 km/s. A time-series analysis of the spectral and photometric data revealed a possible orbital periodicity of 2.85 h, significantly shorter than the reported 3.2 h periodic signal by Zurita et al. (2008). The observed variability properties argue against a low orbital inclination angle and we present several observational arguments in favour of the BH interpretation. However, the measured radial velocity semi-amplitude of the donor star and the short orbital period imply that SWIFT J1753.5-0127 has one of the lowest measured mass function for a BH in a low-mass X-ray binary. We show that the compact object mass in excess of 5 Msun is highly improbable. Thus, SWIFT J1753.5-0127 is a BH binary that has one of the shortest orbital period and hosts probably one of the smallest stellar-mass BH found to date.

### Evidence for Two Distinct Stellar Initial Mass Functions : Probing for Clues to the Dichotomy

We present new measurements of the velocity dispersions of eleven Local Group globular clusters using spatially integrated spectra, to expand our sample of clusters with precise integrated-light velocity dispersions to 29, over 4 different host galaxies. This sample allows us to further our investigation of the stellar mass function among clusters, with a particular emphasis on a search for the driver of the apparent bimodal nature of the inferred stellar initial mass function. We confirm our previous result that clusters fall into two classes. If, as we argue, this behavior reflects a variation in the stellar initial mass function, the cause of that variation is not clear. The variations do not correlate with formation epoch as quantified by age, metallicity quantified by $[ {\rm Fe/H}]$, host galaxy, or internal structure as quantified by velocity dispersion, physical size, relaxation time, or luminosity. The stellar mass-to-light ratios, $\Upsilon_*$, of the high and low $\Upsilon_*$ cluster populations are well-matched to those found in recent studies of early and late type galaxies, respectively.

### The Dynamical Evolution of Stellar Black Holes in Globular Clusters

Our current understanding of the stellar initial mass function and of massive star evolution suggests that young globular clusters (GC) may have formed hundreds to thousands of stellar-mass black holes (BH), the remnants of massive stars with initial masses in the range 20 to 100 MSun. Birth kicks from supernova explosions may eject some of these BHs from their birth clusters, but many if not most should be retained. Using a Monte Carlo method we investigate the long-term dynamical evolution of GCs containing large numbers of BHs. Our parallel Monte Carlo code allows us to construct many models of clusters containing up to 1.6×10^6 stars initially. Here we describe numerical results for 42 models, covering a broad range of realistic initial conditions. In almost all cases we find that significant numbers of BHs (up to 10^3) are retained in the cluster all the way to the present. This is in contrast to previous theoretical expectations that most BHs in clusters should be ejected dynamically on a timescale of a few Gyr. The main reason for this difference is that core collapse driven by BHs (through the Spitzer "mass segregation instability") is easily reverted through three-body processes that form binaries, and involves only a small number of the most massive BHs, while lower-mass BHs remain well mixed with ordinary stars far away from the central cusp. Thus the rapid mass segregation of BHs in a cluster can drive gravothermal oscillations involving the most massive BHs, but it does not lead to a long-term physical separation of most BHs into a dynamically decoupled inner core. Combined with the recent detections of several BH X-ray binary candidates in Galactic GCs, our results suggest that BHs could still be present in large numbers in many GCs today, and that they may play a significant role in shaping the long-term evolution and the present-day dynamical structure of GCs.

### CLASH-VLT: The stellar mass function and stellar mass density profile of the z=0.44 cluster of galaxies MACS J1206.2-0847

Context. The study of the galaxy stellar mass function (SMF) in relation to the galaxy environment and the stellar mass density profile, rho(r), is a powerful tool to constrain models of galaxy evolution. Aims. We determine the SMF of the z=0.44 cluster of galaxies MACS J1206.2-0847 separately for passive and star-forming (SF) galaxies, in different regions of the cluster, from the center out to approximately 2 virial radii. We also determine rho(r) to compare it to the number density and total mass density profiles. Methods. We use the dataset from the CLASH-VLT survey. Stellar masses are obtained by SED fitting on 5-band photometric data obtained at the Subaru telescope. We identify 1363 cluster members down to a stellar mass of 10^9.5 Msolar. Results. The whole cluster SMF is well fitted by a double Schechter function. The SMFs of cluster SF and passive galaxies are statistically different. The SMF of the SF cluster galaxies does not depend on the environment. The SMF of the passive population has a significantly smaller slope (in absolute value) in the innermost (<0.50 Mpc), highest density cluster region, than in more external, lower density regions. The number ratio of giant/subgiant galaxies is maximum in this innermost region and minimum in the adjacent region, but then gently increases again toward the cluster outskirts. This is also reflected in a decreasing radial trend of the average stellar mass per cluster galaxy. On the other hand, the stellar mass fraction, i.e., the ratio of stellar to total cluster mass, does not show any significant radial trend. Conclusions. Our results appear consistent with a scenario in which SF galaxies evolve into passive galaxies due to density-dependent environmental processes, and eventually get destroyed very near the cluster center to become part of a diffuse intracluster medium. (abridged)

### CLASH-VLT: The stellar mass function and stellar mass density profile of the z=0.44 cluster of galaxies MACS J1206.2-0847 [Replacement]

Context. The study of the galaxy stellar mass function (SMF) in relation to the galaxy environment and the stellar mass density profile, rho(r), is a powerful tool to constrain models of galaxy evolution. Aims. We determine the SMF of the z=0.44 cluster of galaxies MACS J1206.2-0847 separately for passive and star-forming (SF) galaxies, in different regions of the cluster, from the center out to approximately 2 virial radii. We also determine rho(r) to compare it to the number density and total mass density profiles. Methods. We use the dataset from the CLASH-VLT survey. Stellar masses are obtained by SED fitting on 5-band photometric data obtained at the Subaru telescope. We identify 1363 cluster members down to a stellar mass of 10^9.5 Msolar. Results. The whole cluster SMF is well fitted by a double Schechter function. The SMFs of cluster SF and passive galaxies are statistically different. The SMF of the SF cluster galaxies does not depend on the environment. The SMF of the passive population has a significantly smaller slope (in absolute value) in the innermost (<0.50 Mpc), highest density cluster region, than in more external, lower density regions. The number ratio of giant/subgiant galaxies is maximum in this innermost region and minimum in the adjacent region, but then gently increases again toward the cluster outskirts. This is also reflected in a decreasing radial trend of the average stellar mass per cluster galaxy. On the other hand, the stellar mass fraction, i.e., the ratio of stellar to total cluster mass, does not show any significant radial trend. Conclusions. Our results appear consistent with a scenario in which SF galaxies evolve into passive galaxies due to density-dependent environmental processes, and eventually get destroyed very near the cluster center to become part of a diffuse intracluster medium.

### Galaxy And Mass Assembly: Deconstructing Bimodality - I. Red ones and blue ones

We measure the mass functions for generically red and blue galaxies, using a z < 0.12 sample of log M* > 8.7 field galaxies from the Galaxy And Mass Assembly (GAMA) survey. Our motivation is that, as we show, the dominant uncertainty in existing measurements stems from how ‘red’ and ‘blue’ galaxies have been selected/defined. Accordingly, we model our data as two naturally overlapping populations, each with their own mass function and colour-mass relation, which enables us characterise the two populations without having to specify a priori which galaxies are ‘red’ and ‘blue’. Our results then provide the means to derive objective operational definitions for the terms ‘red’ and ‘blue’, which are based on the phenomenology of the colour-mass diagrams. Informed by this descriptive modelling, we show that: 1.) after accounting for dust, the stellar colours of ‘blue’ galaxies do not depend strongly on mass; 2.) the tight, flat ‘dead sequence’ does not extend much below log M* ~ 10.5; instead, 3.) the stellar colours of ‘red’ galaxies vary rather strongly with mass, such that lower mass ‘red’ galaxies have bluer stellar populations; 4.) below log M* ~ 9.3, the ‘red’ population dissolves into obscurity, and it becomes problematic to talk about two distinct populations; as a consequence, 5.) it is hard to meaningfully constrain the shape, including the possibility of an upturn, of the ‘red’ galaxy mass function below log M* ~ 9. Points 1-4 provide meaningful targets for models of galaxy formation and evolution to aim for.

### Contribution of stripped nuclear clusters to globular cluster and ultra-compact dwarf galaxy populations

We use the Millennium II cosmological simulation combined with the semi-analytic galaxy formation model of Guo et al. (2011) to predict the contribution of galactic nuclei formed by the tidal stripping of nucleated dwarf galaxies to globular cluster (GC) and ultra-compact dwarf galaxy (UCD) populations of galaxies. We follow the merger trees of galaxies in clusters back in time and determine the absolute number and stellar masses of disrupted galaxies. We assume that at all times nuclei have a distribution in nucleus-to-galaxy mass and nucleation fraction of galaxies similar to that observed in the present day universe. Our results show stripped nuclei follow a mass function $N(M) \sim M^{-1.5}$ in the mass range $10^6 < M/M_\odot < 10^8$, significantly flatter than found for globular clusters. The contribution of stripped nuclei will therefore be most important among high-mass GCs and UCDs. For the Milky Way we predict between 1 and 3 star clusters more massive than $10^5 M_\odot$ come from tidally disrupted dwarf galaxies, with the most massive cluster formed having a typical mass of a few times $10^6 M_\odot$, like omega Centauri. For a galaxy cluster with a mass $7 \times 10^{13} M_\odot$, similar to Fornax, we predict $\sim$19 UCDs more massive than $2\times10^6 M_\odot$ and $\sim$9 UCDs more massive than $10^7 M_\odot$ within a projected distance of 300 kpc come from tidally stripped dwarf galaxies. The observed number of UCDs are $\sim$200 and 23, respectively. We conclude that most UCDs in galaxy clusters are probably simply the high mass end of the GC mass function.

### Gravitational Binding Energy in Charged Cylindrical Symmetry

We consider static cylindrically symmetric charged gravitating object with perfect fluid and investigate the gravitational binding energy. It is found that only the localized part of the mass function provides the gravitational binding energy, whereas the non-localized part generated by the electric coupling does not contribute for such energy.

### The HI Mass Function and Velocity Width Function of Void Galaxies in the Arecibo Legacy Fast ALFA Survey

We measure the HI mass function (HIMF) and velocity width function (WF) across environments over a range of masses $7.2<\log(M_{HI}/M_{\odot})<10.8$, and profile widths $1.3\log(km/s)<\log(W)<2.9\log(km/s)$, using a catalog of ~7,300 HI-selected galaxies from the ALFALFA Survey, located in the region of sky where ALFALFA and SDSS (Data Release 7) North overlap. We divide our galaxy sample into those that reside in large-scale voids (void galaxies) and those that live in denser regions (wall galaxies). We find the void HIMF to be well fit by a Schechter function with normalization $\Phi^*=(1.37\pm0.1)\times10^{-2} h^3Mpc^{-3}$, characteristic mass $\log(M^*/M_{\odot})+2\log h_{70}=9.86\pm0.02$, and low-mass-end slope $\alpha=-1.29\pm0.02$. Similarly, for wall galaxies, we find best-fitting parameters $\Phi^*=(1.82\pm0.03)\times10^{-2} h^3Mpc^{-3}$, $\log(M^*/M_{\odot})+2\log h_{70}=10.00\pm0.01$, and $\alpha=-1.35\pm0.01$. We conclude that void galaxies typically have slightly lower HI masses than their non-void counterparts, which is in agreement with the dark matter halo mass function shift in voids assuming a simple relationship between DM mass and HI mass. We also find that the low-mass slope of the void HIMF is similar to that of the wall HIMF suggesting that there is either no excess of low-mass galaxies in voids or there is an abundance of intermediate HI mass galaxies. We fit a modified Schechter function to the ALFALFA void WF and determine its best-fitting parameters to be $\Phi^*=0.21\pm0.1 h^3Mpc^{-3}$, $\log(W^*)=2.13\pm0.3$, $\alpha=0.52\pm0.5$ and high-width slope $\beta=1.3\pm0.4$. For wall galaxies, the WF parameters are: $\Phi^*=0.022\pm0.009 h^3Mpc^{-3}$, $\log(W^*)=2.62\pm0.5$, $\alpha=-0.64\pm0.2$ and $\beta=3.58\pm1.5$. Because of large uncertainties on the void and wall width functions, we cannot conclude whether the WF is dependent on the environment.

### The HI Mass Function and Velocity Width Function of Void Galaxies in the Arecibo Legacy Fast ALFA Survey [Replacement]

We measure the HI mass function (HIMF) and velocity width function (WF) across environments over a range of masses $7.2<\log(M_{HI}/M_{\odot})<10.8$, and profile widths $1.3\log(km/s)<\log(W)<2.9\log(km/s)$, using a catalog of ~7,300 HI-selected galaxies from the ALFALFA Survey, located in the region of sky where ALFALFA and SDSS (Data Release 7) North overlap. We divide our galaxy sample into those that reside in large-scale voids (void galaxies) and those that live in denser regions (wall galaxies). We find the void HIMF to be well fit by a Schechter function with normalization $\Phi^*=(1.37\pm0.1)\times10^{-2} h^3Mpc^{-3}$, characteristic mass $\log(M^*/M_{\odot})+2\log h_{70}=9.86\pm0.02$, and low-mass-end slope $\alpha=-1.29\pm0.02$. Similarly, for wall galaxies, we find best-fitting parameters $\Phi^*=(1.82\pm0.03)\times10^{-2} h^3Mpc^{-3}$, $\log(M^*/M_{\odot})+2\log h_{70}=10.00\pm0.01$, and $\alpha=-1.35\pm0.01$. We conclude that void galaxies typically have slightly lower HI masses than their non-void counterparts, which is in agreement with the dark matter halo mass function shift in voids assuming a simple relationship between DM mass and HI mass. We also find that the low-mass slope of the void HIMF is similar to that of the wall HIMF suggesting that there is either no excess of low-mass galaxies in voids or there is an abundance of intermediate HI mass galaxies. We fit a modified Schechter function to the ALFALFA void WF and determine its best-fitting parameters to be $\Phi^*=0.21\pm0.1 h^3Mpc^{-3}$, $\log(W^*)=2.13\pm0.3$, $\alpha=0.52\pm0.5$ and high-width slope $\beta=1.3\pm0.4$. For wall galaxies, the WF parameters are: $\Phi^*=0.022\pm0.009 h^3Mpc^{-3}$, $\log(W^*)=2.62\pm0.5$, $\alpha=-0.64\pm0.2$ and $\beta=3.58\pm1.5$. Because of large uncertainties on the void and wall width functions, we cannot conclude whether the WF is dependent on the environment.

### 2FGL J1653.6-0159: A New Low in Evaporating Pulsar Binary Periods

We have identified an optical binary with orbital period P_b=4488s as the probable counterpart of the Fermi source 2FGL J1653.6-0159. Although pulsations have not yet been detected, the source properties are consistent with an evaporating millisecond pulsar binary; this P_b=75min is the record low for a spin-powered system. The heated side of the companion shows coherent radial velocity variations, with amplitude K=666.9+/-7.5 km/s for a large mass function of f(M)=1.60+/-0.05 M_sun. This heating suggests a pulsar luminosity ~3×10^34 erg/s. The colors and spectra show additional hard emission dominating at binary minimum. This system is similar to PSR J1311-3430, with a low mass H-depleted companion, a dense shrouding wind and, likely, a large pulsar mass.

### 2FGL J1653.6-0159: A New Low in Evaporating Pulsar Binary Periods [Replacement]

We have identified an optical binary with orbital period P_b=4488s as the probable counterpart of the Fermi source 2FGL J1653.6-0159. Although pulsations have not yet been detected, the source properties are consistent with an evaporating millisecond pulsar binary; this P_b=75min is the record low for a spin-powered system. The heated side of the companion shows coherent radial velocity variations, with amplitude K=666.9+/-7.5 km/s for a large mass function of f(M)=1.60+/-0.05 M_sun. This heating suggests a pulsar luminosity ~3×10^34 erg/s. The colors and spectra show additional hard emission dominating at binary minimum. Its origin is, at present, unclear. This system is similar to PSR J1311-3430, with a low mass H-depleted companion, a dense shrouding wind and, likely, a large pulsar mass.

### The mass evolution of the first galaxies: stellar mass functions and star formation rates at $4 < z < 7$ in the CANDELS GOODS-South field

We measure new estimates for the galaxy stellar mass function and star formation rates for samples of galaxies at $z \sim 4,~5,~6~\&~7$ using data in the CANDELS GOODS South field. The deep near-infrared observations allow us to construct the stellar mass function at $z \geq 6$ directly for the first time. We estimate stellar masses for our sample by fitting the observed spectral energy distributions with synthetic stellar populations, including nebular line and continuum emission. The observed UV luminosity functions for the samples are consistent with previous observations, however we find that the observed $M_{UV}$ – M$_{*}$ relation has a shallow slope more consistent with a constant mass to light ratio and a normalisation which evolves with redshift. Our stellar mass functions have steep low-mass slopes ($\alpha \approx -1.9$), steeper than previously observed at these redshifts and closer to that of the UV luminosity function. Integrating our new mass functions, we find the observed stellar mass density evolves from $\log_{10} \rho_{*} = 6.64^{+0.58}_{-0.89}$ at $z \sim 7$ to $7.36\pm0.06$ $\text{M}_{\odot} \text{Mpc}^{-3}$ at $z \sim 4$. Finally, combining the measured UV continuum slopes ($\beta$) with their rest-frame UV luminosities, we calculate dust corrected star-formation rates (SFR) for our sample. We find the specific star-formation rate for a fixed stellar mass increases with redshift whilst the global SFR density falls rapidly over this period. Our new SFR density estimates are higher than previously observed at this redshift.

### The low mass star and sub-stellar populations of the 25 Orionis group

We present the results of a survey of the low mass star and brown dwarf population of the 25 Orionis group. Using optical photometry from the CIDA Deep Survey of Orion, near IR photometry from the Visible and Infrared Survey Telescope for Astronomy and low resolution spectroscopy obtained with Hectospec at the MMT, we selected 1246 photometric candidates to low mass stars and brown dwarfs with estimated masses within $0.02 \lesssim M/M_\odot \lesssim 0.8$ and spectroscopically confirmed a sample of 77 low mass stars as new members of the cluster with a mean age of $\sim$7 Myr. We have obtained a system initial mass function of the group that can be well described by either a Kroupa power-law function with indices $\alpha_3=-1.73\pm0.31$ and $\alpha_2=0.68\pm0.41$ in the mass ranges $0.03\leq M/M_\odot\leq 0.08$ and $0.08\leq M/M_\odot\leq0.5$ respectively, or a Scalo log-normal function with coefficients $m_c=0.21^{+0.02}_{-0.02}$ and $\sigma=0.36\pm0.03$ in the mass range $0.03\leq M/M_\odot\leq0.8$. From the analysis of the spatial distribution of this numerous candidate sample, we have confirmed the East-West elongation of the 25 Orionis group observed in previous works, and rule out a possible southern extension of the group. We find that the spatial distributions of low mass stars and brown dwarfs in 25 Orionis are statistically indistinguishable. Finally, we found that the fraction of brown dwarfs showing IR excesses is higher than for low mass stars, supporting the scenario in which the evolution of circumstellar discs around the least massive objects could be more prolonged.

### Nonlinear evolution of dark matter subhalos and applications to warm dark matter [Replacement]

We describe the methodology to include nonlinear evolution, including tidal effects, in the computation of subhalo distribution properties in both cold (CDM) and warm (WDM) dark matter universes. Using semi-analytic modeling, we include effects from dynamical friction, tidal stripping, and tidal heating, allowing us to dynamically evolve the subhalo distribution. We calibrate our nonlinear evolution scheme to the CDM subhalo mass function in the Aquarius N-body simulation, producing a subhalo mass function within the range of simulations. We find tidal effects to be the dominant mechanism of nonlinear evolution in the subhalo population. Finally, we compute the subhalo mass function for $m_\chi=1.5$ keV WDM including the effects of nonlinear evolution, and compare radial number densities and mass density profiles of subhalos in CDM and WDM models. We show that all three signatures differ between the two dark matter models, suggesting that probes of substructure may be able to differentiate between them.

### Nonlinear evolution of dark matter subhalos and applications to warm dark matter

We describe the methodology to include nonlinear evolution, including tidal effects, in the computation of subhalo distribution properties in both cold (CDM) and warm (WDM) dark matter universes. Using semi-analytic modeling, we include effects from dynamical friction, tidal stripping, and tidal heating, allowing us to dynamically evolve the subhalo distribution. We calibrate our nonlinear evolution scheme to the CDM subhalo mass function in the Aquarius N-body simulation, producing a subhalo mass function within the range of simulations. We find tidal effects to be the dominant mechanism of nonlinear evolution in the subhalo population. Finally, we compute the subhalo mass function for $m_\chi=1.5$ keV WDM including the effects of nonlinear evolution, and compare radial number densities and mass density profiles of subhalos in CDM and WDM models. We show that all three signatures differ between the two dark matter models, suggesting that probes of substructure may be able to differentiate between them.

### Galaxy And Mass Assembly (GAMA): Stellar mass functions by Hubble type

We present an estimate of the galaxy stellar mass function and its division by morphological type in the local (0.025 < z < 0.06) Universe. Adopting robust morphological classifications as previously presented (Kelvin et al.) for a sample of 3,727 galaxies taken from the Galaxy And Mass Assembly survey, we define a local volume and stellar mass limited sub-sample of 2,711 galaxies to a lower stellar mass limit of M = 10^9.0 M_sun. We confirm that the galaxy stellar mass function is well described by a double Schechter function given by M* = 10^10.64 M_sun, {\alpha}1 = -0.43, {\phi}*1 = 4.18 dex^-1 Mpc^-3, {\alpha}2 = -1.50 and {\phi}*2 = 0.74 dex^-1 Mpc^-3. The constituent morphological-type stellar mass functions are well sampled above our lower stellar mass limit, excepting the faint little blue spheroid population of galaxies. We find approximately 71+3-4% of the stellar mass in the local Universe is found within spheroid dominated galaxies; ellipticals and S0-Sas. The remaining 29+4-3% falls predominantly within late type disk dominated systems, Sab-Scds and Sd-Irrs. Adopting reasonable bulge-to-total ratios implies that approximately half the stellar mass today resides in spheroidal structures, and half in disk structures. Within this local sample, we find approximate stellar mass proportions for E : S0-Sa : Sab-Scd : Sd-Irr of 34 : 37 : 24 : 5.

### The EAGLE project: Simulating the evolution and assembly of galaxies and their environments [Replacement]

We introduce the Virgo Consortium’s EAGLE project, a suite of hydrodynamical simulations that follow the formation of galaxies and black holes in representative volumes. We discuss the limitations of such simulations in light of their finite resolution and poorly constrained subgrid physics, and how these affect their predictive power. One major improvement is our treatment of feedback from massive stars and AGN in which thermal energy is injected into the gas without the need to turn off cooling or hydrodynamical forces, allowing winds to develop without predetermined speed or mass loading factors. Because the feedback efficiencies cannot be predicted from first principles, we calibrate them to the z~0 galaxy stellar mass function and the amplitude of the galaxy-central black hole mass relation, also taking galaxy sizes into account. The observed galaxy mass function is reproduced to $\lesssim 0.2$ dex over the full mass range, $10^8 < M_*/M_\odot \lesssim 10^{11}$, a level of agreement close to that attained by semi-analytic models, and unprecedented for hydrodynamical simulations. We compare our results to a representative set of low-redshift observables not considered in the calibration, and find good agreement with the observed galaxy specific star formation rates, passive fractions, Tully-Fisher relation, total stellar luminosities of galaxy clusters, and column density distributions of intergalactic CIV and OVI. While the mass-metallicity relations for gas and stars are consistent with observations for $M_* \gtrsim 10^9 M_\odot$, they are insufficiently steep at lower masses. The gas fractions and temperatures are too high for clusters of galaxies, but for groups these discrepancies can be resolved by adopting a higher heating temperature in the subgrid prescription for AGN feedback. EAGLE constitutes a valuable new resource for studies of galaxy formation.

### The EAGLE project: Simulating the evolution and assembly of galaxies and their environments

We introduce the Virgo Consortium’s EAGLE project, a suite of hydrodynamical simulations that follow the formation of galaxies and black holes in representative volumes. We discuss the limitations of such simulations in light of their finite resolution and poorly constrained subgrid physics, and how these affect their predictive power. One major improvement is our treatment of feedback from massive stars and AGN in which thermal energy is injected into the gas without the need to turn off cooling or hydrodynamical forces, allowing winds to develop without predetermined speed or mass loading factors. Because the feedback efficiencies cannot be predicted from first principles, we calibrate them to the z~0 galaxy stellar mass function and the amplitude of the galaxy-central black hole mass relation, also taking galaxy sizes into account. The observed galaxy mass function is reproduced to $\lesssim 0.2$ dex over the full mass range, $10^8 < M_*/M_\odot \lesssim 10^{11}$, a level of agreement close to that attained by semi-analytic models, and unprecedented for hydrodynamical simulations. We compare our results to a representative set of low-redshift observables not considered in the calibration, and find good agreement with the observed galaxy specific star formation rates, passive fractions, Tully-Fisher relation, total stellar luminosities of galaxy clusters, and column density distributions of intergalactic CIV and OVI. While the mass-metallicity relations for gas and stars are consistent with observations for $M_* \gtrsim 10^9 M_\odot$, they are insufficiently steep at lower masses. The gas fractions and temperatures are too high for clusters of galaxies, but for groups these discrepancies can be resolved by adopting a higher heating temperature in the subgrid prescription for AGN feedback. EAGLE constitutes a valuable new resource for studies of galaxy formation.

### The stellar initial mass function of early type galaxies from low to high stellar velocity dispersion: homogeneous analysis of ATLAS$^{\rm 3D}$ and Sloan Lens ACS galaxies [Replacement]

We present an investigation about the shape of the initial mass function (IMF) of early-type galaxies (ETGs), based on a joint lensing and dynamical analysis, and on stellar population synthesis models, for a sample of 55 lens ETGs identified by the Sloan Lens ACS (SLACS) Survey. We construct axisymmetric dynamical models based on the Jeans equations which allow for orbital anisotropy and include a dark matter halo. The models reproduce in detail the observed \textit{HST} photometry and are constrained by the total projected mass within the Einstein radius and the stellar velocity dispersion ($\sigma$) within the SDSS fibers. Comparing the dynamically-derived stellar mass-to-light ratios $(M_*/L)_{\rm dyn}$, obtained for an assumed halo slope $\rho_{\rm h}\propto r^{-1}$, to the stellar population ones $(M_*/L)_{\rm pop}$, derived from full-spectrum fitting and assuming a Salpeter IMF, we infer the mass normalization of the IMF. Our results confirm the previous analysis by the SLACS team that the mass normalization of the IMF of high $\sigma$ galaxies is consistent on average with a Salpeter slope. Our study allows for a fully consistent study of the trend between IMF and $\sigma$ for both the SLACS and \ATLAS samples, which explore quite different $\sigma$ ranges. The two samples are highly complementary, the first being essentially $\sigma$ selected, and the latter volume-limited and nearly mass selected. We find that the two samples merge smoothly into a single trend of the form $\log\alpha =(0.38\pm0.04)\times\log(\sigma_{\rm e}/200\,\mathrm{km~s}^{-1})+(-0.06\pm0.01)$, where $\alpha=(M_*/L)_{\rm dyn}/(M_*/L)_{\rm pop}$ and $\sigma_{\rm e}$ is the luminosity averaged $\sigma$ within one effective radius $R_{\rm e}$. This is consistent with a systematic variation of the IMF normalization from Kroupa to Salpeter in the interval $\sigma_{\rm e}\approx90-270\,\mathrm{km~s}^{-1}$.

### The stellar initial mass function of early type galaxies from low to high stellar velocity dispersion: homogeneous analysis of ATLAS$^{\rm 3D}$ and Sloan Lens ACS galaxies

We present an investigation about the shape of the initial mass function (IMF) of early-type galaxies (ETGs), based on a joint lensing and dynamical analysis, and on stellar population synthesis models, for a sample of 55 lens ETGs identified by the Sloan Lens ACS (SLACS) Survey. We construct axisymmetric dynamical models based on the Jeans equations which allow for orbital anisotropy and include a dark matter halo. The models reproduce in detail the observed HST photometry and are constrained by the total projected mass within the Einstein radius and the stellar velocity dispersion ($\sigma$) within the SDSS fibers. Comparing the dynamically-derived stellar mass-to-light ratios $(M/L)_{\rm dyn}$ to the stellar population ones $(M/L)_{\rm pop}$, derived from full-spectrum fitting and assuming a Salpeter IMF, we infer the mass normalization of the IMF. Our results confirm the previous analysis by the SLACS team that the mass normalization of the IMF of high $\sigma$ galaxies is consistent on average with a Salpeter slope. Our study allows for a fully consistent study of the trend between IMF and $\sigma$ for both the SLACS and ATLAS$^{\rm 3D}$ samples, which explore quite different $\sigma$ ranges. The two samples are highly complementary, the first being essentially $\sigma$ selected, and the latter volume-limited and nearly mass selected. We find that the two samples merge smoothly into a single trend of the form $\log\alpha =(0.38\pm0.04)\times\log(\sigma_e/200\, km s^{-1})+(-0.06\pm0.01)$, where $\alpha=(M/L)_{\rm dyn}/(M/L)_{\rm pop}$ and $\sigma_e$ is the luminosity averaged $\sigma$ within one effective radius $R_e$. This is consistent with a systematic variation of the IMF normalization from Kroupa to Salpeter in the interval $\sigma_e\approx 90-270\,km s^{-1}$.

### Constraints on Core Collapse from the Black Hole Mass Function

We model the observed black hole mass function under the assumption that black hole formation is controlled by the compactness of the stellar core at the time of collapse. Low compactness stars are more likely to explode as supernovae and produce neutron stars, while high compactness stars are more likely to be failed supernovae that produce black holes with the mass of the helium core of the star. Using three sequences of stellar models and marginalizing over a model for the completeness of the black hole mass function, we find that the compactness xi(2.5) above which 50% of core collapses produce black holes is xi(2.5)=0.24 (0.15 < xi(2.5) < 0.37) at 90% confidence). While models with a sharp transition between successful and failed explosions are always the most likely, the width of the transition between the minimum compactness for black hole formation and the compactness above which all core collapses produce black holes is not well constrained. The models also predict that f=0.18 (0.09 < f < 0.39) of core collapses fail assuming a minimum mass for core collapse of 8Msun. We tested four other criteria for black hole formation based on xi(2.0) and xi(3.0), the compactnesses at enclosed masses of 2.0 or 3.0 rather than 2.5Msun, the mass of the iron core, and the mass inside the oxygen burning shell. We found that xi(2.0) works as well as xi(2.5), while the compactness xi(3.0) works significantly worse, as does using the iron core mass or the mass enclosed by the oxygen burning shell. As expected from the high compactness of 20-25Msun stars, black hole formation in this mass range provides a natural explanation of the red supergiant problem.

### The stellar initial mass function at z>1

We explore the stellar initial mass function (IMF) of a sample of 49 massive quiescent galaxies (MQGs) at 0.9<z<1.5. We base our analysis on intermediate resolution spectro-photometric data in the GOODS-N field taken in the near-infrared and optical with the HST/WFC3 G141 grism and the Survey for High-z Absorption Red and Dead Sources (SHARDS). To constrain the slope of the IMF, we have measured the TiO2 spectral feature, whose strength depends strongly on the content of low-mass stars, as well as on stellar age. Using ultraviolet to near-infrared individual and stacked spectral energy distributions, we have independently estimated the stellar ages of our galaxies. For the heaviest z~1 MQGs (M > 10^11.0 Msun) we find an average age of 1.7$\pm$0.3 Gyr and a bottom-heavy IMF ({\Gamma}=3.2$\pm$0.2). Lighter MQGs (10^10.5 < M < 10^11.0 Msun) at the same redshift are younger on average (1.0$\pm$0.2 Gyr) and present a shallower IMF slope ({\Gamma}=2.7$\pm$0.3). Our results are in good agreement with the findings about the IMF slope in early-type galaxies of similar mass in the present-day Universe. This suggests that the IMF, a key characteristic of the stellar populations in galaxies, is bottom-heavier for more massive galaxies and has remained unchanged in the last ~8 Gyr.

### Gravitational collapse of generalised Vaidya spacetime [Replacement]

We study the gravitational collapse of a generalised Vaidya spacetime in the context of the Cosmic Censorship hypothesis. We develop a general mathematical framework to study the conditions on the mass function so that future directed non-spacelike geodesics can terminate at the singularity in the past. Thus our result generalises earlier works on gravitational collapse of the combinations of Type-I and Type-II matter fields. Our analysis shows transparently that there exist classes of generalised Vaidya mass functions for which the collapse terminates with a locally naked central singularity. We calculate the strength of the these singularities to show that they are strong curvature singularities and there can be no extension of spacetime through them.

### Gravitational collapse of generalised Vaidya spacetime [Cross-Listing]

We study the gravitational collapse of a generalised Vaidya spacetime in the context of the Cosmic Censorship hypothesis. We develop a general mathematical framework to study the conditions on the mass function so that future directed non-spacelike geodesics can terminate at the singularity in the past. Thus our result generalises earlier works on gravitational collapse of the combinations of Type-I and Type-II matter fields. Our analysis shows transparently that there exist classes of generalised Vaidya mass functions for which the collapse terminates with a locally naked central singularity. We calculate the strength of the these singularities to show that they are strong curvature singularities and there can be no extension of spacetime through them.

### Gravitational collapse of generalised Vaidya spacetime [Replacement]

We study the gravitational collapse of a generalised Vaidya spacetime in the context of the Cosmic Censorship hypothesis. We develop a general mathematical framework to study the conditions on the mass function so that future directed non-spacelike geodesics can terminate at the singularity in the past. Thus our result generalises earlier works on gravitational collapse of the combinations of Type-I and Type-II matter fields. Our analysis shows transparently that there exist classes of generalised Vaidya mass functions for which the collapse terminates with a locally naked central singularity. We calculate the strength of the these singularities to show that they are strong curvature singularities and there can be no extension of spacetime through them.

### The Extended Zel'dovich Mass Functions of Clusters and Isolated Clusters in the Presence of Primordial Non-Gaussianity

We present new formulae for the mass functions of the clusters and the isolated clusters with non Gaussian initial conditions. For this study, we adopt the Extended Zel’dovich (EZL) model as a basic framework, focusing on the case of primordial non-Gaussianity of the local type whose degree is quantified by a single parameter $f_{nl}$. By making a quantitative comparison with the N-body results, we first demonstrate that the EZL formula with the constant values of three fitting parameters still works remarkably well for the local $f_{nl}$ case. We also modify the EZL formula to find an analytic expression for the mass function of isolated clusters which turns out to have only one fitting parameter other than the overall normalization factor and showed that the modified EZL formula with a constant value of the fitting parameter matches excellently the N-body results with various values of $f_{nl}$ at various redshifts. Given the simplicity of the generalized EZL formulae and their good agreements with the numerical results, we finally conclude that the EZL mass functions of the massive clusters and isolated clusters should be useful as an analytic guideline to constrain the scale dependence of the primordial non-Gaussianity of the local type.

### Can molecular clouds live long?

It is generally accepted that the lifetime of molecular clouds does not exceed $3\cdot 10^7$ yr due to disruption by stellar feedback. We put together some arguments giving evidence that a substantial fraction of molecular clouds (primarily in the outer regions of a disc) may avoid destruction process for at least $10^8$ yr or even longer. A molecular cloud can live long if massive stars are rare or absent. Massive stars capable to destroy a cloud may not form for a long time if a cloud is low massive, or stellar initial mass function is top-light, or if there is a delay of the beginning of active star formation. A long duration of the inactive phase of clouds may be reconciled with the low amount of the observed starless giant molecular clouds if to propose that they were preceded by slowly contraction phase of the magnetized dark gas, non-detected in CO-lines.

### Monte Carlo simulations of post-common-envelope white dwarf + main sequence binaries: The effects of including recombination energy

Detached WD+MS PCEBs are perhaps the most suitable objects for testing predictions of close-compact binary-star evolution theories, in particular, CE evolution. The population of WD+MS PCEBs has been simulated by several authors in the past and compared with observations. However, most of those predictions did not take the possible contributions to the envelope ejection from additional sources of energy (mostly recombination energy) into account. Here we update existing binary population models of WD+MS PCEBs by assuming that a fraction of the recombination energy available within the envelope contributes to ejecting the envelope. We performed Monte Carlo simulations of 10^7 MS+MS binaries for 9 different models using standard assumptions for the initial primary mass function, binary separations, and initial-mass-ratio distribution and evolved these systems using the publicly available BSE code. Including a fraction of recombination energy leads to a clear prediction of a large number of long orbital period (>~10 days) systems mostly containing high-mass WDs. The fraction of systems with He-core WD primaries increases with the CE efficiency and the existence of very low-mass He WDs is only predicted for high values of the CE efficiency (>~0.5). All models predict on average longer orbital periods for PCEBs containing C/O-core WDs than for PCEBs containing He WDs. This effect increases with increasing values of both efficiencies. Longer periods after the CE phase are also predicted for systems containing more massive secondary stars. The initial-mass-ratio distribution affects the distribution of orbital periods, especially the distribution of secondary star masses. Our simulations, in combination with a large and homogeneous observational sample, can provide constraints on the values of the CE efficiencies, as well as on the initial-mass-ratio distribution for MS+MS binary stars.

### Mass segregation in the outer halo globular cluster Palomar 14

We present evidence for mass segregation in the outer-halo globular cluster Palomar 14, which is intuitively unexpected since its present-day two-body relaxation time significantly exceeds the Hubble time. Based on archival Hubble Space Telescope imaging, we analyze the radial dependence of the stellar mass function in the cluster’s inner 39.2 pc in the mass range of 0.53-0.80 M_sun, ranging from the main-sequence turn-off down to a V-band magnitude of 27.1 mag. The mass function at different radii is well approximated by a power law and rises from a shallow slope of 0.6+/-0.2 in the cluster’s core to a slope of 1.6+/-0.3 beyond 18.6 pc. This is seemingly in conflict with the finding by Beccari et al. (2011), who interpret the cluster’s non-segregated population of (more massive) blue straggler stars, compared to (less massive) red giants and horizontal branch stars, as evidence that the cluster has not experienced dynamical segregation yet. We discuss how both results can be reconciled. Our findings indicate that the cluster was either primordially mass-segregated and/or used to be significantly more compact in the past. For the latter case, we propose tidal shocks as the mechanism driving the cluster’s expansion, which would imply that Palomar 14 is on a highly eccentric orbit. Conversely, if the cluster formed already extended and with primordial mass segregation, this could support an accretion origin of the cluster.

(Abridged) We aim at identifying the least massive population of the solar metallicity, young (120 Myr), nearby (133.5 pc) Pleiades star cluster with the ultimate goal of understanding the physical properties of intermediate-age, free-floating, low-mass brown dwarfs and giant planetary-mass objects, and deriving the cluster substellar mass function across the deuterium-burning mass limit at ~0.012 Msol. We performed a deep photometric and astrometric J- and H-band survey covering an area of ~0.8 deg^2. The images with completeness and limiting magnitudes of J,H ~ 20.2 and ~ 21.5 mag were acquired ~9 yr apart (proper motion precision of +/-6 mas/yr). J- and H-band data were complemented with Z, K, and mid-infrared magnitudes up to 4.6 micron coming from UKIDSS, WISE, and follow-up observations of our own. Pleiades member candidates were selected to have proper motions compatible with that of the cluster, and colors following the known Pleiades sequence in the interval J = 15.5-8.8 mag, and Z_UKIDSS – J > 2.3 mag or Z nondetections for J > 18.8 mag. We found a neat sequence of astrometric and photometric Pleiades substellar member candidates in the intervals J = 15.5-21.2 mag and ~0.072-0.008 Msol. The faintest objects show very red near- and mid-infrared colors exceeding those of field high-gravity dwarfs by >0.5 mag. The Pleiades photometric sequence does not show any color turn-over because of the presence of photospheric methane absorption down to J = 20.3 mag, which is about 1 mag fainter than predicted by the color-computed models. Pleiades brown dwarfs have a proper motion dispersion of 6.4-7.5 mas/yr and are dynamically relaxed at the age of the cluster. The Pleiades mass function extends down to the deuterium burning-mass threshold, with a slope fairly similar to that of other young star clusters and stellar associations.

### Nonlinear Bias of Cosmological Halo Formation in the Early Universe

(Abridged) We present estimates of the nonlinear bias of cosmological haloes spanning a wide range in mass, from $\sim 10^{5} M_\odot$ to $\sim 10^{12} M_\odot$, by combining the empirical, average mass function derived from a suite of high-resolution cosmological N-body simulations, and the theoretical nonlinear bias parameter based on the extended Press-Schechter formalism. The halo bias is expressed in terms of the mean bias and stochasticity as a function of local overdensity ($\delta$), based on different filtering scales, which is realized as the density of individual cells in uniform grids. The sampled overdensities span a range large enough to include both linear and nonlinear regimes, allowing us to obtain the fully nonlinear bias effect on the formation of haloes. A very strong correlation between $\delta$ and halo population overdensity $\delta_h$, or nonlinear bias, is found, along with sizable stochasticity. We find that the empirical mean halo bias matches, with good accuracy, the prediction by the peak-background split method based on the excursion set formalism, as long as the empirical, globally-averaged halo mass function is used. Consequently, this bias formalism is insensitive to uncertainties caused by varying halo identification schemes, and can be applied generically. We also find that the probability distribution function of biased halo numbers has wider distribution than the pure Poisson shot noise, which is attributed to the sub-cell scale halo correlation. We explicitly calculate this correlation function and show that both overdense and underdense regions have positive correlation, leading to stochasticity larger than the Poisson shot noise in the range of haloes and halo-collapse epochs we study. Our results can be used to generate mock halo catalogues once a density field is given, such as in cosmological N-body simulations of structure formation. (Abridged)

### Stochastic microhertz gravitational radiation from stellar convection

High-Reynolds-number turbulence driven by stellar convection in main-sequence stars generates stochastic gravitational radiation. We calculate the wave-strain power spectral density as a function of the zero-age main-sequence mass for an individual star and for an isotropic, universal stellar population described by the Salpeter initial mass function and redshift-dependent Hopkins-Beacom star formation rate. The spectrum is a broken power law, which peaks near the turnover frequency of the largest turbulent eddies. The signal from the Sun dominates the universal background. For the Sun, the far-zone power spectral density peaks at $S(f_\mathrm{peak}) = 5.2 \times 10^{-52}$ Hz$^{-1}$ at frequency $f_\mathrm{peak} = 2.3 \times 10^{-7}$ Hz. However, at low observing frequencies $f < 3 \times 10^{-4}$ Hz, the Earth lies inside the Sun’s near zone and the signal is amplified to $S_\mathrm{near}(f_\mathrm{peak}) = 4.1 \times 10^{-27}$ Hz$^{-1}$ because the wave strain scales more steeply with distance ($\propto d^{-5}$) in the near zone than in the far zone ($\propto d^{-1}$). Hence the Solar signal may prove relevant for pulsar timing arrays. Other individual sources and the universal background fall well below the projected sensitivities of the Laser Interferometer Space Antenna and next-generation pulsar timing arrays. Stellar convection sets a fundamental noise floor for more sensitive stochastic gravitational-wave experiments in the more distant future.

### Reconciling the observed star-forming sequence with the observed stellar mass function

We examine the connection between the observed "star-forming sequence" (SFR $\propto$ M$_{*}^{\alpha}$) and the observed evolution of the stellar mass function between $0.2 < z < 2.5$. We find that the star-forming sequence cannot have a slope $\alpha$ $\lesssim$ 0.9 at all masses and redshifts, as this results in a much higher number density at $10 < \log(\mathrm{M}) < 11$ by $z=1$ than is observed. We show that a transition in the slope of the star-forming sequence, such that $\alpha=1$ at $\log(M)<10.5$ and $\alpha=0.7-0.13z$ \citep{whitaker12} at $\log(M)>10.5$, greatly improves agreement with the evolution of the stellar mass function. We then construct a star-forming sequence which exactly reproduces the evolution of the mass function. This star-forming sequence is also well-described by a broken-power law, with a shallow slope at high masses and a steep slope at low masses. At $z=2$, it is offset by $\sim$0.3 dex from the observed star-forming sequence, consistent with the mild disagreement between the cosmic SFR and the growth of the stellar mass density in recent determinations of the mass function. It is unclear whether this problem stems from errors in stellar mass estimates, errors in SFRs, or other effects. We show that a mass-dependent slope is also seen in self-consistent theoretical models of galaxy evolution, including semi-analytical, hydrodynamical, and abundance-matching models. As part of the analysis, we show that neither mergers nor an unknown population of quiescent galaxies are likely to reconcile the evolution of the low-mass stellar mass function and the observed star-forming sequence. These results are supported by observations from Whitaker et al. (2014).

### Number Counts and Dynamical Vacuum Cosmologies

We study non-linear structure formation in an interacting model of the dark sector of the Universe in which the dark energy density decays linearly with the Hubble parameter, $\rho_{\Lambda} \propto H$, leading to a constant-rate creation of cold dark matter. We derive all relevant expressions to calculate the mass function and the cluster number density using the Sheth-Torman formalism and show that the effect of the interaction process is to increase the number of bound structures of large masses ($M \gtrsim 10^{14} M_{\odot}h^{-1}$) when compared to the standard $\Lambda$CDM model. Since these models are not reducible to each other, this number counts signature can in principle be tested in future surveys.

### Statistics of Dark Matter Halos in the Excursion Set Peak Framework

We derive approximated, yet very accurate analytical expressions for the abundance and clustering properties of dark matter halos in the excursion set peak framework; the latter relies on the standard excursion set approach, but also includes the effects of a realistic filtering of the density field, a mass-dependent threshold for collapse, and the prescription from peak theory that halos tend to form around density maxima. We find that our approximations work excellently for diverse power spectra, collapse thresholds and density filters. Moreover, when adopting a cold dark matter power spectra, a tophat filtering and a mass-dependent collapse threshold (supplemented with conceivable scatter), our approximated halo mass function and halo bias represent very well the outcomes of cosmological $N-$body simulations.

### Physical properties, kinetics and mass function of 12 northern infrared dark clouds

The physical, chemical and kinetic characteristics of 12 northern infrared dark clouds (IRDCs) are systematic studied using the $\rm ^{13}CO$ (1-0) and $\rm C^{18}O$ (1-0) lines, observed with the PMO 13.7 m radio telescope, the 1.1 mm Bolocam Galactic Plane Survey (BGPS) data and GLIMPSE Spitzer IRAC $\rm 8 \,\mu m$ data. The molecular lines emission and 1.1 mm continuum emission almost coincide in morphology for each IRDC and both are associated well with the IRDCs. 10 IRDCs present the filamentary structure and substructures. Totally, 41 IRDC cores are identified and a statistic research for them shows that the northern IRDC cores have a typical excitation temperature $8\sim10$ K, a integrated intensity ratio of $\rm ^{13}CO$ to $\rm C^{18}O$ $3\sim6$ and the column density $(1\sim6)\times 10^{22}\, \rm cm^{-2}$. About $57.5\%$ of the IRDC cores are gravitationally bound, which are more compact, warmer and denser. In addition, we study the mass distribution functions of the whole IRDC cores as well as the gravitational bound cores, finding that they almost have the same power-law indexes. This indicates that the evolution of the IRDC cores almost have no effect on the mass spectrum of the molecular cores and thus can be used to study the stellar initial mass function. Moreover, three IRDC cores G24.00-3, G31.38-1 and G34.43-4 are detected to have large-scaled infall motions. Two different outflows are further found for IRDC core G34.43-4 and one of them is in high collimation.

### Mass and Environment as Drivers of Galaxy Evolution III: The constancy of the faint-end slope and the merging of galaxies

We explore using our continuity approach the underlying connections between the evolution of the faint-end slope of the stellar mass function of star-forming galaxies, the logarithmic slope of the sSFR-mass relation and the merging of galaxies. We derive analytically the consequences of the observed constancy of the faint-end slope since redshifts of at least z ~ 2. If the logarithmic slope of the sSFR-mass relation is negative, then the faint-end slope should quickly diverge due to the differential mass increase of galaxies on the star-forming main sequence, and this will also quickly destroy the Schechter form of the mass function. This problem can be solved by removing low mass galaxies by merging them into more massive galaxies. We quantify this process by introducing the specific merger mass rate (sMMR) as the specific rate of mass added to a given galaxy through mergers. For a modest negative value of the logarithmic slope of the sSFR-mass relation of beta ~ -0.1, an average sMMR ~ 0.1sSFR across the population is required to keep the faint-end slope constant with epoch, as observed. This in turn implies a merger rate of ~ 0.2sSFR for major mergers, which is consistent with the available observational estimates. More negative values of beta require higher sMMR and higher merger rates, and the steepening of the mass function becomes impossible to control for beta < ~ -0.6, for an observed value of the faint-end slope of ~ -1.4. The close link that is required between the in situ sSFR and the sMMR probably arises because both are closely linked to the buildup of dark matter haloes. These new findings further develop the formalism for the evolving galaxy population that we introduced earlier, and show how striking symmetries in the galaxy population can emerge as the result of deep links between the physical processes involved.

### AMUSE-Field II. Nucleation of early-type galaxies in the field vs. cluster environment

The optical light profiles of nearby early type galaxies are known to exhibit a smooth transition from nuclear light deficits to nuclear light excesses with decreasing galaxy mass, with as much as 80 per cent of the galaxies with stellar masses below 10^10 Msun hosting a massive nuclear star cluster. At the same time, while all massive galaxies are thought to harbor nuclear super-massive black holes (SMBHs), observational evidence for SMBHs is slim at the low end of the mass function. Here, we explore the environmental dependence of the nucleation fraction by comparing two homogeneous samples of nearby field vs. cluster early type galaxies with uniform Hubble Space Telescope (HST) coverage. Existing Chandra X-ray Telescope data for both samples yield complementary information on low-level accretion onto nuclear SMBHs. Specifically, we report on dual-band (F475W & F850LP) Advanced Camera for Surveys (ACS) imaging data for 28 out of the 103 field early type galaxies that compose the AMUSE-Field Chandra survey, and compare our results against the companion HST and Chandra surveys for a sample of 100 Virgo cluster early types (ACS Virgo Cluster and AMUSE-Virgo surveys, respectively). We model the two-dimensional light profiles of the field targets to identify and characterize NSCs, and find a field nucleation fraction of 26% (+17%, -11%; at the 1-sigma level), consistent with the measured Virgo nucleation fraction of 30% (+17%, -12%), across a comparable mass distribution. Coupled with the Chandra result that SMBH activity is higher for the field, our findings indicate that, since the last epoch of star formation, the funneling of gas to the nuclear regions has been inhibited more effectively for Virgo galaxies, arguably via ram pressure stripping.

### Clues on the Missing Sources of Reionization from Self-consistent Modeling of Milky Way and Dwarf Galaxy Globular Clusters

Globular clusters are unique tracers of ancient star formation. We determine the formation efficiencies of globular clusters across cosmic time by modeling the formation and dynamical evolution of the globular cluster population of a Milky Way type galaxy in hierarchical cosmology, using the merger tree from the Via Lactea II simulation. All of the models are constrained to reproduce the observed specific frequency and initial mass function of globular clusters in isolated dwarfs. Globular cluster orbits are then computed in a time varying gravitational potential after they are either accreted from a satellite halo or formed in situ, within the Milky Way halo. We find that the Galactocentric distances and metallicity distribution of globular clusters are very sensitive to the formation efficiencies of globular clusters as a function of redshift and halo mass. Our most accurate models reveal two distinct peaks in the globular cluster formation efficiency at z~2 and z~7-12 and prefer a formation efficiency that is mildly increasing with decreasing halo mass, the opposite of what expected for feedback-regulated star formation. This model accurately reproduces the positions, velocities, mass function, metallicity distribution, and age distribution of globular clusters in the Milky Way and predicts that ~ 40% formed in situ, within the Milky Way halo, while the other ~ 60% were accreted from about 20 satellite dwarf galaxies with Vc > 30 km/s, and about 29% or all globular clusters formed at redshifts z > 7. These results further strengthen the notion that globular cluster formation was an important mode of star formation in high-redshift galaxies and likely played a significant role in the reionization of the intergalactic medium